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Sample records for plasma kinetic equations

  1. Kinetic equation for spin-polarized plasmas

    International Nuclear Information System (INIS)

    Cowley, S.C.; Kulsrud, R.M.; Valeo, E.

    1984-07-01

    The usual kinetic description of a plasma is extended to include variables to describe the spin. The distribution function, over phase-space and the new spin variables, provides a sufficient description of a spin-polarized plasma. The evolution equation for the distribution function is given. The equations derived are used to calculate depolarization due to four processes, inhomogeneous fields, collisions, collisions in inhomogeneous fields, and waves. It is found that depolarization by field inhomogeneity on scales large compared with the gyroradius is totally negligible. The same is true for collisional depolarization. Collisions in inhomogeneous fields yield a depolarization rate of order 10 -4 S -1 for deuterons and a negligible rate for tritons in a typical fusion reactor design. This is still sufficiently small on reactor time scales. However, small amplitude magnetic fluctuations (of order one gauss) resonant with the spin precession frequency can lead to significant depolarization (depolarises triton in ten seconds and deuteron in a hundred seconds.)

  2. Kinetic equations for the collisional plasma model

    International Nuclear Information System (INIS)

    Rij, W.I. Van; Meier, H.K.; Beasley, C.O. Jr.; McCune, J.E.

    1977-01-01

    Using the Collisional Plasma Model (CPM) representation, expressions are derived for the Vlasov operator, both in its general form and in the drift-kinetic approximation following the recursive derivation by Hazeltine. The expressions for the operators give easily calculated couplings between neighbouring components of the CPM representation. Expressions for various macroscopic observables in the drift-kinetics approximation are also given. (author)

  3. Kinetic equations for an unstable plasma; Equations cinetiques d'un plasma instable

    Energy Technology Data Exchange (ETDEWEB)

    Laval, G; Pellat, R [Commissariat a l' Energie Atomique, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires

    1968-07-01

    In this work, we establish the plasma kinetic equations starting from the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy of equations. We demonstrate that relations existing between correlation functions may help to justify the truncation of the hierarchy. Then we obtain the kinetic equations of a stable or unstable plasma. They do not reduce to an equation for the one-body distribution function, but generally involve two coupled equations for the one-body distribution function and the spectral density of the fluctuating electric field. We study limiting cases where the Balescu-Lenard equation, the quasi-linear theory, the Pines-Schrieffer equations and the equations of weak turbulence in the random phase approximation are recovered. At last we generalise the H-theorem for the system of equations and we define conditions for irreversible behaviour. (authors) [French] Dans ce travail nous etablissons les equations cinetiques d'un plasma a partir des equations de la recurrence de Bogoliubov, Born, Green, Kirkwood et Yvon. Nous demontrons qu'entre les fonctions de correlation d'un plasma existent des relations qui permettent de justifier la troncature de la recurrence. Nous obtenons alors les equations cinetiques d'un plasma stable ou instable. En general elles ne se reduisent pas a une equation d'evolution pour la densite simple, mais se composent de deux equations couplees portant sur la densite simple et la densite spectrale du champ electrique fluctuant. Nous etudions le cas limites ou l'on retrouve l'equation de Balescu-Lenard, les equations de la theorie quasi-lineaire, les equations de Pines et Schrieffer et les equations de la turbulence faible dans l'approximation des phases aleatoires. Enfin, nous generalisons le theoreme H pour ce systeme d'equations et nous precisons les conditions d'evolution irreversible. (auteurs)

  4. Computer models for kinetic equations of magnetically confined plasmas

    International Nuclear Information System (INIS)

    Killeen, J.; Kerbel, G.D.; McCoy, M.G.; Mirin, A.A.; Horowitz, E.J.; Shumaker, D.E.

    1987-01-01

    This paper presents four working computer models developed by the computational physics group of the National Magnetic Fusion Energy Computer Center. All of the models employ a kinetic description of plasma species. Three of the models are collisional, i.e., they include the solution of the Fokker-Planck equation in velocity space. The fourth model is collisionless and treats the plasma ions by a fully three-dimensional particle-in-cell method

  5. Plasma kinetic theory

    International Nuclear Information System (INIS)

    Elliott, J.A.

    1993-01-01

    Plasma kinetic theory is discussed and a comparison made with the kinetic theory of gases. The plasma is described by a modified set of fluid equations and it is shown how these fluid equations can be derived. (UK)

  6. BRIEF COMMUNICATION: On the drift kinetic equation driven by plasma flows

    Science.gov (United States)

    Shaing, K. C.

    2010-07-01

    A drift kinetic equation that is driven by plasma flows has previously been derived by Shaing and Spong 1990 (Phys. Fluids B 2 1190). The terms that are driven by particle speed that is parallel to the magnetic field B have been neglected. Here, such terms are discussed to examine their importance to the equation and to show that these terms do not contribute to the calculations of plasma viscosity in large aspect ratio toroidal plasmas, e.g. tokamaks and stellarators.

  7. Quasi-linear landau kinetic equations for magnetized plasmas: compact propagator formalism, rotation matrices and interaction

    International Nuclear Information System (INIS)

    Misguich, J.H.

    2004-04-01

    As a first step toward a nonlinear renormalized description of turbulence phenomena in magnetized plasmas, the lowest order quasi-linear description is presented here from a unified point of view for collisionless as well as for collisional plasmas in a constant magnetic field. The quasi-linear approximation is applied to a general kinetic equation obtained previously from the Klimontovich exact equation, by means of a generalised Dupree-Weinstock method. The so-obtained quasi-linear description of electromagnetic turbulence in a magnetoplasma is applied to three separate physical cases: -) weak electrostatic turbulence, -) purely magnetic field fluctuations (the classical quasi-linear results are obtained for cosmic ray diffusion in the 'slab model' of magnetostatic turbulence in the solar wind), and -) collisional kinetic equations of magnetized plasmas. This mathematical technique has allowed us to derive basic kinetic equations for turbulent plasmas and collisional plasmas, respectively in the quasi-linear and Landau approximation. In presence of a magnetic field we have shown that the systematic use of rotation matrices describing the helical particle motion allows for a much more compact derivation than usually performed. Moreover, from the formal analogy between turbulent and collisional plasmas, the results derived here in detail for the turbulent plasmas, can be immediately translated to obtain explicit results for the Landau kinetic equation

  8. Quasi-linear landau kinetic equations for magnetized plasmas: compact propagator formalism, rotation matrices and interaction

    Energy Technology Data Exchange (ETDEWEB)

    Misguich, J.H

    2004-04-01

    As a first step toward a nonlinear renormalized description of turbulence phenomena in magnetized plasmas, the lowest order quasi-linear description is presented here from a unified point of view for collisionless as well as for collisional plasmas in a constant magnetic field. The quasi-linear approximation is applied to a general kinetic equation obtained previously from the Klimontovich exact equation, by means of a generalised Dupree-Weinstock method. The so-obtained quasi-linear description of electromagnetic turbulence in a magnetoplasma is applied to three separate physical cases: -) weak electrostatic turbulence, -) purely magnetic field fluctuations (the classical quasi-linear results are obtained for cosmic ray diffusion in the 'slab model' of magnetostatic turbulence in the solar wind), and -) collisional kinetic equations of magnetized plasmas. This mathematical technique has allowed us to derive basic kinetic equations for turbulent plasmas and collisional plasmas, respectively in the quasi-linear and Landau approximation. In presence of a magnetic field we have shown that the systematic use of rotation matrices describing the helical particle motion allows for a much more compact derivation than usually performed. Moreover, from the formal analogy between turbulent and collisional plasmas, the results derived here in detail for the turbulent plasmas, can be immediately translated to obtain explicit results for the Landau kinetic equation.

  9. On the equivalence of convergent kinetic equations for hot dilute plasmas: Generating functions for collision brackets

    NARCIS (Netherlands)

    Cohen, J.S.; Suttorp, L.G.

    1982-01-01

    The generating functions for the collision brackets associated with two alternative convergent kinetic equations are derived for small values of the plasma parameter. It is shown that the first few terms in the asymptotic expansions of these generating functions are identical. Consequently, both

  10. Accelerated procedure to solve kinetic equation for neutral atoms in a hot plasma

    Science.gov (United States)

    Tokar, Mikhail Z.

    2017-12-01

    The recombination of plasma charged components, electrons and ions of hydrogen isotopes, on the wall of a fusion reactor is a source of neutral molecules and atoms, recycling back into the plasma volume. Here neutral species participate, in particular, in charge-exchange (c-x) collisions with the plasma ions and, as a result, atoms of high energies with chaotically directed velocities are generated. Some fraction of these hot atoms hit the wall. Statistical Monte Carlo methods normally used to model c-x atoms are too time consuming for reasonably small level of accident errors and extensive parameter studies are problematic. By applying pass method to evaluate integrals from functions, including the ion velocity distribution, an iteration approach to solve one-dimensional kinetic equation [1], being alternative to Monte Carlo procedure, has been tremendously accelerated, at least by a factor of 30-50 [2]. Here this approach is developed further to solve the 2-D kinetic equation, applied to model the transport of c-x atoms in the vicinity of an opening in the wall, e.g., the entrance of the duct guiding to a diagnostic installation. This is necessary to determine firmly the energy spectrum of c-x atoms penetrating into the duct and to assess the erosion of the installation there. The results of kinetic modeling are compared with those obtained with the diffusion description for c-x atoms, being strictly relevant under plasma conditions of low temperature and high density, where the mean free path length between c-x collisions is much smaller than that till the atom ionization by electrons. It is demonstrated that the previous calculations [3], done with the diffusion approximation for c-x atoms, overestimate the erosion rate of Mo mirrors in a reactor by a factor of 3 compared to the result of the present kinetic study.

  11. KINETIC-J: A computational kernel for solving the linearized Vlasov equation applied to calculations of the kinetic, configuration space plasma current for time harmonic wave electric fields

    Science.gov (United States)

    Green, David L.; Berry, Lee A.; Simpson, Adam B.; Younkin, Timothy R.

    2018-04-01

    We present the KINETIC-J code, a computational kernel for evaluating the linearized Vlasov equation with application to calculating the kinetic plasma response (current) to an applied time harmonic wave electric field. This code addresses the need for a configuration space evaluation of the plasma current to enable kinetic full-wave solvers for waves in hot plasmas to move beyond the limitations of the traditional Fourier spectral methods. We benchmark the kernel via comparison with the standard k →-space forms of the hot plasma conductivity tensor.

  12. Elements of plasma kinetic theory

    International Nuclear Information System (INIS)

    Guasp, J.

    1976-01-01

    The physical foundations of plasma kinetic equations are exposed inside a series of seminars on plasma and fusion physics. The Vlasov and collisional equations with its application range have been discussed. The momenta equations for the macroscopic magnitudes and the more usual approximations have been obtained: two fluid equations for cold and warm plasmas, magnetohydrodynamic equations and the double-adiabatic theory. (author)

  13. Solving kinetic equations with adaptive mesh in phase space for rarefied gas dynamics and plasma physics (Invited)

    International Nuclear Information System (INIS)

    Kolobov, Vladimir; Arslanbekov, Robert; Frolova, Anna

    2014-01-01

    The paper describes an Adaptive Mesh in Phase Space (AMPS) technique for solving kinetic equations with deterministic mesh-based methods. The AMPS technique allows automatic generation of adaptive Cartesian mesh in both physical and velocity spaces using a Tree-of-Trees data structure. We illustrate advantages of AMPS for simulations of rarefied gas dynamics and electron kinetics on low temperature plasmas. In particular, we consider formation of the velocity distribution functions in hypersonic flows, particle kinetics near oscillating boundaries, and electron kinetics in a radio-frequency sheath. AMPS provide substantial savings in computational cost and increased efficiency of the mesh-based kinetic solvers

  14. Solving kinetic equations with adaptive mesh in phase space for rarefied gas dynamics and plasma physics (Invited)

    Energy Technology Data Exchange (ETDEWEB)

    Kolobov, Vladimir [CFD Research Corporation, Huntsville, AL 35805, USA and The University of Alabama in Huntsville, Huntsville, AL 35805 (United States); Arslanbekov, Robert [CFD Research Corporation, Huntsville, AL 35805 (United States); Frolova, Anna [Computing Center of the Russian Academy of Sciences, Moscow, 119333 (Russian Federation)

    2014-12-09

    The paper describes an Adaptive Mesh in Phase Space (AMPS) technique for solving kinetic equations with deterministic mesh-based methods. The AMPS technique allows automatic generation of adaptive Cartesian mesh in both physical and velocity spaces using a Tree-of-Trees data structure. We illustrate advantages of AMPS for simulations of rarefied gas dynamics and electron kinetics on low temperature plasmas. In particular, we consider formation of the velocity distribution functions in hypersonic flows, particle kinetics near oscillating boundaries, and electron kinetics in a radio-frequency sheath. AMPS provide substantial savings in computational cost and increased efficiency of the mesh-based kinetic solvers.

  15. Kinetic equations and fluctuations in μspace of one-component dilute plasmas

    International Nuclear Information System (INIS)

    Tokuyama, Michio; Mori, Hazime

    1977-01-01

    Kinetic equations for a spatially coarse-grained electron density in μ phase space A(p, r; t) with a length cutoff b and for its fluctuations are studied by a scaling method and a time-convolutionless approach developed by the present authors. An electron gas with a small plasma parameter epsilon=1/c (lambda sub(D)) 3 has three characteristic lengths; the Landau cutoff r sub(L)=epsilon lambda sub(D), the Debye length lambda sub(D)=√k sub(B)T/4πe 2 c and the mean free path l sub(f)=lambda sub(D)/epsilon, e and c being electronic charge and mean electron density, respectively. It is shown that there are two characteristic regions of the length cutoff b. One is a coherent region where r sub(L)<< b<< lambda sub(D). Its characteristic scaling is c→0, b→infinity, t→infinity with b√c and t√c being kept constant. The Vlasov equation is derived in this limit. The other is a kinetic region where lambda sub(D)<< b<< l sub(f). Its characteristic scaling is c→0, b→infinity, t→infinity with bc and tc being kept constant. The Vlasov term disappears and the Balescu-Lenard-Boltzmann-Landau equation, which is free of divergence for both close and distant collisions, is derived in this limit. It is shown that the fluctuations of A(p, r; t) obey a Markov process with scaling exponents α=0, β=1/2 in the coherent region near thermal equilibrium, while they obey a Gaussian Markov process with α=0, β=1 in the kinetic region. The present theory does not need the factorization ansatz and Bogoliubov's functional ansatz. (auth.)

  16. Study of carbon dioxide gas treatment based on equations of kinetics in plasma discharge reactor

    Science.gov (United States)

    Abedi-Varaki, Mehdi

    2017-08-01

    Carbon dioxide (CO2) as the primary greenhouse gas, is the main pollutant that is warming earth. CO2 is widely emitted through the cars, planes, power plants and other human activities that involve the burning of fossil fuels (coal, natural gas and oil). Thus, there is a need to develop some method to reduce CO2 emission. To this end, this study investigates the behavior of CO2 in dielectric barrier discharge (DBD) plasma reactor. The behavior of different species and their reaction rates are studied using a zero-dimensional model based on equations of kinetics inside plasma reactor. The results show that the plasma reactor has an effective reduction on the CO2 density inside the reactor. As a result of reduction in the temporal variations of reaction rate, the speed of chemical reactions for CO2 decreases and very low concentration of CO2 molecules inside the plasma reactor is generated. The obtained results are compared with the existing experimental and simulation findings in the literature.

  17. Time-nonlocal kinetic equations, jerk and hyperjerk in plasmas and solar physics

    Science.gov (United States)

    El-Nabulsi, Rami Ahmad

    2018-06-01

    The simulation and analysis of nonlocal effects in fluids and plasmas is an inherently complicated problem due to the massive breadth of physics required to describe the nonlocal dynamics. This is a multi-physics problem that draws upon various miscellaneous fields, such as electromagnetism and statistical mechanics. In this paper we strive to focus on one narrow but motivating mathematical way: the derivation of nonlocal plasma-fluid equations from a generalized nonlocal Liouville derivative operator motivated from Suykens's nonlocal arguments. The paper aims to provide a guideline toward modeling nonlocal effects occurring in plasma-fluid systems by means of a generalized nonlocal Boltzmann equation. The generalized nonlocal equations of fluid dynamics are derived and their implications in plasma-fluid systems are addressed, discussed and analyzed. Three main topics were discussed: Landau damping in plasma electrodynamics, ideal MHD and solar wind. A number of features were revealed, analyzed and confronted with recent research results and observations.

  18. Analysis of Electromagnetic Wave Propagation in a Magnetized Re-Entry Plasma Sheath Via the Kinetic Equation

    Science.gov (United States)

    Manning, Robert M.

    2009-01-01

    Based on a theoretical model of the propagation of electromagnetic waves through a hypersonically induced plasma, it has been demonstrated that the classical radiofrequency communications blackout that is experienced during atmospheric reentry can be mitigated through the appropriate control of an external magnetic field of nominal magnitude. The model is based on the kinetic equation treatment of Vlasov and involves an analytical solution for the electric and magnetic fields within the plasma allowing for a description of the attendant transmission, reflection and absorption coefficients. The ability to transmit through the magnetized plasma is due to the magnetic windows that are created within the plasma via the well-known whistler modes of propagation. The case of 2 GHz transmission through a re-entry plasma is considered. The coefficients are found to be highly sensitive to the prevailing electron density and will thus require a dynamic control mechanism to vary the magnetic field as the plasma evolves through the re-entry phase.

  19. Numerical Calculation of Transport Based on the Drift-Kinetic Equation for Plasmas in General Toroidal Magnetic Geometry: Numerical Methods

    International Nuclear Information System (INIS)

    Reynolds, J. M.; Lopez-Bruna, D.

    2009-01-01

    In this report we continue with the description of a newly developed numerical method to solve the drift kinetic equation for ions and electrons in toroidal plasmas. Several numerical aspects, already outlined in a previous report [Informes Tecnicos Ciemat 1165, mayo 2009], will be treated now in more detail. Aside from discussing the method in the context of other existing codes, various aspects will be now explained from the viewpoint of numerical methods: the way to solve convection equations, the adopted boundary conditions, the real-space meshing procedures along with a new software developed to build them, and some additional questions related with the parallelization and the numerical integration. (Author) 16 refs

  20. Numerical Calculation of Transport Based on the Drift Kinetic Equation for plasmas in General Toroidal Magnetic Geometry

    International Nuclear Information System (INIS)

    Reynolds, J. M.; Lopez-Bruna, D.

    2009-01-01

    This report is the first of a series dedicated to the numerical calculation of the evolution of fusion plasmas in general toroidal geometry, including TJ-II plasmas. A kinetic treatment has been chosen: the evolution equation of the distribution function of one or several plasma species is solved in guiding center coordinates. The distribution function is written as a Maxwellian one modulated by polynomial series in the kinetic coordinates with no other approximations than those of the guiding center itself and the computation capabilities. The code allows also for the inclusion of the three-dimensional electrostatic potential in a self-consistent manner, but the initial objective has been set to solving only the neoclassical transport. A high order conservative method (Spectral Difference Method) has been chosen in order to discretized the equation for its numerical solution. In this first report, in addition to justifying the work, the evolution equation and its approximations are described, as well as the baseline of the numerical procedures. (Author) 28 refs

  1. Kinetic equation solution by inverse kinetic method

    International Nuclear Information System (INIS)

    Salas, G.

    1983-01-01

    We propose a computer program (CAMU) which permits to solve the inverse kinetic equation. The CAMU code is written in HPL language for a HP 982 A microcomputer with a peripheral interface HP 9876 A ''thermal graphic printer''. The CAMU code solves the inverse kinetic equation by taking as data entry the output of the ionization chambers and integrating the equation with the help of the Simpson method. With this program we calculate the evolution of the reactivity in time for a given disturbance

  2. Kinetic equations in dirty superconductors

    International Nuclear Information System (INIS)

    Kraehenbuehl, Y.

    1981-01-01

    Kinetic equations for superconductors in the dirty limit are derived using a method developed for superfluid systems, which allows a systematic expansion in small parameters; exact charge conservation is obeyed. (orig.)

  3. The Balescu kinetic equation with exchange interaction

    International Nuclear Information System (INIS)

    Belyi, V V; Kukharenko, Yu A

    2009-01-01

    Starting with the quantum BBGKY hierarchy for the distribution functions, we have obtained the quantum kinetic equation including the dynamical screening of the interaction potential, which exactly takes into account the exchange scattering in the plasma. The collision integral is expressed in terms of the Green function of the linearized Hartree–Fock equation. The potential energy takes into account the polarization and exchange interaction too

  4. Nonlinear Electrostatic Wave Equations for Magnetized Plasmas

    DEFF Research Database (Denmark)

    Dysthe, K.B.; Mjølhus, E.; Pécseli, Hans

    1984-01-01

    The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed.......The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed....

  5. Kinetic Theory of the Inner Magnetospheric Plasma

    CERN Document Server

    Khazanov, George V

    2011-01-01

    This book provides a broad introduction to the kinetic theory of space plasma physics with the major focus on the inner magnetospheric plasma. It is designed to provide a comprehensive description of the different kinds of transport equations for both plasma particles and waves with an emphasis on the applicability and limitations of each set of equations. The major topics are: Kinetic Theory of Superthermal Electrons, Kinetic Foundation of the Hydrodynamic Description of Space Plasmas (including wave-particle interaction processes), and Kinetic Theory of the Terrestrial Ring Current. Distinguishable features of this book are the analytical solutions of simplified transport equations. Approximate analytic solutions of transport phenomena are very useful because they help us gain physical insight into how the system responds to varying sources of mass, momentum and energy and also to various external boundary conditions. They also provide us a convenient method to test the validity of complicated numerical mod...

  6. Numerical Calculation of Transport Based on the Drift-Kinetic Equation for Plasmas in General Toroidal Magnetic Geometry: Convergence and Testing

    International Nuclear Information System (INIS)

    Reynolds, J. M.; Lopez-Bruna, D.

    2009-01-01

    This report is the third of a series [Informes Tecnicos Ciemat 1165 y 1172] devoted to the development of a new numerical code to solve the guiding center equation for electrons and ions in toroidal plasmas. Two calculation meshes corresponding to axisymmetric tokamaks are now prepared and the kinetic equation is expanded so the standard terms of neoclassical theory --fi rst order terms in the Larmor radius expansion-- can be identified, restricting the calculations correspondingly. Using model density and temperature profiles for the plasma, several convergence test are performed depending on the calculation meshes and the expansions of the distribution function; then the results are compared with the theory [Hinton and Hazeltine, Rev. Mod. Phys. (1976)]. (Author) 18 refs

  7. Non-Abelian plasmons and their kinetics equation

    International Nuclear Information System (INIS)

    Zheng Xiaoping; Li Jiarong

    1998-01-01

    After the fluctuated modes in QGP are treated as plasmons, the kinetics equation for the plasmons in linear approximation is established starting from Yang-Mills fields equation. The kinetics equation can be considered as the balance equation for the number of plasmons, which indicates the balance of the number variation (growth or damping) in space and time because of their motion with velocities that equal to the wave's group velocity and the emission or absorption of plasmons by plasma particles

  8. Quantum-statistical kinetic equations

    International Nuclear Information System (INIS)

    Loss, D.; Schoeller, H.

    1989-01-01

    Considering a homogeneous normal quantum fluid consisting of identical interacting fermions or bosons, the authors derive an exact quantum-statistical generalized kinetic equation with a collision operator given as explicit cluster series where exchange effects are included through renormalized Liouville operators. This new result is obtained by applying a recently developed superoperator formalism (Liouville operators, cluster expansions, symmetrized projectors, P q -rule, etc.) to nonequilibrium systems described by a density operator ρ(t) which obeys the von Neumann equation. By means of this formalism a factorization theorem is proven (being essential for obtaining closed equations), and partial resummations (leading to renormalized quantities) are performed. As an illustrative application, the quantum-statistical versions (including exchange effects due to Fermi-Dirac or Bose-Einstein statistics) of the homogeneous Boltzmann (binary collisions) and Choh-Uhlenbeck (triple collisions) equations are derived

  9. Fundamental aspects of plasma chemical physics kinetics

    CERN Document Server

    Capitelli, Mario; Colonna, Gianpiero; Esposito, Fabrizio; Gorse, Claudine; Hassouni, Khaled; Laricchiuta, Annarita; Longo, Savino

    2016-01-01

    Describing non-equilibrium "cold" plasmas through a chemical physics approach, this book uses the state-to-state plasma kinetics, which considers each internal state as a new species with its own cross sections. Extended atomic and molecular master equations are coupled with Boltzmann and Monte Carlo methods to solve the electron energy distribution function. Selected examples in different applied fields, such as microelectronics, fusion, and aerospace, are presented and discussed including the self-consistent kinetics in RF parallel plate reactors, the optimization of negative ion sources and the expansion of high enthalpy flows through nozzles of different geometries. The book will cover the main aspects of the state-to-state kinetic approach for the description of nonequilibrium cold plasmas, illustrating the more recent achievements in the development of kinetic models including the self-consistent coupling of master equations and Boltzmann equation for electron dynamics. To give a complete portrayal, the...

  10. Kinetic equations with pairing correlations

    International Nuclear Information System (INIS)

    Fauser, R.

    1995-12-01

    The Gorkov equations are derived for a general non-equilibrium system. The Gorkov factorization is generalized by the cumulant expansion of the 2-particle correlation and by a generalized Wick theorem in the case of a perturbation expansion. A stationary solution for the Green functions in the Schwinger-Keldysh formalism is presented taking into account pairing correlations. Especially the effects of collisional broadening on the spectral functions and Green functions is discussed. Kinetic equations are derived in the quasi-particle approximation and in the case of particles with width. Explicit expressions for the self-energies are given. (orig.)

  11. Some Aspects of Extended Kinetic Equation

    Directory of Open Access Journals (Sweden)

    Dilip Kumar

    2015-09-01

    Full Text Available Motivated by the pathway model of Mathai introduced in 2005 [Linear Algebra and Its Applications, 396, 317–328] we extend the standard kinetic equations. Connection of the extended kinetic equation with fractional calculus operator is established. The solution of the general form of the fractional kinetic equation is obtained through Laplace transform. The results for the standard kinetic equation are obtained as the limiting case.

  12. Kinetics and spectroscopy of low temperature plasmas

    CERN Document Server

    Loureiro, Jorge

    2016-01-01

    This is a comprehensive textbook designed for graduate and advanced undergraduate students. Both authors rely on more than 20 years of teaching experience in renowned Physics Engineering courses to write this book addressing the students’ needs. Kinetics and Spectroscopy of Low Temperature Plasmas derives in a full self-consistent way the electron kinetic theory used to describe low temperature plasmas created in the laboratory with an electrical discharge, and presents the main optical spectroscopic diagnostics used to characterize such plasmas. The chapters with the theoretical contents make use of a deductive approach in which the electron kinetic theory applied to plasmas with basis on the electron Boltzmann equation is derived from the basic concepts of Statistical and Plasma Physics. On the other hand, the main optical spectroscopy diagnostics used to characterize experimentally such plasmas are presented and justified from the point of view of the Atomic and Molecular Physics. Low temperature plasmas...

  13. Kinetic theory of gases and plasmas

    International Nuclear Information System (INIS)

    Schram, P.P.J.M.

    1991-01-01

    Kinetic theory provides the link between the non-equilibrium statistical mechanics of many-particle systems and macroscopic or phenomenological physics. This volume deals with the derivation of kinetic equations, their limitations and generalizations,and with the applications of kinetic theory to physical phenomena and the calculation of transport coefficients. This book is divided in 12 chapters which discuss a wide range of topics such as balanced equations, the Klimontovich, Vlasov-Maxwell, and Boltzmann equations, Chapman-Enskog theory, the kinetic theory of plasmas, B.G.K. models, linear response theory, Brownian motion and renormalized kinetic theory. Each chapter is concluded with exercises, which not only enable the readers to test their understanding of the theory, but also present additional examples which complement the text. 151 refs.; 35 figs.; 5 tabs

  14. Numerical Calculation of Transport Based on the Drift-Kinetic Equation for Plasmas in General Toroidal Magnetic Geometry: Numerical Methods; Calculo Numerico de Transporte mediante la Ecuacion Cinetica de Deriva para Plasmas en Geometria Magnetica Toroidal: Metodos Numericos

    Energy Technology Data Exchange (ETDEWEB)

    Reynolds, J. M.; Lopez-Bruna, D.

    2009-10-12

    In this report we continue with the description of a newly developed numerical method to solve the drift kinetic equation for ions and electrons in toroidal plasmas. Several numerical aspects, already outlined in a previous report [Informes Tecnicos Ciemat 1165, mayo 2009], will be treated now in more detail. Aside from discussing the method in the context of other existing codes, various aspects will be now explained from the viewpoint of numerical methods: the way to solve convection equations, the adopted boundary conditions, the real-space meshing procedures along with a new software developed to build them, and some additional questions related with the parallelization and the numerical integration. (Author) 16 refs.

  15. Linearized gyro-kinetic equation

    International Nuclear Information System (INIS)

    Catto, P.J.; Tsang, K.T.

    1976-01-01

    An ordering of the linearized Fokker-Planck equation is performed in which gyroradius corrections are retained to lowest order and the radial dependence appropriate for sheared magnetic fields is treated without resorting to a WKB technique. This description is shown to be necessary to obtain the proper radial dependence when the product of the poloidal wavenumber and the gyroradius is large (k rho much greater than 1). A like particle collision operator valid for arbitrary k rho also has been derived. In addition, neoclassical, drift, finite β (plasma pressure/magnetic pressure), and unperturbed toroidal electric field modifications are treated

  16. Plasma heating by kinetic Alfven wave

    International Nuclear Information System (INIS)

    Assis, A.S. de.

    1982-01-01

    The heating of a nonuniform plasma (electron-ion) due to the resonant excitation of the shear Alfven wave in the low β regime is studied using initially the ideal MHD model and posteriorly using the kinetic model. The Vlasov equation for ions and the drift kinetic equation for electrons have been used. Through the ideal MHD model, it is concluded that the energy absorption is due to the continuous spectrum (phase mixing) which the shear Alfven wave has in a nonuniform plasma. An explicit expression for the energy absorption is derived. Through the kinetic model it is concluded that the energy absorption is due to a resonant mode convertion of the incident wave into the kinetic Alfven wave which propagates away from the resonant region. Its electron Landau damping has been observed. There has been a concordance with the MHD calculations. (Author) [pt

  17. Numerical Calculation of Transport Based on the Drift Kinetic Equation for plasmas in General Toroidal Magnetic Geometry; Calculo Numerico del Transporte mediante la Ecuacion Cinetica de Deriva para Plasmas en Geometria Magnetica Toroidal: Preliminares

    Energy Technology Data Exchange (ETDEWEB)

    Reynolds, J. M.; Lopez-Bruna, D.

    2009-12-11

    This report is the first of a series dedicated to the numerical calculation of the evolution of fusion plasmas in general toroidal geometry, including TJ-II plasmas. A kinetic treatment has been chosen: the evolution equation of the distribution function of one or several plasma species is solved in guiding center coordinates. The distribution function is written as a Maxwellian one modulated by polynomial series in the kinetic coordinates with no other approximations than those of the guiding center itself and the computation capabilities. The code allows also for the inclusion of the three-dimensional electrostatic potential in a self-consistent manner, but the initial objective has been set to solving only the neoclassical transport. A high order conservative method (Spectral Difference Method) has been chosen in order to discretized the equation for its numerical solution. In this first report, in addition to justifying the work, the evolution equation and its approximations are described, as well as the baseline of the numerical procedures. (Author) 28 refs.

  18. Hamiltonian kinetic theory of plasma ponderomotive processes

    International Nuclear Information System (INIS)

    McDonald, S.W.; Kaufman, A.N.

    1982-01-01

    The nonlinear nonresonant interaction of plasma waves and particles is formulated in Hamiltonian kinetic theory which treats the wave-action and particle distributions on an equal footing, thereby displaying reciprocity relations. In the quasistatic limit, a nonlinear wave-kinetic equation is obtained. The generality of the formalism allows for applications to arbitrary geometry, with the nonlinear effects expressed in terms of the linear susceptibility

  19. Hamiltonian kinetic theory of plasma ponderomotive processes

    International Nuclear Information System (INIS)

    McDonald, S.W.; Kaufman, A.N.

    1981-12-01

    The nonlinear nonresonant interaction of plasma waves and particles is formulated in a Hamiltonian kinetic theory which treats the wave-action and particle distributions on an equal footing, thereby displaying reciprocity relations. In the quasistatic limit, a nonlinear wave-kinetic equation is obtained. The generality of the formalism allows for applications to arbitrary geometry, with the nonlinear effects expressed in terms of the linear susceptibility

  20. Numerical Calculation of Transport Based on the Drift-Kinetic Equation for Plasmas in General Toroidal Magnetic Geometry: Convergence and Testing; Calculo Numerico del Transporte mediante la Ecuacion Cinetica de Deriva para Plasmas en Geometria Magnetica Toroidal: Convergencia y Comprobaciones

    Energy Technology Data Exchange (ETDEWEB)

    Reynolds, J. M.; Lopez-Bruna, D.

    2009-12-11

    This report is the third of a series [Informes Tecnicos Ciemat 1165 y 1172] devoted to the development of a new numerical code to solve the guiding center equation for electrons and ions in toroidal plasmas. Two calculation meshes corresponding to axisymmetric tokamaks are now prepared and the kinetic equation is expanded so the standard terms of neoclassical theory --fi rst order terms in the Larmor radius expansion-- can be identified, restricting the calculations correspondingly. Using model density and temperature profiles for the plasma, several convergence test are performed depending on the calculation meshes and the expansions of the distribution function; then the results are compared with the theory [Hinton and Hazeltine, Rev. Mod. Phys. (1976)]. (Author) 18 refs.

  1. Treatment of polymer surfaces in plasma Part I. Kinetic model

    International Nuclear Information System (INIS)

    Tabaliov, N A; Svirachev, D M

    2006-01-01

    The surface tension of the polymer materials depends on functional groups over its surface. As a result from the plasma treatment the kind and concentration of the functional groups can be changed. In the present work, the possible kinetic reactions are defined. They describe the interaction between the plasma and the polymer surface of polyethylene terephthalate (PET). Basing on these reactions, the systems of differential kinetic equations are suggested. The solutions are obtained analytically for the system kinetic equations at defined circumstances

  2. Reduced kinetic equations: An influence functional approach

    International Nuclear Information System (INIS)

    Wio, H.S.

    1985-01-01

    The author discusses a scheme for obtaining reduced descriptions of multivariate kinetic equations based on the 'influence functional' method of Feynmann. It is applied to the case of Fokker-Planck equations showing the form that results for the reduced equation. The possibility of Markovian or non-Markovian reduced description is discussed. As a particular example, the reduction of the Kramers equation to the Smoluchwski equation in the limit of high friction is also discussed

  3. Kinetic simulation on collisional bounded plasma

    International Nuclear Information System (INIS)

    Zhu, S.P.; Sato, Tetsuya; Tomita, Yukihiro; Hatori, Tadatsugu

    1998-01-01

    A self-consistent kinetic simulation model on collisional bounded plasma is presented. The electric field is given by solving Poisson equation and collisions among particles (including charged particles and neutral particles) are included. The excitation and ionization of neutral particle, and recombination are also contained in the present model. The formation of potential structure near a boundary for a discharge system was used as an application of this model. (author)

  4. Kinetic equation of heterogeneous catalytic isotope exchange

    Energy Technology Data Exchange (ETDEWEB)

    Trokhimets, A I [AN Belorusskoj SSR, Minsk. Inst. Fiziko-Organicheskoj Khimii

    1979-12-01

    A kinetic equation is derived for the bimolecular isotope exchange reaction between AXsub(n)sup(*) and BXsub(m)sup(o), all atoms of element X in each molecule being equivalent. The equation can be generalized for homogeneous and heterogeneous catalytic isotope exchange.

  5. Kinetic coefficients for quark-antiquark plasma

    International Nuclear Information System (INIS)

    Czyz, W.; Florkowski, W.

    1986-03-01

    The quark-antiquark plasma near equilibrium is studied. The results are based on the Heinz kinetic equations with the Boltzmann collision operator approximated by a relaxation term with the relaxation time, τ, treated as a small parameter. Linear in τ solutions of these equations are used to calculate the transport coefficients: the non-abelian version of Ohm's law, and the shear and volume viscosities. We introduce new chemical potentials which determine the color density matrix of quarks (antiquarks). Gradients of these potentials generate color currents. 12 refs. (author)

  6. Kinetic electron model for plasma thruster plumes

    Science.gov (United States)

    Merino, Mario; Mauriño, Javier; Ahedo, Eduardo

    2018-03-01

    A paraxial model of an unmagnetized, collisionless plasma plume expanding into vacuum is presented. Electrons are treated kinetically, relying on the adiabatic invariance of their radial action integral for the integration of Vlasov's equation, whereas ions are treated as a cold species. The quasi-2D plasma density, self-consistent electric potential, and electron pressure, temperature, and heat fluxes are analyzed. In particular, the model yields the collisionless cooling of electrons, which differs from the Boltzmann relation and the simple polytropic laws usually employed in fluid and hybrid PIC/fluid plume codes.

  7. A nondissipative simulation method for the drift kinetic equation

    International Nuclear Information System (INIS)

    Watanabe, Tomo-Hiko; Sugama, Hideo; Sato, Tetsuya

    2001-07-01

    With the aim to study the ion temperature gradient (ITG) driven turbulence, a nondissipative kinetic simulation scheme is developed and comprehensively benchmarked. The new simulation method preserving the time-reversibility of basic kinetic equations can successfully reproduce the analytical solutions of asymmetric three-mode ITG equations which are extended to provide a more general reference for benchmarking than the previous work [T.-H. Watanabe, H. Sugama, and T. Sato: Phys. Plasmas 7 (2000) 984]. It is also applied to a dissipative three-mode system, and shows a good agreement with the analytical solution. The nondissipative simulation result of the ITG turbulence accurately satisfies the entropy balance equation. Usefulness of the nondissipative method for the drift kinetic simulations is confirmed in comparisons with other dissipative schemes. (author)

  8. Magnetized plasma kinetic theory

    International Nuclear Information System (INIS)

    Hassan, M.H.A.; Watson, C.J.H.

    1977-01-01

    The magnetized Balescu-Lenard Collision integral for a multi-species plasma in the form derived by Hassan and Watson (1976) is approximated by ignoring wave effects. The resulting collision integral is put in Fokker-Planck form and most of the integrals occurring in the coefficients are performed analytically. The remaining integral is evaluated approximately in various limits for ion-electron, electron-electron and electron-ion interactions. (author)

  9. Kinetic Boltzmann, Vlasov and Related Equations

    CERN Document Server

    Sinitsyn, Alexander; Vedenyapin, Victor

    2011-01-01

    Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in

  10. Hypocoercivity for linear kinetic equations conserving mass

    KAUST Repository

    Dolbeault, Jean; Mouhot, Clé ment; Schmeiser, Christian

    2015-01-01

    We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf

  11. Hypocoercivity for linear kinetic equations conserving mass

    KAUST Repository

    Dolbeault, Jean

    2015-02-03

    We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf

  12. On the kinetic theory of the one-component plasma

    International Nuclear Information System (INIS)

    Cohen, J.S.

    1984-01-01

    In this thesis, kinetic theory is applied to transport phenomena of a one-component plasma. Existing kinetic equations, containing both dynamical screening effects and close binary collisions do not suffer from divergencies. Recently an approximation for the pair correlation function has been proposed that is valid for small values of the plasma collision parameter. Upon insertion of this expression into the general form of the collision integral, one obtains another convergent kinetic equation. This thesis shows that both kinetic equations yield the same coefficient of heat conductivity and viscosity; and that for a hot dilute plasma the arbitrary transport coefficient is rather insensitive to the pair correlation function. In the second part, the author studies the diffusion of a tagged particle in an external magnetic field. It is found that the longitudinal self-diffusion coefficient contra-varies monotonically with the magnetic field strength. (Auth.)

  13. A kinetic equation for irreversible aggregation

    International Nuclear Information System (INIS)

    Zanette, D.H.

    1990-09-01

    We introduce a kinetic equation for describing irreversible aggregation in the ballistic regime, including velocity distributions. The associated evolution for the macroscopic quantities is studied, and the general solution for Maxwell interaction models is obtained in the Fourier representation. (author). 23 refs

  14. Extended symmetries of the kinetic plasma theory models

    International Nuclear Information System (INIS)

    Taranov, V.B.

    2005-01-01

    Symmetry extension of the kinetic theory of collisionless plasma containing particles with equal charge to mass ratio is considered. It is shown that this symmetry allows us to reduce the number of equations. Symmetries obtained for the integro-differential equations of the kinetic theory by the indirect algorithm are compared to those obtained by direct methods. The importance of additional conditions - positiveness and integrability of distribution functions, existence of their moments - is underlined

  15. Multiple spatial scaling and the weak coupling approximation. II. Homogeneous kinetic equation

    Energy Technology Data Exchange (ETDEWEB)

    Kleinsmith, P E [Carnegie-Mellon Univ., Pittsburgh, Pa. (USA)

    1977-08-01

    A modified form of the Bogoliubov plasma cluster expansion is applied to the derivation of a divergence-free kinetic equation from the BBGKY hierarchy. Special attention is given to the conditions under which the Landau kinetic equation may be derived from this more general formulation.

  16. Fractional Bhatnagar-Gross-Krook kinetic equation

    Science.gov (United States)

    Goychuk, Igor

    2017-11-01

    The linear Boltzmann equation (LBE) approach is generalized to describe fractional superdiffusive transport of the Lévy walk type in external force fields. The time distribution between scattering events is assumed to have a finite mean value and infinite variance. It is completely characterized by the two scattering rates, one fractional and a normal one, which defines also the mean scattering rate. We formulate a general fractional LBE approach and exemplify it with a particularly simple case of the Bohm and Gross scattering integral leading to a fractional generalization of the Bhatnagar, Gross and Krook (BGK) kinetic equation. Here, at each scattering event the particle velocity is completely randomized and takes a value from equilibrium Maxwell distribution at a given fixed temperature. We show that the retardation effects are indispensable even in the limit of infinite mean scattering rate and argue that this novel fractional kinetic equation provides a viable alternative to the fractional Kramers-Fokker-Planck (KFP) equation by Barkai and Silbey and its generalization by Friedrich et al. based on the picture of divergent mean time between scattering events. The case of divergent mean time is also discussed at length and compared with the earlier results obtained within the fractional KFP. Also a phenomenological fractional BGK equation without retardation effects is proposed in the limit of infinite scattering rates. It cannot be, however, rigorously derived from a scattering model, being rather clever postulated. It this respect, this retardationless equation is similar to the fractional KFP by Barkai and Silbey. However, it corresponds to the opposite, much more physical limit and, therefore, also presents a viable alternative.

  17. The Gaussian radial basis function method for plasma kinetic theory

    Energy Technology Data Exchange (ETDEWEB)

    Hirvijoki, E., E-mail: eero.hirvijoki@chalmers.se [Department of Applied Physics, Chalmers University of Technology, SE-41296 Gothenburg (Sweden); Candy, J.; Belli, E. [General Atomics, PO Box 85608, San Diego, CA 92186-5608 (United States); Embréus, O. [Department of Applied Physics, Chalmers University of Technology, SE-41296 Gothenburg (Sweden)

    2015-10-30

    Description of a magnetized plasma involves the Vlasov equation supplemented with the non-linear Fokker–Planck collision operator. For non-Maxwellian distributions, the collision operator, however, is difficult to compute. In this Letter, we introduce Gaussian Radial Basis Functions (RBFs) to discretize the velocity space of the entire kinetic system, and give the corresponding analytical expressions for the Vlasov and collision operator. Outlining the general theory, we also highlight the connection to plasma fluid theories, and give 2D and 3D numerical solutions of the non-linear Fokker–Planck equation. Applications are anticipated in both astrophysical and laboratory plasmas. - Highlights: • A radically new method to address the velocity space discretization of the non-linear kinetic equation of plasmas. • Elegant and physically intuitive, flexible and mesh-free. • Demonstration of numerical solution of both 2-D and 3-D non-linear Fokker–Planck relaxation problem.

  18. BOOK REVIEW: Kinetic theory of plasma waves, homogeneous plasmas

    Science.gov (United States)

    Porkolab, Miklos

    1998-11-01

    addition to the literature, for it gives the teacher of the subject a valuable reference where the inquisitive student will be able to read up on and satisfy himself about the practicality and reliability of the Vlasov theory in a hot magnetized and collisionless plasma. The book has excellent treatments of several new topics not included in previous textbooks, for example, the relativistic theory of plasma wave propagation, so important in electron cyclotron heating of magnetically confined fusion plasmas, a discussion of current drive theory and there is a welcome introduction to parametric instabilities in the final chapter. There are some things that make the readability of the book somewhat difficult. In the early parts, certain advanced concepts are introduced without much motivation or explanation, although the author is trying to be helpful by providing a list of relevant references at the end of each chapter. Here the teacher's role will be critical. Again, a certain amount of previous knowledge of the subject would prove to be invaluable to the student. The main content of the book is included in 11 chapters. Use is made of CGS Gaussian units, a favourite of plasma theorists. As the author states, these are still widely used in advanced plasma theory, and the student is well advised to become familiar with this system of units (as well as the SI system for applications). To help the reader in the Introduction, the author defines various expressions often used in plasma physics in practical units (frequencies in hertz, lengths in centimetres, temperatures in kiloelectronvolts and magnetic fields in teslas). Chapter 2 is entitled `Plasma Electrodynamics' and it introduces the Maxwell-Vlasov set of equations, as well as the important fundamentals of wave propagation, such as polarization, dispersion and the dielectric tensor, and energy relations. In Chapter 3, `Elementary Plasma Kinetic Theory', the author derives the Vlasov equation and the Fokker-Planck equation

  19. Metamaterial characterization using Boltzmann's kinetic equation for electrons

    DEFF Research Database (Denmark)

    Novitsky, Andrey; Zhukovsky, Sergei; Novitsky, D.

    2013-01-01

    Statistical properties of electrons in metals are taken into consideration to describe the microscopic motion of electrons. Assuming degenerate electron gas in metal, we introduce the Boltzmann kinetic equation to supplement Maxwell's equations. The solution of these equations clearly shows...

  20. Kinetic Profiles in NSTX Plasmas

    International Nuclear Information System (INIS)

    Bell, R.E.; LeBlanc, B.P.; Bourdelle, C.; Ernst, D.R.; Fredrickson, E.D.; Gates, D.A.; Hosea, J.C.; Johnson, D.W.; Kaye, S.M.; Maingi, R.; Medley, S.; Menard, J.E.; Mueller, D.; Ono, M.; Paoletti, F.; Peng, M.; Sabbagh, S.A.; Stutman, D.; Swain, D.W.; Synakowski, E.J.; Wilson, J.R.

    2001-01-01

    The National Spherical Torus Experiment (NSTX) is a low aspect ratio (R/a approximately 1.3) device with auxiliary heating from neutral-beam injection (NBI) and high-harmonic fast-wave heating (HHFW). Typical NSTX parameters are R(subscript ''0'') = 85 cm, a = 67 cm, I(subscript ''p'') = 0.7-1.4 MA, B(subscript ''phi'') = 0.25-0.45 T. Three co-directed deuterium neutral-beam sources have injected P(subscript ''NB'') less than or equal to 4.7 MW. HHFW plasmas typically have delivered P(subscript ''RF'') less than or equal to 3 MW. Important to the understanding of NSTX confinement are the new kinetic profile diagnostics: a multi-pulse Thomson scattering system (MPTS) and a charge-exchange recombination spectroscopy (CHERS) system. The MPTS diagnostic currently measures electron density and temperature profiles at 30 Hz at ten spatial locations. The CHERS system has recently become available to measure carbon ion temperature and toroidal flow at 17 radial positions spanning the outer half of the minor radius with 20 msec time resolution during NBI. Experiments conducted during the last year have produced a wide range of kinetic profiles in NSTX. Some interesting examples are presented below

  1. Fully implicit kinetic modelling of collisional plasmas

    International Nuclear Information System (INIS)

    Mousseau, V.A.

    1996-05-01

    This dissertation describes a numerical technique, Matrix-Free Newton Krylov, for solving a simplified Vlasov-Fokker-Planck equation. This method is both deterministic and fully implicit, and may not have been a viable option before current developments in numerical methods. Results are presented that indicate the efficiency of the Matrix-Free Newton Krylov method for these fully-coupled, nonlinear integro-differential equations. The use and requirement for advanced differencing is also shown. To this end, implementations of Chang-Cooper differencing and flux limited Quadratic Upstream Interpolation for Convective Kinematics (QUICK) are presented. Results are given for a fully kinetic ion-electron problem with a self consistent electric field calculated from the ion and electron distribution functions. This numerical method, including advanced differencing, provides accurate solutions, which quickly converge on workstation class machines. It is demonstrated that efficient steady-state solutions can be achieved to the non-linear integro-differential equation, obtaining quadratic convergence, without incurring the large memory requirements of an integral operator. Model problems are presented which simulate plasma impinging on a plate with both high and low neutral particle recycling typical of a divertor in a Tokamak device. These model problems demonstrate the performance of the new solution method

  2. The soliton solution of BBGKY quantum kinetic equations chain for different type particles system

    International Nuclear Information System (INIS)

    Rasulova, M.Yu.; Avazov, U.; Hassan, T.

    2006-12-01

    In the present paper on the basis of BBGKY chain of quantum kinetic equations the chain of equations for correlation matrices is derived, describing the evolution of a system of different types particles, which interact by pair potential. The series, which is the solution of this chain of equations for correlation matrices, is suggested. Using this series the solution of the last chain of equations is reduced to a solution of a set of homogeneous and nonhomogeneous von-Neumann's kinetic equations (analogue of Vlasov equations for quantum case). The first and second equations of this set of equations coincide with the first and second kinetic equations of the set, which is used in plasma physics. For an potential in the form of Dirac delta function, the solution of von-Neumann equation is defined through soliton solution of nonlinear Schrodinger equations. Based on von-Neumann equation one can define all terms of series, which is a solution of a chain of equations for correlation matrices. On the basis of these correlation matrices for a system of different types of particles we can define exact solution of BBGKY chain of quantum kinetic equations

  3. NLTE4 Plasma Population Kinetics Database

    Science.gov (United States)

    SRD 159 NLTE4 Plasma Population Kinetics Database (Web database for purchase)   This database contains benchmark results for simulation of plasma population kinetics and emission spectra. The data were contributed by the participants of the 4th Non-LTE Code Comparison Workshop who have unrestricted access to the database. The only limitation for other users is in hidden labeling of the output results. Guest users can proceed to the database entry page without entering userid and password.

  4. Time Dependent Hartree Fock Equation: Gateway to Nonequilibrium Plasmas

    International Nuclear Information System (INIS)

    Dufty, James W.

    2007-01-01

    This is the Final Technical Report for DE-FG02-2ER54677 award 'Time Dependent Hartree Fock Equation - Gateway to Nonequilibrium Plasmas'. Research has focused on the nonequilibrium dynamics of electrons in the presence of ions, both via basic quantum theory and via semi-classical molecular dynamics (MD) simulation. In addition, fundamental notions of dissipative dynamics have been explored for models of grains and dust, and for scalar fields (temperature) in turbulent edge plasmas. The specific topics addressed were Quantum Kinetic Theory for Metallic Clusters, Semi-classical MD Simulation of Plasmas , and Effects of Dissipative Dynamics.

  5. Receptor binding kinetics equations: Derivation using the Laplace transform method.

    Science.gov (United States)

    Hoare, Sam R J

    Measuring unlabeled ligand receptor binding kinetics is valuable in optimizing and understanding drug action. Unfortunately, deriving equations for estimating kinetic parameters is challenging because it involves calculus; integration can be a frustrating barrier to the pharmacologist seeking to measure simple rate parameters. Here, a well-known tool for simplifying the derivation, the Laplace transform, is applied to models of receptor-ligand interaction. The method transforms differential equations to a form in which simple algebra can be applied to solve for the variable of interest, for example the concentration of ligand-bound receptor. The goal is to provide instruction using familiar examples, to enable investigators familiar with handling equilibrium binding equations to derive kinetic equations for receptor-ligand interaction. First, the Laplace transform is used to derive the equations for association and dissociation of labeled ligand binding. Next, its use for unlabeled ligand kinetic equations is exemplified by a full derivation of the kinetics of competitive binding equation. Finally, new unlabeled ligand equations are derived using the Laplace transform. These equations incorporate a pre-incubation step with unlabeled or labeled ligand. Four equations for measuring unlabeled ligand kinetics were compared and the two new equations verified by comparison with numerical solution. Importantly, the equations have not been verified with experimental data because no such experiments are evident in the literature. Equations were formatted for use in the curve-fitting program GraphPad Prism 6.0 and fitted to simulated data. This description of the Laplace transform method will enable pharmacologists to derive kinetic equations for their model or experimental paradigm under study. Application of the transform will expand the set of equations available for the pharmacologist to measure unlabeled ligand binding kinetics, and for other time

  6. The unified description of kinetic and hydrodynamic processes in gases and plasmas

    International Nuclear Information System (INIS)

    Klimontovich, Yu.L.

    1992-01-01

    The unified description of kinetic and hydrodynamic processes in gases and plasmas for all values of the Knudsen number is proposed. The generalized kinetic equation consists of the additional dissipative term and is defined by the diffusion of the distribution function in the coordinate space. This equation is used for the description of nonequilibrium processes in passive and active media. (orig.)

  7. On kinetic description of electromagnetic processes in a quantum plasma

    International Nuclear Information System (INIS)

    Tyshetskiy, Yu.; Vladimirov, S. V.; Kompaneets, R.

    2011-01-01

    A nonlinear kinetic equation for nonrelativistic quantum plasma with electromagnetic interaction of particles is obtained in the Hartree's mean-field approximation. It is cast in a convenient form of Vlasov-Boltzmann-type equation with ''quantum interference integral'', which allows for relatively straightforward modification of existing classical Vlasov codes to incorporate quantum effects (quantum statistics and quantum interference of overlapping particles wave functions), without changing the bulk of the codes. Such modification (upgrade) of existing Vlasov codes may provide a direct and effective path to numerical simulations of nonlinear electrostatic and electromagnetic phenomena in quantum plasmas, especially of processes where kinetic effects are important (e.g., modulational interactions and stimulated scattering phenomena involving plasma modes at short wavelengths or high-order kinetic modes, dynamical screening and interaction of charges in quantum plasma, etc.) Moreover, numerical approaches involving such modified Vlasov codes would provide a useful basis for theoretical analyses of quantum plasmas, as quantum and classical effects can be easily separated there.

  8. Kinetic theory of nonlinear transport phenomena in complex plasmas

    International Nuclear Information System (INIS)

    Mishra, S. K.; Sodha, M. S.

    2013-01-01

    In contrast to the prevalent use of the phenomenological theory of transport phenomena, a number of transport properties of complex plasmas have been evaluated by using appropriate expressions, available from the kinetic theory, which are based on Boltzmann's transfer equation; in particular, the energy dependence of the electron collision frequency has been taken into account. Following the recent trend, the number and energy balance of all the constituents of the complex plasma and the charge balance on the particles is accounted for; the Ohmic loss has also been included in the energy balance of the electrons. The charging kinetics for the complex plasma comprising of uniformly dispersed dust particles, characterized by (i) uniform size and (ii) the Mathis, Rumpl, and Nordsieck power law of size distribution has been developed. Using appropriate expressions for the transport parameters based on the kinetic theory, the system of equations has been solved to investigate the parametric dependence of the complex plasma transport properties on the applied electric field and other plasma parameters; the results are graphically illustrated.

  9. Kinetic computer modeling of microwave surface-wave plasma production

    International Nuclear Information System (INIS)

    Ganachev, Ivan P.

    2004-01-01

    Kinetic computer plasma modeling occupies an intermediate position between the time consuming rigorous particle dynamic simulation and the fast but rather rough cold- or warm-plasma fluid models. The present paper reviews the kinetic modeling of microwave surface-wave discharges with accent on recent kinetic self-consistent models, where the external input parameters are reduced to the necessary minimum (frequency and intensity of the applied microwave field and pressure and geometry of the discharge vessel). The presentation is limited to low pressures, so that Boltzmann equation is solved in non-local approximation and collisional electron heating is neglected. The numerical results reproduce correctly the bi-Maxwellian electron energy distribution functions observed experimentally. (author)

  10. Drift-free kinetic equations for turbulent dispersion

    Science.gov (United States)

    Bragg, A.; Swailes, D. C.; Skartlien, R.

    2012-11-01

    The dispersion of passive scalars and inertial particles in a turbulent flow can be described in terms of probability density functions (PDFs) defining the statistical distribution of relevant scalar or particle variables. The construction of transport equations governing the evolution of such PDFs has been the subject of numerous studies, and various authors have presented formulations for this type of equation, usually referred to as a kinetic equation. In the literature it is often stated, and widely assumed, that these PDF kinetic equation formulations are equivalent. In this paper it is shown that this is not the case, and the significance of differences among the various forms is considered. In particular, consideration is given to which form of equation is most appropriate for modeling dispersion in inhomogeneous turbulence and most consistent with the underlying particle equation of motion. In this regard the PDF equations for inertial particles are considered in the limit of zero particle Stokes number and assessed against the fully mixed (zero-drift) condition for fluid points. A long-standing question regarding the validity of kinetic equations in the fluid-point limit is answered; it is demonstrated formally that one version of the kinetic equation (derived using the Furutsu-Novikov method) provides a model that satisfies this zero-drift condition exactly in both homogeneous and inhomogeneous systems. In contrast, other forms of the kinetic equation do not satisfy this limit or apply only in a limited regime.

  11. Kinetics and hybrid kinetic-fluid models for nonequilibrium gas and plasmas

    International Nuclear Information System (INIS)

    Crouseilles, N.

    2004-12-01

    For a few decades, the application of the physics of plasmas has appeared in different fields like laser-matter interaction, astrophysics or thermonuclear fusion. In this thesis, we are interested in the modeling and the numerical study of nonequilibrium gas and plasmas. To describe such systems, two ways are usually used: the fluid description and the kinetic description. When we study a nonequilibrium system, fluid models are not sufficient and a kinetic description have to be used. However, solving a kinetic model requires the discretization of a large number of variables, which is quite expensive from a numerical point of view. The aim of this work is to propose a hybrid kinetic-fluid model thanks to a domain decomposition method in the velocity space. The derivation of the hybrid model is done in two different contexts: the rarefied gas context and the more complicated plasmas context. The derivation partly relies on Levermore's entropy minimization approach. The so-obtained model is then discretized and validated on various numerical test cases. In a second stage, a numerical study of a fully kinetic model is presented. A collisional plasma constituted of electrons and ions is considered through the Vlasov-Poisson-Fokker-Planck-Landau equation. Then, a numerical scheme which preserves total mass and total energy is presented. This discretization permits in particular a numerical study of the Landau damping. (author)

  12. Nonlinear electromagnetic gyrokinetic equations for rotating axisymmetric plasmas

    International Nuclear Information System (INIS)

    Artun, M.; Tang, W.M.

    1994-03-01

    The influence of sheared equilibrium flows on the confinement properties of tokamak plasmas is a topic of much current interest. A proper theoretical foundation for the systematic kinetic analysis of this important problem has been provided here by presented the derivation of a set of nonlinear electromagnetic gyrokinetic equations applicable to low frequency microinstabilities in a rotating axisymmetric plasma. The subsonic rotation velocity considered is in the direction of symmetry with the angular rotation frequency being a function of the equilibrium magnetic flux surface. In accordance with experimental observations, the rotation profile is chosen to scale with the ion temperature. The results obtained represent the shear flow generalization of the earlier analysis by Frieman and Chen where such flows were not taken into account. In order to make it readily applicable to gyrokinetic particle simulations, this set of equations is cast in a phase-space-conserving continuity equation form

  13. A novel fractional technique for the modified point kinetics equations

    Directory of Open Access Journals (Sweden)

    Ahmed E. Aboanber

    2016-10-01

    Full Text Available A fractional model for the modified point kinetics equations is derived and analyzed. An analytical method is used to solve the fractional model for the modified point kinetics equations. This methodical technique is based on the representation of the neutron density as a power series of the relaxation time as a small parameter. The validity of the fractional model is tested for different cases of step, ramp and sinusoidal reactivity. The results show that the fractional model for the modified point kinetics equations is the best representation of neutron density for subcritical and supercritical reactors.

  14. Solution of the reactor point kinetics equations by MATLAB computing

    Directory of Open Access Journals (Sweden)

    Singh Sudhansu S.

    2015-01-01

    Full Text Available The numerical solution of the point kinetics equations in the presence of Newtonian temperature feedback has been a challenging issue for analyzing the reactor transients. Reactor point kinetics equations are a system of stiff ordinary differential equations which need special numerical treatments. Although a plethora of numerical intricacies have been introduced to solve the point kinetics equations over the years, some of the simple and straightforward methods still work very efficiently with extraordinary accuracy. As an example, it has been shown recently that the fundamental backward Euler finite difference algorithm with its simplicity has proven to be one of the most effective legacy methods. Complementing the back-ward Euler finite difference scheme, the present work demonstrates the application of ordinary differential equation suite available in the MATLAB software package to solve the stiff reactor point kinetics equations with Newtonian temperature feedback effects very effectively by analyzing various classic benchmark cases. Fair accuracy of the results implies the efficient application of MATLAB ordinary differential equation suite for solving the reactor point kinetics equations as an alternate method for future applications.

  15. Development of kinetics equations from the Boltzmann equation; Etablissement des equations de la cinetique a partir de l'equation de Boltzmann

    Energy Technology Data Exchange (ETDEWEB)

    Plas, R.

    1962-07-01

    The author reports a study on kinetics equations for a reactor. He uses the conventional form of these equations but by using a dynamic multiplication factor. Thus, constants related to delayed neutrons are not modified by efficiency factors. The author first describes the theoretic kinetic operation of a reactor and develops the associated equations. He reports the development of equations for multiplication factors.

  16. Fractional Diffusion Limit for Collisional Kinetic Equations

    KAUST Repository

    Mellet, Antoine

    2010-08-20

    This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a diffusion equation. In this paper, we consider situations in which the equilibrium distribution function is a heavy-tailed distribution with infinite variance. We then show that for an appropriate time scale, the small mean free path limit gives rise to a fractional diffusion equation. © 2010 Springer-Verlag.

  17. Kinetic theory of nonideal gases and nonideal plasmas

    CERN Document Server

    Klimontovich, Yu L

    2013-01-01

    Kinetic Theory of Nonideal Gases and Nonideal Plasmas presents the fundamental aspects of the kinetic theory of gases and plasmas. The book consists of three parts, which attempts to present some of the ideas, methods and applications in the study of the kinetic processes in nonideal gases and plasmas. The first part focuses on the classical kinetic theory of nonideal gases. The second part discusses the classical kinetic theory of fully ionized plasmas. The last part is devoted to the quantum kinetic theory of nonideal gases and plasmas. A concluding chapter is included, which presents a shor

  18. Plasma kinetics around a dust grain in an ion flow

    International Nuclear Information System (INIS)

    Maiorov, S.A.; Vladimirov, S.V.; Cramer, N.F.

    2000-01-01

    Full text: In a typical laboratory discharge, dust particles are negatively charged and usually levitate in the sheath or pre-sheath region under the balance of gravitational, electrostatic (due to the sheath electric field) and plasma (such as the ion drag) forces. The ion flow provides not only a direct (dragging) influence, but is also responsible for the generation of associated collective plasma processes which can strongly affect the vertical arrangement of the dust grains. The complete problem of the plasma dynamics around a macroscopic body in the presence of plasma flows is highly nonlinear and therefore its numerical analysis is of major importance. Among various numerical methods, direct integration of the equations of motion of the plasma particles represents a numerical experiment whose significance approaches experiments in the laboratory. Here, we present for the first time the results of a self-consistent molecular dynamics (MD) three-dimensional (3D) simulation of the kinetics of plasma particles (electrons and ions) around a dust grain, taking into account the dust charging. The core of the method includes consideration of the time evolution of the system consisting of positively ('ions') and negatively ('electrons') charged particles confined in a simulation box together with a macroscopic absorbing grain ('dust particle') with infinite mass and an initial (negative) charge. The ions are introduced in the system as a uniform flow defined by its Mach number and the ion temperature. The paths of the ions and electrons are determined through numerical integration of the equations of motion. We demonstrate that the plasma kinetics around a dust grain in the presence of an ion flow involves a strong ion focusing behind the grain. We have also confirmed that the most important of the processes involved is the ion time-scale; the kinetics of the electrons follows a Boltzmann distribution with good agreement. We note that the time constraints involved

  19. Fractional Diffusion Limit for Collisional Kinetic Equations

    KAUST Repository

    Mellet, Antoine; Mischler, Sté phane; Mouhot, Clé ment

    2010-01-01

    This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a

  20. Kinetic theory of two-temperature polyatomic plasmas

    Science.gov (United States)

    Orlac'h, Jean-Maxime; Giovangigli, Vincent; Novikova, Tatiana; Roca i Cabarrocas, Pere

    2018-03-01

    We investigate the kinetic theory of two-temperature plasmas for reactive polyatomic gas mixtures. The Knudsen number is taken proportional to the square root of the mass ratio between electrons and heavy-species, and thermal non-equilibrium between electrons and heavy species is allowed. The kinetic non-equilibrium framework also requires a weak coupling between electrons and internal energy modes of heavy species. The zeroth-order and first-order fluid equations are derived by using a generalized Chapman-Enskog method. Expressions for transport fluxes are obtained in terms of macroscopic variable gradients and the corresponding transport coefficients are expressed as bracket products of species perturbed distribution functions. The theory derived in this paper provides a consistent fluid model for non-thermal multicomponent plasmas.

  1. Hamiltonian formalism of two-dimensional Vlasov kinetic equation.

    Science.gov (United States)

    Pavlov, Maxim V

    2014-12-08

    In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.

  2. Kinetic simulations in plasmas: a general view and some applications

    Energy Technology Data Exchange (ETDEWEB)

    Alves, Maria Virginia [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma]. E-mail: alves@plasma.inpe.br

    1999-07-01

    In these lecture notes we talk about kinetic simulations plasma physics. We present a general view of the different approach that can be given to kinetic plasmas depending on the physical problem to be investigated. Some applications of kinetic simulations to space plasma phenomena and Pierce electrodes are introduced. (author)

  3. Kinetic simulations in plasmas: a general view and some applications

    International Nuclear Information System (INIS)

    Alves, Maria Virginia

    1999-01-01

    In these lecture notes we talk about kinetic simulations plasma physics. We present a general view of the different approach that can be given to kinetic plasmas depending on the physical problem to be investigated. Some applications of kinetic simulations to space plasma phenomena and Pierce electrodes are introduced. (author)

  4. Instabilities and chaos in a kinetic equation for active nematics

    International Nuclear Information System (INIS)

    Shi, Xia-qing; Ma, Yu-qiang; Chaté, Hugues

    2014-01-01

    We study dry active nematics at the kinetic equation level, stressing the differences with the well-known Doi theory for non-active rods near thermal equilibrium. By deriving hydrodynamic equations from the kinetic equation, we show analytically that these two description levels share the same qualitative phase diagram, as defined by the linear instability limits of spatially-homogeneous solutions. In particular, we show that the ordered, homogeneous state is unstable in a region bordering the linear onset of nematic order, and is only linearly stable deeper in the ordered phase. Direct simulations of the kinetic equation reveal that its solutions are chaotic in the region of linear instability of the ordered homogeneous state. The local mechanisms for this large-scale chaos are discussed. (paper)

  5. Uncertainty quantification for hyperbolic and kinetic equations

    CERN Document Server

    Pareschi, Lorenzo

    2017-01-01

    This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo methods, importance sampling, and moment methods. The interest in these topics is rapidly growing, as their applications have now expanded to many areas in engineering, physics, biology and the social sciences. Accordingly, the book provides the scientific community with a topical overview of the latest research efforts.

  6. Verification of continuum drift kinetic equation solvers in NIMROD

    Energy Technology Data Exchange (ETDEWEB)

    Held, E. D.; Ji, J.-Y. [Utah State University, Logan, Utah 84322-4415 (United States); Kruger, S. E. [Tech-X Corporation, Boulder, Colorado 80303 (United States); Belli, E. A. [General Atomics, San Diego, California 92186-5608 (United States); Lyons, B. C. [Program in Plasma Physics, Princeton University, Princeton, New Jersey 08543-0451 (United States)

    2015-03-15

    Verification of continuum solutions to the electron and ion drift kinetic equations (DKEs) in NIMROD [C. R. Sovinec et al., J. Comp. Phys. 195, 355 (2004)] is demonstrated through comparison with several neoclassical transport codes, most notably NEO [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)]. The DKE solutions use NIMROD's spatial representation, 2D finite-elements in the poloidal plane and a 1D Fourier expansion in toroidal angle. For 2D velocity space, a novel 1D expansion in finite elements is applied for the pitch angle dependence and a collocation grid is used for the normalized speed coordinate. The full, linearized Coulomb collision operator is kept and shown to be important for obtaining quantitative results. Bootstrap currents, parallel ion flows, and radial particle and heat fluxes show quantitative agreement between NIMROD and NEO for a variety of tokamak equilibria. In addition, velocity space distribution function contours for ions and electrons show nearly identical detailed structure and agree quantitatively. A Θ-centered, implicit time discretization and a block-preconditioned, iterative linear algebra solver provide efficient electron and ion DKE solutions that ultimately will be used to obtain closures for NIMROD's evolving fluid model.

  7. Modelling opinion formation by means of kinetic equations

    OpenAIRE

    Boudin , Laurent; Salvarani , Francesco

    2010-01-01

    In this chapter, we review some mechanisms of opinion dynamics that can be modelled by kinetic equations. Beside the sociological phenomenon of compromise, naturally linked to collisional operators of Boltzmann kind, many other aspects, already mentioned in the sociophysical literature or no, can enter in this framework. While describing some contributions appeared in the literature, we enlighten some mathematical tools of kinetic theory that can be useful in the context of sociophysics.

  8. Turbulent kinetic energy equation and free mixing

    Science.gov (United States)

    Morel, T.; Torda, T. P.; Bradshaw, P.

    1973-01-01

    Calculation of free shear flows was carried out to investigate the usefulness of several concepts which were previously successfully applied to wall flows. The method belongs to the class of differential approaches. The turbulence is taken into account by the introduction of one additional partial differential equation, the transport equation for the turbulent shear stress. The structure of turbulence is modeled after Bradshaw et al. This model was used successfully in boundary layers and its applicability to other flows is demonstrated. The work reported differs substantially from that of an earlier attempt to use this approach for calculation of free flows. The most important difference is that the region around the center line is treated by invoking the interaction hypothesis (concerning the structure of turbulence in the regions separated by the velocity extrema). The compressibility effects on shear layer spreading at low and moderate Mach numbers were investigated. In the absence of detailed experiments in free flows, the evidence from boundary layers that at low Mach numbers the structure of turbulence is unaffected by the compressibility was relied on. The present model was tested over a range of self-preserving and developing flows including pressure gradients using identical empirical input. The dependence of the structure of turbulence on the spreading rate of the shear layer was established.

  9. Plasma balance equations based on orbit theory

    International Nuclear Information System (INIS)

    Lehnert, B.

    1982-01-01

    A set of plasma balance equations is proposed which is based on orbit theory and the particle distribution function, to provide means for theoretical analysis of a number of finite Larmor radius (FLR) phenomena without use of the Vlasov equation. Several important FLR effects originate from the inhomogeneity of an electric field in the plasma. The exact solution of a simple case shows that this inhomogeneity introduces fundamental changes in the physics of the particle motion. Thus, the periodic Larmor motion (gyration) is shifted in frequency and becomes elliptically polarized. Further, the non-periodic guiding-centre drift obtains additional components, part of which are accelerated such as to make the drift orbits intersect the equipotential surfaces of a static electric field. An attempt is finally made to classify the FLR effects, also with the purpose of identifying phenomena which have so far not been investigated. (author)

  10. Weakly Ionized Plasmas in Hypersonics: Fundamental Kinetics and Flight Applications

    International Nuclear Information System (INIS)

    Macheret, Sergey

    2005-01-01

    The paper reviews some of the recent studies of applications of weakly ionized plasmas to supersonic/hypersonic flight. Plasmas can be used simply as means of delivering energy (heating) to the flow, and also for electromagnetic flow control and magnetohydrodynamic (MHD) power generation. Plasma and MHD control can be especially effective in transient off-design flight regimes. In cold air flow, nonequilibrium plasmas must be created, and the ionization power budget determines design, performance envelope, and the very practicality of plasma/MHD devices. The minimum power budget is provided by electron beams and repetitive high-voltage nanosecond pulses, and the paper describes theoretical and computational modeling of plasmas created by the beams and repetitive pulses. The models include coupled equations for non-local and unsteady electron energy distribution function (modeled in forward-back approximation), plasma kinetics, and electric field. Recent experimental studies at Princeton University have successfully demonstrated stable diffuse plasmas sustained by repetitive nanosecond pulses in supersonic air flow, and for the first time have demonstrated the existence of MHD effects in such plasmas. Cold-air hypersonic MHD devices are shown to permit optimization of scramjet inlets at Mach numbers higher than the design value, while operating in self-powered regime. Plasma energy addition upstream of the inlet throat can increase the thrust by capturing more air (Virtual Cowl), or it can reduce the flow Mach number and thus eliminate the need for an isolator duct. In the latter two cases, the power that needs to be supplied to the plasma would be generated by an MHD generator downstream of the combustor, thus forming the 'reverse energy bypass' scheme. MHD power generation on board reentry vehicles is also discussed

  11. Fractional neutron point kinetics equations for nuclear reactor dynamics

    International Nuclear Information System (INIS)

    Espinosa-Paredes, Gilberto; Polo-Labarrios, Marco-A.; Espinosa-Martinez, Erick-G.; Valle-Gallegos, Edmundo del

    2011-01-01

    The fractional point-neutron kinetics model for the dynamic behavior in a nuclear reactor is derived and analyzed in this paper. The fractional model retains the main dynamic characteristics of the neutron motion in which the relaxation time associated with a rapid variation in the neutron flux contains a fractional order, acting as exponent of the relaxation time, to obtain the best representation of a nuclear reactor dynamics. The physical interpretation of the fractional order is related with non-Fickian effects from the neutron diffusion equation point of view. The numerical approximation to the solution of the fractional neutron point kinetics model, which can be represented as a multi-term high-order linear fractional differential equation, is calculated by reducing the problem to a system of ordinary and fractional differential equations. The numerical stability of the fractional scheme is investigated in this work. Results for neutron dynamic behavior for both positive and negative reactivity and for different values of fractional order are shown and compared with the classic neutron point kinetic equations. Additionally, a related review with the neutron point kinetics equations is presented, which encompasses papers written in English about this research topic (as well as some books and technical reports) published since 1940 up to 2010.

  12. A nonlinear bounce kinetic equation for trapped electrons

    International Nuclear Information System (INIS)

    Gang, F.Y.

    1990-03-01

    A nonlinear bounce averaged drift kinetic equation for trapped electrons is derived. This equation enables one to compute the nonlinear response of the trapped electron distribution function in terms of the field-line projection of a potential fluctuation left-angle e -inqθ φ n right-angle b . It is useful for both analytical and computational studies of the nonlinear evolution of short wavelength (n much-gt 1) trapped electron mode-driven turbulence. 7 refs

  13. Asymptotic behavior of the plasma equation

    International Nuclear Information System (INIS)

    Kwong, Y.C.

    1984-01-01

    This paper is concerned with the plasma equation on a bounded smooth domain the N-dimensional Euclidean Space, with non-negative initial data and a homogenous Dirichlet boundary condition. It is known that there exists a finite extinction time T such that the solution decays to zero at T. Berryman and Holland investigated the stability of the profile of the solution as t is approaching T. However, they obtained their results at the expense of some very strong regularity assumptions. By invoking both the nonlinear semi-group theory and a standard regularizing scheme for the equation, the same results are proved without those assumptions by measuring the rate of decay of the solution and estimates are obtained on the time derivative as t is approaching T. As motivated by the regularity assumptions, both the interior and boundary regularities of the solution are studied. Finally, the nonlinearity of the plasma equation is perturbed and the same aspects for the perturbed equation are studied

  14. GENERAL EQUATIONS OF CARBONIZATION OF EUCALYPTUS SPP KINETIC MECHANISMS

    Directory of Open Access Journals (Sweden)

    Túlio Jardim Raad

    2006-06-01

    Full Text Available In the present work, a set of general equations related to kinetic mechanism of wood compound carbonization: hemicelluloses, cellulose and lignin was obtained by Avrami-Eroffev and Arrhenius equations and Thermogravimetry of Eucalyptus cloeziana, Eucalyptus camaldulensis, Corymbia citriodora, Eucalyptus urophylla and Eucalyptus grandis samples, TG-Isothermal and TG-Dynamic. The different thermal stabilities and decomposition temperature bands of those species compounds were applied as strategy to obtain the kinetic parameters: activation energy, exponential factor and reaction order. The kinetic model developed was validated by thermogravimetric curves from carbonization of others biomass such as coconut. The kinetic parameters found were - Hemicelluloses: E=98,6 kJmol, A=3,5x106s-1 n=1,0; - Cellulose: E=182,2 kJmol, A=1,2x1013s-1 n=1,5; - Lignin: E=46,6 kJmol, A=2,01s-1 n=0,41. The set of equations can be implemented in a mathematical model of wood carbonization simulation (with heat and mass transfer equations with the aim of optimizing the control and charcoal process used to produce pig iron.

  15. Review of Kaganove's solution for the reactor point kinetics equations

    International Nuclear Information System (INIS)

    Couto, R.T.; Santo, A.C.F. de.

    1993-09-01

    A review of Kaganove's method for the reactor point kinetics equations solution is performed. This was method chosen to calculate the power in ATR, a computer program for the analysis of reactivity transients. The reasons for this choice and the adaptation of the method to the purposes of ATR are presented. (author)

  16. Study of the stochastic point reactor kinetic equation

    International Nuclear Information System (INIS)

    Gotoh, Yorio

    1980-01-01

    Diagrammatic technique is used to solve the stochastic point reactor kinetic equation. The method gives exact results which are derived from Fokker-Plank theory. A Green's function dressed with the clouds of noise is defined, which is a transfer function of point reactor with fluctuating reactivity. An integral equation for the correlation function of neutron power is derived using the following assumptions: 1) Green's funntion should be dressed with noise, 2) The ladder type diagrams only contributes to the correlation function. For a white noise and the one delayed neutron group approximation, the norm of the integral equation and the variance to mean-squared ratio are analytically obtained. (author)

  17. Asymptotic kinetic theory of magnetized plasmas: quasi-particle concept

    International Nuclear Information System (INIS)

    Sosenko, P.P.; Zagorodny, A.H.

    2004-01-01

    The asymptotic kinetic theory of magnetized plasmas is elaborated within the context of general statistical approach and asymptotic methods, developed by M. Krylov and M. Bohol'ubov, for linear and non-linear dynamic systems with a rapidly rotating phase. The quasi-particles are introduced already on the microscopic level. Asymptotic expansions enable to close the description for slow processes, and to relate consistently particles and guiding centres to quasi-particles. The kinetic equation for quasi-particles is derived. It makes a basis for the reduced description of slow collective phenomena in the medium. The kinetic equation for quasi-particles takes into account self-consistent interaction fields, quasi-particle collisions and collective-fluctuation-induced relaxation of quasi-particle distribution function. The relationships between the distribution functions for particles, guiding centres and quasi-particles are derived taking into account fluctuations, which can be especially important in turbulent states. In this way macroscopic (statistical) particle properties can be obtained from those of quasi-particles in the general case of non-equilibrium. (authors)

  18. A reduced set of gyrofluid equations for plasma flow in a diverging magnetic field

    International Nuclear Information System (INIS)

    Robertson, Scott

    2016-01-01

    Plasmas are often generated in a small diameter source with a strong magnetic field and subsequently flow into a region with greater diameter and smaller field. The magnetic mirror force that accelerates plasma in a diverging magnetic field appears in the gyrofluid equations developed for applications to toroidal devices, but this force is often absent from fluid equations. A set of gyrofluid equations with reduced complexity is developed in which drifts are assumed negligible and the mirror force is retained. The Chew–Goldberger–Low equations of state are used for a simple closure. These reduced gyrofluid equations are applied to plasma equilibrium in a magnetic mirror, to acceleration of plasma in a magnetic nozzle, and to space charge neutralization of an ion beam by electrons in a diverging magnetic field. The results from gyrofluid theory are compared with results from drift kinetic theory to find the accuracy of the gyrofluid approximation in these applications.

  19. Kinetic Simulations of Dense Plasma Focus Breakdown

    Science.gov (United States)

    Schmidt, A.; Higginson, D. P.; Jiang, S.; Link, A.; Povilus, A.; Sears, J.; Bennett, N.; Rose, D. V.; Welch, D. R.

    2015-11-01

    A dense plasma focus (DPF) device is a type of plasma gun that drives current through a set of coaxial electrodes to assemble gas inside the device and then implode that gas on axis to form a Z-pinch. This implosion drives hydrodynamic and kinetic instabilities that generate strong electric fields, which produces a short intense pulse of x-rays, high-energy (>100 keV) electrons and ions, and (in deuterium gas) neutrons. A strong factor in pinch performance is the initial breakdown and ionization of the gas along the insulator surface separating the two electrodes. The smoothness and isotropy of this ionized sheath are imprinted on the current sheath that travels along the electrodes, thus making it an important portion of the DPF to both understand and optimize. Here we use kinetic simulations in the Particle-in-cell code LSP to model the breakdown. Simulations are initiated with neutral gas and the breakdown modeled self-consistently as driven by a charged capacitor system. We also investigate novel geometries for the insulator and electrodes to attempt to control the electric field profile. The initial ionization fraction of gas is explored computationally to gauge possible advantages of pre-ionization which could be created experimentally via lasers or a glow-discharge. Prepared by LLNL under Contract DE-AC52-07NA27344.

  20. Hydrogen atom kinetics in capacitively coupled plasmas

    Science.gov (United States)

    Nunomura, Shota; Katayama, Hirotaka; Yoshida, Isao

    2017-05-01

    Hydrogen (H) atom kinetics has been investigated in capacitively coupled very high frequency (VHF) discharges at powers of 16-780 mW cm-2 and H2 gas pressures of 0.1-2 Torr. The H atom density has been measured using vacuum ultra violet absorption spectroscopy (VUVAS) with a micro-discharge hollow cathode lamp as a VUV light source. The measurements have been performed in two different electrode configurations of discharges: conventional parallel-plate diode and triode with an intermediate mesh electrode. We find that in the triode configuration, the H atom density is strongly reduced across the mesh electrode. The H atom density varies from ˜1012 cm-3 to ˜1010 cm-3 by crossing the mesh with 0.2 mm in thickness and 36% in aperture ratio. The fluid model simulations for VHF discharge plasmas have been performed to study the H atom generation, diffusion and recombination kinetics. The simulations suggest that H atoms are generated in the bulk plasma, by the electron impact dissociation (e + H2 \\to e + 2H) and the ion-molecule reaction (H2 + + H2 \\to {{{H}}}3+ + H). The diffusion of H atoms is strongly limited by a mesh electrode, and thus the mesh geometry influences the spatial distribution of the H atoms. The loss of H atoms is dominated by the surface recombination.

  1. Kinetic theory of plasma adiabatic major radius compression in tokamaks

    International Nuclear Information System (INIS)

    Gorelenkova, M.V.; Gorelenkov, N.N.; Azizov, E.A.; Romannikov, A.N.; Herrmann, H.W.

    1998-01-01

    In order to understand the individual charged particle behavior as well as plasma macroparameters (temperature, density, etc.) during the adiabatic major radius compression (R-compression) in a tokamak, a kinetic approach is used. The perpendicular electric field from the Ohm close-quote s law at zero resistivity is made use of in order to describe particle motion during the R-compression. Expressions for both passing and trapped particle energy and pitch angle change are derived for a plasma with high aspect ratio and circular magnetic surfaces. The particle behavior near the passing trapped boundary during the compression is studied to simulate the compression-induced collisional losses of alpha particles. Qualitative agreement is obtained with the alphas loss measurements in deuterium-tritium (D-T) experiments in the Tokamak Fusion Test Reactor (TFTR) [World Survey of Activities in Controlled Fusion Research [Nucl. Fusion special supplement (1991)] (International Atomic Energy Agency, Vienna, 1991)]. The plasma macroparameters evolution at the R-compression is calculated by solving the gyroaveraged drift kinetic equation. copyright 1998 American Institute of Physics

  2. Taylor's series method for solving the nonlinear point kinetics equations

    International Nuclear Information System (INIS)

    Nahla, Abdallah A.

    2011-01-01

    Highlights: → Taylor's series method for nonlinear point kinetics equations is applied. → The general order of derivatives are derived for this system. → Stability of Taylor's series method is studied. → Taylor's series method is A-stable for negative reactivity. → Taylor's series method is an accurate computational technique. - Abstract: Taylor's series method for solving the point reactor kinetics equations with multi-group of delayed neutrons in the presence of Newtonian temperature feedback reactivity is applied and programmed by FORTRAN. This system is the couples of the stiff nonlinear ordinary differential equations. This numerical method is based on the different order derivatives of the neutron density, the precursor concentrations of i-group of delayed neutrons and the reactivity. The r th order of derivatives are derived. The stability of Taylor's series method is discussed. Three sets of applications: step, ramp and temperature feedback reactivities are computed. Taylor's series method is an accurate computational technique and stable for negative step, negative ramp and temperature feedback reactivities. This method is useful than the traditional methods for solving the nonlinear point kinetics equations.

  3. The nonlocal electron kinetics for a low-pressure glow discharge dusty plasma

    Science.gov (United States)

    Liang, Yonggan; Wang, Ying; Li, Hui; Tian, Ruihuan; Yuan, Chengxun; Kudryavtsev, A. A.; Rabadanov, K. M.; Wu, Jian; Zhou, Zhongxiang; Tian, Hao

    2018-05-01

    The nonlocal electron kinetic model based on the Boltzmann equation is developed in low-pressure argon glow discharge dusty plasmas. The additional electron-dust elastic and inelastic collision processes are considered when solving the kinetic equation numerically. The orbital motion limited theory and collision enhanced collection approximation are employed to calculate the dust surface potential. The electron energy distribution function (EEDF), effective electron temperature Teff, and dust surface potential are investigated under different plasma and dust conditions by solving the Boltzmann and the dust charging current balance equations self-consistently. A comparison of the calculation results obtained from nonlocal and local kinetic models is made. It is shown that the appearance of dust particles leads to a deviation of the EEDF from its original profile for both nonlocal and local kinetic models. With the increase in dust density and size, the effective electron temperature and dust surface potential decrease due to the high-energy electron loss on the dust surface. Meanwhile, the nonlocal and local results differ much from each other under the same calculation condition. It is concluded that, for low-pressure (PR ≤ 1 cm*Torr) glow discharge dusty plasmas, the existence of dust particles will amplify the difference of local and nonlocal EEDFs, which makes the local kinetic model more improper to determine the main parameters of the positive column. The nonlocal kinetic model should be used for the calculation of the EEDFs and dusty plasma parameters.

  4. Comparative analysis of solution methods of the punctual kinetic equations

    International Nuclear Information System (INIS)

    Hernandez S, A.

    2003-01-01

    The following one written it presents a comparative analysis among different analytical solutions for the punctual kinetics equation, which present two variables of interest: a) the temporary behavior of the neutronic population, and b) The temporary behavior of the different groups of precursors of delayed neutrons. The first solution is based on a method that solves the transfer function of the differential equation for the neutronic population, in which intends to obtain the different poles that give the stability of this transfer function. In this section it is demonstrated that the temporary variation of the reactivity of the system can be managed as it is required, since the integration time for this method doesn't affect the result. However, the second solution is based on an iterative method like that of Runge-Kutta or the Euler method where the algorithm was only used to solve first order differential equations giving this way solution to each differential equation that conforms the equations of punctual kinetics. In this section it is demonstrated that only it can obtain a correct temporary behavior of the neutronic population when it is integrated on an interval of very short time, forcing to the temporary variation of the reactivity to change very quick way without one has some control about the time. In both methods the same change is used so much in the reactivity of the system like in the integration times, giving validity to the results graph the one the temporary behavior of the neutronic population vs. time. (Author)

  5. Kinetic parameters for plasma β-endorphin in lean and obese Zucker rats

    International Nuclear Information System (INIS)

    Rodd, D.; Farrell, P.A.; Caston, A.L.; Green, M.H.

    1991-01-01

    To determine plasma clearance kinetics for β-endorphin (BE) by empirical compartmental analysis, a bolus of radioactive labeled 125I-BE was rapidly injected into a carotid artery catheter of unanesthetized lean (L) and obese (O) Zucker rats. The plasma disappearance of 125I was followed over a 3-h period. A 3-component exponential equation provided the best fit for plasma data. Plasma transit times were very short (10 s); however, plasma fractional catabolic rate was much slower. Plasma mean residence time was similar for both groups (50 min) as was recycle time (1.3 min). These data suggest that BE plasma disappearance kinetics are similar in L and O rats

  6. Kinetic parameters for plasma. beta. -endorphin in lean and obese Zucker rats

    Energy Technology Data Exchange (ETDEWEB)

    Rodd, D.; Farrell, P.A.; Caston, A.L.; Green, M.H. (Department of Exercise and Sport Science, Pennsylvania State University, University Park (USA))

    1991-03-01

    To determine plasma clearance kinetics for {beta}-endorphin (BE) by empirical compartmental analysis, a bolus of radioactive labeled 125I-BE was rapidly injected into a carotid artery catheter of unanesthetized lean (L) and obese (O) Zucker rats. The plasma disappearance of 125I was followed over a 3-h period. A 3-component exponential equation provided the best fit for plasma data. Plasma transit times were very short (10 s); however, plasma fractional catabolic rate was much slower. Plasma mean residence time was similar for both groups (50 min) as was recycle time (1.3 min). These data suggest that BE plasma disappearance kinetics are similar in L and O rats.

  7. Initial value problem for the equations of reactor kinetics

    International Nuclear Information System (INIS)

    Kyncl, J.

    1987-08-01

    The initial value problem for the equations of reactor kinetics is solved while taking temperature feedback into account. The space where the problem is solved is chosen such as to correspond to the mathematical properties of cross-section models. The local solution is found by the iterative method, its uniqueness is proved and it is also shown that the existence of global solution is ensured in most cases. Finally, the problem of a weak solution is discussed. (author). 5 refs

  8. Kinetic theory of flocking: derivation of hydrodynamic equations.

    Science.gov (United States)

    Ihle, Thomas

    2011-03-01

    It is shown how to explicitly coarse-grain the microscopic dynamics of the rule-based Vicsek model for self-propelled agents. The hydrodynamic equations are derived by means of an Enskog-type kinetic theory. Expressions for all transport coefficients are given. The transition from a disordered to a flocking state, which at large particle speeds appears to be a fluctuation-induced first-order phase transition, is studied numerically and analytically.

  9. Kinetic coefficients for quark-antiquark plasma with quantal treatment of color

    International Nuclear Information System (INIS)

    Dyrek, A.; Florkowski, W.

    1986-07-01

    We discuss the near-equilibrium state of the q-bar q plasma treated as a system of classical particles with quantized color charges. The matrix of the kinetic coefficients is calculated (in the relaxation approximation of the transport equation) and compared with its classical version. The color Ohm law is recovered but the structure of the kinetic matrix is different. 5 refs. (author)

  10. A Global Modeling Framework for Plasma Kinetics: Development and Applications

    Science.gov (United States)

    Parsey, Guy Morland

    The modern study of plasmas, and applications thereof, has developed synchronously with com- puter capabilities since the mid-1950s. Complexities inherent to these charged-particle, many- body, systems have resulted in the development of multiple simulation methods (particle-in-cell, fluid, global modeling, etc.) in order to both explain observed phenomena and predict outcomes of plasma applications. Recognizing that different algorithms are chosen to best address specific topics of interest, this thesis centers around the development of an open-source global model frame- work for the focused study of non-equilibrium plasma kinetics. After verification and validation of the framework, it was used to study two physical phenomena: plasma-assisted combustion and the recently proposed optically-pumped rare gas metastable laser. Global models permeate chemistry and plasma science, relying on spatial averaging to focus attention on the dynamics of reaction networks. Defined by a set of species continuity and energy conservation equations, the required data and constructed systems are conceptually similar across most applications, providing a light platform for exploratory and result-search parameter scan- ning. Unfortunately, it is common practice for custom code to be developed for each application-- an enormous duplication of effort which negatively affects the quality of the software produced. Presented herein, the Python-based Kinetic Global Modeling framework (KGMf) was designed to support all modeling phases: collection and analysis of reaction data, construction of an exportable system of model ODEs, and a platform for interactive evaluation and post-processing analysis. A symbolic ODE system is constructed for interactive manipulation and generation of a Jacobian, both of which are compiled as operation-optimized C-code. Plasma-assisted combustion and ignition (PAC/PAI) embody the modernization of burning fuel by opening up new avenues of control and optimization

  11. Kinetic treatment of nonlinear ion-acoustic waves in multi-ion plasma

    Science.gov (United States)

    Ahmad, Zulfiqar; Ahmad, Mushtaq; Qamar, A.

    2017-09-01

    By applying the kinetic theory of the Valsove-Poisson model and the reductive perturbation technique, a Korteweg-de Vries (KdV) equation is derived for small but finite amplitude ion acoustic waves in multi-ion plasma composed of positive and negative ions along with the fraction of electrons. A correspondent equation is also derived from the basic set of fluid equations of adiabatic ions and isothermal electrons. Both kinetic and fluid KdV equations are stationary solved with different nature of coefficients. Their differences are discussed both analytically and numerically. The criteria of the fluid approach as a limiting case of kinetic theory are also discussed. The presence of negative ion makes some modification in the solitary structure that has also been discussed with its implication at the laboratory level.

  12. On coupling fluid plasma and kinetic neutral physics models

    Directory of Open Access Journals (Sweden)

    I. Joseph

    2017-08-01

    Full Text Available The coupled fluid plasma and kinetic neutral physics equations are analyzed through theory and simulation of benchmark cases. It is shown that coupling methods that do not treat the coupling rates implicitly are restricted to short time steps for stability. Fast charge exchange, ionization and recombination coupling rates exist, even after constraining the solution by requiring that the neutrals are at equilibrium. For explicit coupling, the present implementation of Monte Carlo correlated sampling techniques does not allow for complete convergence in slab geometry. For the benchmark case, residuals decay with particle number and increase with grid size, indicating that they scale in a manner that is similar to the theoretical prediction for nonlinear bias error. Progress is reported on implementation of a fully implicit Jacobian-free Newton–Krylov coupling scheme. The present block Jacobi preconditioning method is still sensitive to time step and methods that better precondition the coupled system are under investigation.

  13. Kinetic theory of surface waves in plasma jets

    International Nuclear Information System (INIS)

    Shokri, B.

    2002-01-01

    The kinetic theory analysis of surface waves propagating along a semi-bounded plasma jet is presented. The frequency spectra and their damping rate are obtained in both the high and low frequency regions. Finally, the penetration of the static field in the plasma jet under the condition that the plasma jet velocity is smaller than the sound velocity is studied

  14. Statistical approach to LHCD modeling using the wave kinetic equation

    International Nuclear Information System (INIS)

    Kupfer, K.; Moreau, D.; Litaudon, X.

    1993-04-01

    Recent work has shown that for parameter regimes typical of many present day current drive experiments, the orbits of the launched LH rays are chaotic (in the Hamiltonian sense), so that wave energy diffuses through the stochastic layer and fills the spectral gap. We have analyzed this problem using a statistical approach, by solving the wave kinetic equation for the coarse-grained spectral energy density. An interesting result is that the LH absorption profile is essentially independent of both the total injected power and the level of wave stochastic diffusion

  15. Nonequilibrium Statistical Operator Method and Generalized Kinetic Equations

    Science.gov (United States)

    Kuzemsky, A. L.

    2018-01-01

    We consider some principal problems of nonequilibrium statistical thermodynamics in the framework of the Zubarev nonequilibrium statistical operator approach. We present a brief comparative analysis of some approaches to describing irreversible processes based on the concept of nonequilibrium Gibbs ensembles and their applicability to describing nonequilibrium processes. We discuss the derivation of generalized kinetic equations for a system in a heat bath. We obtain and analyze a damped Schrödinger-type equation for a dynamical system in a heat bath. We study the dynamical behavior of a particle in a medium taking the dissipation effects into account. We consider the scattering problem for neutrons in a nonequilibrium medium and derive a generalized Van Hove formula. We show that the nonequilibrium statistical operator method is an effective, convenient tool for describing irreversible processes in condensed matter.

  16. Non-equilibrium reaction rates in chemical kinetic equations

    Science.gov (United States)

    Gorbachev, Yuriy

    2018-05-01

    Within the recently proposed asymptotic method for solving the Boltzmann equation for chemically reacting gas mixture, the chemical kinetic equations has been derived. Corresponding one-temperature non-equilibrium reaction rates are expressed in terms of specific heat capacities of the species participate in the chemical reactions, bracket integrals connected with the internal energy transfer in inelastic non-reactive collisions and energy transfer coefficients. Reactions of dissociation/recombination of homonuclear and heteronuclear diatomic molecules are considered. It is shown that all reaction rates are the complex functions of the species densities, similarly to the unimolecular reaction rates. For determining the rate coefficients it is recommended to tabulate corresponding bracket integrals, additionally to the equilibrium rate constants. Correlation of the obtained results with the irreversible thermodynamics is established.

  17. On the kinetic collisional theory of beam-plasma system (relativistic dielectric tensor). Vol. 2.

    Energy Technology Data Exchange (ETDEWEB)

    Khalil, Sh M; Sayed, Y A; Zaki, N G [Plasma Physics and Nuclear Fusion Department, Nuclear Research Center, Atomic Energy Authority, Cairo, (Egypt)

    1996-03-01

    Calculation of the dielectric tensor is useful for calculating and oscillations the stability of an inhomogeneous plasma. If the dielectric tensor is known, the problem of oscillations is reduced the derivation of the Maxwellian equations. In this case, there is no need to derive the equations of the motion of charged particles every time. The properties of the plasma, especially those connected to its instability, may be equally well specified through permittivity as through conductivity. The features of plasma instabilities and the plasma dielectric tensor are essentially affected by the presence of collision. Coloumb collisions (C.C.) are very important in the process of no linear saturation of some plasma instabilities (e.g., ion cyclotron instability, electron-ion two stream instability). For C.C., two basic properties are considered; (i) the cross section decreases rapidly as the particle velocity increases, (ii) the dominate contribution arises from a commutative effect of small-angle scattering or small-momentum transfer processes. If allowance is made for C.C. to derive the kinetic wave equations in a homogeneous plasma, it will remove the divergance in the matrix elements describing nonlinear interactions. In this paper, the collisional kinetic wave equation in cylindrical hot plasma is studied. The dielectric and polarizing tensor elements which describes the kinetic relativistic electron beam (REB) interaction with magnetized plasma into consideration the effect of pair C.C. is derived. Most research carried out in this direction has neglected the effect of C.C. In the absence of collisions, a `plauste` is formed on the distribution function, and the adsorption of the energy by the plasma stops. 1 fig.

  18. A consistent hierarchy of generalized kinetic equation approximations to the master equation applied to surface catalysis.

    Science.gov (United States)

    Herschlag, Gregory J; Mitran, Sorin; Lin, Guang

    2015-06-21

    We develop a hierarchy of approximations to the master equation for systems that exhibit translational invariance and finite-range spatial correlation. Each approximation within the hierarchy is a set of ordinary differential equations that considers spatial correlations of varying lattice distance; the assumption is that the full system will have finite spatial correlations and thus the behavior of the models within the hierarchy will approach that of the full system. We provide evidence of this convergence in the context of one- and two-dimensional numerical examples. Lower levels within the hierarchy that consider shorter spatial correlations are shown to be up to three orders of magnitude faster than traditional kinetic Monte Carlo methods (KMC) for one-dimensional systems, while predicting similar system dynamics and steady states as KMC methods. We then test the hierarchy on a two-dimensional model for the oxidation of CO on RuO2(110), showing that low-order truncations of the hierarchy efficiently capture the essential system dynamics. By considering sequences of models in the hierarchy that account for longer spatial correlations, successive model predictions may be used to establish empirical approximation of error estimates. The hierarchy may be thought of as a class of generalized phenomenological kinetic models since each element of the hierarchy approximates the master equation and the lowest level in the hierarchy is identical to a simple existing phenomenological kinetic models.

  19. Theory of warm ionized gases: equation of state and kinetic Schottky anomaly.

    Science.gov (United States)

    Capolupo, A; Giampaolo, S M; Illuminati, F

    2013-10-01

    Based on accurate Lennard-Jones-type interaction potentials, we derive a closed set of state equations for the description of warm atomic gases in the presence of ionization processes. The specific heat is predicted to exhibit peaks in correspondence to single and multiple ionizations. Such kinetic analog in atomic gases of the Schottky anomaly in solids is enhanced at intermediate and low atomic densities. The case of adiabatic compression of noble gases is analyzed in detail and the implications on sonoluminescence are discussed. In particular, the predicted plasma electron density in a sonoluminescent bubble turns out to be in good agreement with the value measured in recent experiments.

  20. Nonlinear quantum fluid equations for a finite temperature Fermi plasma

    International Nuclear Information System (INIS)

    Eliasson, Bengt; Shukla, Padma K

    2008-01-01

    Nonlinear quantum electron fluid equations are derived, taking into account the moments of the Wigner equation and by using the Fermi-Dirac equilibrium distribution for electrons with an arbitrary temperature. A simplified formalism with the assumptions of incompressibility of the distribution function is used to close the moments in velocity space. The nonlinear quantum diffraction effects into the fluid equations are incorporated. In the high-temperature limit, we retain the nonlinear fluid equations for a dense hot plasma and in the low-temperature limit, we retain the correct fluid equations for a fully degenerate plasma

  1. Corrections to classical kinetic and transport theory for a two-temparature, fully ionized plasma in electromagnetic fields

    International Nuclear Information System (INIS)

    Oeien, A.H.

    1977-06-01

    Sets of lower order and higher order kinetic and macroscopic equations are developed for a plasma where collisions are important but electrons and ions are allowed to have different temperatures when transports, due to gradients and fields, set in. Solving the lower order kinetic equations and taking appropriate velocity moments we show that usual classical transports emerge. From the higher order kinetic equations special notice is taken of some new correction terms to the classical transports. These corrections are linear in gradients and fields, some of which are found in a two-temperature state only. (Auth.)

  2. HIDENEK: an implicit particle simulation of kinetic-MHD phenomena in three-dimensional plasmas

    International Nuclear Information System (INIS)

    Tanaka, Motohiko.

    1993-05-01

    An advanced 'kinetic-MHD' simulation method and its applications to plasma physics are given in this lecture. This method is quite suitable for studying strong nonlinear, kinetic processes associated with large space-scale, low-frequency electromagnetic phenomena of plasmas. A full set of the Maxwell equations, and the Newton-Lorentz equations of motion for particle ions and guiding-center electrons are adopted. In order to retain only the low-frequency waves and instabilities, implicit particle-field equations are derived. The present implicit-particle method is proved to reproduce the MHD eigenmodes such as Alfven, magnetosonic and kinetic Alfven waves in a thermally near-equilibrium plasma. In the second part of the lecture, several physics applications are shown. These include not only the growth of the instabilities of beam ions against the background plasmas and helical kink of the current, but they also demonstrate nonlinear results such as pitch-angle scattering of the ions. Recent progress in the simulation of the Kelvin-Helmholtz instability is also presented with a special emphasis on the mixing of plasma particles. (author)

  3. From quantum to semiclassical kinetic equations: Nuclear matter estimates

    International Nuclear Information System (INIS)

    Galetti, D.; Mizrahi, S.S.; Nemes, M.C.; Toledo Piza, A.F.R. de

    1985-01-01

    Starting from the exact microscopic time evolution of the quantum one body density associated with a many fermion system semiclassical approximations are derived to it. In the limit where small momentum transfer two body collisions are dominant we get a Fokker-Planck equation and work out friction and diffusion tensors explicitly for nuclear matter. If arbitrary momentum transfers are considered a Boltzmann equation is derived and used to calculate the viscosity coefficient of nuclear matter. A derivation is given of the collision term used by Landau to describe the damping of zero sound waves at low temperature in Plasmas. Memory effects are essential for this. The damping of zero sound waves in nuclear matter is also calculated and the value so obtained associated with the bulk value of the damping of giant resonances in finite nuclei. The bulk value is estimated to be quite small indicating the importance of the nuclear surface for the damping. (Author) [pt

  4. Kinetic modelling of runaway electron avalanches in tokamak plasmas

    International Nuclear Information System (INIS)

    Nilsson, E; Peysson, Y; Saint-Laurent, F; Decker, J; Granetz, R S; Vlainic, M

    2015-01-01

    Runaway electrons can be generated in tokamak plasmas if the accelerating force from the toroidal electric field exceeds the collisional drag force owing to Coulomb collisions with the background plasma. In ITER, disruptions are expected to generate runaway electrons mainly through knock-on collisions (Hender et al 2007 Nucl. Fusion 47 S128–202), where enough momentum can be transferred from existing runaways to slow electrons to transport the latter beyond a critical momentum, setting off an avalanche of runaway electrons. Since knock-on runaways are usually scattered off with a significant perpendicular component of the momentum with respect to the local magnetic field direction, these particles are highly magnetized. Consequently, the momentum dynamics require a full 3D kinetic description, since these electrons are highly sensitive to the magnetic non-uniformity of a toroidal configuration. For this purpose, a bounce-averaged knock-on source term is derived. The generation of runaway electrons from the combined effect of Dreicer mechanism and knock-on collision process is studied with the code LUKE, a solver of the 3D linearized bounce-averaged relativistic electron Fokker–Planck equation (Decker and Peysson 2004 DKE: a fast numerical solver for the 3D drift kinetic equation Report EUR-CEA-FC-1736, Euratom-CEA), through the calculation of the response of the electron distribution function to a constant parallel electric field. The model, which has been successfully benchmarked against the standard Dreicer runaway theory now describes the runaway generation by knock-on collisions as proposed by Rosenbluth (Rosenbluth and Putvinski 1997 Nucl. Fusion 37 1355–62). This paper shows that the avalanche effect can be important even in non-disruptive scenarios. Runaway formation through knock-on collisions is found to be strongly reduced when taking place off the magnetic axis, since trapped electrons can not contribute to the runaway electron population. Finally

  5. Modified mean generation time parameter in the neutron point kinetics equations

    Energy Technology Data Exchange (ETDEWEB)

    Diniz, Rodrigo C.; Gonçalves, Alessandro C.; Rosa, Felipe S.S., E-mail: alessandro@nuclear.ufrj.br, E-mail: frosa@if.ufrj.br [Coordenacao de Pos-Graduacao e Pesquisa de Engenharia (PEN/COPPE/UFRJ), Rio de Janeiro, RJ (Brazil)

    2017-07-01

    This paper proposes an approximation for the modified point kinetics equations proposed by NUNES et. al, 2015, through the adjustment of a kinetic parameter. This approximation consists of analyzing the terms of the modified point kinetics equations in order to identify the least important ones for the solution, resulting in a modification of the mean generation time parameter that incorporates all influences of the additional terms of the modified kinetics. This approximation is applied on the inverse kinetics, to compare the results with the inverse kinetics from the modified kinetics in order to validate the proposed model. (author)

  6. Modified mean generation time parameter in the neutron point kinetics equations

    International Nuclear Information System (INIS)

    Diniz, Rodrigo C.; Gonçalves, Alessandro C.; Rosa, Felipe S.S.

    2017-01-01

    This paper proposes an approximation for the modified point kinetics equations proposed by NUNES et. al, 2015, through the adjustment of a kinetic parameter. This approximation consists of analyzing the terms of the modified point kinetics equations in order to identify the least important ones for the solution, resulting in a modification of the mean generation time parameter that incorporates all influences of the additional terms of the modified kinetics. This approximation is applied on the inverse kinetics, to compare the results with the inverse kinetics from the modified kinetics in order to validate the proposed model. (author)

  7. Solution of the non-stationary electron Boltzmann equation for a weakly ionized collision dominated plasma

    International Nuclear Information System (INIS)

    Winkler, R.; Wilhelm, J.

    A detailed description is presented of calculating the nonstationary electron distribution function in a weakly ionized collision-dominated plasma from the Boltzmann kinetic equation respecting the effects of the time-dependent electric field, collision processes and the electron formation and loss. The finite difference approximation was used for numerical solution. Using the Crank-Nicolson method and parabolic interpolation between the grid points the Boltzmann equation was transformed to a system of linear equations which was then solved by iterations at a preset accuracy. Using the calculated distribution function values, the macroscopic plasma parameters were determined and the balance of electron density and energy checked in each time step. The mathematical procedure is illustrated using a neon plasma perturbed by a rectangular electric pulse. The time development shown of the distribution function at moments when the pulse was switched on and off demonstrates the great stability of the numerical solution. (J.U.)

  8. Hydrodynamic limits of kinetic equations for polyatomic and reactive gases

    Directory of Open Access Journals (Sweden)

    Bisi M.

    2017-03-01

    Full Text Available Starting from a kinetic BGK-model for a rarefied polyatomic gas, based on a molecular structure of discrete internal energy levels, an asymptotic Chapman-Enskog procedure is developed in the asymptotic continuum limit in order to derive consistent fluid-dynamic equations for macroscopic fields at Navier-Stokes level. In this way, the model allows to treat the gas as a mixture of mono-atomic species. Explicit expressions are given not only for dynamical pressure, but also for shear stress, diffusion velocities, and heat flux. The analysis is shown to deal properly also with a mixture of reactive gases, endowed for simplicity with translational degrees of freedom only, in which frame analogous results can be achieved.

  9. Measuring the equations of state in a relaxed magnetohydrodynamic plasma

    Science.gov (United States)

    Kaur, M.; Barbano, L. J.; Suen-Lewis, E. M.; Shrock, J. E.; Light, A. D.; Brown, M. R.; Schaffner, D. A.

    2018-01-01

    We report measurements of the equations of state of a fully relaxed magnetohydrodynamic (MHD) laboratory plasma. Parcels of magnetized plasma, called Taylor states, are formed in a coaxial magnetized plasma gun, and are allowed to relax and drift into a closed flux conserving volume. Density, ion temperature, and magnetic field are measured as a function of time as the Taylor states compress and heat. The theoretically predicted MHD and double adiabatic equations of state are compared to experimental measurements. We find that the MHD equation of state is inconsistent with our data.

  10. Plasma kinetics of 125I beta endorphin turnover in lean and obese Zucker rats

    International Nuclear Information System (INIS)

    Rodd, D.; Caston, A.L.; Green, M.H.; Farrell, P.A.

    1990-01-01

    Plasma clearance kinetics for Beta Endorphin (BEP) are not well-defined and no definitive data exist for lean versus obese animals. To determine such kinetic parameters, a bolus of 125 I BEP (1μCi/kg) was infused into awake lean(L) and obese(O) Zucker rats. Arterial blood samples were withdrawn initially at 20 seconds intervals and less frequently as a 3-hour experimental period progressed. Donor rat blood was infused (venous catheter) to replace withdrawn blood. At 180 minutes approximately 10% of the initial dose remained in the plasma. Clearance kinetics for 125 I BEP were analyzed by compartmental analysis. A 3-component equation (i.e., 3 compartment model) provided the best fit for both L and O groups. Plasma transit times were very rapid; however, plasma fractional catabolic rate was low. Plasma mean residence time was similar for both groups (50 minutes) as was recycle time. These data suggest that BEP kinetics are similar in L and O rats, and that this peptide may undergo extensive recycling into and out of the plasma compartment. The identity of the other two compartments requires further investigation

  11. Plasma kinetics of sup 125 I beta endorphin turnover in lean and obese Zucker rats

    Energy Technology Data Exchange (ETDEWEB)

    Rodd, D.; Caston, A.L.; Green M.H.; Farrell, P.A. (Pennsylvania State Univ., University Park (United States))

    1990-02-26

    Plasma clearance kinetics for Beta Endorphin (BEP) are not well-defined and no definitive data exist for lean versus obese animals. To determine such kinetic parameters, a bolus of {sup 125}I BEP (1{mu}Ci/kg) was infused into awake lean(L) and obese(O) Zucker rats. Arterial blood samples were withdrawn initially at 20 seconds intervals and less frequently as a 3-hour experimental period progressed. Donor rat blood was infused (venous catheter) to replace withdrawn blood. At 180 minutes approximately 10% of the initial dose remained in the plasma. Clearance kinetics for {sup 125}I BEP were analyzed by compartmental analysis. A 3-component equation (i.e., 3 compartment model) provided the best fit for both L and O groups. Plasma transit times were very rapid; however, plasma fractional catabolic rate was low. Plasma mean residence time was similar for both groups (50 minutes) as was recycle time. These data suggest that BEP kinetics are similar in L and O rats, and that this peptide may undergo extensive recycling into and out of the plasma compartment. The identity of the other two compartments requires further investigation.

  12. Kinetic and radiation processes in cluster plasmas

    International Nuclear Information System (INIS)

    Smirnov, B.M.

    1996-01-01

    The analysis of processes is made for a cluster plasma which is a xenon arc plasma of a high pressure with an admixture of tungsten cluster ions. Because cluster ions emit radiation, this system is a light source which parameters are determined by various processes such as heat release and transport of charged particles in the plasma, radiative processes involving clusters, processes of cluster evaporation and attachment of atoms to it that leads to an equilibrium between clusters and vapor of their atoms, processes of cluster generation, processes of the ionization equilibrium between cluster ions and plasma electrons, transport of cluster ions in the discharge plasma in all directions. These processes govern by properties of a specific cluster plasma under consideration. (author)

  13. One-dimensional hybrid-direct kinetic simulation of the discharge plasma in a Hall thruster

    International Nuclear Information System (INIS)

    Hara, Kentaro; Boyd, Iain D.; Kolobov, Vladimir I.

    2012-01-01

    In order to model the non-equilibrium plasma within the discharge region of a Hall thruster, the velocity distribution functions (VDFs) must be obtained accurately. A direct kinetic (DK) simulation method that directly solves the plasma Boltzmann equation can achieve better resolution of VDFs in comparison to particle simulations, such as the particle-in-cell (PIC) method that inherently include statistical noise. In this paper, a one-dimensional hybrid-DK simulation, which uses a DK simulation for heavy species and a fluid model for electrons, is developed and compared to a hybrid-PIC simulation. Time-averaged results obtained from the hybrid-DK simulation are in good agreement with hybrid-PIC results and experimental data. It is shown from a comparison of using a kinetic simulation and solving the continuity equation that modeling of the neutral atoms plays an important role for simulations of the Hall thruster discharge plasma. In addition, low and high frequency plasma oscillations are observed. Although the kinetic nature of electrons is not resolved due to the use of a fluid model, the hybrid-DK model provides spatially and temporally well-resolved plasma properties and an improved resolution of VDFs for heavy species with less statistical noise in comparison to the hybrid-PIC method.

  14. An auxiliary differential equation FDTD method for anisotropic magnetized plasmas

    International Nuclear Information System (INIS)

    Liu Shaobin; Mo Jinjun; Yuan Naichang

    2004-01-01

    An auxiliary differential equation finite-difference time-domain (ADE-FDTD) methodology for anisotropic magnetized plasmas is derived. The method is based on a difference approximation of the auxiliary differential equation. A comparison with the JEC method is included. The CPU time saving by several times and accuracy of the method are confirmed by computing the reflection and transmission through a magnetized plasma layer with the direction of propagation parallel to the direction of the biasing field

  15. Energy Conservation Tests of a Coupled Kinetic-kinetic Plasma-neutral Transport Code

    Energy Technology Data Exchange (ETDEWEB)

    Stotler, D. P.; Chang, C. S.; Ku, S. H.; Lang, J.; Park, G.

    2012-08-29

    A Monte Carlo neutral transport routine, based on DEGAS2, has been coupled to the guiding center ion-electron-neutral neoclassical PIC code XGC0 to provide a realistic treatment of neutral atoms and molecules in the tokamak edge plasma. The DEGAS2 routine allows detailed atomic physics and plasma-material interaction processes to be incorporated into these simulations. The spatial pro le of the neutral particle source used in the DEGAS2 routine is determined from the uxes of XGC0 ions to the material surfaces. The kinetic-kinetic plasma-neutral transport capability is demonstrated with example pedestal fueling simulations.

  16. Iterative Addition of Kinetic Effects to Cold Plasma RF Wave Solvers

    Science.gov (United States)

    Green, David; Berry, Lee; RF-SciDAC Collaboration

    2017-10-01

    The hot nature of fusion plasmas requires a wave vector dependent conductivity tensor for accurate calculation of wave heating and current drive. Traditional methods for calculating the linear, kinetic full-wave plasma response rely on a spectral method such that the wave vector dependent conductivity fits naturally within the numerical method. These methods have seen much success for application to the well-confined core plasma of tokamaks. However, quantitative prediction of high power RF antenna designs for fusion applications has meant a requirement of resolving the geometric details of the antenna and other plasma facing surfaces for which the Fourier spectral method is ill-suited. An approach to enabling the addition of kinetic effects to the more versatile finite-difference and finite-element cold-plasma full-wave solvers was presented by where an operator-split iterative method was outlined. Here we expand on this approach, examine convergence and present a simplified kinetic current estimator for rapidly updating the right-hand side of the wave equation with kinetic corrections. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725.

  17. Global weak solution for a equations in plasma

    International Nuclear Information System (INIS)

    Guo Boling; Huang Daiwen

    2010-01-01

    The existence of global weak solutions of the initial boundary value problem to a simplified equations, derived from the equations of two fluid system in plasma, is proven by using energy method and some embedding theorems in Sobolev-Orlicz space.

  18. Kinetic theory of plasma in the limiter-scrape-off layer

    International Nuclear Information System (INIS)

    Daybelge, U.; Bein, B.

    1977-01-01

    An asymptotic solution is given for the ion-drift-kinetic equation with a full Fokker--Planck term for the limiter-scrape-off layer in a tokamak. In this layer, the plasma is assumed to consist of hot, collisionless ions, and cold, collisional electrons. From the solution of the boundary-layer problem, ion and electron particle and energy losses to the limiter are calculated. Limiter load profiles due to ions are explicitly given as functions of the poloidal angle

  19. The classical equation of state of fully ionized plasmas

    Science.gov (United States)

    Eisa, Dalia Ahmed

    2011-03-01

    The aim of this paper is to calculate the analytical form of the equation of state until the third virial coefficient of a classical system interacting via an effective potential of fully Ionized Plasmas. The excess osmotic pressure is represented in the forms of a convergent series expansions in terms of the plasma Parameter μ _{ab} = {{{e_a e_b χ } over {DKT}}}, where χ2 is the square of the inverse Debye radius. We consider only the thermal equilibrium plasma.

  20. Kinetic Modifications to MHD Phenomena in Toroidal Plasmas

    International Nuclear Information System (INIS)

    Cheng, C.Z.; Gorelenkov, N.N.; Kramer, G.J.; Fredrickson, E.

    2004-01-01

    Particle kinetic effects involving small spatial and fast temporal scales can strongly affect MHD phenomena and the long time behavior of plasmas. In particular, kinetic effects such as finite ion gyroradii, trapped particle dynamics, and wave-particle resonances have been shown to greatly modify the stability of MHD modes. Here, the kinetic effects of trapped electron dynamics and finite ion gyroradii are shown to have a large stabilizing effect on kinetic ballooning modes in low aspect ratio toroidal plasmas such as NSTX [National Spherical Torus Experiment]. We also present the analysis of Toroidicity-induced Alfven Eigenmodes (TAEs) destabilized by fast neutral-beam injected ions in NSTX experiments and TAE stability in ITER due to alpha-particles and MeV negatively charged neutral beam injected ions

  1. Kinetic calculation of plasma deposition in castellated tile gaps

    International Nuclear Information System (INIS)

    Dejarnac, R.; Gunn, J.P.

    2007-01-01

    Plasma-facing divertors and limiters are armoured with castellated tiles to withstand intense heat fluxes. Recent experimental studies show that a non-negligible amount of deuterium is deposited in the gaps between tiles. We present here a numerical study of plasma deposition in this critical region. For this purpose we have developed a particle-in-cell code with realistic boundary conditions determined from kinetic calculations. We find a strong asymmetry of plasma deposition into the gaps. A significant fraction of the plasma influx is expelled from the gap to be deposited on the leading edge of the downstream tile

  2. Effective potential kinetic theory for strongly coupled plasmas

    Science.gov (United States)

    Baalrud, Scott D.; Daligault, Jérôme

    2016-11-01

    The effective potential theory (EPT) is a recently proposed method for extending traditional plasma kinetic and transport theory into the strongly coupled regime. Validation from experiments and molecular dynamics simulations have shown it to be accurate up to the onset of liquid-like correlation parameters (corresponding to Γ ≃ 10-50 for the one-component plasma, depending on the process of interest). Here, this theory is briefly reviewed along with comparisons between the theory and molecular dynamics simulations for self-diffusivity and viscosity of the one-component plasma. A number of new results are also provided, including calculations of friction coefficients, energy exchange rates, stopping power, and mobility. The theory is also cast in the Landau and Fokker-Planck kinetic forms, which may prove useful for enabling efficient kinetic computations.

  3. Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation

    Science.gov (United States)

    Karney, C. F. F.

    1977-01-01

    Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.

  4. Study on the numerical analysis of nuclear reactor kinetics equations

    International Nuclear Information System (INIS)

    Yang, J.C.

    1980-01-01

    A two-step alternating direction explict method is proposed for the solution of the space-and time-dependent diffusion theory reactor kinetics equations in two space dimensions as a special case of the general class of alternating direction implicit method and the truncation error of this method is estimated. To test the validity of this method it is applied to the Pressurized Water Reactor and CANDU-PHW reactor which have been operating and underconstructing in Korea. The time dependent neutron flux of the PWR reactor during control rod insertion and time dependent neutronic power of CANDU-PHW reactor in the case of postulated loss of coolant accident are obtained from the numerical calculation results. The results of the PWR reactor problem are shown the close agreement between implicit-difference method used in the TWIGL program and this method, and the results of the CANDU-PHW reactor are compared with the results of improved quasistic method and modal method. (Author)

  5. Charge exchange of muons in gases: I. Kinetic equations

    International Nuclear Information System (INIS)

    Turner, R.E.

    1983-06-01

    Kinetic equations for the spin density operators of the diamagnetic and paramagnetic states of the positive muon are obtained for the description of the slowing-down process encountered when high energy muons thermalize in a single component gas. The motion of this two species system is generated by the Liouville superoperators associated with the diamagnetic and paramagnetic spin Hamiltonians and by time-dependent rate superoperators which depict the probabilities per collision that an electron is captured or lost. These rates are translational averages of the appropriate Boltzmann collision operators. That is, they are momentum and position integrals of the product of either the electron capture or loss total cross section with the single particle translational density operators for the muon (or muonium) and a gas particle. These rates are time dependent because the muon (or muonium) translational density operator is time dependent. The initial amplitudes and phases of the observed thermal spin polarization in μSR experiments are then obtained in terms of the spin density operators emerging from the stopping regime

  6. Charge exchange of muons in gases. Kinetic equations

    International Nuclear Information System (INIS)

    Turner, R.E.

    1983-01-01

    Kinetic equations for the spin-density operators of the diamagnetic and paramagnetic states of the positive muon are obtained for the description of the slowing-down process encountered when high-energy muons thermalize in a single-component gas. The motion of this two-species system is generated by the Liouville superoperators associated with the diamagnetic and paramagnetic spin Hamiltonians and by time-dependent rate superoperators which depict the probabilities per collision that an electron is captured or lost. These rates are translational averages of the appropriate Boltzmann collision operators. That is, they are momentum and position integrals of the product of either the electron capture or loss total cross section with the single-particle translational density operators for the muon (or muonium) and a gas particle. These rates are time dependent because the muon (or muonium) translational density operator is time dependent. The initial amplitudes and phases of the observed thermal spin polarization in muon-spin-rotation (μSR) experiments are then obtained in terms of the spin-density operators emerging from the stopping regime

  7. A multi water bag model of drift kinetic electron plasma

    International Nuclear Information System (INIS)

    Morel, P.; Dreydemy Ghiro, F.; Berionni, V.; Gurcan, O.D.; Coulette, D.; Besse, N.

    2014-01-01

    A Multi Water Bag model is proposed for describing drift kinetic plasmas in a magnetized cylindrical geometry, relevant for various experimental devices, solar wind modeling... The Multi Water Bag (MWB) model is adapted to the description of a plasma with kinetic electrons as well as an arbitrary number of kinetic ions. This allows to describe the kinetic dynamics of the electrons, making possible the study of electron temperature gradient (ETG) modes, in addition to the effects of non adiabatic electrons on the ion temperature gradient (ITG) modes, that are of prime importance in the magnetized plasmas micro-turbulence [X. Garbet, Y. Idomura, L. Villard, T.H. Watanabe, Nucl. Fusion 50, 043002 (2010); J.A. Krommes, Ann. Rev. Fluid Mech. 44, 175 (2012)]. The MWB model is shown to link kinetic and fluid descriptions, depending on the number of bags considered. Linear stability of the ETG modes is presented and compared to the existing results regarding cylindrical ITG modes [P. Morel, E. Gravier, N. Besse, R. Klein, A. Ghizzo, P. Bertrand, W. Garbet, Ph. Ghendrih, V. Grandgirard, Y. Sarazin, Phys. Plasmas 14, 112109 (2007)]. (authors)

  8. Hydrodynamization and transient modes of expanding plasma in kinetic theory

    CERN Document Server

    Heller, Michal P.; Spalinski, Michal

    2016-01-01

    We study the transition to hydrodynamics in a weakly-coupled model of quark-gluon plasma given by kinetic theory in the relaxation time approximation. Our studies uncover qualitative similarities to the results on hydrodynamization in strongly coupled gauge theories. In particular, we demonstrate that the gradient expansion in this model has vanishing radius of convergence. The asymptotic character of the hydrodynamic gradient expansion is crucial for the recently discovered applicability of hydrodynamics at large gradients. Furthermore, the analysis of the resurgent properties of the series provides, quite remarkably, indication for the existence of a novel transient, damped oscillatory mode of expanding plasmas in kinetic theory.

  9. Fully kinetic simulations of megajoule-scale dense plasma focus

    Energy Technology Data Exchange (ETDEWEB)

    Schmidt, A.; Link, A.; Tang, V.; Halvorson, C.; May, M. [Lawrence Livermore National Laboratory, Livermore California 94550 (United States); Welch, D. [Voss Scientific, LLC, Albuquerque, New Mexico 87108 (United States); Meehan, B. T.; Hagen, E. C. [National Security Technologies, LLC, Las Vegas, Nevada 89030 (United States)

    2014-10-15

    Dense plasma focus (DPF) Z-pinch devices are sources of copious high energy electrons and ions, x-rays, and neutrons. Megajoule-scale DPFs can generate 10{sup 12} neutrons per pulse in deuterium gas through a combination of thermonuclear and beam-target fusion. However, the details of the neutron production are not fully understood and past optimization efforts of these devices have been largely empirical. Previously, we reported on the first fully kinetic simulations of a kilojoule-scale DPF and demonstrated that both kinetic ions and kinetic electrons are needed to reproduce experimentally observed features, such as charged-particle beam formation and anomalous resistivity. Here, we present the first fully kinetic simulation of a MegaJoule DPF, with predicted ion and neutron spectra, neutron anisotropy, neutron spot size, and time history of neutron production. The total yield predicted by the simulation is in agreement with measured values, validating the kinetic model in a second energy regime.

  10. Kinetic description of quasi-stationary axisymmetric collisionless accretion disk plasmas with arbitrary magnetic field configurations

    International Nuclear Information System (INIS)

    Cremaschini, Claudio; Miller, John C.; Tessarotto, Massimo

    2011-01-01

    A kinetic treatment is developed for collisionless magnetized plasmas occurring in high-temperature, low-density astrophysical accretion disks, such as are thought to be present in some radiatively inefficient accretion flows onto black holes. Quasi-stationary configurations are investigated, within the framework of a Vlasov-Maxwell description. The plasma is taken to be axisymmetric and subject to the action of slowly time-varying gravitational and electromagnetic fields. The magnetic field is assumed to be characterized by a family of locally nested but open magnetic surfaces. The slow collisionless dynamics of these plasmas is investigated, yielding a reduced gyrokinetic Vlasov equation for the kinetic distribution function. For doing this, an asymptotic quasi-stationary solution is first determined, represented by a generalized bi-Maxwellian distribution expressed in terms of the relevant adiabatic invariants. The existence of the solution is shown to depend on having suitable kinetic constraints and conditions leading to particle trapping phenomena. With this solution, one can treat temperature anisotropy, toroidal and poloidal flow velocities, and finite Larmor-radius effects. An asymptotic expansion for the distribution function permits analytic evaluation of all the relevant fluid fields. Basic theoretical features of the solution and their astrophysical implications are discussed. As an application, the possibility of describing the dynamics of slowly time-varying accretion flows and the self-generation of magnetic field by means of a ''kinetic dynamo effect'' are discussed. Both effects are shown to be related to intrinsically kinetic physical mechanisms.

  11. Viriato: a Fourier-Hermite spectral code for strongly magnetised fluid-kinetic plasma dynamics

    Science.gov (United States)

    Loureiro, Nuno; Dorland, William; Fazendeiro, Luis; Kanekar, Anjor; Mallet, Alfred; Zocco, Alessandro

    2015-11-01

    We report on the algorithms and numerical methods used in Viriato, a novel fluid-kinetic code that solves two distinct sets of equations: (i) the Kinetic Reduced Electron Heating Model equations [Zocco & Schekochihin, 2011] and (ii) the kinetic reduced MHD (KRMHD) equations [Schekochihin et al., 2009]. Two main applications of these equations are magnetised (Alfvnénic) plasma turbulence and magnetic reconnection. Viriato uses operator splitting to separate the dynamics parallel and perpendicular to the ambient magnetic field (assumed strong). Along the magnetic field, Viriato allows for either a second-order accurate MacCormack method or, for higher accuracy, a spectral-like scheme. Perpendicular to the field Viriato is pseudo-spectral, and the time integration is performed by means of an iterative predictor-corrector scheme. In addition, a distinctive feature of Viriato is its spectral representation of the parallel velocity-space dependence, achieved by means of a Hermite representation of the perturbed distribution function. A series of linear and nonlinear benchmarks and tests are presented, with focus on 3D decaying kinetic turbulence. Work partially supported by Fundação para a Ciência e Tecnologia via Grants UID/FIS/50010/2013 and IF/00530/2013.

  12. Two new proofs of the test particle superposition principle of plasma kinetic theory

    International Nuclear Information System (INIS)

    Krommes, J.A.

    1975-12-01

    The test particle superposition principle of plasma kinetic theory is discussed in relation to the recent theory of two-time fluctuations in plasma given by Williams and Oberman. Both a new deductive and a new inductive proof of the principle are presented. The fundamental observation is that two-time expectations of one-body operators are determined completely in terms of the (x,v) phase space density autocorrelation, which to lowest order in the discreteness parameter obeys the linearized Vlasov equation with singular initial condition. For the deductive proof, this equation is solved formally using time-ordered operators, and the solution then rearranged into the superposition principle. The inductive proof is simpler than Rostoker's, although similar in some ways; it differs in that first order equations for pair correlation functions need not be invoked. It is pointed out that the superposition principle is also applicable to the short-time theory of neutral fluids

  13. KINETIC THEORY OF PLASMA WAVES: Part II: Homogeneous Plasma

    NARCIS (Netherlands)

    Westerhof, E.

    2010-01-01

    The theory of electromagnetic waves in a homogeneous plasma is reviewed. The linear response of the plasma to the waves is obtained in the form of the dielectric tensor. Waves ranging from the low frequency Alfven to the high frequency electron cyclotron waves are discussed in the limit of the cold

  14. Kinetic theory of plasma waves: Part II homogeneous plasma

    NARCIS (Netherlands)

    Westerhof, E.

    2000-01-01

    The theory of electromagnetic waves in a homogeneous plasma is reviewed. The linear response of the plasma to the waves is obtained in the form of the dielectric tensor. Waves ranging from the low frequency Alfven to the high frequency electron cyclotron waves are discussed in the limit of the cold

  15. Kinetic theory of plasma waves - Part II: Homogeneous plasma

    NARCIS (Netherlands)

    Westerhof, E.

    2008-01-01

    The theory of electromagnetic waves in a homogeneous plasma is reviewed. The linear response of the plasma to the waves is obtained in the form of the dielectric tensor. Waves ranging from the low frequency Alfven to the high frequency electron cyclotron waves axe discussed in the limit of the cold

  16. On a closed form solution of the point kinetics equations with reactivity feedback of temperature

    International Nuclear Information System (INIS)

    Silva, Jeronimo J.A.; Vilhena, Marco T.M.B.; Petersen, Claudio Z.; Bodmann, Bardo E.J.; Alvim, Antonio C.M.

    2011-01-01

    An analytical solution of the point kinetics equations to calculate reactivity as a function of time by the Decomposition method has recently appeared in the literature. In this paper, we go one step forward, by considering the neutron point kinetics equations together with temperature feedback effects. To accomplish that, we extended the point kinetics by a temperature perturbation, obtaining a second order nonlinear ordinary differential equation. This equation is then solved by the Decomposition Method, that is, by expanding the neutron density in a series and the nonlinear terms into Adomian Polynomials. Substituting these expansions into the nonlinear ordinary equation, we construct a recursive set of linear problems that can be solved by the methodology previously mentioned for the point kinetics equation. We also report on numerical simulations and comparisons against literature results. (author)

  17. Probes, Moons, and Kinetic Plasma Wakes

    Science.gov (United States)

    Hutchinson, I. H.; Malaspina, D.; Zhou, C.

    2017-10-01

    Nonmagnetic objects as varied as probes in tokamaks or moons in space give rise to flowing plasma wakes in which strong distortions of the ion and electron velocity distributions cause electrostatic instabilities. Non-linear phenomena such as electron holes are then produced. Historic probe theory largely ignores the resulting unstable character of the wake, but since we can now simulate computationally the non-linear wake phenomena, a timely challenge is to reassess the influence of these instabilities both on probe measurements and on the wakes themselves. Because the electron instability wavelengths are very short (typically a few Debye-lengths), controlled laboratory experiments face serious challenges in diagnosing them. That is one reason why they have long been neglected as an influence in probe interpretation. Space-craft plasma observations, by contrast, easily obtain sub-Debye-length resolution, but have difficulty with larger-scale reconstruction of the plasma spatial variation. In addition to surveying our developing understanding of wakes in magnetized plasmas, ongoing analysis of Artemis data concerning electron holes observed in the solar-wind lunar wake will be featured. Work partially supported by NASA Grant NNX16AG82G.

  18. A generalized electron energy probability function for inductively coupled plasmas under conditions of nonlocal electron kinetics

    Science.gov (United States)

    Mouchtouris, S.; Kokkoris, G.

    2018-01-01

    A generalized equation for the electron energy probability function (EEPF) of inductively coupled Ar plasmas is proposed under conditions of nonlocal electron kinetics and diffusive cooling. The proposed equation describes the local EEPF in a discharge and the independent variable is the kinetic energy of electrons. The EEPF consists of a bulk and a depleted tail part and incorporates the effect of the plasma potential, Vp, and pressure. Due to diffusive cooling, the break point of the EEPF is eVp. The pressure alters the shape of the bulk and the slope of the tail part. The parameters of the proposed EEPF are extracted by fitting to measure EEPFs (at one point in the reactor) at different pressures. By coupling the proposed EEPF with a hybrid plasma model, measurements in the gaseous electronics conference reference reactor concerning (a) the electron density and temperature and the plasma potential, either spatially resolved or at different pressure (10-50 mTorr) and power, and (b) the ion current density of the electrode, are well reproduced. The effect of the choice of the EEPF on the results is investigated by a comparison to an EEPF coming from the Boltzmann equation (local electron kinetics approach) and to a Maxwellian EEPF. The accuracy of the results and the fact that the proposed EEPF is predefined renders its use a reliable alternative with a low computational cost compared to stochastic electron kinetic models at low pressure conditions, which can be extended to other gases and/or different electron heating mechanisms.

  19. On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity

    Directory of Open Access Journals (Sweden)

    Nikolai N. Bogoliubov (Jr.

    2007-01-01

    Full Text Available A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.

  20. Effective computation of stochastic protein kinetic equation by reducing stiffness via variable transformation

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Lijin, E-mail: ljwang@ucas.ac.cn [School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049 (China)

    2016-06-08

    The stochastic protein kinetic equations can be stiff for certain parameters, which makes their numerical simulation rely on very small time step sizes, resulting in large computational cost and accumulated round-off errors. For such situation, we provide a method of reducing stiffness of the stochastic protein kinetic equation by means of a kind of variable transformation. Theoretical and numerical analysis show effectiveness of this method. Its generalization to a more general class of stochastic differential equation models is also discussed.

  1. An analytical solution of the one-dimensional neutron diffusion kinetic equation in cartesian geometry

    International Nuclear Information System (INIS)

    Ceolin, Celina; Vilhena, Marco T.; Petersen, Claudio Z.

    2009-01-01

    In this work we report an analytical solution for the monoenergetic neutron diffusion kinetic equation in cartesian geometry. Bearing in mind that the equation for the delayed neutron precursor concentration is a first order linear differential equation in the time variable, to make possible the application of the GITT approach to the kinetic equation, we introduce a fictitious diffusion term multiplied by a positive small value ε. By this procedure, we are able to solve this set of equations. Indeed, applying the GITT technique to the modified diffusion kinetic equation, we come out with a matrix differential equation which has a well known analytical solution when ε goes to zero. We report numerical simulations as well study of numerical convergence of the results attained. (author)

  2. Nonlinear electrostatic wave equations for magnetized plasmas - II

    DEFF Research Database (Denmark)

    Dysthe, K. B.; Mjølhus, E.; Pécseli, H. L.

    1985-01-01

    For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent (electrosta......For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent...... (electrostatic) cut-off implies that various cases must be considered separately, leading to equations with rather different properties. Various equations encountered previously in the literature are recovered as limiting cases....

  3. Numerical solution of plasma fluid equations using locally refined grids

    International Nuclear Information System (INIS)

    Colella, P.

    1997-01-01

    This paper describes a numerical method for the solution of plasma fluid equations on block-structured, locally refined grids. The plasma under consideration is typical of those used for the processing of semiconductors. The governing equations consist of a drift-diffusion model of the electrons and an isothermal model of the ions coupled by Poisson's equation. A discretization of the equations is given for a uniform spatial grid, and a time-split integration scheme is developed. The algorithm is then extended to accommodate locally refined grids. This extension involves the advancement of the discrete system on a hierarchy of levels, each of which represents a degree of refinement, together with synchronization steps to ensure consistency across levels. A brief discussion of a software implementation is followed by a presentation of numerical results

  4. Numerical treatment of linearized equations describing inhomogeneous collisionless plasmas

    International Nuclear Information System (INIS)

    Lewis, H.R.

    1979-01-01

    The equations governing the small-signal response of spatially inhomogeneous collisionless plasmas have practical significance in physics, for example in controlled thermonuclear fusion research. Although the solutions are very complicated and the equations are different to solve numerically, effective methods for them are being developed which are applicable when the equilibrium involves only one nonignorable coordinate. The general theoretical framework probably will provide a basis for progress when there are two or three nonignorable coordinates

  5. Equation of state of strongly coupled plasma mixtures

    International Nuclear Information System (INIS)

    DeWitt, H.E.

    1984-01-01

    Thermodynamic properties of strongly coupled (high density) plasmas of mixtures of light elements have been obtained by Monte Carlo simulations. For an assumed uniform charge background the equation of state of ionic mixtures is a simple extension of the one-component plasma EOS. More realistic electron screening effects are treated in linear response theory and with an appropriate electron dielectric function. Results have been obtained for the ionic pair distribution functions, and for the electric microfield distribution

  6. A quiver kinetic formulation of radio frequency heating and confinement in collisional edge plasmas

    International Nuclear Information System (INIS)

    Catto, P.J.; Myra, J.R.

    1989-01-01

    The near fields in the collisional edge plasma of a radio frequency heated tokamak can cause one or more charged species to oscillate in the applied field with a quiver (or jitter) speed comparable to its thermal speed. By assuming the quiver motion dominates over drifts and gyromotion a completely new kinetic description of the flows in an edge plasma is formulated which retains Coulomb collisions and the relevant atomic processes. Moment equations are employed to obtain a description in which only a lowest order quiver kinetic equation need be solved to evaluate the slow time particle fluxes and current induced by the applied fields. The electron heating by collisional randomization of their quiver motion (inverse bremsstrahlung) is balanced by impact excitation losses since equilibration with the ions is too weak. A model plasma of electrons, neutrals, and a single cold ion species is considered to illustrate the utility of the quiver kinetic formulation. The model predicts local electrostatic potential changes and a local /rvec E//times//rvec B/ convective flux that is of the same magnitude and scaling as would be predicted by Bohm diffusion. 30 refs

  7. Preliminary scaling laws for plasma current, ion kinetic temperature, and plasma number density in the NASA Lewis bumpy torus plasma

    Science.gov (United States)

    Roth, J. R.

    1976-01-01

    Parametric variation of independent variables which may affect the characteristics of bumpy torus plasma have identified those which have a significant effect on the plasma current, ion kinetic temperature, and plasma number density, and those which do not. Empirical power law correlations of the plasma current, and the ion kinetic temperature and number density were obtained as functions of potential applied to the midplane electrode rings, the background neutral gas pressure, and the magnetic field strength. Additional parameters studied included the type of gas, the polarity of the midplane electrode rings, the mode of plasma operation, and the method of measuring the plasma number density. No significant departures from the scaling laws appear to occur at the highest ion kinetic temperatures or number densities obtained to date.

  8. Astrophysical Gyrokinetics: Kinetic and Fluid Turbulent Cascades In Magentized Weakly Collisional Plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Schekochihin, A. A.; Cowley, S. C.; Dorland, W.; Hammett, G. W.; Howes, G. G.; Quataert, E.; Tatsuno, T.

    2009-04-23

    This paper presents a theoretical framework for understanding plasma turbulence in astrophysical plasmas. It is motivated by observations of electromagnetic and density fluctuations in the solar wind, interstellar medium and galaxy clusters, as well as by models of particle heating in accretion disks. All of these plasmas and many others have turbulentmotions at weakly collisional and collisionless scales. The paper focuses on turbulence in a strong mean magnetic field. The key assumptions are that the turbulent fluctuations are small compared to the mean field, spatially anisotropic with respect to it and that their frequency is low compared to the ion cyclotron frequency. The turbulence is assumed to be forced at some system-specific outer scale. The energy injected at this scale has to be dissipated into heat, which ultimately cannot be accomplished without collisions. A kinetic cascade develops that brings the energy to collisional scales both in space and velocity. The nature of the kinetic cascade in various scale ranges depends on the physics of plasma fluctuations that exist there. There are four special scales that separate physically distinct regimes: the electron and ion gyroscales, the mean free path and the electron diffusion scale. In each of the scale ranges separated by these scales, the fully kinetic problem is systematically reduced to a more physically transparent and computationally tractable system of equations, which are derived in a rigorous way. In the "inertial range" above the ion gyroscale, the kinetic cascade separates into two parts: a cascade of Alfvenic fluctuations and a passive cascade of density and magnetic-fieldstrength fluctuations. The former are governed by the Reduced Magnetohydrodynamic (RMHD) equations at both the collisional and collisionless scales; the latter obey a linear kinetic equation along the (moving) field lines associated with the Alfvenic component (in the collisional limit, these compressive fluctuations

  9. Astrophysical Gyrokinetics: Kinetic and Fluid Turbulent Cascades In Magnetized Weakly Collisional Plasmas

    International Nuclear Information System (INIS)

    Schekochihin, A.A.; Cowley, S.C.; Dorland, W.; Hammett, G.W.; Howes, G.G.; Quataert, E.; Tatsuno, T.

    2009-01-01

    This paper presents a theoretical framework for understanding plasma turbulence in astrophysical plasmas. It is motivated by observations of electromagnetic and density fluctuations in the solar wind, interstellar medium and galaxy clusters, as well as by models of particle heating in accretion disks. All of these plasmas and many others have turbulent motions at weakly collisional and collisionless scales. The paper focuses on turbulence in a strong mean magnetic field. The key assumptions are that the turbulent fluctuations are small compared to the mean field, spatially anisotropic with respect to it and that their frequency is low compared to the ion cyclotron frequency. The turbulence is assumed to be forced at some system-specific outer scale. The energy injected at this scale has to be dissipated into heat, which ultimately cannot be accomplished without collisions. A kinetic cascade develops that brings the energy to collisional scales both in space and velocity. The nature of the kinetic cascade in various scale ranges depends on the physics of plasma fluctuations that exist there. There are four special scales that separate physically distinct regimes: the electron and ion gyroscales, the mean free path and the electron diffusion scale. In each of the scale ranges separated by these scales, the fully kinetic problem is systematically reduced to a more physically transparent and computationally tractable system of equations, which are derived in a rigorous way. In the 'inertial range' above the ion gyroscale, the kinetic cascade separates into two parts: a cascade of Alfvenic fluctuations and a passive cascade of density and magnetic-field strength fluctuations. The former are governed by the Reduced Magnetohydrodynamic (RMHD) equations at both the collisional and collisionless scales; the latter obey a linear kinetic equation along the (moving) field lines associated with the Alfvenic component (in the collisional limit, these compressive fluctuations

  10. Kinetic extensions of magnetohydrodynamic models for axisymmetric toroidal plasmas

    International Nuclear Information System (INIS)

    Cheng, C.Z.

    1989-04-01

    A nonvariational kinetic-MHD stability code (NOVA-K) has been developed to integrate a set of non-Hermitian integro-differential eigenmode equations due to energetic particles for axisymmetric toroidal plasmas in a general flux coordinate system with an arbitrary Jacobian. The NOVA-K code employs the Galerkin method involving Fourier expansions in the generalized poloidal angle θ and generalized toroidal angle /zeta/ directions, and cubic-B spline finite elements in the radial /Psi/ direction. Extensive comparisons with the existing variational ideal MHD codes show that the ideal MHD version of the NOVA-K code converges faster and gives more accurate results. The NOVA-K code is employed to study the effects of energetic particles on MHD-type modes: the stabilization of ideal MHD internal kink modes and the excitation of ''fishbone'' internal kink modes; and the alpha particle destabilization of toroidicity-induced Alfven eigenmodes (TAE) via transit resonances. Analytical theories are also presented to help explain the NOVA-K results. For energetic trapped particles generated by neutral beam injection (NBI) or ion cyclotron resonant heating (ICRH), a stability window for the n = 1 internal kink mode in the hot particle beta space exists even in the absence of the core ion finite Larmor radius effect. On the other hand, the trapped alpha particles are found to have negligible effects on the stability of the n = 1 internal kink mode, but the circulating alpha particles can strongly destabilize TAE modes via inverse Landau damping associated with the spatial gradient of the alpha particle pressure. 60 refs., 24 figs., 1 tab

  11. Intermediate modeling between kinetic equations and hydrodynamic limits: derivation, analysis and simulations

    International Nuclear Information System (INIS)

    Parisot, M.

    2011-01-01

    This work is dedicated study of a problem resulting from plasma physics: the thermal transfer of electrons in a plasma close to equilibrium Maxwellian. Firstly, a dimensional study of the Vlasov-Fokker-Planck-Maxwell system is performed, allowing one hand to identify a physically relevant parameter of scale and also to define mathematically the contours of validity domain. The asymptotic regime called Spitzer-Harm is studied for a relatively general class of collision operator. The following part of this work is devoted to the derivation and study of the hydrodynamic limit of the system of Vlasov-Maxwell-Landau outside the strictly asymptotic. A model proposed by Schurtz and Nicolais located in this context and analyzed. The particularity of this model lies in the application of a delocalization operation in the heat flux. The link with non-local models of Luciani and Mora is established as well as mathematics properties as the principle of maximum and entropy dissipation. Then a formal derivation from the Vlasov equations with a simplified collision operator, is proposed. The derivation, inspired by the recent work of D. Levermore, involves decomposition methods according to the spherical harmonics and methods of closing called diffusion methods. A hierarchy of intermediate models between the kinetic equations and the hydrodynamic limit is described. In particular a new hydrodynamic system integro-differential by nature, is proposed. The Schurtz and Nicolai model appears as a simplification of the system resulting from the derivation, assuming a steady flow of heat. The above results are then generalized to account for the internal energy dependence which appears naturally in the equation establishment. The existence and uniqueness of the solution of the nonstationary system are established in a simplified framework. The last part is devoted was the implementation of a specific numerical scheme to solve these models. We propose a finite volume approach can be

  12. Tokamak plasma shape identification based on the boundary integral equations

    International Nuclear Information System (INIS)

    Kurihara, Kenichi; Kimura, Toyoaki

    1992-05-01

    A necessary condition for tokamak plasma shape identification is discussed and a new identification method is proposed in this article. This method is based on the boundary integral equations governing a vacuum region around a plasma with only the measurement of either magnetic fluxes or magnetic flux intensities. It can identify various plasmas with low to high ellipticities with the precision determined by the number of the magnetic sensors. This method is applicable to real-time control and visualization using a 'table-look-up' procedure. (author)

  13. Hybrid Fluid/Kinetic Modeling Of Magnetized High Energy Density Plasmas

    Science.gov (United States)

    Hansen, David; Held, Eric; King, Jacob; Stoltz, Peter; Masti, Robert; Srinivasan, Bhuvana

    2017-10-01

    MHD modeling with an equation of state (EOS) of the Rayleigh-Taylor (RT) instabily in Z indicates that it is seeded by the electro-thermal instability. Large thermodynamic drives associated with gradients at the interface between the liner and the coronal regions distort distribution functions and likely lead to non-local transport effects in a plasma which varies from weakly to strongly coupled. In this work, we discuss using effective potential theory along with a Chapman-Ensksog-like (CEL) formalism to develop hybrid fluid/kinetic modeling capabilities for these plasmas. Effective potential theory addresses the role of Coulomb collisions on transport across coupling regimes and the CEL approach bridges the gap between full-blow kinetic simulations and the EOS tables, which only depend locally on density and temperature. Quantitative results on the Spitzer problem across coupling coupling regimes will be presented as a first step. DOE Grant No. DE-SC0016525.

  14. Small amplitude Kinetic Alfven waves in a superthermal electron-positron-ion plasma

    Science.gov (United States)

    Adnan, Muhammad; Mahmood, Sahahzad; Qamar, Anisa; Tribeche, Mouloud

    2016-11-01

    We are investigating the propagating properties of coupled Kinetic Alfven-acoustic waves in a low beta plasma having superthermal electrons and positrons. Using the standard reductive perturbation method, a nonlinear Korteweg-de Vries (KdV) type equation is derived which describes the evolution of Kinetic Alfven waves. It is found that nonlinearity and Larmor radius effects can compromise and give rise to solitary structures. The parametric role of superthermality and positron content on the characteristics of solitary wave structures is also investigated. It is found that only sub-Alfvenic and compressive solitons are supported in the present model. The present study may find applications in a low β electron-positron-ion plasma having superthermal electrons and positrons.

  15. Empiric model for mean generation time adjustment factor for classic point kinetics equations

    Energy Technology Data Exchange (ETDEWEB)

    Goes, David A.B.V. de; Martinez, Aquilino S.; Goncalves, Alessandro da C., E-mail: david.goes@poli.ufrj.br, E-mail: aquilino@lmp.ufrj.br, E-mail: alessandro@con.ufrj.br [Coordenacao de Pos-Graduacao e Pesquisa de Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Departamento de Engenharia Nuclear

    2017-11-01

    Point reactor kinetics equations are the easiest way to observe the neutron production time behavior in a nuclear reactor. These equations are derived from the neutron transport equation using an approximation called Fick's law leading to a set of first order differential equations. The main objective of this study is to review classic point kinetics equation in order to approximate its results to the case when it is considered the time variation of the neutron currents. The computational modeling used for the calculations is based on the finite difference method. The results obtained with this model are compared with the reference model and then it is determined an empirical adjustment factor that modifies the point reactor kinetics equation to the real scenario. (author)

  16. Empiric model for mean generation time adjustment factor for classic point kinetics equations

    International Nuclear Information System (INIS)

    Goes, David A.B.V. de; Martinez, Aquilino S.; Goncalves, Alessandro da C.

    2017-01-01

    Point reactor kinetics equations are the easiest way to observe the neutron production time behavior in a nuclear reactor. These equations are derived from the neutron transport equation using an approximation called Fick's law leading to a set of first order differential equations. The main objective of this study is to review classic point kinetics equation in order to approximate its results to the case when it is considered the time variation of the neutron currents. The computational modeling used for the calculations is based on the finite difference method. The results obtained with this model are compared with the reference model and then it is determined an empirical adjustment factor that modifies the point reactor kinetics equation to the real scenario. (author)

  17. Modeling of subtle kinetic processes in plasma simulation

    International Nuclear Information System (INIS)

    Sydora, R.D.; Decyk, V.K.; Dawson, J.M.

    1988-01-01

    A new diagnostic method for plasma simulation models is presented which enables one to probe the subtle dielectric properties of the plasma medium. The procedure involves the removal of the background plasma response in order to isolate the effects of small perturbing influences which are externally added. We have found the technique accurately describes fundamental kinetic plasma behavior such as the shielding of individual test charges and currents. Wave emission studies and drag of test particles has been carried out in explicit particle algorithms as well as large time step implicit and gyrokinetic models. Accurate plasma behavior is produced and it is possible to investigate in detail, processes which can be compared with plasma kinetic theory. The technique of subtraction is not only limited to particle simulation models but also can be used in MHD or fluid models where resolution is difficult due to the intensity of the background response relative to the phenomena one is interested in measuring, such as a weakly grouwing instability or nonlinear mode coupling effect. (author)

  18. Kinetic Analysis of Weakly ionized Plasmas in presence of collecting walls

    Science.gov (United States)

    Gonzalez, J.; Donoso, J. M.

    2018-02-01

    Description of plasmas in contact with a wall able to collecting or emitting charged particles is a research topic of great importance. This situation arises in a great variety of phenomena such as the characterization of plasmas by means of electric probes, in the surface treatment of materials and in the service-life of coatings in electric thrusters. In particular, in this work we devote attention to the dynamics of an argon weakly ionized plasma in the presence of a collecting wall. It is proposed a kinetic model in a 1D1V planar phase-space geometry. The model accounts for the electric field coupled to the system by solving the associated Poisson’s equation. To solve numerically the resulting non-linear system of equations, the Propagator Integral Method is used in conjunction with a slabbing method. On each interrelating plasma slab the integral advancing scheme operates in velocity space, in such a way that the all the species dynamics dominating the system evolution are kinetically described.

  19. Kinetic equations within the formalism of non-equilibrium thermo field dynamics

    International Nuclear Information System (INIS)

    Arimitsu, Toshihico

    1988-01-01

    After reviewing the real-time formalism of dissipative quantum field theory, i.e. non-equilibrium thermo field dynamics (NETFD), a kinetic equation, a self-consistent equation for the dissipation coefficient and a ''mass'' or ''chemical potential'' renormalization equation for non-equilibrium transient situations are extracted out of the two-point Green's function of the Heisenberg field, in their most general forms upon the basic requirements of NETFD. The formulation is applied to the electron-phonon system, as an example, where the gradient expansion and the quasi-particle approximation are performed. The formalism of NETFD is reinvestigated in connection with the kinetic equations. (orig.)

  20. Suppression of Phase Mixing in Drift-Kinetic Plasma Turbulence

    Science.gov (United States)

    Parker, J. T.; Dellar, P. J.; Schekochihin, A. A.; Highcock, E. G.

    2017-12-01

    The solar wind and interstellar medium are examples of strongly magnetised, weakly collisional, astrophysical plasmas. Their turbulent fluctuations are strongly anisotropic, with small amplitudes, and frequencies much lower than the Larmor frequency. This regime is described by gyrokinetic theory, a reduced five-dimensional kinetic system describing averages over Larmor orbits. A turbulent plasma may transfer free energy, a measure of fluctuation amplitudes, from injection at large scales, typically by an instability, to dissipation at small physical scales like a turbulent fluid. Alternatively, a turbulent plasma may form fine scale structures in velocity space via phase-mixing, the mechanism that leads to Landau damping in linear plasma theory. Macroscopic plasma properties like heat and momentum transport are affected by both mechanisms. While each is understood in isolation, their interaction is not. We study this interaction using a Hankel-Hermite velocity space representation of gyrokinetic theory. The Hankel transform interacts neatly with the Bessel functions that arise from averaging over Larmor orbits, so the perpendicular velocity space is decoupled for linearized problems. The Hermite transform expresses phase mixing as nearest-neighbor coupling between parallel velocity space scales represented by Hermite mode numbers. We use this representation to study transfer mechanisms in drift-kinetic plasma turbulence, the long wavelength limit of gyrokinetic theory. We show that phase space is divided into two regions, with one transfer mechanism dominating in each. Most energy is contained in the region where the fluid-like nonlinear cascade dominates. Moreover, in that region the nonlinear cascade interferes with phase mixing by exciting an "anti phase mixing" transfer of free energy from small to large velocity space scales. This cancels out the usual phase mixing, and renders the overall behavior fluid-like. These results profoundly change our understanding

  1. On Generalized Fractional Kinetic Equations Involving Generalized Bessel Function of the First Kind

    Directory of Open Access Journals (Sweden)

    Dinesh Kumar

    2015-01-01

    Full Text Available We develop a new and further generalized form of the fractional kinetic equation involving generalized Bessel function of the first kind. The manifold generality of the generalized Bessel function of the first kind is discussed in terms of the solution of the fractional kinetic equation in the paper. The results obtained here are quite general in nature and capable of yielding a very large number of known and (presumably new results.

  2. Transport and relaxation properties of superfluid 3He. I. Kinetic equation and Bogoliubov quasiparticle relaxation rate

    International Nuclear Information System (INIS)

    Einzel, D.; Woelfle, P.

    1978-01-01

    The kinetic equation for Bogoliubov quasiparticles for both the A and B phases of superfluid 3 He is derived from the general matrix kinetic equation. A condensed expression for the exact spin-symmetric collision integral is given. The quasiparticle relaxation rate is calculated for the BW state using the s--p approximation for the quasiparticle scattering amplitude. By using the results for the quasiparticle relaxation rate, the mean free path of Bogoliubov quasiparticles is calculated for all temperatures

  3. Kinetic theory of the interdiffusion coefficient in dense plasmas

    International Nuclear Information System (INIS)

    Boercker, D.B.

    1986-08-01

    Naive applications of Spitzer's theory to very dense plasmas can lead to negative diffusion coefficients. The interdiffusion coefficients in Binary Ionic Mixtures (two species of point ions in a uniform neutralizing background) have been calculated recently using molecular dynamics techniques. These calculations can provide useful benchmarks for theoretical evaluations of the diffusion coefficient in dense plasma mixtures. This paper gives a brief description of a kinetic theoretic approximation to the diffusion coefficient which generalizes Spitzer to high density and is in excellent agreement with the computer simulations. 15 refs., 1 fig., 2 tabs

  4. Species separation and kinetic effects in collisional plasma shocks

    Energy Technology Data Exchange (ETDEWEB)

    Bellei, C., E-mail: bellei1@llnl.gov; Wilks, S. C.; Amendt, P. A. [Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550 (United States); Rinderknecht, H.; Zylstra, A.; Rosenberg, M.; Sio, H.; Li, C. K.; Petrasso, R. [Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

    2014-05-15

    The properties of collisional shock waves propagating in uniform plasmas are studied with ion-kinetic calculations, in both slab and spherical geometry and for the case of one and two ion species. Despite the presence of an electric field at the shock front—and in contrast to the case where an interface is initially present [C. Bellei et al., Phys. Plasmas 20, 044702 (2013)]—essentially no ion reflection at the shock front is observed due to collisions, with a probability of reflection ≲10{sup −4} for the cases presented. A kinetic two-ion-species spherical convergent shock is studied in detail and compared against an average-species calculation, confirming effects of species separation and differential heating of the ion species at the shock front. The effect of different ion temperatures on the DT and D{sup 3}He fusion reactivity is discussed in the fluid limit and is estimated to be moderately important.

  5. Parameter Estimates in Differential Equation Models for Chemical Kinetics

    Science.gov (United States)

    Winkel, Brian

    2011-01-01

    We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data. We estimate the parameters present in several differential equation models of chemical reactions of order n, where n = 0, 1, 2, and apply more general…

  6. Kinetic equations for clean superconductors: Application to the flux flow hall effect

    International Nuclear Information System (INIS)

    Kopnin, N.B.

    1994-01-01

    The kinetic equations for clean superconductors (l>>ζ) are derived. expanding the equations for the time dependent Green functions in the quasiclassical parameter, the new contributions are found which contain the derivatives of the distribution functions with respect to the quasiparticle momentum. The transition from the ultra-clean case (no relaxation) to a relaxation-dominated behavior, for which the kinetic equations coincide with the usual quasiclassical approximation, occurs for the relaxation time of the order of ℎE F /Δ 2 . The kinetic equations can be used for various dynamic processes in superconductors including the flux-flow Hall effect. The derived equations, after necessary modifications for the p-wave pairing, are especially suitable for nonstationary problems in the theory of superfluidity of 3 He

  7. Unequilibrium kinetic of collisionless boundary layers in binary plasmas

    International Nuclear Information System (INIS)

    Kotelnikov, V.A.; Nikolaev, F.A.; Cherepanov, V.V.

    1985-01-01

    Relaxation processes of kinetic nonequilibrium collisionless boundary layers near spherical charged full absorbing surfaces in binary low-temperature plasmas are investigated. The effect of magnetic field on relaxation processes was neglected. The dynamics of components of the ionized gas was treated near the boundary layer. The potential distribution and the space dependence of concentration were calculated numerically. These results agree well with the experimental data. (D.Gy.)

  8. Exact solutions for a system of nonlinear plasma fluid equations

    International Nuclear Information System (INIS)

    Prahovic, M.G.; Hazeltine, R.D.; Morrison, P.J.

    1991-04-01

    A method is presented for constructing exact solutions to a system of nonlinear plasma fluid equations that combines the physics of reduced magnetohydrodynamics and the electrostatic drift-wave description of the Charney-Hasegawa-Mima equation. The system has nonlinearities that take the form of Poisson brackets involving the fluid field variables. The method relies on modifying a class of simple equilibrium solutions, but no approximations are made. A distinguishing feature is that the original nonlinear problem is reduced to the solution of two linear partial differential equations, one fourth-order and the other first-order. The first-order equation has Hamiltonian characteristics and is easily integrated, supplying information about the general structure of solutions. 6 refs

  9. Kinetic electromagnetic instabilities in an ITB plasma with weak magnetic shear

    Science.gov (United States)

    Chen, W.; Yu, D. L.; Ma, R. R.; Shi, P. W.; Li, Y. Y.; Shi, Z. B.; Du, H. R.; Ji, X. Q.; Jiang, M.; Yu, L. M.; Yuan, B. S.; Li, Y. G.; Yang, Z. C.; Zhong, W. L.; Qiu, Z. Y.; Ding, X. T.; Dong, J. Q.; Wang, Z. X.; Wei, H. L.; Cao, J. Y.; Song, S. D.; Song, X. M.; Liu, Yi.; Yang, Q. W.; Xu, M.; Duan, X. R.

    2018-05-01

    Kinetic Alfvén and pressure gradient driven instabilities are very common in magnetized plasmas, both in space and the laboratory. These instabilities will be easily excited by energetic particles (EPs) and/or pressure gradients in present-day fusion and future burning plasmas. This will not only cause the loss and redistribution of the EPs, but also affect plasma confinement and transport. Alfvénic ion temperature gradient (AITG) instabilities with the frequency ω_BAE<ω<ω_TAE and the toroidal mode numbers n=2{-}8 are found to be unstable in NBI internal transport barrier plasmas with weak shear and low pressure gradients, where ω_BAE and ω_TAE are the frequencies of the beta- and toroidicity-induced Alfvén eigenmodes, respectively. The measured results are consistent with the general fishbone-like dispersion relation and kinetic ballooning mode equation, and the modes become more unstable the smaller the magnetic shear is in low pressure gradient regions. The interaction between AITG activity and EPs also needs to be investigated with greater attention in fusion plasmas, such as ITER (Tomabechi and The ITER Team 1991 Nucl. Fusion 31 1135), since these fluctuations can be enhanced by weak magnetic shear and EPs.

  10. A Unified Gas Kinetic Scheme for Transport and Collision Effects in Plasma

    Directory of Open Access Journals (Sweden)

    Dongxin Pan

    2018-05-01

    Full Text Available In this study, the Boltzmann equation with electric acceleration term is discretized and solved by the unified gas-kinetic scheme (UGKS. The charged particle transport driven by electric field is included in the electric acceleration term. To capture non-equilibrium distribution function, the probability distribution functions of gas is discretized in a discrete velocity space. After discretization, the numerical flux for distribution function is computed to update the microscopic and macroscopic states. The flux is decided by an integral solution of Boltzmann equation based on characteristic problem. An electron-ion collision model is introduced in the Boltzmann Bhatnagar-Gross-Krook (BGK equation. This finite volume method for the UGKS couples the free transport and long-range interaction between particles. For simplicity, the electric field induced by charged particles is controlled by the Poisson’s equation, which is solved using the Green’s function for two dimensional plasma system subjected to the symmetry or periodic boundary conditions. Two numerical cases, linear Landau damping and Gaussian beam, are carried out to validate the proposed method. The linear electron plasma wave damping is simulated based on electron-ion collision operator. Comparison results show good accuracy and higher efficiency than particle based methods. Difference between Poisson’s equation and complete electromagnetic Maxwell equation is presented by numerical results based on the two models. Highly non-equilibrium and rarefied plasma flows, such as electron flows driven by electromagnetic field, can be simulated easily. The UGKS-Poisson model is proved to be promising in plasma flow simulation.

  11. Plasma kinetics of 14C-uric acid in bulls

    International Nuclear Information System (INIS)

    Cetinkaya, N.

    1999-01-01

    Plasma kinetics of uric acid were followed by 14C labelled uric acid to measure the effects of feed intake upon kinetic parameters. Two bulls (average L W 346±79 kg) were given an intravenous administration of a tracer (8-14C-uric acid, 250μCi/50 ml) by single injection via a jugular catheter. Animals were fed a mixed diet containing 30% wheat straw and 70% compounded feed as 95 and 60 % of the voluntary intake. Voluntary intakes were 8 kg/d as fed for two bulls. Blood samples, were collected at 0, 0.5,1, 2, 3, 4, 6, 8, 12, 16, 24 and 28 h after tracer administration. Fractional rates of clearance from the blood and pool size of compartments in the blood were estimated using plasma 8-14C-counts, following the method proposed by Chen and Franklin. The mean values of fractional rates (K 2,1 , K 1,2 ) and compartments pool size (V 1 , V 2 ) and the total pool size of compartments I and 2 at 60% and 95% feeding level were 1.97 and 1.44, 1.06 and 0.78; 76.9 L and 94.5 L, 137.01 L and 163.51 L; 214.0 L and 250.3 L respectively. Plasma kinetic parameters of 14C-uric acid were not affected at different feed intakes

  12. Plasma norepinephrine in humans: limitations in assessment of whole body norepinephrine kinetics and plasma clearance

    DEFF Research Database (Denmark)

    Christensen, N J; Henriksen, Jens Henrik Sahl

    1989-01-01

    ]IP and 131I-hippurate, whole body clearance from plasma of [3H]NE, as obtained from infusion rate divided by plasma concentration of tracer [1.74 +/- 0.64 (SD) 1/min] was significantly higher than the value obtained by total tracer infusion divided by total plasma area of tracer (1.27 +/- 0.51, P less than 0...... irreversible removal of NE, is smaller than previously estimated due to recycling through the plasma space. Attention has been drawn to limitations of [3H]NE kinetics....

  13. Temperature waves and the Boltzmann kinetic equation for phonons

    International Nuclear Information System (INIS)

    Urushev, D.; Borisov, M.; Vavrek, A.

    1988-01-01

    The ordinary parabolic equation for thermal conduction based on the Fourier empiric law as well as the generalized thermal conduction equation based on the Maxwell law have been derived from the Boltzmann equation for the phonons within the relaxation time approximation. The temperature waves of the so-called second sound in crystals at low temperatures are transformed into Fourier waves at low frequencies with respect to the characteristic frequency of the U-processes. These waves are transformed into temperature waves similar to the second sound waves in He II at frequences higher than the U-processes characteristic. 1 fig., 19 refs

  14. Plasma kinetics issues in an ESA study for a plasma laboratory in space

    International Nuclear Information System (INIS)

    Annaratone, B M; Biancalani, A; Ceccherini, F; Pegoraro, F; Bruno, D; Capitelli, M; Pascale, O de; Longo, S; Daly, E; Hilgers, A; Diomede, P; D'Ammando, G; Marcuccio, S; Mendonca, J T; Nagnibeda, V; Sanmartin, J R

    2008-01-01

    A study supported by the European Space Agency (ESA), in the context of its General Studies Programme, performed an investigation of the possible use of space for studies in pure and applied plasma physics, in areas not traditionally covered by 'space plasma physics'. A set of experiments have been identified that can potentially provide access to new phenomena and to allow advances in several fields of plasma science. These experiments concern phenomena on a spatial scale (10 1 -10 4 m) intermediate between what is achievable on the ground and the usual solar system plasma observations. Detailed feasibility studies have been performed for three experiments: active magnetic experiments, large-scale discharges and long tether-plasma interactions. The perspectives opened by these experiments are discussed for magnetic reconnection, instabilities, MHD turbulence, atomic excited states kinetics, weakly ionized plasmas, plasma diagnostics, artificial auroras and atmospheric studies. The discussion is also supported by results of numerical simulations and estimates

  15. A conservative scheme of drift kinetic electrons for gyrokinetic simulation of kinetic-MHD processes in toroidal plasmas

    Science.gov (United States)

    Bao, J.; Liu, D.; Lin, Z.

    2017-10-01

    A conservative scheme of drift kinetic electrons for gyrokinetic simulations of kinetic-magnetohydrodynamic processes in toroidal plasmas has been formulated and verified. Both vector potential and electron perturbed distribution function are decomposed into adiabatic part with analytic solution and non-adiabatic part solved numerically. The adiabatic parallel electric field is solved directly from the electron adiabatic response, resulting in a high degree of accuracy. The consistency between electrostatic potential and parallel vector potential is enforced by using the electron continuity equation. Since particles are only used to calculate the non-adiabatic response, which is used to calculate the non-adiabatic vector potential through Ohm's law, the conservative scheme minimizes the electron particle noise and mitigates the cancellation problem. Linear dispersion relations of the kinetic Alfvén wave and the collisionless tearing mode in cylindrical geometry have been verified in gyrokinetic toroidal code simulations, which show that the perpendicular grid size can be larger than the electron collisionless skin depth when the mode wavelength is longer than the electron skin depth.

  16. Equation of state of partially-ionized dense plasmas

    International Nuclear Information System (INIS)

    Rogers, F.J.

    1989-01-01

    This paper describes methods for calculating the equation of state of partially-ionized dense plasmas. The term dense plasma is used rather than strongly coupled plasma, since it is possible that at plasma conditions such that only a few levels can be observed spectroscopically the plasma coupling parameters are not large. Due mainly to their importance in theoretical astrophysics, the properties of partially ionized plasmas have been of interest for a long while. More recently, this interest has intensified due to the development of methods for producing partially ionized plasmas in the laboratory. This has opened up large programs of experimental investigation and of practical application. In this paper we consider detailed statistical mechanical methods that explicitly treat the distribution over ionic species and their energy level structure. These detailed approaches are generally characterized as being in the ''chemical picture'' when a free energy expression is minimized or in the ''physical picture'' when the starting point is the grand canonical ensemble. 52 refs., 2 tabs

  17. Homotopy analysis solutions of point kinetics equations with one delayed precursor group

    International Nuclear Information System (INIS)

    Zhu Qian; Luo Lei; Chen Zhiyun; Li Haofeng

    2010-01-01

    Homotopy analysis method is proposed to obtain series solutions of nonlinear differential equations. Homotopy analysis method was applied for the point kinetics equations with one delayed precursor group. Analytic solutions were obtained using homotopy analysis method, and the algorithm was analysed. The results show that the algorithm computation time and precision agree with the engineering requirements. (authors)

  18. Elementary Processes and Kinetic Modeling for Hydrogen and Helium Plasmas

    Directory of Open Access Journals (Sweden)

    Roberto Celiberto

    2017-05-01

    Full Text Available We report cross-sections and rate coefficients for excited states colliding with electrons, heavy particles and walls useful for the description of H 2 /He plasma kinetics under different conditions. In particular, the role of the rotational states in resonant vibrational excitations of the H 2 molecule by electron impact and the calculation of the related cross-sections are illustrated. The theoretical determination of the cross-section for the rovibrational energy exchange and dissociation of H 2 molecule, induced by He atom impact, by using the quasi-classical trajectory method is discussed. Recombination probabilities of H atoms on tungsten and graphite, relevant for the determination of the nascent vibrational distribution, are also presented. An example of a state-to-state plasma kinetic model for the description of shock waves operating in H 2 and He-H 2 mixtures is presented, emphasizing also the role of electronically-excited states in affecting the electron energy distribution function of free electrons. Finally, the thermodynamic properties and the electrical conductivity of non-ideal, high-density hydrogen plasma are finally discussed, in particular focusing on the pressure ionization phenomenon in high-pressure high-temperature plasmas.

  19. Atomic kinetics of a neon photoionized plasma experiment at Z

    Science.gov (United States)

    Mayes, Daniel C.; Mancini, Roberto; Bailey, James E.; Loisel, Guillaume; Rochau, Gregory; ZAPP Collaboration

    2018-06-01

    We discuss an experimental effort to study the atomic kinetics in astrophysically relevant photoionized plasmas via K-shell line absorption spectroscopy. The experiment employs the intense x-ray flux emitted at the collapse of a Z-pinch to heat and backlight a photoionized plasma contained within a cm-scale gas cell placed at a variable distance from the Z-pinch and filled with neon gas pressures in the range from 3.5 to 30 Torr. The experimental platform affords an order of magnitude range in the ionization parameter characterizing the photoionized plasma at the peak of the x-ray drive from about 5 to 80 erg*cm/s. Thus, the experiment allows for the study of trends in ionization distribution as a function of the ionization parameter. An x-ray crystal spectrometer capable of time-integrated and/or time-gated configurations is used to collect absorption spectra. The spectra show line absorption by several ionization stages of neon, including Be-, Li-, He-, and H-like ions. Analysis of these spectra yields ion areal densities and charge state distributions, which can be compared with simulation results from atomic kinetics codes. In addition, the electron temperature is extracted from level population ratios of nearby energy levels in Li- and Be-like ions, which can be used to test heating models of photoionized plasmas.

  20. An efficient technique for the point reactor kinetics equations with Newtonian temperature feedback effects

    International Nuclear Information System (INIS)

    Nahla, Abdallah A.

    2011-01-01

    Highlights: → An efficient technique for the nonlinear reactor kinetics equations is presented. → This method is based on Backward Euler or Crank Nicholson and fundamental matrix. → Stability of efficient technique is defined and discussed. → This method is applied to point kinetics equations of six-groups of delayed neutrons. → Step, ramp, sinusoidal and temperature feedback reactivities are discussed. - Abstract: The point reactor kinetics equations of multi-group of delayed neutrons in the presence Newtonian temperature feedback effects are a system of stiff nonlinear ordinary differential equations which have not any exact analytical solution. The efficient technique for this nonlinear system is based on changing this nonlinear system to a linear system by the predicted value of reactivity and solving this linear system using the fundamental matrix of the homogenous linear differential equations. The nonlinear point reactor kinetics equations are rewritten in the matrix form. The solution of this matrix form is introduced. This solution contains the exponential function of a variable coefficient matrix. This coefficient matrix contains the unknown variable, reactivity. The predicted values of reactivity in the explicit form are determined replacing the exponential function of the coefficient matrix by two kinds, Backward Euler and Crank Nicholson, of the rational approximations. The nonlinear point kinetics equations changed to a linear system of the homogenous differential equations. The fundamental matrix of this linear system is calculated using the eigenvalues and the corresponding eigenvectors of the coefficient matrix. Stability of the efficient technique is defined and discussed. The efficient technique is applied to the point kinetics equations of six-groups of delayed neutrons with step, ramp, sinusoidal and the temperature feedback reactivities. The results of these efficient techniques are compared with the traditional methods.

  1. An Explicit Finite Difference scheme for numerical solution of fractional neutron point kinetic equation

    International Nuclear Information System (INIS)

    Saha Ray, S.; Patra, A.

    2012-01-01

    Highlights: ► In this paper fractional neutron point kinetic equation has been analyzed. ► The numerical solution for fractional neutron point kinetic equation is obtained. ► Explicit Finite Difference Method has been applied. ► Supercritical reactivity, critical reactivity and subcritical reactivity analyzed. ► Comparison between fractional and classical neutron density is presented. - Abstract: In the present article, a numerical procedure to efficiently calculate the solution for fractional point kinetics equation in nuclear reactor dynamics is investigated. The Explicit Finite Difference Method is applied to solve the fractional neutron point kinetic equation with the Grunwald–Letnikov (GL) definition (). Fractional Neutron Point Kinetic Model has been analyzed for the dynamic behavior of the neutron motion in which the relaxation time associated with a variation in the neutron flux involves a fractional order acting as exponent of the relaxation time, to obtain the best operation of a nuclear reactor dynamics. Results for neutron dynamic behavior for subcritical reactivity, supercritical reactivity and critical reactivity and also for different values of fractional order have been presented and compared with the classical neutron point kinetic (NPK) equation as well as the results obtained by the learned researchers .

  2. Computer simulation of kinetic properties of plasmas. Progress report, October 1, 1977--September 30, 1978

    International Nuclear Information System (INIS)

    Denavit, J.

    1978-01-01

    The research is directed toward the development and testing of new numerical methods for particle and hybrid simulation of plasmas and their application to physical problems of current significance to Magnetic Fusion Energy. During the past year, research on the project has been concerned with the following specific problems: (1) analysis and computer simulations of the dissipative trapped-electron instability in tokamaks; (2) long-time-scale algorithms for numerical solutions of the drift-kinetic equation; and (3) computer simulation of field-reversed ion ring stability

  3. Computer simulation of kinetic properties of plasmas. Progress report, October 1, 1978-June 30, 1979

    International Nuclear Information System (INIS)

    Denavit, J.

    1979-01-01

    The research is directed toward the development and testing of new numerical methods for particle and hybrid simulation of plasmas, and their application to physical problems of current significance to Magnetic Fusion Energy. During the present period, research on the project has been concerned with the following specific problems: (1) Computer simulations of drift and dissipative trapped-electron instabilities in tokamaks, including radial dependence and shear stabilization. (2) Long-time-scale algorithms for numerical solutions of the drift-kinetic equation. (3) Computer simulation of field-reversed ion ring stability. (4) Nonlinear, single-mode saturation of the bump-on-tail instability

  4. Correlations and the Ring-Kinetic Equation in Dense Sheared Granular Flows

    Science.gov (United States)

    Kumaran, V.

    A formal way of deriving fluctuation-correlation relations in densesheared granular media, starting with the Enskog approximation for the collision integral in the Chapman-Enskog theory, is discussed. The correlation correction to the viscosity is obtained using the ring-kinetic equation, in terms of the correlations in the hydrodynamic modes of the linearised Enskog equation. It is shown that the Green-Kubo formula for the shear viscosity emerges from the two-body correlation function obtained from the ring-kinetic equation.

  5. Numerical solution of the point reactor kinetics equations with fuel burn-up and temperature feedback

    International Nuclear Information System (INIS)

    Tashakor, S.; Jahanfarnia, G.; Hashemi-Tilehnoee, M.

    2010-01-01

    Point reactor kinetics equations are solved numerically using one group of delayed neutrons and with fuel burn-up and temperature feedback included. To calculate the fraction of one-group delayed neutrons, a group of differential equations are solved by an implicit time method. Using point reactor kinetics equations, changes in mean neutrons density, temperature, and reactivity are calculated in different times during the reactor operation. The variation of reactivity, temperature, and maximum power with time are compared with the predictions by other methods.

  6. Self-Consistent System of Equations for a Kinetic Description of the Low-Pressure Discharges Accounting for the Nonlocal and Collisionless Electron Dynamics

    International Nuclear Information System (INIS)

    Kaganovich, Igor D.; Polomarov, Oleg

    2003-01-01

    In low-pressure discharges, when the electron mean free path is larger or comparable with the discharge length, the electron dynamics is essentially non-local. Moreover, the electron energy distribution function (EEDF) deviates considerably from a Maxwellian. Therefore, an accurate kinetic description of the low-pressure discharges requires knowledge of the non-local conductivity operator and calculation of the non-Maxwellian EEDF. The previous treatments made use of simplifying assumptions: a uniform density profile and a Maxwellian EEDF. In the present study a self-consistent system of equations for the kinetic description of nonlocal, non-uniform, nearly collisionless plasmas of low-pressure discharges is derived. It consists of the nonlocal conductivity operator and the averaged kinetic equation for calculation of the non-Maxwellian EEDF. The importance of accounting for the non-uniform plasma density profile on both the current density profile and the EEDF is demonstrated

  7. Derivation of a new kinetic equation. Application to the determination of viscosity coefficients

    International Nuclear Information System (INIS)

    Frey, Jean-Jacques

    1970-01-01

    By introducing a new hypothesis concerning the closure in the B.B.G.K.Y. equation system, an approximate expression for f 12 is obtained. By inserting this expression in the first B.B.G.K.Y. equation, a new kinetic equation results. It is verified that this equation does in fact give the fluid mechanics equations, and new expressions for the shear and expansion viscosity coefficients are obtained. The numerical calculations which have been carried out show that very satisfactory agreement exists with experimental results. (author) [fr

  8. Kinetic and Related Determinants of Plasma Triglyceride Concentration in Abdominal Obesity: Multicenter Tracer Kinetic Study.

    Science.gov (United States)

    Borén, Jan; Watts, Gerald F; Adiels, Martin; Söderlund, Sanni; Chan, Dick C; Hakkarainen, Antti; Lundbom, Nina; Matikainen, Niina; Kahri, Juhani; Vergès, Bruno; Barrett, P Hugh R; Taskinen, Marja-Riitta

    2015-10-01

    Patients with obesity and diabetes mellitus have increased risk of cardiovascular disease. A major cause is an atherogenic dyslipidemia related primarily to elevated plasma concentrations of triglyceride-rich lipoproteins. The aim of this study was to clarify determinants of plasma triglyceride concentration. We focused on factors that predict the kinetics of very-low density lipoprotein 1 (VLDL1) triglycerides. A multicenter study using dual stable isotopes (deuterated leucine and glycerol) and multicompartmental modeling was performed to elucidate the kinetics of triglycerides and apoB in VLDL1 in 46 subjects with abdominal obesity and additional cardiometabolic risk factors. Results showed that plasma triglyceride concentrations were dependent on both the secretion rate (r=0.44, Ptriglycerides and VLDL1-apoB. Liver fat mass was independently and directly associated with secretion rates of VLDL1-triglycerides (r=0.56, Ptriglycerides (r=0.48, Ptriglyceride concentrations in abdominal obesity are determined by the kinetics of VLDL1 subspecies, catabolism being mainly dependent on apoC-III concentration and secretion on liver fat content. Reduction in liver fat and targeting apoC-III may be an effective approach for correcting triglyceride metabolism atherogenic dyslipidemia in obesity. © 2015 American Heart Association, Inc.

  9. MAIA, Eigenvalues for MHD Equation of Tokamak Plasma Stability Problems

    International Nuclear Information System (INIS)

    Tanaka, Y.; Azumi, M.; Kurita, G.; Tsunematsu, T.; Takeda, T.

    1986-01-01

    1 - Description of program or function: This program solves an eigenvalue problem zBx=Ax where A and B are real block tri-diagonal matrices. This eigenvalue problem is derived from a reduced set of linear resistive MHD equations which is often employed to study tokamak plasma stability problem. 2 - Method of solution: Both the determinant and inverse iteration methods are employed. 3 - Restrictions on the complexity of the problem: The eigenvalue z must be real

  10. Numerical solution of the kinetic equation in reactor shielding

    International Nuclear Information System (INIS)

    Germogenova, T.A.

    1975-01-01

    A review is made of methods of solving marginal problems of multi-group systems of equations of neutron and γ radiation transfer. The first stage of the solution - the quantification of the basic task, is determined by the qualitative behaviour of the solution - is the nature of its performance and asymptotics. In the second stage - solution of the approximating system, various modifications of the iterative method are as a rule used. A description is given of the features of the major Soviet complexes of programmes (ROZ and RADUGA) for the solution of multi-group systems of transfer equations and some methodological research findings are presented. (author)

  11. Calculation of statistic estimates of kinetic parameters from substrate uncompetitive inhibition equation using the median method

    Directory of Open Access Journals (Sweden)

    Pedro L. Valencia

    2017-04-01

    Full Text Available We provide initial rate data from enzymatic reaction experiments and tis processing to estimate the kinetic parameters from the substrate uncompetitive inhibition equation using the median method published by Eisenthal and Cornish-Bowden (Cornish-Bowden and Eisenthal, 1974; Eisenthal and Cornish-Bowden, 1974. The method was denominated the direct linear plot and consists in the calculation of the median from a dataset of kinetic parameters Vmax and Km from the Michaelis–Menten equation. In this opportunity we present the procedure to applicate the direct linear plot to the substrate uncompetitive inhibition equation; a three-parameter equation. The median method is characterized for its robustness and its insensibility to outlier. The calculations are presented in an Excel datasheet and a computational algorithm was developed in the free software Python. The kinetic parameters of the substrate uncompetitive inhibition equation Vmax, Km and Ks were calculated using three experimental points from the dataset formed by 13 experimental points. All the 286 combinations were calculated. The dataset of kinetic parameters resulting from this combinatorial was used to calculate the median which corresponds to the statistic estimator of the real kinetic parameters. A comparative statistical analyses between the median method and the least squares was published in Valencia et al. [3].

  12. Analytic solutions of the multigroup space-time reactor kinetics equations

    International Nuclear Information System (INIS)

    Lee, C.E.; Rottler, S.

    1986-01-01

    The development of analytical and numerical solutions to the reactor kinetics equations is reviewed. Analytic solutions of the multigroup space-time reactor kinetics equations are developed for bare and reflected slabs and spherical reactors for zero flux, zero current and extrapolated endpoint boundary conditions. The material properties of the reactors are assumed constant in space and time, but spatially-dependent source terms and initial conditions are investigated. The system of partial differential equations is reduced to a set of linear ordinary differential equations by the Laplace transform method. These equations are solved by matrix Green's functions yielding a general matrix solution for the neutron flux and precursor concentration in the Laplace transform space. The detailed pole structure of the Laplace transform matrix solutions is investigated. The temporally- and spatially-dependent solutions are determined from the inverse Laplace transform using the Cauchy residue theorem, the theorem of Frobenius, a knowledge of the detailed pole structure and matrix operators. (author)

  13. Stability of generalized Runge-Kutta methods for stiff kinetics coupled differential equations

    International Nuclear Information System (INIS)

    Aboanber, A E

    2006-01-01

    A stability and efficiency improved class of generalized Runge-Kutta methods of order 4 are developed for the numerical solution of stiff system kinetics equations for linear and/or nonlinear coupled differential equations. The determination of the coefficients required by the method is precisely obtained from the so-called equations of condition which in turn are derived by an approach based on Butcher series. Since the equations of condition are fewer in number, free parameters can be chosen for optimizing any desired feature of the process. A further related coefficient set with different values of these parameters and the region of absolute stability of the method have been introduced. In addition, the A(α) stability properties of the method are investigated. Implementing the method in a personal computer estimated the accuracy and speed of calculations and verified the good performances of the proposed new schemes for several sample problems of the stiff system point kinetics equations with reactivity feedback

  14. Contribution to the modelling and multi-scale numerical simulation of kinetic electron transport in hot plasma

    International Nuclear Information System (INIS)

    Mallet, J.

    2012-01-01

    This research thesis stands at the crossroad of plasma physics, numerical analysis and applied mathematics. After an introduction presenting the problematic and previous works, the author recalls some basis of classical kinetic models for plasma physics (collisionless kinetic theory and Vlasov equation, collisional kinetic theory with the non-relativistic Maxwell-Fokker-Plansk system) and describes the fundamental properties of the collision operators such as conservation laws, entropy dissipation, and so on. He reports the improvement of a deterministic numerical method to solve the non-relativistic Vlasov-Maxwell system coupled with Fokker-Planck-Landau type operators. The efficiency of each high order scheme is compared. The evolution of the hot spot is studied in the case of thermonuclear reactions in the centre of the pellet in a weakly collisional regime. The author focuses on the simulation of the kinetic electron collisional transport in inertial confinement fusion (ICF) between the laser absorption zone and the ablation front. A new approach is then introduced to reduce the huge computation time obtained with kinetic models. In a last chapter, the kinetic continuous equation in spherical domain is described and a new model is chosen for collisions in order to preserve collision properties

  15. An accurate solution of point reactor neutron kinetics equations of multi-group of delayed neutrons

    International Nuclear Information System (INIS)

    Yamoah, S.; Akaho, E.H.K.; Nyarko, B.J.B.

    2013-01-01

    Highlights: ► Analytical solution is proposed to solve the point reactor kinetics equations (PRKE). ► The method is based on formulating a coefficient matrix of the PRKE. ► The method was applied to solve the PRKE for six groups of delayed neutrons. ► Results shows good agreement with other traditional methods in literature. ► The method is accurate and efficient for solving the point reactor kinetics equations. - Abstract: The understanding of the time-dependent behaviour of the neutron population in a nuclear reactor in response to either a planned or unplanned change in the reactor conditions is of great importance to the safe and reliable operation of the reactor. In this study, an accurate analytical solution of point reactor kinetics equations with multi-group of delayed neutrons for specified reactivity changes is proposed to calculate the change in neutron density. The method is based on formulating a coefficient matrix of the homogenous differential equations of the point reactor kinetics equations and calculating the eigenvalues and the corresponding eigenvectors of the coefficient matrix. A small time interval is chosen within which reactivity relatively stays constant. The analytical method was applied to solve the point reactor kinetics equations with six-groups delayed neutrons for a representative thermal reactor. The problems of step, ramp and temperature feedback reactivities are computed and the results compared with other traditional methods. The comparison shows that the method presented in this study is accurate and efficient for solving the point reactor kinetics equations of multi-group of delayed neutrons

  16. A new variational formulation of kinetic plasma theory and the application of moving finite elements

    International Nuclear Information System (INIS)

    Glasser, A.H.

    1991-01-01

    A new variational formulation has been developed for the system of equations governing kinetic plasmas and electromagnetic fields. It is used to apply the method of Moving Finite Elements to the electromagnetic fields. The fields are expanded in a basis of linear finite elements on a movable, unstructured grid of triangles in 2D or tetrahedra in 3D, while the plasma distribution function is expanded in a basis of super particles. Minimization of the variational with respect to the time derivatives of the field quantities yields a coupled system of equations for simultaneously advancing the amplitudes and node positions, resulting in adaptive grid motion. The adaptivity of the grid may save a large factor in the size of the grid and the number of particles required in many problems. Minimization of the variational with respect to the time derivatives of the particle positions and velocities gives the equations of motion, providing consistent prescriptions for assigning particles to the grid and fields to the particles. Orthogonality conditions on the particles are derived as conditions for keeping their equations of motion independent. Collisions can be included in a natural way. The relationship between PIC methods and alternative methods of discretizing phase space is clarified

  17. Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria

    International Nuclear Information System (INIS)

    Frieman, E.A.; Chen, L.

    1981-10-01

    A nonlinear gyrokinetic formalism for low-frequency (less than the cyclotron frequency) microscopic electromagnetic perturbations in general magnetic field configurations is developed. The nonlinear equations thus derived are valid in the strong-turbulence regime and contain effects due to finite Larmor radius, plasma inhomogeneities, and magentic field geometries. The specific case of axisymmetric tokamaks is then considered, and a model nonlinear equation is derived for electrostatic drift waves. Also, applying the formalism to the shear Alfven wave heating sceme, it is found that nonlinear ion Landau damping of kinetic shear-Alfven waves is modified, both qualitatively and quantitatively, by the diamagnetic drift effects. In particular, wave energy is found to cascade in wavenumber instead of frequency

  18. Numerical simulation of stochastic point kinetic equation in the dynamical system of nuclear reactor

    International Nuclear Information System (INIS)

    Saha Ray, S.

    2012-01-01

    Highlights: ► In this paper stochastic neutron point kinetic equations have been analyzed. ► Euler–Maruyama method and Strong Taylor 1.5 order method have been discussed. ► These methods are applied for the solution of stochastic point kinetic equations. ► Comparison between the results of these methods and others are presented in tables. ► Graphs for neutron and precursor sample paths are also presented. -- Abstract: In the present paper, the numerical approximation methods, applied to efficiently calculate the solution for stochastic point kinetic equations () in nuclear reactor dynamics, are investigated. A system of Itô stochastic differential equations has been analyzed to model the neutron density and the delayed neutron precursors in a point nuclear reactor. The resulting system of Itô stochastic differential equations are solved over each time-step size. The methods are verified by considering different initial conditions, experimental data and over constant reactivities. The computational results indicate that the methods are simple and suitable for solving stochastic point kinetic equations. In this article, a numerical investigation is made in order to observe the random oscillations in neutron and precursor population dynamics in subcritical and critical reactors.

  19. Linear kinetic enlightenment of a slab of nonuniform plasma

    International Nuclear Information System (INIS)

    Revenchuk, S.M.

    1996-01-01

    A phenomenon of linear kinetic regeneration of a harmonic electric-field perturbation beyond the nonuniform opacity barrier due to electrons trapped by a potential well is investigated. Such electrons are reflected by the well walls without loss of phase memory about the external perturbation, which is rehabilitated on the other side of the barrier. The incidence of the electromagnetic wave polarized in the plane of incidence on a plasma slab. Analytic expressions for the regenerated electric field and regeneration coefficient are obtained in the ballistic approximation. The dependence of the regeneration coefficient on shape of the electrostatic potential confining the wave barrier is discussed

  20. Different seeds to solve the equations of stochastic point kinetics using the Euler-Maruyama method

    International Nuclear Information System (INIS)

    Suescun D, D.; Oviedo T, M.

    2017-09-01

    In this paper, a numerical study of stochastic differential equations that describe the kinetics in a nuclear reactor is presented. These equations, known as the stochastic equations of punctual kinetics they model temporal variations in neutron population density and concentrations of deferred neutron precursors. Because these equations are probabilistic in nature (since random oscillations in the neutrons and population of precursors were considered to be approximately normally distributed, and these equations also possess strong coupling and stiffness properties) the proposed method for the numerical simulations is the Euler-Maruyama scheme that provides very good approximations for calculating the neutron population and concentrations of deferred neutron precursors. The method proposed for this work was computationally tested for different seeds, initial conditions, experimental data and forms of reactivity for a group of precursors and then for six groups of deferred neutron precursors at each time step with 5000 Brownian movements per seed. In a paper reported in the literature, the Euler-Maruyama method was proposed, but there are many doubts about the reported values, in addition to not reporting the seed used, so in this work is expected to rectify the reported values. After taking the average of the different seeds used to generate the pseudo-random numbers the results provided by the Euler-Maruyama scheme will be compared in mean and standard deviation with other methods reported in the literature and results of the deterministic model of the equations of the punctual kinetics. This comparison confirms in particular that the Euler-Maruyama scheme is an efficient method to solve the equations of stochastic point kinetics but different from the values found and reported by another author. The Euler-Maruyama method is simple and easy to implement, provides acceptable results for neutron population density and concentration of deferred neutron precursors and

  1. Time discretization of the point kinetic equations using matrix exponential method and First-Order Hold

    International Nuclear Information System (INIS)

    Park, Yujin; Kazantzis, Nikolaos; Parlos, Alexander G.; Chong, Kil To

    2013-01-01

    Highlights: • Numerical solution for stiff differential equations using matrix exponential method. • The approximation is based on First Order Hold assumption. • Various input examples applied to the point kinetics equations. • The method shows superior useful and effective activity. - Abstract: A system of nonlinear differential equations is derived to model the dynamics of neutron density and the delayed neutron precursors within a point kinetics equation modeling framework for a nuclear reactor. The point kinetic equations are mathematically characterized as stiff, occasionally nonlinear, ordinary differential equations, posing significant challenges when numerical solutions are sought and traditionally resulting in the need for smaller time step intervals within various computational schemes. In light of the above realization, the present paper proposes a new discretization method inspired by system-theoretic notions and technically based on a combination of the matrix exponential method (MEM) and the First-Order Hold (FOH) assumption. Under the proposed time discretization structure, the sampled-data representation of the nonlinear point kinetic system of equations is derived. The performance of the proposed time discretization procedure is evaluated using several case studies with sinusoidal reactivity profiles and multiple input examples (reactivity and neutron source function). It is shown, that by applying the proposed method under a First-Order Hold for the neutron density and the precursor concentrations at each time step interval, the stiffness problem associated with the point kinetic equations can be adequately addressed and resolved. Finally, as evidenced by the aforementioned detailed simulation studies, the proposed method retains its validity and accuracy for a wide range of reactor operating conditions, including large sampling periods dictated by physical and/or technical limitations associated with the current state of sensor and

  2. Kinetic theory of spectral line broadening in plasmas

    International Nuclear Information System (INIS)

    Hussey, T.W.

    1974-01-01

    A formal kinetic theory is used to cast the line shape function into a form that, while similar to the ''unified'' theories of Smith, Cooper, and Vidal and of Voslamber, does not introduce some of the usual approximations. The resulting line shape function explicitly includes the initial correlations between the atom and perturbers, and also demonstrates the natural separation of plasma mean field and collisional effects. The classical path and no-quenching approximations are discussed and ultimately employed; however, they are not required in the formal development. The weak coupling limit is considered as a systematic approximation to the formal results. It is shown tha different ways of applying this limit lead to different expressions for the memory operator, some of which correspond to existing theories. One approximation is considered which systematically incorporates the effects of electron correlations within the framework of a unified theory. In addition, a practical approximation suitable for a strongly interacting plasma is discussed

  3. Simulating Chemical Kinetics Without Differential Equations: A Quantitative Theory Based on Chemical Pathways.

    Science.gov (United States)

    Bai, Shirong; Skodje, Rex T

    2017-08-17

    A new approach is presented for simulating the time-evolution of chemically reactive systems. This method provides an alternative to conventional modeling of mass-action kinetics that involves solving differential equations for the species concentrations. The method presented here avoids the need to solve the rate equations by switching to a representation based on chemical pathways. In the Sum Over Histories Representation (or SOHR) method, any time-dependent kinetic observable, such as concentration, is written as a linear combination of probabilities for chemical pathways leading to a desired outcome. In this work, an iterative method is introduced that allows the time-dependent pathway probabilities to be generated from a knowledge of the elementary rate coefficients, thus avoiding the pitfalls involved in solving the differential equations of kinetics. The method is successfully applied to the model Lotka-Volterra system and to a realistic H 2 combustion model.

  4. Initial state dependence of nonlinear kinetic equations: The classical electron gas

    International Nuclear Information System (INIS)

    Marchetti, M.C.; Cohen, E.G.D.; Dorfman, J.R.; Kirkpatrick, T.R.

    1985-01-01

    The method of nonequilibrium cluster expansion is used to study the decay to equilibrium of a weakly coupled inhomogeneous electron gas prepared in a local equilibrium state at the initial time, t=0. A nonlinear kinetic equation describing the long time behavior of the one-particle distribution function is obtained. For consistency, initial correlations have to be taken into account. The resulting kinetic equation-differs from that obtained when the initial state of the system is assumed to be factorized in a product of one-particle functions. The question of to what extent correlations in the initial state play an essential role in determining the form of the kinetic equation at long times is discussed. To that end, the present calculations are compared wih results obtained before for hard sphere gases and in general with strong short-range forces. A partial answer is proposed and some open questions are indicated

  5. Kinetic theory of cross-modulation in a weakly ionized plasma

    International Nuclear Information System (INIS)

    Garrett, A.J.M.

    1991-01-01

    Cross-modulation in plasma is an electromagnetic wave interaction in which the modulation of one 'disturbing' wave is imposed nonlinearly on the transport properties of the medium, and thence onto a second, 'wanted' wave propagating linearly through it. This analysis is restricted to weakly ionized plasma with allowance for ambient magnetic field, as in the lower ionosphere. A kinetic description is used, based on the Boltzmann equation for the electrons, with electron-molecule collisions described by Boltzmann's collision integral. Because of the small mass ratio this simplifies to a differential form. There is no cross-modulation if the collision frequency is independent of collision speed, when contributions from all parts of velocity space cancel. (author)

  6. Neoclassical kinetic theory near the edge of a diverted tokamak plasma

    International Nuclear Information System (INIS)

    Solano, E.R.; Hazeltine, R.D.

    1993-01-01

    In a diverted plasma, the poloidal magnetic field has a strong poloidal variation, approaching zero near the X-point. Typically, neoclassical theory is based on ordering assumptions about the 3 characteristic frequencies present in the problem: streaming, collisions and drift. In a circular geometry, the streaming freuency is constant, while the drift frequency has a sin(θ) variation. In a shaped plasma, the streaming frequency also has a poloidal variation. The ordering is now established by the amplitude of these frequencies. With a model poloidal flux function, the authors solve the drift kinetic equation inside, but near, the separatrix. Both the plateau and collisional regime are considered. Ion rotation rates, and their poloidal variation, are calculated. It is shown that the standard neoclassical rotation predictions still hold, when correctly interpreted. Other neoclassical fluxes are calculated as well

  7. The solution of the neutron point kinetics equation with stochastic extension: an analysis of two moments

    Energy Technology Data Exchange (ETDEWEB)

    Silva, Milena Wollmann da; Vilhena, Marco Tullio M.B.; Bodmann, Bardo Ernst J.; Vasques, Richard, E-mail: milena.wollmann@ufrgs.br, E-mail: vilhena@mat.ufrgs.br, E-mail: bardobodmann@ufrgs.br, E-mail: richard.vasques@fulbrightmail.org [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica

    2015-07-01

    The neutron point kinetics equation, which models the time-dependent behavior of nuclear reactors, is often used to understand the dynamics of nuclear reactor operations. It consists of a system of coupled differential equations that models the interaction between (i) the neutron population; and (II) the concentration of the delayed neutron precursors, which are radioactive isotopes formed in the fission process that decay through neutron emission. These equations are deterministic in nature, and therefore can provide only average values of the modeled populations. However, the actual dynamical process is stochastic: the neutron density and the delayed neutron precursor concentrations vary randomly with time. To address this stochastic behavior, Hayes and Allen have generalized the standard deterministic point kinetics equation. They derived a system of stochastic differential equations that can accurately model the random behavior of the neutron density and the precursor concentrations in a point reactor. Due to the stiffness of these equations, this system was numerically implemented using a stochastic piecewise constant approximation method (Stochastic PCA). Here, we present a study of the influence of stochastic fluctuations on the results of the neutron point kinetics equation. We reproduce the stochastic formulation introduced by Hayes and Allen and compute Monte Carlo numerical results for examples with constant and time-dependent reactivity, comparing these results with stochastic and deterministic methods found in the literature. Moreover, we introduce a modified version of the stochastic method to obtain a non-stiff solution, analogue to a previously derived deterministic approach. (author)

  8. The solution of the neutron point kinetics equation with stochastic extension: an analysis of two moments

    International Nuclear Information System (INIS)

    Silva, Milena Wollmann da; Vilhena, Marco Tullio M.B.; Bodmann, Bardo Ernst J.; Vasques, Richard

    2015-01-01

    The neutron point kinetics equation, which models the time-dependent behavior of nuclear reactors, is often used to understand the dynamics of nuclear reactor operations. It consists of a system of coupled differential equations that models the interaction between (i) the neutron population; and (II) the concentration of the delayed neutron precursors, which are radioactive isotopes formed in the fission process that decay through neutron emission. These equations are deterministic in nature, and therefore can provide only average values of the modeled populations. However, the actual dynamical process is stochastic: the neutron density and the delayed neutron precursor concentrations vary randomly with time. To address this stochastic behavior, Hayes and Allen have generalized the standard deterministic point kinetics equation. They derived a system of stochastic differential equations that can accurately model the random behavior of the neutron density and the precursor concentrations in a point reactor. Due to the stiffness of these equations, this system was numerically implemented using a stochastic piecewise constant approximation method (Stochastic PCA). Here, we present a study of the influence of stochastic fluctuations on the results of the neutron point kinetics equation. We reproduce the stochastic formulation introduced by Hayes and Allen and compute Monte Carlo numerical results for examples with constant and time-dependent reactivity, comparing these results with stochastic and deterministic methods found in the literature. Moreover, we introduce a modified version of the stochastic method to obtain a non-stiff solution, analogue to a previously derived deterministic approach. (author)

  9. Hydrodynamic and kinetic models for spin-1/2 electron-positron quantum plasmas: Annihilation interaction, helicity conservation, and wave dispersion in magnetized plasmas

    International Nuclear Information System (INIS)

    Andreev, Pavel A.

    2015-01-01

    We discuss the complete theory of spin-1/2 electron-positron quantum plasmas, when electrons and positrons move with velocities mach smaller than the speed of light. We derive a set of two fluid quantum hydrodynamic equations consisting of the continuity, Euler, spin (magnetic moment) evolution equations for each species. We explicitly include the Coulomb, spin-spin, Darwin and annihilation interactions. The annihilation interaction is the main topic of the paper. We consider the contribution of the annihilation interaction in the quantum hydrodynamic equations and in the spectrum of waves in magnetized electron-positron plasmas. We consider the propagation of waves parallel and perpendicular to an external magnetic field. We also consider the oblique propagation of longitudinal waves. We derive the set of quantum kinetic equations for electron-positron plasmas with the Darwin and annihilation interactions. We apply the kinetic theory to the linear wave behavior in absence of external fields. We calculate the contribution of the Darwin and annihilation interactions in the Landau damping of the Langmuir waves. We should mention that the annihilation interaction does not change number of particles in the system. It does not related to annihilation itself, but it exists as a result of interaction of an electron-positron pair via conversion of the pair into virtual photon. A pair of the non-linear Schrodinger equations for the electron-positron plasmas including the Darwin and annihilation interactions is derived. Existence of the conserving helicity in electron-positron quantum plasmas of spinning particles with the Darwin and annihilation interactions is demonstrated. We show that the annihilation interaction plays an important role in the quantum electron-positron plasmas giving the contribution of the same magnitude as the spin-spin interaction

  10. Comparative analysis among several methods used to solve the point kinetic equations

    International Nuclear Information System (INIS)

    Nunes, Anderson L.; Goncalves, Alessandro da C.; Martinez, Aquilino S.; Silva, Fernando Carvalho da

    2007-01-01

    The main objective of this work consists on the methodology development for comparison of several methods for the kinetics equations points solution. The evaluated methods are: the finite differences method, the stiffness confinement method, improved stiffness confinement method and the piecewise constant approximations method. These methods were implemented and compared through a systematic analysis that consists basically of confronting which one of the methods consume smaller computational time with higher precision. It was calculated the relative which function is to combine both criteria in order to reach the goal. Through the analyses of the performance factor it is possible to choose the best method for the solution of point kinetics equations. (author)

  11. Comparative analysis among several methods used to solve the point kinetic equations

    Energy Technology Data Exchange (ETDEWEB)

    Nunes, Anderson L.; Goncalves, Alessandro da C.; Martinez, Aquilino S.; Silva, Fernando Carvalho da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear; E-mails: alupo@if.ufrj.br; agoncalves@con.ufrj.br; aquilino@lmp.ufrj.br; fernando@con.ufrj.br

    2007-07-01

    The main objective of this work consists on the methodology development for comparison of several methods for the kinetics equations points solution. The evaluated methods are: the finite differences method, the stiffness confinement method, improved stiffness confinement method and the piecewise constant approximations method. These methods were implemented and compared through a systematic analysis that consists basically of confronting which one of the methods consume smaller computational time with higher precision. It was calculated the relative which function is to combine both criteria in order to reach the goal. Through the analyses of the performance factor it is possible to choose the best method for the solution of point kinetics equations. (author)

  12. An analytical solution for the two-group kinetic neutron diffusion equation in cylindrical geometry

    International Nuclear Information System (INIS)

    Fernandes, Julio Cesar L.; Vilhena, Marco Tullio; Bodmann, Bardo Ernst

    2011-01-01

    Recently the two-group Kinetic Neutron Diffusion Equation with six groups of delay neutron precursor in a rectangle was solved by the Laplace Transform Technique. In this work, we report on an analytical solution for this sort of problem but in cylindrical geometry, assuming a homogeneous and infinite height cylinder. The solution is obtained applying the Hankel Transform to the Kinetic Diffusion equation and solving the transformed problem by the same procedure used in the rectangle. We also present numerical simulations and comparisons against results available in literature. (author)

  13. Beyond the Cahn-Hilliard equation: a vacancy-based kinetic theory

    International Nuclear Information System (INIS)

    Nastar, M.

    2011-01-01

    A Self-Consistent Mean Field (SCMF) kinetic theory including an explicit description of the vacancy diffusion mechanism is developed. The present theory goes beyond the usual local equilibrium hypothesis. It is applied to the study of the early time spinodal decomposition in alloys. The resulting analytical expression of the structure function highlights the contribution of the vacancy diffusion mechanism. Instead of the single amplification rate of the Cahn-Hillard linear theory, the linearized SCMF kinetic equations involve three constant rates, first one describing the vacancy relaxation kinetics, second one related to the kinetic coupling between local concentrations and pair correlations and the third one representing the spinodal amplification rate. Starting from the same vacancy diffusion model, we perform kinetic Monte Carlo simulations of a Body Centered Cubic (BCC) demixting alloy. The resulting spherically averaged structure function is compared to the SCMF predictions. Both qualitative and quantitative agreements are satisfying. (authors)

  14. Is the kinetic equation for turbulent gas-particle flows ill posed?

    Science.gov (United States)

    Reeks, M; Swailes, D C; Bragg, A D

    2018-02-01

    This paper is about the kinetic equation for gas-particle flows, in particular its well-posedness and realizability and its relationship to the generalized Langevin model (GLM) probability density function (PDF) equation. Previous analyses, e.g. [J.-P. Minier and C. Profeta, Phys. Rev. E 92, 053020 (2015)PLEEE81539-375510.1103/PhysRevE.92.053020], have concluded that this kinetic equation is ill posed, that in particular it has the properties of a backward heat equation, and as a consequence, its solution will in the course of time exhibit finite-time singularities. We show that this conclusion is fundamentally flawed because it ignores the coupling between the phase space variables in the kinetic equation and the time and particle inertia dependence of the phase space diffusion tensor. This contributes an extra positive diffusion that always outweighs the negative diffusion associated with the dispersion along one of the principal axes of the phase space diffusion tensor. This is confirmed by a numerical evaluation of analytic solutions of these positive and negative contributions to the particle diffusion coefficient along this principal axis. We also examine other erroneous claims and assumptions made in previous studies that demonstrate the apparent superiority of the GLM PDF approach over the kinetic approach. In so doing, we have drawn attention to the limitations of the GLM approach, which these studies have ignored or not properly considered, to give a more balanced appraisal of the benefits of both PDF approaches.

  15. A new integral method for solving the point reactor neutron kinetics equations

    International Nuclear Information System (INIS)

    Li Haofeng; Chen Wenzhen; Luo Lei; Zhu Qian

    2009-01-01

    A numerical integral method that efficiently provides the solution of the point kinetics equations by using the better basis function (BBF) for the approximation of the neutron density in one time step integrations is described and investigated. The approach is based on an exact analytic integration of the neutron density equation, where the stiffness of the equations is overcome by the fully implicit formulation. The procedure is tested by using a variety of reactivity functions, including step reactivity insertion, ramp input and oscillatory reactivity changes. The solution of the better basis function method is compared to other analytical and numerical solutions of the point reactor kinetics equations. The results show that selecting a better basis function can improve the efficiency and accuracy of this integral method. The better basis function method can be used in real time forecasting for power reactors in order to prevent reactivity accidents.

  16. Non-equilibrium plasma kinetics of reacting CO: an improved state to state approach

    Science.gov (United States)

    Pietanza, L. D.; Colonna, G.; Capitelli, M.

    2017-12-01

    Non-equilibrium plasma kinetics of reacting CO for conditions typically met in microwave discharges have been developed based on the coupling of excited state kinetics and the Boltzmann equation for the electron energy distribution function (EEDF). Particular attention is given to the insertion in the vibrational kinetics of a complete set of electron molecule resonant processes linking the whole vibrational ladder of the CO molecule, as well as to the role of Boudouard reaction, i.e. the process of forming CO2 by two vibrationally excited CO molecules, in shaping the vibrational distribution of CO and promoting reaction channels assisted by vibrational excitation (pure vibrational mechanisms, PVM). PVM mechanisms can become competitive with electron impact dissociation processes (DEM) in the activation of CO. A case study reproducing the conditions of a microwave discharge has been considered following the coupled kinetics also in the post discharge conditions. Results include the evolution of EEDF in discharge and post discharge conditions highlighting the role of superelastic vibrational and electronic collisions in shaping the EEDF. Moreover, PVM rate coefficients and DEM ones are studied as a function of gas temperature, showing a non-Arrhenius behavior, i.e. the rate coefficients increase with decreasing gas temperature as a result of a vibrational-vibrational (V-V) pumping up mechanism able to form plateaux in the vibrational distribution function. The accuracy of the results is discussed in particular in connection to the present knowledge of the activation energy of the Boudouard process.

  17. Gabor Wave Packet Method to Solve Plasma Wave Equations

    International Nuclear Information System (INIS)

    Pletzer, A.; Phillips, C.K.; Smithe, D.N.

    2003-01-01

    A numerical method for solving plasma wave equations arising in the context of mode conversion between the fast magnetosonic and the slow (e.g ion Bernstein) wave is presented. The numerical algorithm relies on the expansion of the solution in Gaussian wave packets known as Gabor functions, which have good resolution properties in both real and Fourier space. The wave packets are ideally suited to capture both the large and small wavelength features that characterize mode conversion problems. The accuracy of the scheme is compared with a standard finite element approach

  18. Three species one-dimensional kinetic model for weakly ionized plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Gonzalez, J., E-mail: jorge.gonzalez@upm.es; Donoso, J. M.; Tierno, S. P. [Department of Applied Physics, Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, 28040 Madrid (Spain)

    2016-06-15

    A three species one-dimensional kinetic model is presented for a spatially homogeneous weakly ionized plasma subjected to the action of a time varying electric field. Planar geometry is assumed, which means that the plasma evolves in the privileged direction of the field. The energy transmitted to the electric charges is channelized to the neutrals thanks to collisions, a mechanism that influences the plasma dynamics. Charge-charge interactions have been designed as a one-dimensional collision term equivalent to the Landau operator used for fully ionized plasmas. Charge-neutral collisions are modelled by a conservative drift-diffusion operator in the Dougherty's form. The resulting set of coupled integro-differential equations is solved with the stable and robust propagator integral method. This semi–analytical method feasibility accounts for non–linear effects without appealing to linearisation or simplifications, providing conservative physically meaningful solutions even for initial or emerging sharp velocity distribution function profiles. It is found that charge-neutral collisions exert a significant effect since a quite different plasma evolution arises if compared to the collisionless limit. In addition, substantial differences in the system motion are found for constant and temperature dependent collision frequencies cases.

  19. Kinetic study on non-thermal volumetric plasma decay in the early afterglow of air discharge generated by a short pulse microwave or laser

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Wei, E-mail: yangwei861212@126.com; Zhou, Qianhong; Dong, Zhiwei [Institute of Applied Physics and Computational Mathematics, Beijing 100094 (China)

    2016-08-28

    This paper reports a kinetic study on non-thermal plasma decay in the early afterglow of air discharge generated by short pulse microwave or laser. A global self-consistent model is based on the particle balance of complex plasma chemistry, electron energy equation, and gas thermal balance equation. Electron-ion Coulomb collision is included in the steady state Boltzmann equation solver to accurately describe the electron mobility and other transport coefficients. The model is used to simulate the afterglow of microsecond to nanosecond pulse microwave discharge in N{sub 2}, O{sub 2}, and air, as well as femtosecond laser filament discharge in dry and humid air. The simulated results for electron density decay are in quantitative agreement with the available measured ones. The evolution of plasma decay under an external electric field is also investigated, and the effect of gas heating is considered. The underlying mechanism of plasma density decay is unveiled through the above kinetic modeling.

  20. Numerical solution of multi groups point kinetic equations by simulink toolbox of Matlab software

    International Nuclear Information System (INIS)

    Hadad, K.; Mohamadi, A.; Sabet, H.; Ayobian, N.; Khani, M.

    2004-01-01

    The simulink toolbox of Matlab Software was employed to solve the point kinetics equation with six group delayed neutrons. The method of Adams-Bash ford showed a good convergence in solving the system of simultaneous equations and the obtained results showed good agreements with other numerical schemes. The flexibility of the package in changing the system parameters and the user friendly interface makes this approach a reliable educational package in revealing the affects of reactivity changes on power incursions

  1. Analytical solution of point kinetic equations for sub-critical systems

    International Nuclear Information System (INIS)

    Henrice Junior, Edson; Goncalves, Alessandro C.

    2013-01-01

    This article presents an analytical solution for the set of point kinetic equations for sub-critical reactors. This solution stems from the ordinary, non-homogeneous differential equation that rules the neutron density and that presents the incomplete Gamma function in its functional form. The method used proved advantageous and allowed practical applications such as the linear insertion of reactivity, considering an external constant source or with both varying linearly. (author)

  2. Solution of the kinetic equation in the P3-approximation in a plane geometry

    International Nuclear Information System (INIS)

    Vlasov, Yu.A.

    1975-01-01

    A method and a program are described for solving single-velocity kinetic equations of neutron transfer for the plane geometry in the finite-difference approximation. A difference high-accuracy scheme and a matrix factorization method are used for the differential-difference equation systems. The program is written in the ALGOL-60 language and is adapted for M-20, M-220, M-222 and BESM-4 computers

  3. Generalized multivariate Fokker-Planck equations derived from kinetic transport theory and linear nonequilibrium thermodynamics

    International Nuclear Information System (INIS)

    Frank, T.D.

    2002-01-01

    We study many particle systems in the context of mean field forces, concentration-dependent diffusion coefficients, generalized equilibrium distributions, and quantum statistics. Using kinetic transport theory and linear nonequilibrium thermodynamics we derive for these systems a generalized multivariate Fokker-Planck equation. It is shown that this Fokker-Planck equation describes relaxation processes, has stationary maximum entropy distributions, can have multiple stationary solutions and stationary solutions that differ from Boltzmann distributions

  4. Unified implicit kinetic scheme for steady multiscale heat transfer based on the phonon Boltzmann transport equation

    Science.gov (United States)

    Zhang, Chuang; Guo, Zhaoli; Chen, Songze

    2017-12-01

    An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a macroscopic equation to accelerate the convergence in the diffusive regime. The macroscopic equation can be taken as a moment equation for phonon BTE. The heat flux in the macroscopic equation is evaluated from the nonequilibrium distribution function in the BTE, while the equilibrium state in BTE is determined by the macroscopic equation. These two processes exchange information from different scales, such that the method is applicable to the problems with a wide range of Knudsen numbers. Implicit discretization is implemented to solve both the macroscopic equation and the BTE. In addition, a memory reduction technique, which is originally developed for the stationary kinetic equation, is also extended to phonon BTE. Numerical comparisons show that the present scheme can predict reasonable results both in ballistic and diffusive regimes with high efficiency, while the memory requirement is on the same order as solving the Fourier law of heat conduction. The excellent agreement with benchmark and the rapid converging history prove that the proposed macro-micro coupling is a feasible solution to multiscale heat transfer problems.

  5. Two new proofs of the test particle superposition principle of plasma kinetic theory

    International Nuclear Information System (INIS)

    Krommes, J.A.

    1976-01-01

    The test particle superposition principle of plasma kinetic theory is discussed in relation to the recent theory of two-time fluctuations in plasma given by Williams and Oberman. Both a new deductive and a new inductive proof of the principle are presented; the deductive approach appears here for the first time in the literature. The fundamental observation is that two-time expectations of one-body operators are determined completely in terms of the (x,v) phase space density autocorrelation, which to lowest order in the discreteness parameter obeys the linearized Vlasov equation with singular initial condition. For the deductive proof, this equation is solved formally using time-ordered operators, and the solution is then re-arranged into the superposition principle. The inductive proof is simpler than Rostoker's although similar in some ways; it differs in that first-order equations for pair correlation functions need not be invoked. It is pointed out that the superposition principle is also applicable to the short-time theory of neutral fluids

  6. Kinetic Study of Nonequilibrium Plasma-Assisted Methane Steam Reforming

    Directory of Open Access Journals (Sweden)

    Hongtao Zheng

    2014-01-01

    Full Text Available To develop a detailed reaction mechanism for plasma-assisted methane steam reforming, a comprehensive numerical and experimental study of effect laws on methane conversion and products yield is performed at different steam to methane molar ratio (S/C, residence time s, and reaction temperatures. A CHEMKIN-PRO software with sensitivity analysis module and path flux analysis module was used for simulations. A set of comparisons show that the developed reaction mechanism can accurately predict methane conversion and the trend of products yield in different operating conditions. Using the developed reaction mechanism in plasma-assisted kinetic model, the reaction path flux analysis was carried out. The result shows that CH3 recombination is the limiting reaction for CO production and O is the critical species for CO production. Adding 40 wt.% Ni/SiO2 in discharge region has significantly promoted the yield of H2, CO, or CO2 in dielectric packed bed (DPB reactor. Plasma catalytic hybrid reforming experiment verifies the reaction path flux analysis tentatively.

  7. Analytic solution of boundary-value problems for nonstationary model kinetic equations

    International Nuclear Information System (INIS)

    Latyshev, A.V.; Yushkanov, A.A.

    1993-01-01

    A theory for constructing the solutions of boundary-value problems for non-stationary model kinetic equations is constructed. This theory was incorrectly presented equation, separation of the variables is used, this leading to a characteristic equation. Eigenfunctions are found in the space of generalized functions, and the eigenvalue spectrum is investigated. An existence and uniqueness theorem for the expansion of the Laplace transform of the solution with respect to the eigenfunctions is proved. The proof is constructive and gives explicit expressions for the expansion coefficients. An application to the Rayleigh problem is obtained, and the corresponding result of Cercignani is corrected

  8. Comparison of two forms of Vlasov-type relativistic kinetic equations in hadrodynamics

    International Nuclear Information System (INIS)

    Mashnik, S.G.; Maino, G.

    1996-01-01

    A comparison of two methods in the relativistic kinetic theory of the Fermi systems is carried out assuming, as an example, the simplest σω-version of quantum hadrodynamics with allowance for strong mean meson fields. It is shown that the Vlasov-type relativistic kinetic equation (VRKE) obtained by means of the procedure of squaring at an intermediate step is responsible for unphysical features. A direct method of derivation of kinetic equations is proposed. This method does not contain such drawback and gives rise to VRKE in hydrodynamics of a non-contradictory form in which both spin degrees of freedom and states with positive and negative energies are taken into account. 17 refs

  9. Kinetic and spectral descriptions of autoionization phenomena associated with atomic processes in plasmas

    Science.gov (United States)

    Jacobs, Verne L.

    2017-06-01

    This investigation has been devoted to the theoretical description and computer modeling of atomic processes giving rise to radiative emission in energetic electron and ion beam interactions and in laboratory plasmas. We are also interested in the effects of directed electron and ion collisions and of anisotropic electric and magnetic fields. In the kinetic-theory description, we treat excitation, de-excitation, ionization, and recombination in electron and ion encounters with partially ionized atomic systems, including the indirect contributions from processes involving autoionizing resonances. These fundamental collisional and electromagnetic interactions also provide particle and photon transport mechanisms. From the spectral perspective, the analysis of atomic radiative emission can reveal detailed information on the physical properties in the plasma environment, such as non-equilibrium electron and charge-state distributions as well as electric and magnetic field distributions. In this investigation, a reduced-density-matrix formulation is developed for the microscopic description of atomic electromagnetic interactions in the presence of environmental (collisional and radiative) relaxation and decoherence processes. Our central objective is a fundamental microscopic description of atomic electromagnetic processes, in which both bound-state and autoionization-resonance phenomena can be treated in a unified and self-consistent manner. The time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations of the reduced-density-matrix approach are developed in a unified and self-consistent manner. This is necessary for our ultimate goal of a systematic and self-consistent treatment of non-equilibrium (possibly coherent) atomic-state kinetics and high-resolution (possibly overlapping) spectral-line shapes. We thereby propose the introduction of a generalized collisional-radiative atomic-state kinetics model based on a reduced

  10. On the exact solution for the multi-group kinetic neutron diffusion equation in a rectangle

    International Nuclear Information System (INIS)

    Petersen, C.Z.; Vilhena, M.T.M.B. de; Bodmann, B.E.J.

    2011-01-01

    In this work we consider the two-group bi-dimensional kinetic neutron diffusion equation. The solution procedure formalism is general with respect to the number of energy groups, neutron precursor families and regions with different chemical compositions. The fast and thermal flux and the delayed neutron precursor yields are expanded in a truncated double series in terms of eigenfunctions that, upon insertion into the kinetic equation and upon taking moments, results in a first order linear differential matrix equation with source terms. We split the matrix appearing in the transformed problem into a sum of a diagonal matrix plus the matrix containing the remaining terms and recast the transformed problem into a form that can be solved in the spirit of Adomian's recursive decomposition formalism. Convergence of the solution is guaranteed by the Cardinal Interpolation Theorem. We give numerical simulations and comparisons with available results in the literature. (author)

  11. Kinetics of subdiffusion-assisted reactions: non-Markovian stochastic Liouville equation approach

    International Nuclear Information System (INIS)

    Shushin, A I

    2005-01-01

    Anomalous specific features of the kinetics of subdiffusion-assisted bimolecular reactions (time-dependence, dependence on parameters of systems, etc) are analysed in detail with the use of the non-Markovian stochastic Liouville equation (SLE), which has been recently derived within the continuous-time random-walk (CTRW) approach. In the CTRW approach, subdiffusive motion of particles is modelled by jumps whose onset probability distribution function is of a long-tailed form. The non-Markovian SLE allows for rigorous describing of some peculiarities of these reactions; for example, very slow long-time behaviour of the kinetics, non-analytical dependence of the reaction rate on the reactivity of particles, strong manifestation of fluctuation kinetics showing itself in very slowly decreasing behaviour of the kinetics at very long times, etc

  12. Advances in petascale kinetic plasma simulation with VPIC and Roadrunner

    Energy Technology Data Exchange (ETDEWEB)

    Bowers, Kevin J [Los Alamos National Laboratory; Albright, Brian J [Los Alamos National Laboratory; Yin, Lin [Los Alamos National Laboratory; Daughton, William S [Los Alamos National Laboratory; Roytershteyn, Vadim [Los Alamos National Laboratory; Kwan, Thomas J T [Los Alamos National Laboratory

    2009-01-01

    VPIC, a first-principles 3d electromagnetic charge-conserving relativistic kinetic particle-in-cell (PIC) code, was recently adapted to run on Los Alamos's Roadrunner, the first supercomputer to break a petaflop (10{sup 15} floating point operations per second) in the TOP500 supercomputer performance rankings. They give a brief overview of the modeling capabilities and optimization techniques used in VPIC and the computational characteristics of petascale supercomputers like Roadrunner. They then discuss three applications enabled by VPIC's unprecedented performance on Roadrunner: modeling laser plasma interaction in upcoming inertial confinement fusion experiments at the National Ignition Facility (NIF), modeling short pulse laser GeV ion acceleration and modeling reconnection in magnetic confinement fusion experiments.

  13. Kinetic global analysis of Alfven eigenmodes in toroidal plasmas

    International Nuclear Information System (INIS)

    Fukuyama, A.

    2002-01-01

    Systematic study on low to medium n (toroidal mode number) Alfven eigenmodes (AE) in tokamaks and helical systems is presented. Linear stability of AE in the presence of energetic ions was studied using the kinetic full-wave code TASK/WM.We have reproduced the destabilizing effect of toroidal co-rotation on TAE for JT-60U parameters. We have found the existence of reversed-shear-induced Alfven eigenmode (RSAE) which localizes near the q minimum in a reversed magnetic shear configuration. Two kinds of mode structures are identified for energetic particle mode (EPM) below the TAE frequency gap. The coupling to lower-frequency modes such as drift waves and MHD modes as well as the effect of trapped particles are also taken into account. For a helical plasma, the existence of GAE in the central region and TAE in the off-axis region was confirmed. (author)

  14. MAGNETIC NULL POINTS IN KINETIC SIMULATIONS OF SPACE PLASMAS

    International Nuclear Information System (INIS)

    Olshevsky, Vyacheslav; Innocenti, Maria Elena; Cazzola, Emanuele; Lapenta, Giovanni; Deca, Jan; Divin, Andrey; Peng, Ivy Bo; Markidis, Stefano

    2016-01-01

    We present a systematic attempt to study magnetic null points and the associated magnetic energy conversion in kinetic particle-in-cell simulations of various plasma configurations. We address three-dimensional simulations performed with the semi-implicit kinetic electromagnetic code iPic3D in different setups: variations of a Harris current sheet, dipolar and quadrupolar magnetospheres interacting with the solar wind, and a relaxing turbulent configuration with multiple null points. Spiral nulls are more likely created in space plasmas: in all our simulations except lunar magnetic anomaly (LMA) and quadrupolar mini-magnetosphere the number of spiral nulls prevails over the number of radial nulls by a factor of 3–9. We show that often magnetic nulls do not indicate the regions of intensive energy dissipation. Energy dissipation events caused by topological bifurcations at radial nulls are rather rare and short-lived. The so-called X-lines formed by the radial nulls in the Harris current sheet and LMA simulations are rather stable and do not exhibit any energy dissipation. Energy dissipation is more powerful in the vicinity of spiral nulls enclosed by magnetic flux ropes with strong currents at their axes (their cross sections resemble 2D magnetic islands). These null lines reminiscent of Z-pinches efficiently dissipate magnetic energy due to secondary instabilities such as the two-stream or kinking instability, accompanied by changes in magnetic topology. Current enhancements accompanied by spiral nulls may signal magnetic energy conversion sites in the observational data

  15. Ultrafast dynamics of laser-pulse excited semiconductors: non-Markovian quantum kinetic equations with nonequilibrium correlations

    Directory of Open Access Journals (Sweden)

    V.V.Ignatyuk

    2004-01-01

    Full Text Available Non-Markovian kinetic equations in the second Born approximation are derived for a two-zone semiconductor excited by a short laser pulse. Both collision dynamics and running nonequilibrium correlations are taken into consideration. The energy balance and relaxation of the system to equilibrium are discussed. Results of numerical solution of the kinetic equations for carriers and phonons are presented.

  16. Electron kinetics with attachment and ionization from higher order solutions of Boltzmann's equation

    International Nuclear Information System (INIS)

    Winkler, R.; Wilhelm, J.; Braglia, G.L.

    1989-01-01

    An appropriate approach is presented for solving the Boltzmann equation for electron swarms and nonstationary weakly ionized plasmas in the hydrodynamic stage, including ionization and attachment processes. Using a Legendre-polynomial expansion of the electron velocity distribution function the resulting eigenvalue problem has been solved at any even truncation-order. The technique has been used to study velocity distribution, mean collision frequencies, energy transfer rates, nonstationary behaviour and power balance in hydrodynamic stage, of electrons in a model plasma and a plasma of pure SF 6 . The calculations have been performed for increasing approximation-orders, up to the converged solution of the problem. In particular, the transition from dominant attachment to prevailing ionization when increasing the field strength has been studied. Finally the establishment of the hydrodynamic stage for a selected case in the model plasma has been investigated by solving the nonstationary, spatially homogeneous Boltzmann equation in twoterm approximation. (author)

  17. The plasma transport equations derived by multiple time-scale expansions and turbulent transport. I. General theory

    International Nuclear Information System (INIS)

    Edenstrasser, J.W.

    1995-01-01

    A multiple time-scale derivative expansion scheme is applied to the dimensionless Fokker--Planck equation and to Maxwell's equations, where the parameter range of a typical fusion plasma was assumed. Within kinetic theory, the four time scales considered are those of Larmor gyration, particle transit, collisions, and classical transport. The corresponding magnetohydrodynamic (MHD) time scales are those of ion Larmor gyration, Alfven, MHD collision, and resistive diffusion. The solution of the zeroth-order equations results in the force-free equilibria and ideal Ohm's law. The solution of the first-order equations leads under the assumption of a weak collisional plasma to the ideal MHD equations. On the MHD-collision time scale, not only the full set of the MHD transport equations is obtained, but also turbulent terms, where the related transport quantities are one order in the expansion parameter larger than those of classical transport. Finally, at the resistive diffusion time scale the known transport equations are arrived at including, however, also turbulent contributions. copyright 1995 American Institute of Physics

  18. Balance of liquid-phase turbulence kinetic energy equation for bubble-train flow

    International Nuclear Information System (INIS)

    Ilic, Milica; Woerner, Martin; Cacuci, Dan Gabriel

    2004-01-01

    In this paper the investigation of bubble-induced turbulence using direct numerical simulation (DNS) of bubbly two-phase flow is reported. DNS computations are performed for a bubble-driven liquid motion induced by a regular train of ellipsoidal bubbles rising through an initially stagnant liquid within a plane vertical channel. DNS data are used to evaluate balance terms in the balance equation for the liquid phase turbulence kinetic energy. The evaluation comprises single-phase-like terms (diffusion, dissipation and production) as well as the interfacial term. Special emphasis is placed on the procedure for evaluation of interfacial quantities. Quantitative analysis of the balance equation for the liquid phase turbulence kinetic energy shows the importance of the interfacial term which is the only source term. The DNS results are further used to validate closure assumptions employed in modelling of the liquid phase turbulence kinetic energy transport in gas-liquid bubbly flows. In this context, the performance of respective closure relations in the transport equation for liquid turbulence kinetic energy within the two-phase k-ε and the two-phase k-l model is evaluated. (author)

  19. Effect of impurities on kinetic transport processes in fusion plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Braun, Stefanie

    2010-12-10

    prominent role in stellarators than in tokamaks. In the final chapter of this thesis, analytical expressions for the particle and heat fluxes in an impure, collisional plasma are derived from first principles. Contrary to the tokamak case, where collisional transport is exclusively caused directly by friction, in stellarators an additional source of transport exists, namely anisotropy between the pressures parallel and perpendicular to the magnetic field. Whereas this anisotropy term does not contribute much to the overall fluxes at high collisionality since it is then considerably smaller than the friction contributions, it is nonetheless important since it is not ambipolar and therefore of relevance to the ambipolar electric field. Based on these results, the behaviour of heavy impurity ions under the influence of strong radial temperature and density gradients of the background plasma is studied. It is shown that a redistribution of the impurity ions within each magnetic flux surface arises. The effect of 3D geometry is studied. Since the resulting partial differential equations are too complicated for an analytical treatment, different limits are considered analytically and the full equation is solved numerically. The redistribution is driven by parallel friction and qualitatively influenced by the radial temperature gradient of the background plasma and the spatially varying E x B rotation due to the radial electric potential. The resulting impurity density patterns on the flux surface are sensitive to the exact geometry of the device and can be determined with the help of numerical databases of the magnetic configurations of different experiments. (orig.)

  20. Modified Gompertz equation for electrotherapy murine tumor growth kinetics: predictions and new hypotheses

    International Nuclear Information System (INIS)

    Cabrales, Luis E Bergues; Mateus, Miguel A O'Farril; Brooks, Soraida C Acosta; Palencia, Fabiola Suárez; Zamora, Lisset Ortiz; Quevedo, María C Céspedes; Seringe, Sarah Edward; Cuitié, Vladimir Crombet; Cabrales, Idelisa Bergues; González, Gustavo Sierra; Nava, Juan J Godina; Aguilera, Andrés Ramírez; Joa, Javier A González; Ciria, Héctor M Camué; González, Maraelys Morales; Salas, Miriam Fariñas; Jarque, Manuel Verdecia; González, Tamara Rubio

    2010-01-01

    Electrotherapy effectiveness at different doses has been demonstrated in preclinical and clinical studies; however, several aspects that occur in the tumor growth kinetics before and after treatment have not yet been revealed. Mathematical modeling is a useful instrument that can reveal some of these aspects. The aim of this paper is to describe the complete growth kinetics of unperturbed and perturbed tumors through use of the modified Gompertz equation in order to generate useful insight into the mechanisms that underpin this devastating disease. The complete tumor growth kinetics for control and treated groups are obtained by interpolation and extrapolation methods with different time steps, using experimental data of fibrosarcoma Sa-37. In the modified Gompertz equation, a delay time is introduced to describe the tumor's natural history before treatment. Different graphical strategies are used in order to reveal new information in the complete kinetics of this tumor type. The first stage of complete tumor growth kinetics is highly non linear. The model, at this stage, shows different aspects that agree with those reported theoretically and experimentally. Tumor reversibility and the proportionality between regions before and after electrotherapy are demonstrated. In tumors that reach partial remission, two antagonistic post-treatment processes are induced, whereas in complete remission, two unknown antitumor mechanisms are induced. The modified Gompertz equation is likely to lead to insights within cancer research. Such insights hold promise for increasing our understanding of tumors as self-organizing systems and, the possible existence of phase transitions in tumor growth kinetics, which, in turn, may have significant impacts both on cancer research and on clinical practice

  1. Differential equation methods for simulation of GFP kinetics in non-steady state experiments.

    Science.gov (United States)

    Phair, Robert D

    2018-03-15

    Genetically encoded fluorescent proteins, combined with fluorescence microscopy, are widely used in cell biology to collect kinetic data on intracellular trafficking. Methods for extraction of quantitative information from these data are based on the mathematics of diffusion and tracer kinetics. Current methods, although useful and powerful, depend on the assumption that the cellular system being studied is in a steady state, that is, the assumption that all the molecular concentrations and fluxes are constant for the duration of the experiment. Here, we derive new tracer kinetic analytical methods for non-steady state biological systems by constructing mechanistic nonlinear differential equation models of the underlying cell biological processes and linking them to a separate set of differential equations governing the kinetics of the fluorescent tracer. Linking the two sets of equations is based on a new application of the fundamental tracer principle of indistinguishability and, unlike current methods, supports correct dependence of tracer kinetics on cellular dynamics. This approach thus provides a general mathematical framework for applications of GFP fluorescence microscopy (including photobleaching [FRAP, FLIP] and photoactivation to frequently encountered experimental protocols involving physiological or pharmacological perturbations (e.g., growth factors, neurotransmitters, acute knockouts, inhibitors, hormones, cytokines, and metabolites) that initiate mechanistically informative intracellular transients. When a new steady state is achieved, these methods automatically reduce to classical steady state tracer kinetic analysis. © 2018 Phair. This article is distributed by The American Society for Cell Biology under license from the author(s). Two months after publication it is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

  2. Using packaged software for solving two differential equation problems that arise in plasma physics

    International Nuclear Information System (INIS)

    Gaffney, P.W.

    1980-01-01

    Experience in using packaged numerical software for solving two related problems that arise in Plasma physics is described. These problems are (i) the solution of the reduced resistive MHD equations and (ii) the solution of the Grad-Shafranov equation

  3. Quantum degeneracy corrections to plasma line emission and to Saha equation

    International Nuclear Information System (INIS)

    Molinari, V.G.; Mostacci, D.; Rocchi, F.; Sumini, M.

    2003-01-01

    The effect of quantum degeneracy on the electron collisional excitation is investigated, and its effects on line emission evaluated for applications to spectroscopy of dense, cold plasmas. A correction to Saha equation for weakly-degenerate plasmas is also presented

  4. Equations for the kinetic modeling of supersonically flowing electrically excited lasers

    International Nuclear Information System (INIS)

    Lind, R.C.

    1973-01-01

    The equations for the kinetic modeling of a supersonically flowing electrically excited laser system are presented. The work focuses on the use of diatomic gases, in particular carbon monoxide mixtures. The equations presented include the vibrational rate equation which describes the vibrational population distribution, the electron, ion and electronic level rate equations, the gasdynamic equations for an ionized gas in the presence of an applied electric field, and the free electron Boltzmann equation including flow and gradient coupling terms. The model developed accounts for vibration--vibration collisions, vibration-translation collisions, electron-molecule inelastic excitation and superelastic de-excitation collisions, charge particle collisions, ionization and three body recombination collisions, elastic collisions, and radiative decay, all of which take place in such a system. A simplified form of the free electron Boltzmann equation is developed and discussed with emphasis placed on its coupling with the supersonic flow. A brief description of a possible solution procedure for the set of coupled equations is discussed

  5. Derivation of a reduced kinetic equation using Lie-transform techniques

    International Nuclear Information System (INIS)

    Brizard, A.

    1991-01-01

    The asymptotic elimination of fast time scales from a general kinetic equation, of the form: ∂ t f+z·∂ x f = C[f], facilitates the study of the long time behavior of its solution f(z,t). Here z describe the single-particle Hamiltonian dynamics and the operator C, which may possess nonlinear functional dependence on f, describes processes (such as discrete-particle effects, resonant wave-particle effects, or effects due to external sources) which cause changes in f as it is convectively transported along a Hamiltonian phase-space trajectory. When a fast time scale is associated with z through the dependence on a fast angle θ (whose frequency θ = Ω satisfies ε ≡ 1/Ωτ much-lt 1, where τ is a slow time scale of interest), a near-identity phase-space transformation T ε :z→Z (carried out with Lie-transform techniques) yields reduced Hamiltonian dynamical equations Z ε which are θ-independent. The corresponding transformed kinetic equation is derived. Averaging this equation over the fast angle θ yields a kinetic equation for left-angle F right-angle, the θ-averaged part of F. In general, the θ-dependence of C ε couples the kinetic equations for left-angle F right-angle and F, the θ-dependent part of F. One solves for the Fourier coefficient F l (associated with e ilθ ) as a functional of left-angle F right-angle. One obtains a reduced kinetic equation for left-angle F right-angle: d R left-angle F right-angle/dt = C R [left-angle F right-angle]. General expressions for C R are given, as well as expressions for the guiding-center and oscillation-center phase-space transformations of a linear Fokker-Planck operator. A discussion of the relationship with Mynick's work is presented

  6. An equation of state for purely kinetic k-essence inspired by cosmic topological defects

    Energy Technology Data Exchange (ETDEWEB)

    Cordero, Ruben; Gonzalez, Eduardo L.; Queijeiro, Alfonso [Instituto Politecnico Nacional, Departamento de Fisica, Escuela Superior de Fisica y Matematicas, Ciudad de Mexico (Mexico)

    2017-06-15

    We investigate the physical properties of a purely kinetic k-essence model with an equation of state motivated in superconducting membranes. We compute the equation of state parameter w and discuss its physical evolution via a nonlinear equation of state. Using the adiabatic speed of sound and energy density, we restrict the range of parameters of the model in order to have an acceptable physical behavior. We study the evolution of the scale factor and address the question of the possible existence of finite-time future singularities. Furthermore, we analyze the evolution of the luminosity distance d{sub L} with redshift z by comparing (normalizing) it with the ΛCDM model. Since the equation of state parameter is z-dependent the evolution of the luminosity distance is also analyzed using the Alcock-Paczynski test. (orig.)

  7. An integral equation method for discrete and continuous distribution of centres in thermoluminescence kinetics

    International Nuclear Information System (INIS)

    Kantorovich, L.N.; Fogel, G.M.; Gotlib, V.I.

    1990-01-01

    Thermoluminescence kinetics is discussed within the framework of a band model containing an arbitrary number of types of recombination and trapping centres at an arbitrary correlation of all centre parameters. It is shown that the initial system of kinetic equations is reduced to an equivalent system consisting of two integro-differential equations which permit one to perform an accurate generalisation, in the case of a continuous centre distribution, to their parameters for the description of irradiation and thermoluminescence, taking into account charge carrier redistribution to both types of centre. In addition, if only one electron (hole) channel is taken into account, only one integro-differential equation is obtained. On the basis of this equation a precise algebraic equation is obtained for calculation of the area of an arbitrary part of the thermoluminescence curve (TLC), consisting of one or several peaks, which slightly overlap with other peaks. It is shown that at doses which are less than the saturation dose, when the centres are not completely filled by the charge carriers, the dose dependences of such a part of the TLC may have a non-linear character at a simultaneous linear dependence of the area of the whole TLC. At doses which are greater than the saturation dose, the dose dependences of the area of the whole TLC, as well as of its separate parts, undergo breaks at the saturation doses. (author)

  8. Analytic solution of vector model kinetic equations with constant kernel and their applications

    International Nuclear Information System (INIS)

    Latyshev, A.V.

    1993-01-01

    For the first time exact solutions the heif-space boundary value problems for model kinetic equations is obtained. Here x > 0, μ is an element of (-∞, 0) union (0, +∞), Σ = diag {σ 1 , σ 2 }, C = [c ij ] - 2 x 2-matrix, Ψ (x, μ) is vector-column with elements ψ 1 and ψ 2 . Exact solution of the diffusion slip flow of the binary gas mixture as a application for the model Boltzmann equation with collision operator in the McCormack's form is found. 18 refs

  9. Numerical instability of time-discretized one-point kinetic equations

    International Nuclear Information System (INIS)

    Hashimoto, Kengo; Ikeda, Hideaki; Takeda, Toshikazu

    2000-01-01

    The one-point kinetic equations with numerical errors induced by the explicit, implicit and Crank-Nicolson integration methods are derived. The zero-power transfer functions based on the present equations are demonstrated to investigate the numerical stability of the discretized systems. These demonstrations indicate unconditional stability for the implicit and Crank-Nicolson methods but present the possibility of numerical instability for the explicit method. An upper limit of time mesh spacing for the stability is formulated and several numerical calculations are made to confirm the validity of this formula

  10. Relativistic electron kinetic effects on laser diagnostics in burning plasmas

    Science.gov (United States)

    Mirnov, V. V.; Den Hartog, D. J.

    2018-02-01

    Toroidal interferometry/polarimetry (TIP), poloidal polarimetry (PoPola), and Thomson scattering systems (TS) are major optical diagnostics being designed and developed for ITER. Each of them relies upon a sophisticated quantitative understanding of the electron response to laser light propagating through a burning plasma. Review of the theoretical results for two different applications is presented: interferometry/polarimetry (I/P) and polarization of Thomson scattered light, unified by the importance of relativistic (quadratic in vTe/c) electron kinetic effects. For I/P applications, rigorous analytical results are obtained perturbatively by expansion in powers of the small parameter τ = Te/me c2, where Te is electron temperature and me is electron rest mass. Experimental validation of the analytical models has been made by analyzing data of more than 1200 pulses collected from high-Te JET discharges. Based on this validation the relativistic analytical expressions are included in the error analysis and design projects of the ITER TIP and PoPola systems. The polarization properties of incoherent Thomson scattered light are being examined as a method of Te measurement relevant to ITER operational regimes. The theory is based on Stokes vector transformation and Mueller matrices formalism. The general approach is subdivided into frequency-integrated and frequency-resolved cases. For each of them, the exact analytical relativistic solutions are presented in the form of Mueller matrix elements averaged over the relativistic Maxwellian distribution function. New results related to the detailed verification of the frequency-resolved solutions are reported. The precise analytic expressions provide output much more rapidly than relativistic kinetic numerical codes allowing for direct real-time feedback control of ITER device operation.

  11. High fidelity kinetic modeling of magnetic reconnection in laboratory plasma

    Science.gov (United States)

    Stanier, A.; Daughton, W. S.

    2017-12-01

    Over the past decade, a great deal of progress has been made towards understanding the physics of magnetic reconnection in weakly collisional regimes of relevance to both fusion devices, and to space and astrophysical plasmas. However, there remain some outstanding unsolved problems in reconnection physics, such as the generation and influence of plasmoids (flux ropes) within reconnection layers, the development of magnetic turbulence, the role of current driven and streaming instabilities, and the influence of electron pressure anisotropy on the layer structure. Due to the importance of these questions, new laboratory reconnection experiments are being built to allow controlled and reproducible study of such questions with the simultaneous acquisition of high time resolution measurements at a large number of spatial points. These experiments include the FLARE facility at Princeton University and the T-REX experiment at the University of Wisconsin. To guide and interpret these new experiments, and to extrapolate the results to space applications, new investments in kinetic modeling tools are required. We have recently developed a cylindrical version of the VPIC Particle-In-Cell code with the capability to perform first-principles kinetic simulations that approach experimental device size with more realistic geometry and drive coils. This cylindrical version inherits much of the optimization work that has been done recently for the next generation many-cores architectures with wider vector registers, and achieves comparable conservation properties as the Cartesian code. Namely it features exact discrete charge conservation, and a so-called "energy-conserving" scheme where the energy is conserved in the limit of continuous time, i.e. without contribution from spatial discretization (Lewis, 1970). We will present initial results of modeling magnetic reconnection in the experiments mentioned above. Since the VPIC code is open source (https

  12. Solving the master equation without kinetic Monte Carlo: Tensor train approximations for a CO oxidation model

    International Nuclear Information System (INIS)

    Gelß, Patrick; Matera, Sebastian; Schütte, Christof

    2016-01-01

    In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO 2 (110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.

  13. Solving the master equation without kinetic Monte Carlo: Tensor train approximations for a CO oxidation model

    Science.gov (United States)

    Gelß, Patrick; Matera, Sebastian; Schütte, Christof

    2016-06-01

    In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO2(110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.

  14. Solving the master equation without kinetic Monte Carlo: Tensor train approximations for a CO oxidation model

    Energy Technology Data Exchange (ETDEWEB)

    Gelß, Patrick, E-mail: p.gelss@fu-berlin.de; Matera, Sebastian, E-mail: matera@math.fu-berlin.de; Schütte, Christof, E-mail: schuette@mi.fu-berlin.de

    2016-06-01

    In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO{sub 2}(110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.

  15. Compactness and robustness: Applications in the solution of integral equations for chemical kinetics and electromagnetic scattering

    Science.gov (United States)

    Zhou, Yajun

    This thesis employs the topological concept of compactness to deduce robust solutions to two integral equations arising from chemistry and physics: the inverse Laplace problem in chemical kinetics and the vector wave scattering problem in dielectric optics. The inverse Laplace problem occurs in the quantitative understanding of biological processes that exhibit complex kinetic behavior: different subpopulations of transition events from the "reactant" state to the "product" state follow distinct reaction rate constants, which results in a weighted superposition of exponential decay modes. Reconstruction of the rate constant distribution from kinetic data is often critical for mechanistic understandings of chemical reactions related to biological macromolecules. We devise a "phase function approach" to recover the probability distribution of rate constants from decay data in the time domain. The robustness (numerical stability) of this reconstruction algorithm builds upon the continuity of the transformations connecting the relevant function spaces that are compact metric spaces. The robust "phase function approach" not only is useful for the analysis of heterogeneous subpopulations of exponential decays within a single transition step, but also is generalizable to the kinetic analysis of complex chemical reactions that involve multiple intermediate steps. A quantitative characterization of the light scattering is central to many meteoro-logical, optical, and medical applications. We give a rigorous treatment to electromagnetic scattering on arbitrarily shaped dielectric media via the Born equation: an integral equation with a strongly singular convolution kernel that corresponds to a non-compact Green operator. By constructing a quadratic polynomial of the Green operator that cancels out the kernel singularity and satisfies the compactness criterion, we reveal the universality of a real resonance mode in dielectric optics. Meanwhile, exploiting the properties of

  16. Application of the reactor kinetics equations to the reactor safety analysis

    International Nuclear Information System (INIS)

    Sdouz, G.

    1976-01-01

    The reactor kinetics equations which can be solved by the computer program AIREK-III are used to describe the behavior of fast reactivity transients. By supplementing this computer program it was possible to solve additional safety problems, e.g. the course of reactor excursions induced by any form of reactivity input, the control of reactivity input as a function of a threshold-energy and the computation of produced energy. (author)

  17. Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations

    International Nuclear Information System (INIS)

    EL Safadi, M.

    2007-03-01

    We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C ∞ regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

  18. Application of the fractional neutron point kinetic equation: Start-up of a nuclear reactor

    International Nuclear Information System (INIS)

    Polo-Labarrios, M.-A.; Espinosa-Paredes, G.

    2012-01-01

    Highlights: ► Neutron density behavior at reactor start up with fractional neutron point kinetics. ► There is a relaxation time associated with a rapid variation in the neutron flux. ► Physical interpretation of the fractional order is related with non-Fickian effects. ► Effect of the anomalous diffusion coefficient and the relaxation time is analyzed. ► Neutron density is related with speed and duration of the control rods lifting. - Abstract: In this paper we present the behavior of the variation of neutron density when the nuclear reactor power is increased using the fractional neutron point kinetic (FNPK) equation with a single-group of delayed neutron precursor. It is considered that there is a relaxation time associated with a rapid variation in the neutron flux and its physical interpretation of the fractional order is related with non-Fickian effects from the neutron diffusion equation point of view. We analyzed the case of increase the nuclear reactor power when reactor is cold start-up which is a process of inserting reactivity by lifting control rods discontinuously. The results show that for short time scales of the start-up the neutronic density behavior with FNPK shows sub-diffusive effects whose absorption are government by control rods velocity. For large times scale, the results shows that the classical equation of the neutron point kinetics over predicted the neutron density regarding to FNPK.

  19. Kinetic instabilities in plasmas: from electromagnetic fluctuations to collisionless shocks

    International Nuclear Information System (INIS)

    Ruyer, Charles

    2014-01-01

    Collisionless shocks play a major role in powerful astrophysical objects (e.g., gamma-ray bursts, supernova remnants, pulsar winds, etc.), where they are thought to be responsible for non-thermal particle acceleration and radiation. Numerical simulations have shown that, in the absence of an external magnetic field, these self-organizing structures originate from electromagnetic instabilities triggered by high-velocity colliding flows. These Weibel-like instabilities are indeed capable of producing the magnetic turbulence required for both efficient scattering and Fermi-type acceleration. Along with rapid advances in their theoretical understanding, intense effort is now underway to generate collisionless shocks in the laboratory using energetic lasers. In a first part we study the (w,k)-resolved electromagnetic thermal spectrum sustained by a drifting relativistic plasma. In particular, we obtain analytical formulae for the fluctuation spectra, the latter serving as seeds for growing magnetic modes in counterstreaming plasmas. Distinguishing between sub-luminal and supra-luminal thermal fluctuations, we derived analytical formulae of their respective spectral contributions. Comparisons with particle-in-cell (PIC) simulations are made, showing close agreement in the sub-luminal regime along with some discrepancy in the supra-luminal regime. Our formulae are then used to estimate the saturation time of the Weibel instability of relativistic pair plasmas. Our predictions are shown to match 2-D particle-in-cell (PIC) simulations over a three-decade range in flow energy. We then develop a predictive kinetic model of the nonlinear phase of the Weibel instability induced by two counter-streaming, symmetric and non-relativistic ion beams. This self consistent, fully analytical model allows us to follow the evolution of the beams' properties up to a stage close to complete isotropization and thus to shock formation. Its predictions are supported by 2D and 3D particle

  20. Fast, kinetically self-consistent simulation of RF modulated plasma boundary sheaths

    International Nuclear Information System (INIS)

    Shihab, Mohammed; Ziegler, Dennis; Brinkmann, Ralf Peter

    2012-01-01

    A mathematical model is presented which enables the efficient, kinetically self-consistent simulation of RF modulated plasma boundary sheaths in all technically relevant discharge regimes. It is defined on a one-dimensional geometry where a Cartesian x-axis points from the electrode or wall at x E ≡ 0 towards the plasma bulk. An arbitrary endpoint x B is chosen ‘deep in the bulk’. The model consists of a set of kinetic equations for the ions, Boltzmann's relation for the electrons and Poisson's equation for the electrical field. Boundary conditions specify the ion flux at x B and a periodically—not necessarily harmonically—modulated sheath voltage V(t) or sheath charge Q(t). The equations are solved in a statistical sense. However, it is not the well-known particle-in-cell (PIC) scheme that is employed, but an alternative iterative algorithm termed ensemble-in-spacetime (EST). The basis of the scheme is a discretization of the spacetime, the product of the domain [x E , x B ] and the RF period [0, T]. Three modules are called in a sequence. A Monte Carlo module calculates the trajectories of a large set of ions from their start at x B until they reach the electrode at x E , utilizing the potential values on the nodes of the spatio-temporal grid. A harmonic analysis module reconstructs the Fourier modes n im (x) of the ion density n i (x, t) from the calculated trajectories. A field module finally solves the Boltzmann-Poisson equation with the calculated ion densities to generate an updated set of potential values for the spatio-temporal grid. The iteration is started with the potential values of a self-consistent fluid model and terminates when the updates become sufficiently small, i.e. when self-consistency is achieved. A subsequent post-processing determines important quantities, in particular the phase-resolved and phase-averaged values of the ion energy and angular distributions and the total energy flux at the electrode. A drastic reduction of the

  1. Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas

    International Nuclear Information System (INIS)

    Zawaideh, E.S.

    1985-01-01

    A new set of two-fluid equations which are valid from collisional to weakly collisional limits are derived. Starting from gyrokinetic equations in flux coordinates with no zeroth order drifts, a set of moment equations describing plasma transport along the field lines of a space and time dependent magnetic field are derived. No restriction on the anisotropy of the ion distribution function is imposed. In the highly collisional limit, these equations reduce to those of Braginskii while in the weakly collisional limit, they are similar to the double adiabatic or Chew, Goldberger, and Low (CGL) equations. The new transport equations are used to study the effects of collisionality, magnetic field structure, and plasma anisotropy on plasma parallel transport. Numerical examples comparing these equations with conventional transport equations show that the conventional equations may contain large errors near the sound speed (M approx. = 1). It is also found that plasma anisotropy, which is not included in the conventional equations, is a critical parameter in determining plasma transport in varying magnetic field. The new transport equations are also used to study axial confinement in multiple mirror devices from the strongly to weakly collisional regime. A new ion conduction model was worked out to extend the regime of validity of the transport equations to the low density multiple mirror regime

  2. Relations between the kinetic equation and the Langevin models in two-phase flow modelling

    International Nuclear Information System (INIS)

    Minier, J.P.; Pozorski, J.

    1997-05-01

    The purpose of this paper is to discuss PDF and stochastic models which are used in two-phase flow modelling. The aim of the present analysis is essentially to try to determine relations and consistency between different models. It is first recalled that different approaches actually correspond to PDF models written either in terms of the process trajectories or in terms of the PDF itself. The main difference lies in the choice of the independent variables which are retained. Two particular models are studied, the Kinetic Equation and the Langevin Equation model. The latter uses a Langevin equation to model the fluid velocities seen along particle trajectories. The Langevin model is more general since it contains an additional variable. It is shown that, in certain cases, this variable can be summed up exactly to retrieve the Kinetic Equation model as a marginal PDF. A joint fluid and solid particle PDF which includes the characteristics of both phases is proposed at the end of the paper. (author)

  3. Solution for the multigroup neutron space kinetics equations by the modified Picard algorithm

    Energy Technology Data Exchange (ETDEWEB)

    Tavares, Matheus G.; Petersen, Claudio Z., E-mail: matheus.gulartetavares@gmail.com [Universidade Federal de Pelotas (UFPEL), Capao do Leao, RS (Brazil). Departamento de Matematica e Estatistica; Schramm, Marcelo, E-mail: schrammmarcelo@gmail.com [Universidade Federal de Pelotas (UFPEL), RS (Brazil). Centro de Engenharias; Zanette, Rodrigo, E-mail: rodrigozanette@hotmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Instituto de Matematica e Estatistica

    2017-07-01

    In this work, we used a modified Picards method to solve the Multigroup Neutron Space Kinetics Equations (MNSKE) in Cartesian geometry. The method consists in assuming an initial guess for the neutron flux and using it to calculate a fictitious source term in the MNSKE. A new source term is calculated applying its solution, and so on, iteratively, until a stop criterion is satisfied. For the solution of the fast and thermal neutron fluxes equations, the Laplace Transform technique is used in time variable resulting in a rst order linear differential matrix equation, which are solved by classical methods in the literature. After each iteration, the scalar neutron flux and the delayed neutron precursors are reconstructed by polynomial interpolation. We obtain the fluxes and precursors through Numerical Inverse Laplace Transform using the Stehfest method. We present numerical simulations and comparisons with available results in literature. (author)

  4. Solution for the multigroup neutron space kinetics equations by the modified Picard algorithm

    International Nuclear Information System (INIS)

    Tavares, Matheus G.; Petersen, Claudio Z.; Schramm, Marcelo; Zanette, Rodrigo

    2017-01-01

    In this work, we used a modified Picards method to solve the Multigroup Neutron Space Kinetics Equations (MNSKE) in Cartesian geometry. The method consists in assuming an initial guess for the neutron flux and using it to calculate a fictitious source term in the MNSKE. A new source term is calculated applying its solution, and so on, iteratively, until a stop criterion is satisfied. For the solution of the fast and thermal neutron fluxes equations, the Laplace Transform technique is used in time variable resulting in a rst order linear differential matrix equation, which are solved by classical methods in the literature. After each iteration, the scalar neutron flux and the delayed neutron precursors are reconstructed by polynomial interpolation. We obtain the fluxes and precursors through Numerical Inverse Laplace Transform using the Stehfest method. We present numerical simulations and comparisons with available results in literature. (author)

  5. Magnetoresistance in organic semiconductors: Including pair correlations in the kinetic equations for hopping transport

    Science.gov (United States)

    Shumilin, A. V.; Kabanov, V. V.; Dediu, V. I.

    2018-03-01

    We derive kinetic equations for polaron hopping in organic materials that explicitly take into account the double occupation possibility and pair intersite correlations. The equations include simplified phenomenological spin dynamics and provide a self-consistent framework for the description of the bipolaron mechanism of the organic magnetoresistance. At low applied voltages, the equations can be reduced to those for an effective resistor network that generalizes the Miller-Abrahams network and includes the effect of spin relaxation on the system resistivity. Our theory discloses the close relationship between the organic magnetoresistance and the intersite correlations. Moreover, in the absence of correlations, as in an ordered system with zero Hubbard energy, the magnetoresistance vanishes.

  6. Non-relativistic and relativistic quantum kinetic equations in nuclear physics

    International Nuclear Information System (INIS)

    Botermans, W.M.M.

    1989-01-01

    In this thesis an attempt is made to draw up a quantummechanical tranport equation for the explicit calculation oof collision processes between two (heavy) ions, by making proper approaches of the exact equations (non-rel.: N-particles Schroedinger equation; rel.: Euler-Lagrange field equations.). An important starting point in the drag-up of the theory is the behaviour of nuclear matter in equilibrium which is determined by individual as well as collective effects. The central point in this theory is the effective interaction between two nucleons both surrounded by other nucleons. In the derivation of the tranport equations use is made of the green's function formalism as developed by Schwinger and Keldys. For the Green's function kinematic equations are drawn up and are solved by choosing a proper factorization of three- and four-particle Green's functions in terms of one- and two-particle Green's functions. The necessary boundary condition is obtained by explicitly making use of Boltzmann's assumption that colliding particles are statistically uncorrelated. Finally a transport equation is obtained in which the mean field as well as the nucleon-nucleon collisions are given by the same (medium dependent) interaction. This interaction is the non-equilibrium extension of the interaction as given in the Brueckner theory of nuclear matter. Together, kinetic equation and interaction, form a self-consistent set of equations for the case of a non-relativistic as well as for the case of a relativistic starting point. (H.W.) 148 refs.; 6 figs.; 411 schemes

  7. Kinetic Theory of quasi-electrostatic waves in non-gyrotropic plasmas

    Science.gov (United States)

    Arshad, K.; Poedts, S.; Lazar, M.

    2017-12-01

    The orbital angular momentum (OAM) is a trait of helically phased light or helical (twisted) electric field. Lasers carrying orbital angular momentum (OAM) revolutionized many scientific and technological paradigms like microscopy, imaging and ionospheric radar facility to analyze three dimensional plasma dynamics in ionosphere, ultra-intense twisted laser pulses, twisted gravitational waves and astrophysics. This trend has also been investigated in plasma physics. Laguerre-Gaussian type solutions are predicted for magnetic tornadoes and Alfvénic tornadoes which exhibit spiral, split and ring-like morphologies. The ring shape morphology is ideal to fit the observed solar corona, solar atmosphere and Earth's ionosphere. The orbital angular momentum indicates the mediation of electrostatic and electromagnetic waves in new phenomena like Raman and Brillouin scattering. A few years ago, some new effects have been included in studies of orbital angular momentum in plasma regimes such as wave-particle interaction in the presence of helical electric field. Therefore, kinetic studies are carried out to investigate the Landau damping of the waves and growth of the instabilities in the presence helical electric field carrying orbital angular momentum for the Maxwellian distributed plasmas. Recently, a well suited approach involving a kappa distribution function has been adopted to model the twisted space plasmas. This leads to the development of new theoretical grounds for the study of Lorentzian or kappa distributed twisted Langmuir, ion acoustic, dust ion acoustic and dust acoustic modes. The quasi-electrostatic twisted waves have been studied now for the non-gyrotropic dusty plasmas in the presence of the orbital angular momentum of the helical electric field using Generalized Lorentzian or kappa distribution function. The Laguerre-Gaussian (LG) mode function is employed to decompose the perturbed distribution function and electric field into planar (longitudinal) and

  8. Low-frequency linear waves and instabilities in uniform and stratified plasmas: the role of kinetic effects

    Directory of Open Access Journals (Sweden)

    K. M. Ferrière

    2004-01-01

    Full Text Available We review the basic approximations underlying magnetohydrodynamic (MHD theory, with special emphasis on the closure approximations, i.e. the approximations used in any fluid approach to close the hierarchy of moment equations. We then present the main closure models that have been constructed for collisionless plasmas in the large-scale regime, and we describe our own mixed MHD-kinetic model, which is designed to study low-frequency linear waves and instabilities in collisionless plasmas. We write down the full dispersion relation in a new, general form, which gathers all the specific features of our MHD-kinetic model into four polytropic indices, and which can be applied to standard adiabatic MHD and to double-adiabatic MHD through a simple change in the expressions of the polytropic indices. We study the mode solutions and the stability properties of the full dispersion relation in each of these three theories, first in the case of a uniform plasma, and then in the case of a stratified plasma. In both cases, we show how the results are affected by the collisionless nature of the plasma.

  9. A Reduced-order NLTE Kinetic Model for Radiating Plasmas of Outer Envelopes of Stellar Atmospheres

    Energy Technology Data Exchange (ETDEWEB)

    Munafò, Alessandro [Aerospace Engineering Department, University of Illinois at Urbana-Champaign, 206A Talbot Lab., 104 S. Wright Street, Urbana, IL 61801 (United States); Mansour, Nagi N. [NASA Ames Research Center, Moffett Field, 94035 CA (United States); Panesi, Marco, E-mail: munafo@illinois.edu, E-mail: nagi.n.mansour@nasa.gov, E-mail: m.panesi@illinois.edu [Aerospace Engineering Department, University of Illinois at Urbana-Champaign, 306 Talbot Lab., 104 S. Wright Street, Urbana, IL 61801 (United States)

    2017-04-01

    The present work proposes a self-consistent reduced-order NLTE kinetic model for radiating plasmas found in the outer layers of stellar atmospheres. A detailed collisional-radiative kinetic mechanism is constructed by leveraging the most up-to-date set of ab initio and experimental data available in the literature. This constitutes the starting point for the derivation of a reduced-order model, obtained by lumping the bound energy states into groups. In order to determine the needed thermo-physical group properties, uniform and Maxwell–Boltzmann energy distributions are used to reconstruct the energy population of each group. Finally, the reduced set of governing equations for the material gas and the radiation field is obtained based on the moment method. Applications consider the steady flow across a shock wave in partially ionized hydrogen. The results clearly demonstrate that adopting a Maxwell–Boltzmann grouping allows, on the one hand, for a substantial reduction of the number of unknowns and, on the other, to maintain accuracy for both gas and radiation quantities. Also, it is observed that, when neglecting line radiation, the use of two groups already leads to a very accurate resolution of the photo-ionization precursor, internal relaxation, and radiative cooling regions. The inclusion of line radiation requires adopting just one additional group to account for optically thin losses in the α , β , and γ lines of the Balmer and Paschen series. This trend has been observed for a wide range of shock wave velocities.

  10. Plasma kinetics of Ar/O2 magnetron discharge by two-dimensional multifluid modeling

    International Nuclear Information System (INIS)

    Costin, C.; Minea, T. M.; Popa, G.; Gousset, G.

    2010-01-01

    Multifluid two-dimensional model was developed to describe the plasma kinetics of the direct current Ar/O 2 magnetron, coupling two modules: charged particles and neutrals. The first module deals with three positive ions - Ar + , O 2 + , and O + - and two negative species - e - and O - - treated by the moments of Boltzmann's equation. The second one follows seven neutral species (Ar, O 2 , O, O 3 , and related metastables) by the multicomponent diffusion technique. The two modules are self-consistently coupled by the mass conservation and kinetic coefficients taking into account more than 100 volume reactions. The steady state is obtained when the overall convergence is achieved. Calculations for 10%O 2 in Ar/O 2 mixture at 2.67 and 4 Pa show that the oxygen excited species are mainly created by electron collisions in the negative glow of the discharge. Decreasing the pressure down to 0.67 Pa, the model reveals the nonlocal behavior of the reactive species. The density gradient of O 2 ground state is reversed with respect to all gradients of the other reactive species, since the latter ones originate from the molecular ground state of oxygen. It is also found that the wall reactions drastically modify the space gradient of neutral reactive species, at least as much as the pressure, even if the discharge operates in compound mode.

  11. Plasma kinetics of Ar/O{sub 2} magnetron discharge by two-dimensional multifluid modeling

    Energy Technology Data Exchange (ETDEWEB)

    Costin, C.; Minea, T. M.; Popa, G.; Gousset, G. [LPGP, UMR 8578, CNRS-Paris-Sud XI University, Bat. 210, Orsay Cedex 91405, France and Faculty of Physics, Al. I. Cuza University, 11 Carol I Blvd., Iasi 700506 (Romania); LPGP, UMR 8578, CNRS-Paris-Sud XI University, Bat. 210, Orsay Cedex 91405 (France); Faculty of Physics, Al. I. Cuza University, 11 Carol I Blvd., Iasi 700506 (Romania); LPGP, UMR 8578, CNRS-Paris-Sud XI University, Bat. 210, Orsay Cedex 91405 (France)

    2010-03-15

    Multifluid two-dimensional model was developed to describe the plasma kinetics of the direct current Ar/O{sub 2} magnetron, coupling two modules: charged particles and neutrals. The first module deals with three positive ions - Ar{sup +}, O{sub 2}{sup +}, and O{sup +} - and two negative species - e{sup -} and O{sup -} - treated by the moments of Boltzmann's equation. The second one follows seven neutral species (Ar, O{sub 2}, O, O{sub 3}, and related metastables) by the multicomponent diffusion technique. The two modules are self-consistently coupled by the mass conservation and kinetic coefficients taking into account more than 100 volume reactions. The steady state is obtained when the overall convergence is achieved. Calculations for 10%O{sub 2} in Ar/O{sub 2} mixture at 2.67 and 4 Pa show that the oxygen excited species are mainly created by electron collisions in the negative glow of the discharge. Decreasing the pressure down to 0.67 Pa, the model reveals the nonlocal behavior of the reactive species. The density gradient of O{sub 2} ground state is reversed with respect to all gradients of the other reactive species, since the latter ones originate from the molecular ground state of oxygen. It is also found that the wall reactions drastically modify the space gradient of neutral reactive species, at least as much as the pressure, even if the discharge operates in compound mode.

  12. Effect of antenna size on electron kinetics in inductively coupled plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Hyo-Chang; Chung, Chin-Wook [Department of Electrical Engineering, Hanyang University, Seoul 133-791 (Korea, Republic of)

    2013-10-15

    Spatially resolved measurements of electron energy distribution functions (EEDFs) are investigated in inductively coupled plasmas with two planar antenna coils. When the plasma is sustained by the antenna with a diameter of 18 cm, the nonlocal kinetics is preserved in the argon gas pressure range from 2 mTorr to 20 mTorr. However, electron kinetics transit from nonlocal kinetics to local kinetics in discharge sustained by the antenna coil with diameter 34 cm. The results suggest that antenna size as well as chamber length are important parameters for the transition of the electron kinetics. Spatial variations of plasma potential, effective electron temperature, and EEDF in terms of total electron energy scale are also presented.

  13. Kinetic effects in the conversion of fast waves in pre-heated, low aspect ratio tokamak plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Kommoshvili, K [School of Physics and Astronomy, Tel Aviv University, 69978 Tel Aviv (Israel); Cuperman, S [School of Physics and Astronomy, Tel Aviv University, 69978 Tel Aviv (Israel); Bruma, C [School of Physics and Astronomy, Tel Aviv University, 69978 Tel Aviv (Israel)

    2003-03-01

    Kinetic effects in the conversion of fast waves to Alfven waves and their subsequent deposition in low aspect ratio (spherical) tokamaks (LARTs) have been investigated theoretically. More specifically, we have considered the consequences of incorporation of kinetic effects in the electron parallel (to the ambient magnetic field) dynamics derived by following the drift-tearing mode analysis of Chen et al (Chen L, Rutherford P H and Tang W M 1977 Phys. Rev. Lett. 39 460), and particle-conserving Krook collision operator for the passing electrons involved (Mett R R and Mahajan S M 1992 Phys. Fluids B 4 2885). The perpendicular plasma dynamics is described by a quite general resistive two-fluid (2F) model based dielectric tensor-operator (Cuperman S, Bruma C and Komoshvili K 2002 Solution of the resistive 2F wave equations for Alfvenic modes in spherical tokamak plasmas J. Plasma Phys. accepted for publication). The full-wave electromagnetic equations, formulated in terms of the vector and scalar potentials, have been solved by the aid of an advanced finite elements numerical code (Sewell G 1993 Adv. Eng. Software 17 105). Detailed solutions of the full-wave equations are obtained and compared with those corresponding to a pure resistive 2F model, this, for the illustrative pre-heated START-type device (Sykes 1994). Our results quantitatively confirm the general theory of the conversion of fast waves with subsequent power dissipation for the conditions of spherical tokamaks thus providing the required auxiliary energy source for the successful operation of LARTs. Moreover, these results indicate the absolute necessity of using a full model for the parallel electron dynamics, i.e. including both kinetic and collisional effects.

  14. Kinetic effects in the conversion of fast waves in pre-heated, low aspect ratio tokamak plasmas

    International Nuclear Information System (INIS)

    Kommoshvili, K; Cuperman, S; Bruma, C

    2003-01-01

    Kinetic effects in the conversion of fast waves to Alfven waves and their subsequent deposition in low aspect ratio (spherical) tokamaks (LARTs) have been investigated theoretically. More specifically, we have considered the consequences of incorporation of kinetic effects in the electron parallel (to the ambient magnetic field) dynamics derived by following the drift-tearing mode analysis of Chen et al (Chen L, Rutherford P H and Tang W M 1977 Phys. Rev. Lett. 39 460), and particle-conserving Krook collision operator for the passing electrons involved (Mett R R and Mahajan S M 1992 Phys. Fluids B 4 2885). The perpendicular plasma dynamics is described by a quite general resistive two-fluid (2F) model based dielectric tensor-operator (Cuperman S, Bruma C and Komoshvili K 2002 Solution of the resistive 2F wave equations for Alfvenic modes in spherical tokamak plasmas J. Plasma Phys. accepted for publication). The full-wave electromagnetic equations, formulated in terms of the vector and scalar potentials, have been solved by the aid of an advanced finite elements numerical code (Sewell G 1993 Adv. Eng. Software 17 105). Detailed solutions of the full-wave equations are obtained and compared with those corresponding to a pure resistive 2F model, this, for the illustrative pre-heated START-type device (Sykes 1994). Our results quantitatively confirm the general theory of the conversion of fast waves with subsequent power dissipation for the conditions of spherical tokamaks thus providing the required auxiliary energy source for the successful operation of LARTs. Moreover, these results indicate the absolute necessity of using a full model for the parallel electron dynamics, i.e. including both kinetic and collisional effects

  15. Kinetic effects in the conversion of fast waves in pre-heated, low aspect ratio tokamak plasmas

    Science.gov (United States)

    Kommoshvili, K.; Cuperman, S.; Bruma, C.

    2003-03-01

    Kinetic effects in the conversion of fast waves to Alfvèn waves and their subsequent deposition in low aspect ratio (spherical) tokamaks (LARTs) have been investigated theoretically. More specifically, we have considered the consequences of incorporation of kinetic effects in the electron parallel (to the ambient magnetic field) dynamics derived by following the drift-tearing mode analysis of Chen et al (Chen L, Rutherford P H and Tang W M 1977 Phys. Rev. Lett. 39 460), and particle-conserving Krook collision operator for the passing electrons involved (Mett R R and Mahajan S M 1992 Phys. Fluids B 4 2885). The perpendicular plasma dynamics is described by a quite general resistive two-fluid (2F) model based dielectric tensor-operator (Cuperman S, Bruma C and Komoshvili K 2002 Solution of the resistive 2F wave equations for Alfvènic modes in spherical tokamak plasmas J. Plasma Phys. accepted for publication). The full-wave electromagnetic equations, formulated in terms of the vector and scalar potentials, have been solved by the aid of an advanced finite elements numerical code (Sewell G 1993 Adv. Eng. Software 17 105). Detailed solutions of the full-wave equations are obtained and compared with those corresponding to a pure resistive 2F model, this, for the illustrative pre-heated START-type device (Sykes 1994). Our results quantitatively confirm the general theory of the conversion of fast waves with subsequent power dissipation for the conditions of spherical tokamaks thus providing the required auxilliary energy source for the succesful operation of LARTs. Moreover, these results indicate the absolute necessity of using a full model for the parallel electron dynamics, i.e. including both kinetic and collisional effects.

  16. Low frequency, electrodynamic simulation of kinetic plasmas with the DArwin Direct Implicit Particle-In-Cell (DADIPIC) method

    International Nuclear Information System (INIS)

    Gibbons, M.R.

    1995-06-01

    This dissertation describes a new algorithm for simulating low frequency, kinetic phenomena in plasmas. DArwin Direct Implicit Particle-in-Cell (DADIPIC), as its name implies, is a combination of the Darwin and direct implicit methods. One of the difficulties in simulating plasmas lies in the enormous disparity between the fundamental scale lengths of a plasma and the scale lengths of the phenomena of interest. The objective is to create models which can ignore the fundamental constraints without eliminating relevant plasma properties. Over the past twenty years several PIC methods have been investigated for overcoming the constraints on explicit electrodynamic PIC. These models eliminate selected high frequency plasma phenomena while retaining kinetic phenomena at low frequency. This dissertation shows that the combination of Darwin and Direct Implicit allows them to operate better than they have been shown to operate in the past. Through the Darwin method the hyperbolic Maxwell's equations are reformulated into a set of elliptic equations. Propagating light waves do not exist in the formulation so the Courant constraint on the time step is eliminated. The Direct Implicit method is applied only to the electrostatic field with the result that electrostatic plasma oscillations do not have to be resolved for stability. With the elimination of these constraints spatial and temporal discretization can be much larger than that possible with explicit, electrodynamic PIC. The code functions in a two dimensional Cartesian region and has been implemented with all components of the particle velocities, the E-field, and the B-field. Internal structures, conductors or dielectrics, may be placed in the simulation region, can be set at desired potentials, and driven with specified currents

  17. On a closed form approach to the fractional neutron point kinetics equation with temperature feedback

    International Nuclear Information System (INIS)

    Schramm, Marcelo; Bodmann, Bardo E.J.; Vilhena, Marco T.M.B.; Petersen, Claudio Z.; Alvim, Antonio C.M.

    2013-01-01

    Following the quest to find analytical solutions, we extend the methodology applied successfully to timely fractional neutron point kinetics (FNPK) equations by adding the effects of temperature. The FNPK equations with temperature feedback correspond to a nonlinear system and “stiff” type for the neutron density and the concentration of delayed neutron precursors. These variables determine the behavior of a nuclear reactor power with time and are influenced by the position of control rods, for example. The solutions of kinetics equations provide time information about the dynamics in a nuclear reactor in operation and are useful, for example, to understand the power fluctuations with time that occur during startup or shutdown of the reactor, due to adjustments of the control rods. The inclusion of temperature feedback in the model introduces an estimate of the transient behavior of the power and other variables, which are strongly coupled. Normally, a single value of reactivity is used across the energy spectrum. Especially in case of power change, the neutron energy spectrum changes as well as physical parameters such as the average cross sections. However, even knowing the importance of temperature effects on the control of the reactor power, the character of the set of nonlinear equations governing this system makes it difficult to obtain a purely analytical solution. Studies have been published in this sense, using numerical approaches. Here the idea is to consider temperature effects to make the model more realistic and thus solve it in a semi-analytical way. Therefore, the main objective of this paper is to obtain an analytical representation of fractional neutron point kinetics equations with temperature feedback, without having to resort to approximations inherent in numerical methods. To this end, we will use the decomposition method, which has been successfully used by the authors to solve neutron point kinetics problems. The results obtained will

  18. On a closed form approach to the fractional neutron point kinetics equation with temperature feedback

    Energy Technology Data Exchange (ETDEWEB)

    Schramm, Marcelo; Bodmann, Bardo E.J.; Vilhena, Marco T.M.B., E-mail: marceloschramm@hotmail.com, E-mail: bardo.bodmann@ufrgs.br, E-mail: mtmbvilhena@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Departamento de Engenharia Mecanica; Petersen, Claudio Z., E-mail: claudiopetersen@yahoo.com.br [Universidade Federal de Pelotas (UFPel), RS (Brazil). Departamento de Matematica; Alvim, Antonio C.M., E-mail: alvim@nuclear.ufrj.br [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Instituto Alberto Luiz Coimbra de Pos-Graduacao e Pesquisa em Engenharia

    2013-07-01

    Following the quest to find analytical solutions, we extend the methodology applied successfully to timely fractional neutron point kinetics (FNPK) equations by adding the effects of temperature. The FNPK equations with temperature feedback correspond to a nonlinear system and “stiff” type for the neutron density and the concentration of delayed neutron precursors. These variables determine the behavior of a nuclear reactor power with time and are influenced by the position of control rods, for example. The solutions of kinetics equations provide time information about the dynamics in a nuclear reactor in operation and are useful, for example, to understand the power fluctuations with time that occur during startup or shutdown of the reactor, due to adjustments of the control rods. The inclusion of temperature feedback in the model introduces an estimate of the transient behavior of the power and other variables, which are strongly coupled. Normally, a single value of reactivity is used across the energy spectrum. Especially in case of power change, the neutron energy spectrum changes as well as physical parameters such as the average cross sections. However, even knowing the importance of temperature effects on the control of the reactor power, the character of the set of nonlinear equations governing this system makes it difficult to obtain a purely analytical solution. Studies have been published in this sense, using numerical approaches. Here the idea is to consider temperature effects to make the model more realistic and thus solve it in a semi-analytical way. Therefore, the main objective of this paper is to obtain an analytical representation of fractional neutron point kinetics equations with temperature feedback, without having to resort to approximations inherent in numerical methods. To this end, we will use the decomposition method, which has been successfully used by the authors to solve neutron point kinetics problems. The results obtained will

  19. AIREK-MOD, Time Dependent Reactor Kinetics with Feedback Differential Equation

    International Nuclear Information System (INIS)

    Tamagnini, C.

    1984-01-01

    1 - Nature of physical problem solved: Solves the reactor kinetic equations with respect to time. A standard form for the reactivity behaviour has been introduced in which the reactivity is given by the sum of a polynomial, sine, cosine and exponential expansion. Tabular form is also included. The presence of feedback differential equations in which the dependence on variables different from the considered one is considered enables many heat-exchange problems to be dealt with. 2 - Method of solution: The method employed for the solution of the differential equations is the one developed by E.R. Cohen (Geneva Conference, 1958). 3 - Restrictions on the complexity of the problem: The maximum number of differential equations that can be solved simultaneously is 50. Within this limitation there may be n delayed neutron groups (n less than or equal to 25), on m other linear feedback equations (n+m less than or equal to 49). CDC 1604 version was offered by EIR (Institut Federal de Recherches en matiere de reacteurs, Switzerland)

  20. Application of Elovich equation on uptake kinetics of 137Cs by living freshwater macrophytes - a short duration laboratory study

    International Nuclear Information System (INIS)

    Jaison, T.J.; Patra, A.K.; Ravi, P.M.; Tripathi, R.M.

    2014-01-01

    Application of Elovich equation on uptake kinetics of 137 Cs by two living macrophytes during controlled experiments on short duration exposure is studied. Compliance to 2 nd order kinetics indicates the mechanism could be chemi-sorption, involving polar functional groups present on the extracelluar surface of the macrophytes. Data analysis suggests that Myriophyllum s. exhibits faster adsorption rate than Hydrilla v. As Myriophyllum s. exhibits better kinetics than Hydrilla v., former could be a better natural adsorbing media for 137 Cs. (author)

  1. Kinetic effects in the propagation of ion-acoustic negative solitons in plasmas with negative ions

    International Nuclear Information System (INIS)

    Roberto, M.

    1986-12-01

    The existence of ion-acoustic negative (rarefactive) solitons in plasmas was experimentally verified and explained by means of the Korteweg-de Vries equation, obtained from a fluid model. The experimental results obtained in a double-plasma machine of the Institute for Space Research, however, have provided values of Mach number larger than predicted by this simple model. In order to improve the analysis of the phenomenon, Kinetic effects resultant from the occurrence of reflected electrons and trapped ions in the soliton potential were considered, using the theory of Sagdeev potential. For the description of the negative ion dynamics the fluid model treatment was preserved. It was verified that the effects of the finite temperature and trapping of the positive ions modify the results predicted by the simple KdV model in such a way that the Mach number is reduced as the ion temperature increases. It was shown that reflection of electrons is consistent with the large experimental values of Mach number. (Author) [pt

  2. An accurate technique for the solution of the nonlinear point kinetics equations

    International Nuclear Information System (INIS)

    Picca, Paolo; Ganapol, Barry D.; Furfaro, Roberto

    2011-01-01

    A novel methodology for the solution of non-linear point kinetic (PK) equations is proposed. The technique is based on a piecewise constant approximation of PK system of ODEs and explicitly accounts for reactivity feedback effects, through an iterative cycle. High accuracy is reached by introducing a sub-mesh for the numerical evaluation of integrals involved and by correcting the source term to include the non-linear effect on a finer time scale. The use of extrapolation techniques for convergence acceleration is also explored. Results for adiabatic feedback model are reported and compared with other benchmarks in literature. The convergence trend makes the algorithm particularly attractive for applications, including in multi-point kinetics and quasi-static frameworks. (author)

  3. Analytical solution of Luedeking-Piret equation for a batch fermentation obeying Monod growth kinetics.

    Science.gov (United States)

    Garnier, Alain; Gaillet, Bruno

    2015-12-01

    Not so many fermentation mathematical models allow analytical solutions of batch process dynamics. The most widely used is the combination of the logistic microbial growth kinetics with Luedeking-Piret bioproduct synthesis relation. However, the logistic equation is principally based on formalistic similarities and only fits a limited range of fermentation types. In this article, we have developed an analytical solution for the combination of Monod growth kinetics with Luedeking-Piret relation, which can be identified by linear regression and used to simulate batch fermentation evolution. Two classical examples are used to show the quality of fit and the simplicity of the method proposed. A solution for the combination of Haldane substrate-limited growth model combined with Luedeking-Piret relation is also provided. These models could prove useful for the analysis of fermentation data in industry as well as academia. © 2015 Wiley Periodicals, Inc.

  4. DKE: a fast numerical solver for the 3-D relativistic bounce-averaged electron drift kinetic equation

    Energy Technology Data Exchange (ETDEWEB)

    Decker, J.; Peysson, Y

    2004-12-01

    A new original code for solving the 3-D relativistic and bounce-averaged electron drift kinetic equation is presented. It designed for the current drive problem in tokamak with an arbitrary magnetic equilibrium. This tool allows self-consistent calculations of the bootstrap current in presence of other external current sources. RF current drive for arbitrary type of waves may be used. Several moments of the electron distribution function are determined, like the exact and effective fractions of trapped electrons, the plasma current, absorbed RF power, runaway and magnetic ripple loss rates and non-thermal Bremsstrahlung. Advanced numerical techniques have been used to make it the first fully implicit (reverse time) 3-D solver, particularly well designed for implementation in a chain of code for realistic current drive calculations in high {beta}{sub p} plasmas. All the details of the physics background and the numerical scheme are presented, as well a some examples to illustrate main code capabilities. Several important numerical points are addressed concerning code stability and potential numerical and physical limitations. (authors)

  5. DKE: a fast numerical solver for the 3-D relativistic bounce-averaged electron drift kinetic equation

    International Nuclear Information System (INIS)

    Decker, J.; Peysson, Y.

    2004-12-01

    A new original code for solving the 3-D relativistic and bounce-averaged electron drift kinetic equation is presented. It designed for the current drive problem in tokamak with an arbitrary magnetic equilibrium. This tool allows self-consistent calculations of the bootstrap current in presence of other external current sources. RF current drive for arbitrary type of waves may be used. Several moments of the electron distribution function are determined, like the exact and effective fractions of trapped electrons, the plasma current, absorbed RF power, runaway and magnetic ripple loss rates and non-thermal Bremsstrahlung. Advanced numerical techniques have been used to make it the first fully implicit (reverse time) 3-D solver, particularly well designed for implementation in a chain of code for realistic current drive calculations in high β p plasmas. All the details of the physics background and the numerical scheme are presented, as well a some examples to illustrate main code capabilities. Several important numerical points are addressed concerning code stability and potential numerical and physical limitations. (authors)

  6. Kadomstev–Petviashvili (KP) equation in warm dusty plasma with ...

    Indian Academy of Sciences (India)

    In this work, the propagation of nonlinear waves in warm dusty plasmas with ... Mamun et al [7] have also derived rarefactive solitary waves in low-temperature dusty plasmas such as those in laboratory and astrophysical environments. ... plasma environments that clearly indicate the presence of nonthermal electron pop-.

  7. An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations

    International Nuclear Information System (INIS)

    Sun, Wenjun; Jiang, Song; Xu, Kun

    2015-01-01

    The solutions of radiative transport equations can cover both optical thin and optical thick regimes due to the large variation of photon's mean-free path and its interaction with the material. In the small mean free path limit, the nonlinear time-dependent radiative transfer equations can converge to an equilibrium diffusion equation due to the intensive interaction between radiation and material. In the optical thin limit, the photon free transport mechanism will emerge. In this paper, we are going to develop an accurate and robust asymptotic preserving unified gas kinetic scheme (AP-UGKS) for the gray radiative transfer equations, where the radiation transport equation is coupled with the material thermal energy equation. The current work is based on the UGKS framework for the rarefied gas dynamics [14], and is an extension of a recent work [12] from a one-dimensional linear radiation transport equation to a nonlinear two-dimensional gray radiative system. The newly developed scheme has the asymptotic preserving (AP) property in the optically thick regime in the capturing of diffusive solution without using a cell size being smaller than the photon's mean free path and time step being less than the photon collision time. Besides the diffusion limit, the scheme can capture the exact solution in the optical thin regime as well. The current scheme is a finite volume method. Due to the direct modeling for the time evolution solution of the interface radiative intensity, a smooth transition of the transport physics from optical thin to optical thick can be accurately recovered. Many numerical examples are included to validate the current approach

  8. Interaction of the Modulated Electron Beam with Plasma: Kinetic Effects

    International Nuclear Information System (INIS)

    Anisimov, I.O.; Kiyanchuk, M.J.; Soroka, S.V.; Velikanets', D.M.

    2006-01-01

    Evolution of the velocity distribution functions of plasma and beam electrons during modulated electron beam propagation in homogeneous and inhomogeneous plasmas was studied numerically. Velocity distribution function of plasma electrons at the late time moments strongly differs from the initially Maxwellian one. In the regions of strong electric field plasma electrons' bunches are formed. Comparison of distribution functions of beam electrons for modulated and non-modulated beams shows that deep initial modulation suppresses resonant instability development. In the inhomogeneous plasma acceleration of electrons in the plasma resonance point can be observed

  9. Full Tokamak discharge simulation and kinetic plasma profile control for ITER

    International Nuclear Information System (INIS)

    Hee Kim, S.

    2009-10-01

    technique that simplifies the active real-time control of several kinetic plasma profiles in ITER. The response of the plasma profiles to power changes of auxiliary H and CD systems is modelled. To allow real-time update of the plasma profile response model, the related physics is simplified with several assumptions. The electron temperature profile response is modelled by simplifying the electron heat transport equation. The q profile response is modelled by directly relating it to the changes of source current density profiles. The required actuator power changes are calculated using the singular value decomposition (SVD) technique, taking the saturation of the actuator powers into account. The potential of this control technique has been shown by applying it to simulations of the ITER hybrid mode operation. (author)

  10. Microscopic theory of warm ionized gases: equation of state and kinetic Schottky anomaly

    International Nuclear Information System (INIS)

    Capolupo, A; Giampaolo, S M; Illuminati, F

    2013-01-01

    Based on accurate Lennard-Jones type interaction potentials, we derive a closed set of state equations for the description of warm atomic gases in the presence of ionization processes. The specific heat is predicted to exhibit peaks in correspondence to single and multiple ionizations. Such kinetic analogue in atomic gases of the Schottky anomaly in solids is enhanced at intermediate and low atomic densities. The case of adiabatic compression of noble gases is analyzed in detail and the implications on sonoluminescence are discussed.

  11. Simulation of light generation in cholesteric liquid crystals using kinetic equations: Time-independent solution

    Energy Technology Data Exchange (ETDEWEB)

    Shtykov, N. M., E-mail: nshtykov@mail.ru; Palto, S. P.; Umanskii, B. A. [Russian Academy of Sciences, Shubnikov Institute of Crystallography (Russian Federation)

    2013-08-15

    We report on the results of calculating the conditions for light generation in cholesteric liquid crystals doped with fluorescent dyes using kinetic equations. Specific features of spectral properties of the chiral cholesteric medium as a photonic structure and spatially distributed type of the feedback in the active medium are taken into account. The expression is derived for the threshold pump radiation intensity as a function of the dye concentration and sample thickness. The importance of taking into account the distributed loss level in the active medium for calculating the optimal parameters of the medium and for matching the calculated values with the results of experiments is demonstrated.

  12. Effect of Landau damping on kinetic Alfven and ion-acoustic solitary waves in a magnetized nonthermal plasma with warm ions

    International Nuclear Information System (INIS)

    Bandyopadhyay, Anup; Das, K.P.

    2002-01-01

    The evolution equations describing both kinetic Alfven wave and ion-acoustic wave in a nonthermal magnetized plasma with warm ions including weak nonlinearity and weak dispersion with the effect of Landau damping have been derived. These equations reduce to two coupled equations constituting the KdV-ZK (Korteweg-de Vries-Zakharov-Kuznetsov) equation for both kinetic Alfven wave and ion-acoustic wave, including an extra term accounting for the effect of Landau damping. When the coefficient of the nonlinear term of the evolution equation for ion-acoustic wave vanishes, the nonlinear behavior of ion-acoustic wave, including the effect of Landau damping, is described by two coupled equations constituting the modified KdV-ZK (MKdV-ZK) equation, including an extra term accounting for the effect of Landau damping. It is found that there is no effect of Landau damping on the solitary structures of the kinetic Alfven wave. Both the macroscopic evolution equations for the ion-acoustic wave admits solitary wave solutions, the former having a sech 2 profile and the latter having a sech profile. In either case, it is found that the amplitude of the ion-acoustic solitary wave decreases slowly with time

  13. Waves in plasmas (part 1 - wave-plasma interaction general background)

    International Nuclear Information System (INIS)

    Dumont, R.

    2004-01-01

    This document gathers a series of transparencies presented in the framework of the week-long lectures 'hot plasmas 2004' and dedicated to the physics of wave-plasma interaction. The structure of this document is as follows: 1) wave and diverse plasmas, 2) basic equations (Maxwell equations), 3) waves in a fluid plasma, and 4) waves in a kinetic plasma (collisionless plasma)

  14. Strong plasma shock structures based on the Navier--Stokes equations

    International Nuclear Information System (INIS)

    Abe, K.

    1975-01-01

    The structure of a plasma collisional shock wave is examined on the basis of the Navier--Stokes equations and simultaneously on the basis of the Fokker--Planck equation. The resultant structures are compared to check the validity of the Navier--Stokes equations applied to the structures of strong shock waves. The Navier--Stokes equations give quite correct structures for weak shock waves. For the strong shock waves, the detailed structures obtained from the Navier--Stokes equations differ from the results of the Fokker--Planck equation, but the shock thicknesses of the two shock waves are in relatively close agreement

  15. Extending the collisional fluid equations into the long mean-free-path regime in toroidal plasmas. IV. Banana regime

    International Nuclear Information System (INIS)

    Shaing, K. C.

    2007-01-01

    In Part I [Phys. Fluids B 2, 1190 (1990)] and Part II [Phys. Plasmas 12, 082508 (2005)], it was emphasized that the equilibrium plasma viscous forces when applied for the magnetohydrodynamic (MHD) modes are only rigorously valid at the mode rational surface where m-nq=0. Here, m is the poloidal mode number, n is the toroidal mode number, and q is the safety factor. This important fact has been demonstrated explicitly by calculating the viscous forces in the plateau regime in Parts I and II. Here, the effective viscous forces in the banana regime are calculated for MHD modes by solving the linear drift kinetic equation that is driven by the plasma flows first derived in Part I. At the mode rational surface, the equilibrium plasma viscous forces are reproduced. However, it is found that away from the mode rational surface, the viscous forces for MHD modes decrease, a behavior similar to that observed in the viscous forces for the plateau regime. The proper form of the momentum equation that is appropriate for the modeling of the MHD modes is also discussed

  16. Some aspects of transformation of the nonlinear plasma equations to the space-independent frame

    International Nuclear Information System (INIS)

    Paul, S.N.; Chakraborty, B.

    1982-01-01

    Relativistically correct transformation of nonlinear plasma equations are derived in a space-independent frame. This transformation is useful in many ways because in place of partial differential equations one obtains a set of ordinary differential equations in a single independent variable. Equations of Akhiezer and Polovin (1956) for nonlinear plasma oscillations have been generalized and the results of Arons and Max (1974), and others for wave number shift and precessional rotation of electromagnetic wave are recovered in a space-independent frame. (author)

  17. Simulation studies of plasma waves in the electron foreshock - The transition from reactive to kinetic instability

    Science.gov (United States)

    Dum, C. T.

    1990-01-01

    Particle simulation experiments were used to analyze the electron beam-plasma instability. It is shown that there is a transition from the reactive state of the electron beam-plasma instability to the kinetic instability of Langmuir waves. Quantitative tests, which include an evaluation of the dispersion relation for the evolving non-Maxwellian beam distribution, show that a quasi-linear theory describes the onset of this transition and applies again fully to the kinetic stage. This stage is practically identical to the late stage seen in simulations of plasma waves in the electron foreshock described by Dum (1990).

  18. Simulation of kinetic processes in the nuclear-excited helium non-ideal dusty plasma

    International Nuclear Information System (INIS)

    Budnik, A.P.; Kosarev, V.A.; Rykov, V.A.; Fortov, V.E.; Vladimirov, V.I.; Deputatova, L.V.

    2009-01-01

    The paper is devoted to the studying of kinetic processes in the nuclear-excited plasma of the helium gas with the fine uranium (or its chemical compounds) particles admixture. A new theoretical model for the mathematical simulation of the kinetic processes in dusty plasma of helium gas was developed. The main goal of this investigation is to determine possibilities of a creation of non-ideal dusty plasma, containing nano- and micro-particles, and excited by fission fragments (copyright 2009 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

  19. Comprehensive kinetic analysis of the plasma-wall transition layer in a strongly tilted magnetic field

    International Nuclear Information System (INIS)

    Tskhakaya, D. D.; Kos, L.

    2014-01-01

    The magnetized plasma-wall transition (MPWT) layer at the presence of the obliquity of the magnetic field to the wall consists of three sub-layers: the Debye sheath (DS), the magnetic pre-sheath (MPS), and the collisional pre-sheath (CPS) with characteristic lengths λ D (electron Debye length), ρ i (ion gyro-radius), and ℓ (the smallest relevant collision length), respectively. Tokamak plasmas are usually assumed to have the ordering λ D ≪ρ i ≪ℓ, when the above-mentioned sub-layers can be distinctly distinguished. In the limits of ε Dm (λ D /ρ i )→0 and ε mc (ρ i /ℓ)→0 (“asymptotic three-scale (A3S) limits”), these sub-layers are precisely defined. Using the smallness of the tilting angle of the magnetic field to the wall, the ion distribution functions are found for three sub-regions in the analytic form. The equations and characteristic length-scales governing the transition (intermediate) regions between the neighboring sub-layers (CPS – MPS and MPS – DS) are derived, allowing to avoid the singularities arising from the ε Dm →0 and ε mc →0 approximations. The MPS entrance and the related kinetic form of the Bohm–Chodura condition are successfully defined for the first time. At the DS entrance, the Bohm condition maintains its usual form. The results encourage further study and understanding of physics of the MPWT layers in the modern plasma facilities

  20. Using Equation-Free Computation to Accelerate Network-Free Stochastic Simulation of Chemical Kinetics.

    Science.gov (United States)

    Lin, Yen Ting; Chylek, Lily A; Lemons, Nathan W; Hlavacek, William S

    2018-06-21

    The chemical kinetics of many complex systems can be concisely represented by reaction rules, which can be used to generate reaction events via a kinetic Monte Carlo method that has been termed network-free simulation. Here, we demonstrate accelerated network-free simulation through a novel approach to equation-free computation. In this process, variables are introduced that approximately capture system state. Derivatives of these variables are estimated using short bursts of exact stochastic simulation and finite differencing. The variables are then projected forward in time via a numerical integration scheme, after which a new exact stochastic simulation is initialized and the whole process repeats. The projection step increases efficiency by bypassing the firing of numerous individual reaction events. As we show, the projected variables may be defined as populations of building blocks of chemical species. The maximal number of connected molecules included in these building blocks determines the degree of approximation. Equation-free acceleration of network-free simulation is found to be both accurate and efficient.

  1. A highly accurate algorithm for the solution of the point kinetics equations

    International Nuclear Information System (INIS)

    Ganapol, B.D.

    2013-01-01

    Highlights: • Point kinetics equations for nuclear reactor transient analysis are numerically solved to extreme accuracy. • Results for classic benchmarks found in the literature are given to 9-digit accuracy. • Recent results of claimed accuracy are shown to be less accurate than claimed. • Arguably brings a chapter of numerical evaluation of the PKEs to a close. - Abstract: Attempts to resolve the point kinetics equations (PKEs) describing nuclear reactor transients have been the subject of numerous articles and texts over the past 50 years. Some very innovative methods, such as the RTS (Reactor Transient Simulation) and CAC (Continuous Analytical Continuation) methods of G.R. Keepin and J. Vigil respectively, have been shown to be exceptionally useful. Recently however, several authors have developed methods they consider accurate without a clear basis for their assertion. In response, this presentation will establish a definitive set of benchmarks to enable those developing PKE methods to truthfully assess the degree of accuracy of their methods. Then, with these benchmarks, two recently published methods, found in this journal will be shown to be less accurate than claimed and a legacy method from 1984 will be confirmed

  2. The solution of the point kinetics equations via converged accelerated Taylor series (CATS)

    Energy Technology Data Exchange (ETDEWEB)

    Ganapol, B.; Picca, P. [Dept. of Aerospace and Mechanical Engineering, Univ. of Arizona (United States); Previti, A.; Mostacci, D. [Laboratorio di Montecuccolino, Alma Mater Studiorum - Universita di Bologna (Italy)

    2012-07-01

    This paper deals with finding accurate solutions of the point kinetics equations including non-linear feedback, in a fast, efficient and straightforward way. A truncated Taylor series is coupled to continuous analytical continuation to provide the recurrence relations to solve the ordinary differential equations of point kinetics. Non-linear (Wynn-epsilon) and linear (Romberg) convergence accelerations are employed to provide highly accurate results for the evaluation of Taylor series expansions and extrapolated values of neutron and precursor densities at desired edits. The proposed Converged Accelerated Taylor Series, or CATS, algorithm automatically performs successive mesh refinements until the desired accuracy is obtained, making use of the intermediate results for converged initial values at each interval. Numerical performance is evaluated using case studies available from the literature. Nearly perfect agreement is found with the literature results generally considered most accurate. Benchmark quality results are reported for several cases of interest including step, ramp, zigzag and sinusoidal prescribed insertions and insertions with adiabatic Doppler feedback. A larger than usual (9) number of digits is included to encourage honest benchmarking. The benchmark is then applied to the enhanced piecewise constant algorithm (EPCA) currently being developed by the second author. (authors)

  3. Coupled kinetic equations for fermions and bosons in the relaxation-time approximation

    Science.gov (United States)

    Florkowski, Wojciech; Maksymiuk, Ewa; Ryblewski, Radoslaw

    2018-02-01

    Kinetic equations for fermions and bosons are solved numerically in the relaxation-time approximation for the case of one-dimensional boost-invariant geometry. Fermions are massive and carry baryon number, while bosons are massless. The conservation laws for the baryon number, energy, and momentum lead to two Landau matching conditions, which specify the coupling between the fermionic and bosonic sectors and determine the proper-time dependence of the effective temperature and baryon chemical potential of the system. The numerical results illustrate how a nonequilibrium mixture of fermions and bosons approaches hydrodynamic regime described by the Navier-Stokes equations with appropriate forms of the kinetic coefficients. The shear viscosity of a mixture is the sum of the shear viscosities of fermion and boson components, while the bulk viscosity is given by the formula known for a gas of fermions, however, with the thermodynamic variables characterising the mixture. Thus, we find that massless bosons contribute in a nontrivial way to the bulk viscosity of a mixture, provided fermions are massive. We further observe the hydrodynamization effect, which takes place earlier in the shear sector than in the bulk one. The numerical studies of the ratio of the longitudinal and transverse pressures show, to a good approximation, that it depends on the ratio of the relaxation and proper times only. This behavior is connected with the existence of an attractor solution for conformal systems.

  4. The equation of state and ionization equilibrium of dense aluminum plasma with conductivity verification

    International Nuclear Information System (INIS)

    Wang, Kun; Shi, Zongqian; Shi, Yuanjie; Bai, Jun; Wu, Jian; Jia, Shenli

    2015-01-01

    The equation of state, ionization equilibrium, and conductivity are the most important parameters for investigation of dense plasma. The equation of state is calculated with the non-ideal effects taken into consideration. The electron chemical potential and pressure, which are commonly used thermodynamic quantities, are calculated by the non-ideal free energy and compared with results of a semi-empirical equation of state based on Thomas-Fermi-Kirzhnits model. The lowering of ionization potential, which is a crucial factor in the calculation of non-ideal Saha equation, is settled according to the non-ideal free energy. The full coupled non-ideal Saha equation is applied to describe the ionization equilibrium of dense plasma. The conductivity calculated by the Lee-More-Desjarlais model combined with non-ideal Saha equation is compared with experimental data. It provides a possible approach to verify the accuracy of the equation of state and ionization equilibrium

  5. Inverse kinetics equations for on line measurement of reactivity using personal computer

    International Nuclear Information System (INIS)

    Ratemi, Wajdi; El Gadamsi, Walied; Beleid, Abdul Kariem

    1993-01-01

    Computer with their astonishing speed of calculations along with their easy connection to real systems, are very appropriate for digital measurements of real system variables. In the nuclear industry, such computer application will produce compact control rooms of real power plants, where information and results display can be obtained through push button concept. In our study, we use two personal computers for the purpose of simulation and measurement. One of them is used as a digital simulator to a real reactor, where we effectively simulate the reactor power through a cross talk network. The computed power is passed at certain chosen sampling time to the other computer. The purpose of the other computer is to use the inverse kinetics equations to calculate the reactivity parameter based on the received power and then it performs on line display of the power curve and the reactivity curve using color graphics. In this study, we use the one group version of the inverse kinetics algorithm which can easily be extended to larger group version. The language of programming used in Turbo BASIC, which is very comparable, in terms of efficiency, to FORTRAN language, besides its effective graphics routines. With the use of the extended version of the Inverse Kinetics algorithm, we can effectively apply this techniques of measurement for the purpose of on line display of the reactivity of the Tajoura Research Reactor. (author)

  6. Chemical kinetics and relaxation of non-equilibrium air plasma generated by energetic photon and electron beams

    International Nuclear Information System (INIS)

    Maulois, Melissa; Ribière, Maxime; Eichwald, Olivier; Yousfi, Mohammed; Azaïs, Bruno

    2016-01-01

    The comprehension of electromagnetic perturbations of electronic devices, due to air plasma-induced electromagnetic field, requires a thorough study on air plasma. In the aim to understand the phenomena at the origin of the formation of non-equilibrium air plasma, we simulate, using a volume average chemical kinetics model (0D model), the time evolution of a non-equilibrium air plasma generated by an energetic X-ray flash. The simulation is undertaken in synthetic air (80% N_2 and 20% O_2) at ambient temperature and atmospheric pressure. When the X-ray flash crosses the gas, non-relativistic Compton electrons (low energy) and a relativistic Compton electron beam (high energy) are simultaneously generated and interact with the gas. The considered chemical kinetics scheme involves 26 influent species (electrons, positive ions, negative ions, and neutral atoms and molecules in their ground or metastable excited states) reacting following 164 selected reactions. The kinetics model describing the plasma chemistry was coupled to the conservation equation of the electron mean energy, in order to calculate at each time step of the non-equilibrium plasma evolution, the coefficients of reactions involving electrons while the energy of the heavy species (positive and negative ions and neutral atoms and molecules) is assumed remaining close to ambient temperature. It has been shown that it is the relativistic Compton electron beam directly created by the X-ray flash which is mainly responsible for the non-equilibrium plasma formation. Indeed, the low energy electrons (i.e., the non-relativistic ones) directly ejected from molecules by Compton collisions contribute to less than 1% on the creation of electrons in the plasma. In our simulation conditions, a non-equilibrium plasma with a low electron mean energy close to 1 eV and a concentration of charged species close to 10"1"3" cm"−"3 is formed a few nanoseconds after the peak of X-ray flash intensity. 200 ns after the

  7. Kinetic modelling of runaway electron avalanches in tokamak plasmas.

    Czech Academy of Sciences Publication Activity Database

    Nilsson, E.; Decker, J.; Peysson, Y.; Granetz, R.S.; Saint-Laurent, F.; Vlainic, Milos

    2015-01-01

    Roč. 57, č. 9 (2015), č. článku 095006. ISSN 0741-3335 EU Projects: European Commission(XE) 633053 - EUROfusion Institutional support: RVO:61389021 Keywords : plasma physics * runaway electrons * knock-on collisions * tokamak * Fokker-Planck * runaway avalanches Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 2.404, year: 2015

  8. Quantum kinetic field theory in curved spacetime: Covariant Wigner function and Liouville-Vlasov equations

    International Nuclear Information System (INIS)

    Calzetta, E.; Habib, S.; Hu, B.L.

    1988-01-01

    We consider quantum fields in an external potential and show how, by using the Fourier transform on propagators, one can obtain the mass-shell constraint conditions and the Liouville-Vlasov equation for the Wigner distribution function. We then consider the Hadamard function G 1 (x 1 ,x 2 ) of a real, free, scalar field in curved space. We postulate a form for the Fourier transform F/sup (//sup Q//sup )/(X,k) of the propagator with respect to the difference variable x = x 1 -x 2 on a Riemann normal coordinate centered at Q. We show that F/sup (//sup Q//sup )/ is the result of applying a certain Q-dependent operator on a covariant Wigner function F. We derive from the wave equations for G 1 a covariant equation for the distribution function and show its consistency. We seek solutions to the set of Liouville-Vlasov equations for the vacuum and nonvacuum cases up to the third adiabatic order. Finally we apply this method to calculate the Hadamard function in the Einstein universe. We show that the covariant Wigner function can incorporate certain relevant global properties of the background spacetime. Covariant Wigner functions and Liouville-Vlasov equations are also derived for free fermions in curved spacetime. The method presented here can serve as a basis for constructing quantum kinetic theories in curved spacetime or for near-uniform systems under quasiequilibrium conditions. It can also be useful to the development of a transport theory of quantum fields for the investigation of grand unification and post-Planckian quantum processes in the early Universe

  9. Balance equations for a relativistic plasma. Pt. 1

    International Nuclear Information System (INIS)

    Hebenstreit, H.

    1983-01-01

    Relativistic power moments of the four-momentum are decomposed according to a macroscopic four-velocity. The thus obtained quantities are identified as relativistic generalization of the nonrelativistic orthogonal moments, e.g. diffusion flow, heat flow, pressure, etc. From the relativistic Boltzmann equation we then derive balance equations for these quantities. Explicit expressions for the relativistic mass conservation, energy balance, pressure balance, heat flow balance are presented. The weak relativistic limit is discussed. The derivation of higher order balance equations is sketched. (orig.)

  10. DISPL-1, 2. Order Nonlinear Partial Differential Equation System Solution for Kinetics Diffusion Problems

    International Nuclear Information System (INIS)

    Leaf, G.K.; Minkoff, M.

    1982-01-01

    1 - Description of problem or function: DISPL1 is a software package for solving second-order nonlinear systems of partial differential equations including parabolic, elliptic, hyperbolic, and some mixed types. The package is designed primarily for chemical kinetics- diffusion problems, although not limited to these problems. Fairly general nonlinear boundary conditions are allowed as well as inter- face conditions for problems in an inhomogeneous medium. The spatial domain is one- or two-dimensional with rectangular Cartesian, cylindrical, or spherical (in one dimension only) geometry. 2 - Method of solution: The numerical method is based on the use of Galerkin's procedure combined with the use of B-Splines (C.W.R. de-Boor's B-spline package) to generate a system of ordinary differential equations. These equations are solved by a sophisticated ODE software package which is a modified version of Hindmarsh's GEAR package, NESC Abstract 592. 3 - Restrictions on the complexity of the problem: The spatial domain must be rectangular with sides parallel to the coordinate geometry. Cross derivative terms are not permitted in the PDE. The order of the B-Splines is at most 12. Other parameters such as the number of mesh points in each coordinate direction, the number of PDE's etc. are set in a macro table used by the MORTRAn2 preprocessor in generating the object code

  11. Numerical solution of the 1D kinetics equations using a cubic reduced nodal scheme

    International Nuclear Information System (INIS)

    Gomez T, A.M.; Valle G, E. del; Delfin L, A.; Alonso V, G.

    2003-01-01

    In this work a finite differences technique centered in mesh based on a cubic reduced nodal scheme type finite element to solve the equations of the kinetics 1 D that include the equations corresponding to the concentrations of precursors of delayed neutrons is described. The technique of finite elements used is that of Galerkin where so much the neutron flux as the concentrations of precursors its are spatially approached by means of a three grade polynomial. The matrices of rigidity and of mass that arise during this discretization process are numerically evaluated using the open quadrature non standard of Newton-Cotes and that of Radau respectively. The purpose of the application of these quadratures is the one of to eliminate in the global matrices the couplings among the values of the flow in points of the discretization with the consequent advantages as for the reduction of the order of the matrix associated to the discreet problem that is to solve. As for the time dependent part the classical integration scheme known as Θ scheme is applied. After carrying out the one reordering of unknown and equations it arrives to a reduced system that it can be solved but quickly. With the McKin compute program developed its were solved three benchmark problems and those results are shown for the relative powers. (Author)

  12. Solution of fractional kinetic equation by a class of integral transform of pathway type

    Science.gov (United States)

    Kumar, Dilip

    2013-04-01

    Solutions of fractional kinetic equations are obtained through an integral transform named Pα-transform introduced in this paper. The Pα-transform is a binomial type transform containing many class of transforms including the well known Laplace transform. The paper is motivated by the idea of pathway model introduced by Mathai [Linear Algebra Appl. 396, 317-328 (2005), 10.1016/j.laa.2004.09.022]. The composition of the transform with differential and integral operators are proved along with convolution theorem. As an illustration of applications to the general theory of differential equations, a simple differential equation is solved by the new transform. Being a new transform, the Pα-transform of some elementary functions as well as some generalized special functions such as H-function, G-function, Wright generalized hypergeometric function, generalized hypergeometric function, and Mittag-Leffler function are also obtained. The results for the classical Laplace transform is retrieved by letting α → 1.

  13. 'Kinetic calculation of plasma deposition in castellated tile gaps'.

    Czech Academy of Sciences Publication Activity Database

    Dejarnac, Renaud; Gunn, J. P.

    363-365, - (2007), s. 560-564 ISSN 0022-3115 Grant - others:-(XE) EURATOM fellowship contract no.012801 Institutional research plan: CEZ:AV0Z20430508 Keywords : Edge modeling * Divertor plasma * Ion-surface interactions * ITER * Sheaths Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 1.643, year: 2007

  14. Investigation of diffusion kinetics of plasma paste borided AISI 8620 ...

    Indian Academy of Sciences (India)

    Henríquez 2009), plasma boriding (Rodríguez et al 1999) and plasma paste boriding (Gunes et al 2011; Yoon et al ... symmetric geometry with monochromatized radiation (Cu Kα, λ = 0.15418 nm). ..... cate the degree of reliability of the predicted results, when compared with that of the experiments. ... low alloy steels. Surf.

  15. Coupled electron and atomic kinetics through the solution of the Boltzmann equation for generating time-dependent X-ray spectra

    International Nuclear Information System (INIS)

    Sherrill, M.E.; Abdallah, J. Jr.; Csanak, G.; Kilcrease, D.P.; Dodd, E.S.; Fukuda, Y.; Akahane, Y.; Aoyama, M.; Inoue, N.; Ueda, H.; Yamakawa, K.; Faenov, A.Ya.; Magunov, A.I.; Pikuz, T.A.; Skobelev, I.Yu.

    2006-01-01

    In this work, we present a model that solves self-consistently the electron and atomic kinetics to characterize highly non-equilibrium plasmas, in particular for those systems where both the electron distribution function is far from Maxwellian and the evolution of the ion level populations are dominated by time-dependent atomic kinetics. In this model, level populations are obtained from a detailed collisional-radiative model where collision rates are computed from a time varying electron distribution function obtained from the solution of the zero-dimensional Boltzmann equation. The Boltzmann collision term includes the effects of electron-electron collisions, electron collisional ionization, excitation and de-excitation. An application for He α spectra from a short pulse laser irradiated argon cluster target will be shown to illustrate the results of our model

  16. Coupled electron and atomic kinetics through the solution of the Boltzmann equation for generating time-dependent X-ray spectra

    Energy Technology Data Exchange (ETDEWEB)

    Sherrill, M.E. [Los Alamos National Laboratory, T-4, Los Alamos, NM 87545 (United States)]. E-mail: manolo@t4.lanl.gov; Abdallah, J. Jr. [Los Alamos National Laboratory, T-4, Los Alamos, NM 87545 (United States); Csanak, G. [Los Alamos National Laboratory, T-4, Los Alamos, NM 87545 (United States); Kilcrease, D.P. [Los Alamos National Laboratory, T-4, Los Alamos, NM 87545 (United States); Dodd, E.S. [Los Alamos National Laboratory, X-1, Los Alamos, NM 87545 (United States); Fukuda, Y. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Akahane, Y. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Aoyama, M. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Inoue, N. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Ueda, H. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Yamakawa, K. [Advanced Photon Research Center, JAERI, Kyoto 619-0215 (Japan); Faenov, A.Ya. [Multicharged Ions Spectra Data Center of VNIIFTRI, Mendeleevo, Moscow Region 141570 (Russian Federation); Magunov, A.I. [Multicharged Ions Spectra Data Center of VNIIFTRI, Mendeleevo, Moscow Region 141570 (Russian Federation); Pikuz, T.A. [Multicharged Ions Spectra Data Center of VNIIFTRI, Mendeleevo, Moscow Region 141570 (Russian Federation); Skobelev, I.Yu. [Multicharged Ions Spectra Data Center of VNIIFTRI, Mendeleevo, Moscow Region 141570 (Russian Federation)

    2006-05-15

    In this work, we present a model that solves self-consistently the electron and atomic kinetics to characterize highly non-equilibrium plasmas, in particular for those systems where both the electron distribution function is far from Maxwellian and the evolution of the ion level populations are dominated by time-dependent atomic kinetics. In this model, level populations are obtained from a detailed collisional-radiative model where collision rates are computed from a time varying electron distribution function obtained from the solution of the zero-dimensional Boltzmann equation. The Boltzmann collision term includes the effects of electron-electron collisions, electron collisional ionization, excitation and de-excitation. An application for He{sub {alpha}} spectra from a short pulse laser irradiated argon cluster target will be shown to illustrate the results of our model.

  17. 3-D resistive MHD calculations for tokamak plasmas: beyond the simple reduced set of equations

    International Nuclear Information System (INIS)

    Carreras, B.A.; Garcia, L.; Hender, T.C.; Hicks, H.R.; Holmes, J.A.; Lynch, V.E.; Masden, B.F.

    1983-01-01

    Numerical studies of the resistive stability of tokamak plasmas in cylindrical geometry have been performed using: (1) the full set of resistive Magnetohydrodynamic (MHD) equations and (2) an extended version of the reduced set of resistive MHD equations including diamagnetic and electron temperature effects. In particular, the nonlinear interaction of tearing modes of many helicities has been investigated. The numerical results confirm many of the features uncovered previously using the simple reduced equations. (author)

  18. Reduced, three-dimensional, nonlinear equations for high-β plasmas including toroidal effects

    International Nuclear Information System (INIS)

    Schmalz, R.

    1980-11-01

    The resistive MHD equations for toroidal plasma configurations are reduced by expanding to the second order in epsilon, the inverse aspect ratio, allowing for high β = μsub(o)p/B 2 of order epsilon. The result is a closed system of nonlinear, three-dimensional equations where the fast magnetohydrodynamic time scale is eliminated. In particular, the equation for the toroidal velocity remains decoupled. (orig.)

  19. On the kinetic theory of parametric resonance in relativistic plasma

    International Nuclear Information System (INIS)

    El-Ashry, M.Y.

    1982-08-01

    The instability of relativistic hot plasma located in high-frequency external electric field is studied. The dispersion relation, in the case when the plasma electrons have relativistic oscillatory motion, is obtained. It is shown that if the electron Deby's radius is less than the wave length of plasma oscillation and far from the resonance on the overtones of the external field frequency, the oscillation build-up is possible. It is also shown that taking into account the relativistic motion of electrons leads to a considerable decrease in the frequency at which the parametric resonance takes place. (author)

  20. Hamiltonian structure of reduced fluid models for plasmas obtained from a kinetic description

    International Nuclear Information System (INIS)

    Guillebon, L. de; Chandre, C.

    2012-01-01

    We consider the Hamiltonian structure of reduced fluid models obtained from a kinetic description of collisionless plasmas by Vlasov–Maxwell equations. We investigate the possibility of finding Poisson subalgebras associated with fluid models starting from the Vlasov–Maxwell Poisson algebra. In this way, we show that the only possible Poisson subalgebra involves the moments of zeroth and first order of the Vlasov distribution, meaning the fluid density and the fluid velocity. We find that the bracket derived in [B.A. Shadwick, G.M. Tarkenton, E.H. Esarey, Phys. Rev. Lett. 93 (2004) 175002] which involves moments of order 2 is not a Poisson bracket since it does not satisfy the Jacobi identity. -- Highlights: ► We investigate fluid reductions from the Vlasov–Maxwell Poisson bracket. ► The only Poisson subalgebra involves fluid density and fluid velocity. ► The bracket derived in [B.A. Shadwick, G.M. Tarkenton, E.H. Esarey, Phys. Rev. Lett. 93 (2004) 175002] is not Hamiltonian.

  1. Shear viscosity of the quark-gluon plasma in a kinetic theory approach

    International Nuclear Information System (INIS)

    Puglisi, A.; Plumari, S.; Scardina, F.; Greco, V.

    2014-01-01

    One of the main results of heavy ions collision (HIC) at relativistic energy experiments is the very small shear viscosity to entropy density ratio of the Quark-Gluon Plasma, close to the conjectured lower bound η/s=1/4π for systems in the infinite coupling limit. Transport coefficients like shear viscosity are responsible of non-equilibrium properties of a system: Green-Kubo relations give us an exact expression to compute these coefficients. We compute shear viscosity numerically using Green-Kubo relation in the framework of Kinetic Theory solving the relativistic transport Boltzmann equation in a finite box with periodic boundary conditions. We investigate a system of particles interacting via anisotropic and energy dependent cross-section in the range of temperature of interest for HIC. Green-Kubo results are in agreement with Chapman-Enskog approximation while Relaxation Time approximation can underestimates the viscosity of a factor 2. The correct analytic formula for shear viscosity can be used to develop a transport theory with a fixed η/s and have a comparison with physical observables like elliptic flow

  2. Transport coefficients of Quark-Gluon Plasma in a Kinetic Theory approach

    International Nuclear Information System (INIS)

    Puglisi, A; Plumari, S; Scardina, F; Greco, V

    2014-01-01

    One of the main results of heavy ions collision at relativistic energy experiments is the very small shear viscosity to entropy density ratio of the Quark-Gluon Plasma, close to the conjectured lower bound η/s = 1/4π for systems in the infinite coupling limit. Transport coefficients like shear viscosity are responsible of non-equilibrium properties of a system: Green- Kubo relations give us an exact expression to compute these coefficients. We computed shear viscosity numerically using Green-Kubo relation in the framework of Kinetic Theory solving the relativistic transport Boltzmann equation in a finite box with periodic boundary conditions. We investigated different cases of particles, for one component system (gluon matter), interacting via isotropic or anisotropic cross-section in the range of temperature of interest for HIC. Green-Kubo results are in agreement with Chapman-Enskog approximation while Relaxation Time approximation can underestimates the viscosity of a factor 2. Another transport coefficient of interest is the electric conductivity σ el which determines the response of QGP to the electromagnetic fields present in the early stage of the collision. We study the σ el dependence on microscopic details of interaction and we find also in this case that Relaxation Time Approximation is a good approximation only for isotropic cross-section.

  3. Plasma-assisted ignition and combustion: nanosecond discharges and development of kinetic mechanisms

    Science.gov (United States)

    Starikovskaia, S. M.

    2014-09-01

    This review covers the results obtained in the period 2006-2014 in the field of plasma-assisted combustion, and in particular the results on ignition and combustion triggered or sustained by pulsed nanosecond discharges in different geometries. Some benefits of pulsed high voltage discharges for kinetic study and for applications are demonstrated. The necessity of and the possibility of building a particular kinetic mechanism of plasma-assisted ignition and combustion are discussed. The most sensitive regions of parameters for plasma-combustion kinetic mechanisms are selected. A map of the pressure and temperature parameters (P-T diagram) is suggested, to unify the available data on ignition delay times, ignition lengths and densities of intermediate species reported by different authors.

  4. Polynomial approach method to solve the neutron point kinetics equations with use of the analytic continuation

    Energy Technology Data Exchange (ETDEWEB)

    Tumelero, Fernanda; Petersen, Claudio Zen; Goncalves, Glenio Aguiar [Universidade Federal de Pelotas, Capao do Leao, RS (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Schramm, Marcelo [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica

    2016-12-15

    In this work, we report a solution to solve the Neutron Point Kinetics Equations applying the Polynomial Approach Method. The main idea is to expand the neutron density and delayed neutron precursors as a power series considering the reactivity as an arbitrary function of the time in a relatively short time interval around an ordinary point. In the first interval one applies the initial conditions and the analytical continuation is used to determine the solutions of the next intervals. A genuine error control is developed based on an analogy with the Rest Theorem. For illustration, we also report simulations for different approaches types (linear, quadratic and cubic). The results obtained by numerical simulations for linear approximation are compared with results in the literature.

  5. A Gas-kinetic Discontinuous Galerkin Method for Viscous Flow Equations

    International Nuclear Information System (INIS)

    Liu, Hongwei; Xu, Kun

    2007-01-01

    This paper presents a Runge-Kutta discontinuous Galerkin (RKDG) method for viscous flow computation. The construction of the RKDG method is based on a gas-kinetic formulation, which not only couples the convective and dissipative terms together, but also includes both discontinuous and continuous representation in the flux evaluation at the cell interface through a simple hybrid gas distribution function. Due to the intrinsic connection between the gaskinetic BGK model and the Navier-Stokes equations, the Navier-Stokes flux is automatically obtained by the present method. Numerical examples for both one dimensional (10) and two dimensional(20) compressible viscous flows are presented to demonstrate the accuracy and shock capturing capability of the current RKDG method

  6. Integration of the three-dimensional Vlasov equation for a magnetized plasma

    International Nuclear Information System (INIS)

    Cheng, C.Z.

    1976-04-01

    A second order splitting scheme is developed to integrate the three dimensional Vlasov equation for a plasma in a magnetic field. The integration of the Vlasov equation is divided into a series of intermediate steps and Fourier interpolation and the ASD method with a third order Taylor expansion are used to integrate the fractional equations. Numerical experiments related to cyclotron waves in 2 and 2 1 / 2 D are demonstrated with high accuracy and efficiency. The computer storage requirements are modest; for example, a typical 2D nonlinear electron plasma simulation requires only 4000 ''particles.''

  7. Relativistic simulation of the Vlasov equation for plasma expansion into vacuum

    Directory of Open Access Journals (Sweden)

    H Abbasi

    2012-12-01

    Full Text Available   In this study, relativistic Vlasov simulation of plasma for expansion of collisionless plasma for into vacuum is presented. The model is based on 1+1 dimensional phase space and electrostatic approximation. For this purpose, the electron dynamics is studied by the relativistic Vlasov equation. Regardless of the ions temperature, fluid equations are used for their dynamics. The initial electrons distribution function is the relativistic Maxwellian. The results show that due to the electrons relativistic temperature, the process of the plasma expansion takes place faster, the resulting electric field is stronger and the ions are accelerated to higher velocities, in comparison to the non-relativistic case.

  8. The kinetics of nonequilibrium chain plasma-chemical oxidation in heterogeneous media

    International Nuclear Information System (INIS)

    Deminskii, M.A.; Potapkin, B.V.; Rusanov, V.D.

    1994-01-01

    The kinetics of oxidation of low-impurity components in air mixtures under heterogeneous conditions was studied. The principal kinetic features of the process were determined on the basis of theoretical analysis of plasma-chemical oxidation in heterogeneous media. The analysis also showed that low concentrations of impurities in liquid aerosol particles can be efficiently oxidized via a chain process induced by reactive species formed in the gas

  9. Non Equilbrium Vibrational Kinetics in Expanding Plasma Flows

    International Nuclear Information System (INIS)

    Colonna, Gianpiero

    2008-01-01

    The supersonic expansion of a plasma is a system of interest for aerospace applications, ranging from propulsion to hypersonic wind tunnels. Under these conditions the plasma shows significant departures from chemical and thermal equilibrium, similarly to post-discharge conditions. The multitemperature description is not adequate because the internal level distributions show tails overpopulated with respect to a Boltzmann distribution. The state-to-state approach has to be used, including the interaction with free electrons which follow non-maxwellian distributions.

  10. Intensity dependence of non-linear kinetic behaviour of stimulated Raman scattering in fusion relevant plasmas

    Czech Academy of Sciences Publication Activity Database

    Mašek, Martin; Rohlena, Karel

    2015-01-01

    Roč. 69, č. 4 (2015), s. 109 ISSN 1434-6060 R&D Projects: GA ČR GAP205/11/0571; GA MŠk(CZ) LD14089 Institutional support: RVO:68378271 Keywords : plasma physics * Vlasov equation * numerical-simulation electromagnetic - waves * acceleration Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 1.208, year: 2015

  11. Approximate method for stochastic chemical kinetics with two-time scales by chemical Langevin equations

    International Nuclear Information System (INIS)

    Wu, Fuke; Tian, Tianhai; Rawlings, James B.; Yin, George

    2016-01-01

    The frequently used reduction technique is based on the chemical master equation for stochastic chemical kinetics with two-time scales, which yields the modified stochastic simulation algorithm (SSA). For the chemical reaction processes involving a large number of molecular species and reactions, the collection of slow reactions may still include a large number of molecular species and reactions. Consequently, the SSA is still computationally expensive. Because the chemical Langevin equations (CLEs) can effectively work for a large number of molecular species and reactions, this paper develops a reduction method based on the CLE by the stochastic averaging principle developed in the work of Khasminskii and Yin [SIAM J. Appl. Math. 56, 1766–1793 (1996); ibid. 56, 1794–1819 (1996)] to average out the fast-reacting variables. This reduction method leads to a limit averaging system, which is an approximation of the slow reactions. Because in the stochastic chemical kinetics, the CLE is seen as the approximation of the SSA, the limit averaging system can be treated as the approximation of the slow reactions. As an application, we examine the reduction of computation complexity for the gene regulatory networks with two-time scales driven by intrinsic noise. For linear and nonlinear protein production functions, the simulations show that the sample average (expectation) of the limit averaging system is close to that of the slow-reaction process based on the SSA. It demonstrates that the limit averaging system is an efficient approximation of the slow-reaction process in the sense of the weak convergence.

  12. Relativistic Kinetic Theory

    Science.gov (United States)

    Vereshchagin, Gregory V.; Aksenov, Alexey G.

    2017-02-01

    Preface; Acknowledgements; Acronyms and definitions; Introduction; Part I. Theoretical Foundations: 1. Basic concepts; 2. Kinetic equation; 3. Averaging; 4. Conservation laws and equilibrium; 5. Relativistic BBGKY hierarchy; 6. Basic parameters in gases and plasmas; Part II. Numerical Methods: 7. The basics of computational physics; 8. Direct integration of Boltzmann equations; 9. Multidimensional hydrodynamics; Part III. Applications: 10. Wave dispersion in relativistic plasma; 11. Thermalization in relativistic plasma; 12. Kinetics of particles in strong fields; 13. Compton scattering in astrophysics and cosmology; 14. Self-gravitating systems; 15. Neutrinos, gravitational collapse and supernovae; Appendices; Bibliography; Index.

  13. PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY

    Energy Technology Data Exchange (ETDEWEB)

    Tsai, Shang-Hsi; Yang, Jaw-Yen, E-mail: shanghsi@gmail.com [Institute of Applied Mechanics, National Taiwan University, Taipei 10764, Taiwan (China)

    2015-07-20

    A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.

  14. Multi-scale method for the resolution of the neutronic kinetics equations

    International Nuclear Information System (INIS)

    Chauvet, St.

    2008-10-01

    In this PhD thesis and in order to improve the time/precision ratio of the numerical simulation calculations, we investigate multi-scale techniques for the resolution of the reactor kinetics equations. We choose to focus on the mixed dual diffusion approximation and the quasi-static methods. We introduce a space dependency for the amplitude function which only depends on the time variable in the standard quasi-static context. With this new factorization, we develop two mixed dual problems which can be solved with Cea's solver MINOS. An algorithm is implemented, performing the resolution of these problems defined on different scales (for time and space). We name this approach: the Local Quasi-Static method. We present here this new multi-scale approach and its implementation. The inherent details of amplitude and shape treatments are discussed and justified. Results and performances, compared to MINOS, are studied. They illustrate the improvement on the time/precision ratio for kinetics calculations. Furthermore, we open some new possibilities to parallelize computations with MINOS. For the future, we also introduce some improvement tracks with adaptive scales. (author)

  15. Derivation of regularized Grad's moment system from kinetic equations: modes, ghosts and non-Markov fluxes

    Science.gov (United States)

    Karlin, Ilya

    2018-04-01

    Derivation of the dynamic correction to Grad's moment system from kinetic equations (regularized Grad's 13 moment system, or R13) is revisited. The R13 distribution function is found as a superposition of eight modes. Three primary modes, known from the previous derivation (Karlin et al. 1998 Phys. Rev. E 57, 1668-1672. (doi:10.1103/PhysRevE.57.1668)), are extended into the nonlinear parameter domain. Three essentially nonlinear modes are identified, and two ghost modes which do not contribute to the R13 fluxes are revealed. The eight-mode structure of the R13 distribution function implies partition of R13 fluxes into two types of contributions: dissipative fluxes (both linear and nonlinear) and nonlinear streamline convective fluxes. Physical interpretation of the latter non-dissipative and non-local in time effect is discussed. A non-perturbative R13-type solution is demonstrated for a simple Lorentz scattering kinetic model. The results of this study clarify the intrinsic structure of the R13 system. This article is part of the theme issue `Hilbert's sixth problem'.

  16. Potential formation in a one-dimensional bounded plasma system containing a two-electron temperature plasma: Kinetic model and PIC simulation

    International Nuclear Information System (INIS)

    Gyergyek, T.; Jurcic-Zlobec, B.; Cercek, M.

    2008-01-01

    Potential formation in a bounded plasma system that contains electrons with a two-temperature velocity distribution and is terminated by a floating, electron emitting electrode (collector) is studied by a one-dimensional kinetic model. A method on how to determine the boundary conditions at the collector for the numerical solution of the Poisson equation is presented. The difference between the regular and the irregular numerical solutions of the Poisson equation is explained. The regular numerical solution of the Poisson equation fulfills the boundary conditions at the source and can be computed for any distance from the collector. The irregular solution does not fulfill the source boundary conditions and the computation breaks down at some distance from the collector. An excellent agreement of the values of the potential at the inflection point found from the numerical solution of the Poisson equation with the values predicted by the analytical model is obtained. Potential, electric field, and particle density profiles found by the numerical solution of the Poisson equation are compared to the profiles obtained with the particle in cell computer simulation. A very good quantitative agreement of the potential and electric field profiles is obtained. For certain values of the parameters the analytical model predicts three possible values of the potential at the inflection point. In such cases always only one of the corresponding numerical solutions of the Poisson equation is regular, while the other two are irregular. The regular numerical solution of the Poisson equation always corresponds to the solution of the model that predicts the largest ion flux to the collector

  17. Point kinetics equations for subcritical systems based on the importance function associated to an external neutron source

    International Nuclear Information System (INIS)

    Carvalho Gonçalves, Wemerson de; Martinez, Aquilino Senra; Carvalho da Silva, Fernando

    2015-01-01

    Highlights: • We define the new function importance. • We calculate the kinetic parameters Λ, β, Γ and Q to: 0.95, 0.96, 0.97, 0.98 and 0.99. • We compared the results with those obtained by the main important functions. • We found that the calculated kinetic parameters are physically consistent. - Abstract: This paper aims to determine the parameters for a new set of equations of point kinetic subcritical systems, based on the concept of importance of Heuristic Generalized Perturbation Theory (HGPT). The importance function defined here is related to both the subcriticality and the external neutron source worth (which keeps the system at steady state). The kinetic parameters defined in this work are compared with the corresponding parameters when adopting the importance functions proposed by Gandini and Salvatores (2002), Dulla et al. (2006) and Nishihara et al. (2003). Furthermore, the point kinetics equations developed here are solved for two different transients, considering the parameters obtained with different importance functions. The results collected show that there is a similar behavior of the solution of the point kinetics equations, when used with the parameters obtained by the importance functions proposed by Gandini and Salvatores (2002) and Dulla et al. (2006), specially near the criticality. However, this is not verified as the system gets farther from criticality

  18. Kinetic approach to plasma end loss from linear devices

    International Nuclear Information System (INIS)

    Dreicer, H.

    1976-01-01

    A first step in the direction of a kinetic approach to end loss has been presented. This approach brings to light some fundamental processes not uncovered by the magnetohydrodynamic or guiding center approach. Attention was focused on the basically transient phenomenon in a way that describes the quite different behavior of collision dominated and collisionless ions, but ignores the magnetic nozzle effects near the ends of the system. The treatment illuminates some of the roles played by the parameter l/sub ii//L, and suggests the direction for more detailed investigations. End loss from linear systems is a very many faceted problem. Kinetic effects, magnetic effects, heat flow, etc. are all intermixed, and it will require a strong long term experimental and theoretical program to unravel all of its mysteries

  19. Solution of the neutron point kinetics equations with temperature feedback effects applying the polynomial approach method

    Energy Technology Data Exchange (ETDEWEB)

    Tumelero, Fernanda, E-mail: fernanda.tumelero@yahoo.com.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Petersen, Claudio Z.; Goncalves, Glenio A.; Lazzari, Luana, E-mail: claudiopeteren@yahoo.com.br, E-mail: gleniogoncalves@yahoo.com.br, E-mail: luana-lazzari@hotmail.com [Universidade Federal de Pelotas (DME/UFPEL), Capao do Leao, RS (Brazil). Instituto de Fisica e Matematica

    2015-07-01

    In this work, we present a solution of the Neutron Point Kinetics Equations with temperature feedback effects applying the Polynomial Approach Method. For the solution, we consider one and six groups of delayed neutrons precursors with temperature feedback effects and constant reactivity. The main idea is to expand the neutron density, delayed neutron precursors and temperature as a power series considering the reactivity as an arbitrary function of the time in a relatively short time interval around an ordinary point. In the first interval one applies the initial conditions of the problem and the analytical continuation is used to determine the solutions of the next intervals. With the application of the Polynomial Approximation Method it is possible to overcome the stiffness problem of the equations. In such a way, one varies the time step size of the Polynomial Approach Method and performs an analysis about the precision and computational time. Moreover, we compare the method with different types of approaches (linear, quadratic and cubic) of the power series. The answer of neutron density and temperature obtained by numerical simulations with linear approximation are compared with results in the literature. (author)

  20. Solution of the neutron point kinetics equations with temperature feedback effects applying the polynomial approach method

    International Nuclear Information System (INIS)

    Tumelero, Fernanda; Petersen, Claudio Z.; Goncalves, Glenio A.; Lazzari, Luana

    2015-01-01

    In this work, we present a solution of the Neutron Point Kinetics Equations with temperature feedback effects applying the Polynomial Approach Method. For the solution, we consider one and six groups of delayed neutrons precursors with temperature feedback effects and constant reactivity. The main idea is to expand the neutron density, delayed neutron precursors and temperature as a power series considering the reactivity as an arbitrary function of the time in a relatively short time interval around an ordinary point. In the first interval one applies the initial conditions of the problem and the analytical continuation is used to determine the solutions of the next intervals. With the application of the Polynomial Approximation Method it is possible to overcome the stiffness problem of the equations. In such a way, one varies the time step size of the Polynomial Approach Method and performs an analysis about the precision and computational time. Moreover, we compare the method with different types of approaches (linear, quadratic and cubic) of the power series. The answer of neutron density and temperature obtained by numerical simulations with linear approximation are compared with results in the literature. (author)

  1. Simulation of the organic-waste processing in plasma with allowance for kinetics of thermochemical transformations

    Science.gov (United States)

    Messerle, V. E.; Ustimenko, A. B.

    2017-07-01

    Kinetic calculations of the plasma processing/utilization process of organic waste in air and steam ambient were carried out. It is shown that, during the time of waste residence in the plasma reactor, 0.7 and 1.2 s, at the exit from the reactor there forms a high-calorific fuel gas with a combustion heat of 3540 and 5070 kcal/kg, respectively. In this process, 1 kg of waste yields 1.16 kg of fuel gas at air gasification of waste and 0.87 kg of pure synthesis gas at steam gasification. The energy efficiency of the waste gasification process, defined by the ratio between the calorific value of the resultant fuel gas and the initial calorific value of the waste amounts to 91 % in air plasma and 98 % in steam plasma. A comparison between the results of kinetic and thermodynamic calculations has revealed their good agreement.

  2. Kinetics of HIV-1 in cerebrospinal fluid and plasma in cryptococcal meningitis

    Directory of Open Access Journals (Sweden)

    Jorge A. Benetucci

    2012-04-01

    Full Text Available In order to determine HIV-1 kinetics in cerebrospinal fluid (CSF and plasma in patients with cryptococcal meningitis (CM, we undertook a prospective collection of paired CSF/plasma samples from antiretroviral therapy- free HIV-infected patients with CM. Samples were obtained at baseline (S1 and at the second (S2 and third (S3 weeks of antifungal therapy. HIV-1 CSF concentrations were significantly lower in both S2 and S3 with respect to S1. Plasma concentrations remained stable. HIV-1 concentrations were higher in plasma than CSF in all cases. Patients who survived the episode of CM (but not those who died showed a decrease in CSF viral load, what suggests different viral kinetics of HIV-1 in the CSF according to the clinical course of this opportunistic disease.

  3. Center manifolds for a class of degenerate evolution equations and existence of small-amplitude kinetic shocks

    Science.gov (United States)

    Pogan, Alin; Zumbrun, Kevin

    2018-06-01

    We construct center manifolds for a class of degenerate evolution equations including the steady Boltzmann equation and related kinetic models, establishing in the process existence and behavior of small-amplitude kinetic shock and boundary layers. Notably, for Boltzmann's equation, we show that elements of the center manifold decay in velocity at near-Maxwellian rate, in accord with the formal Chapman-Enskog picture of near-equilibrium flow as evolution along the manifold of Maxwellian states, or Grad moment approximation via Hermite polynomials in velocity. Our analysis is from a classical dynamical systems point of view, with a number of interesting modifications to accommodate ill-posedness of the underlying evolution equation.

  4. Electron screening and kinetic-energy oscillations in a strongly coupled plasma

    International Nuclear Information System (INIS)

    Chen, Y.C.; Simien, C.E.; Laha, S.; Gupta, P.; Martinez, Y.N.; Mickelson, P.G.; Nagel, S.B.; Killian, T.C.

    2004-01-01

    We study equilibration of strongly coupled ions in an ultracold neutral plasma produced by photoionizing laser-cooled and trapped atoms. By varying the electron temperature, we show that electron screening modifies the equilibrium ion temperature. Even with few electrons in a Debye sphere, the screening is well described by a model using a Yukawa ion-ion potential. We also observe damped oscillations of the ion kinetic energy that are a unique feature of equilibration of a strongly coupled plasma

  5. Tracer kinetics: Modelling by partial differential equations of inhomogeneous compartments with age-dependent elimination rates. Pt. 2

    International Nuclear Information System (INIS)

    Winkler, E.

    1991-01-01

    The general theory of inhomogeneous compartments with age-dependent elimination rates is illustrated by examples. Mathematically, it turns out that models consisting of partial differential equations include ordinary, delayed and integro-differential equations, a general fact which is treated here in the context of linear tracer kinetics. The examples include standard compartments as a degenerate case, systems of standard compartments (compartment blocks), models resulting in special residence time distributions, models with pipes, and systems with heterogeneous particles. (orig./BBR) [de

  6. Fractional Boltzmann equation for multiple scattering of resonance radiation in low-temperature plasma

    Energy Technology Data Exchange (ETDEWEB)

    Uchaikin, V V; Sibatov, R T, E-mail: vuchaikin@gmail.com, E-mail: ren_sib@bk.ru [Ulyanovsk State University, 432000, 42 Leo Tolstoy str., Ulyanovsk (Russian Federation)

    2011-04-08

    The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start with the standard Boltzmann equation; averaging over photon frequencies leads to the appearance of a fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of a fractional material derivative in the equation is concordant with heavy tailed distribution of photon path lengths and with spatiotemporal coupling peculiar to the process. We discuss some methods of solving the obtained equation and demonstrate numerical results in some simple cases.

  7. Fractional Boltzmann equation for multiple scattering of resonance radiation in low-temperature plasma

    International Nuclear Information System (INIS)

    Uchaikin, V V; Sibatov, R T

    2011-01-01

    The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start with the standard Boltzmann equation; averaging over photon frequencies leads to the appearance of a fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of a fractional material derivative in the equation is concordant with heavy tailed distribution of photon path lengths and with spatiotemporal coupling peculiar to the process. We discuss some methods of solving the obtained equation and demonstrate numerical results in some simple cases.

  8. Modelling of thermal transport using Fokker-Planck equations in laser produced plasma

    International Nuclear Information System (INIS)

    Nakarmi, J.J.; Jha, L.N.

    1996-12-01

    The kinetic equation with Fokker-Planck collision term has been presented to obtain the distribution function in the corona of inertial confinement fusion, in the presence of the self generated magnetic field. The resulting distribution has non-local form with the convolution in Maxwellian. An expression for thermal flux with self generated magnetic field is obtained. (author). 22 refs

  9. Linear relativistic gyrokinetic equation in general magnetically confined plasmas

    International Nuclear Information System (INIS)

    Tsai, S.T.; Van Dam, J.W.; Chen, L.

    1983-08-01

    The gyrokinetic formalism for linear electromagnetic waves of arbitrary frequency in general magnetic-field configurations is extended to include full relativistic effects. The derivation employs the small adiabaticity parameter rho/L 0 where rho is the Larmor radius and L 0 the equilibrium scale length. The effects of the plasma and magnetic field inhomogeneities and finite Larmor-radii effects are also contained

  10. Kinetic theory of interaction of high frequency waves with a rotating plasma

    International Nuclear Information System (INIS)

    Chiu, S. C.; Chan, V. S.; Chu, M. S.; Lin-Liu, Y. R.

    2000-01-01

    The equations of motion of charged particles of a strongly magnetized flowing plasma under the influence of high frequency waves are derived in the guiding center approximation. A quasilinear theory of the interactions of waves with rotating plasmas is formulated. This is applied to investigate the effect of radio frequency waves on a rotating tokamak plasma with a heated minority species. The angular momentum drive is mainly due to the rf-induced radial minority current. The return current by the bulk plasma gives an equal and opposite rotation drive on the bulk. Using moment equations and a small banana width approximation, the JxB drive was evaluated for the bulk plasma. Quite remarkably, although collisions are included, the net rotation drive is due to a term which can be obtained by neglecting collisions. (c) 2000 American Institute of Physics

  11. Growth kinetics and initial stage growth during plasma-enhanced Ti atomic layer deposition

    CERN Document Server

    Kim, H

    2002-01-01

    We have investigated the growth kinetics of plasma-enhanced Ti atomic layer deposition (ALD) using a quartz crystal microbalance. Ti ALD films were grown at temperatures from 20 to 200 deg. C using TiCl sub 4 as a source gas and rf plasma-produced atomic H as the reducing agent. Postdeposition ex situ chemical analyses of thin films showed that the main impurity is oxygen, mostly incorporated during the air exposure prior to analysis. The thickness per cycle, corresponding to the growth rate, was measured by quartz crystal microbalance as a function of various key growth parameters, including TiCl sub 4 and H exposure time, rf plasma power, and sample temperature. The growth rates were independent of TiCl sub 4 exposure above 1x10 sup 3 L, indicating typical ALD mode growth. The key kinetic parameters for Cl extraction reaction and TiCl sub 4 adsorption kinetics were obtained and the growth kinetics were modeled to predict the growth rates based upon these results. Also, the dependency of growth kinetics on d...

  12. Gas-kinetic unified algorithm for hypersonic flows covering various flow regimes solving Boltzmann model equation in nonequilibrium effect

    International Nuclear Information System (INIS)

    Li, Zhihui; Ma, Qiang; Wu, Junlin; Jiang, Xinyu; Zhang, Hanxin

    2014-01-01

    Based on the Gas-Kinetic Unified Algorithm (GKUA) directly solving the Boltzmann model equation, the effect of rotational non-equilibrium is investigated recurring to the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant. The molecular velocity distribution function is integrated by the weight factor on the internal energy, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The optimization selection technique of discrete velocity ordinate points and numerical quadrature rules for macroscopic flow variables with dynamic updating evolvement are developed to simulate hypersonic flows, and the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in thermodynamic non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of Boltzmann model equation involving non-equilibrium effect is presented for the whole range of flow regimes. The hypersonic flows involving non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-Ma-25, the planar ramp flow with the whole range of Knudsen numbers of 0.0009-Kn-10 and the three-dimensional re-entering flows around tine double-cone body

  13. ALICE: A non-LTE plasma atomic physics, kinetics and lineshape package

    Science.gov (United States)

    Hill, E. G.; Pérez-Callejo, G.; Rose, S. J.

    2018-03-01

    All three parts of an atomic physics, atomic kinetics and lineshape code, ALICE, are described. Examples of the code being used to model the emissivity and opacity of plasmas are discussed and interesting features of the code which build on the existing corpus of models are shown throughout.

  14. ASPECTS OF KINETICS AUTOTHERMAL THERMOPHILIC AEROBIC DIGESTION OF SEWAGE SLUDGE - THE USE OF EQUATIONS OF VARIOUS ORDERS

    Directory of Open Access Journals (Sweden)

    Magdalena Filkiewicz

    2016-12-01

    Work to identify the kinetics of the process are aimed at, among others, creating a model describing the speed of the process, including obtaining an answer whether the above equations can be the basis for further work on identifying the factors influencing the stabilization process.

  15. Energy Transfer and Dual Cascade in Kinetic Magnetized Plasma Turbulence

    International Nuclear Information System (INIS)

    Plunk, G. G.; Tatsuno, T.

    2011-01-01

    The question of how nonlinear interactions redistribute the energy of fluctuations across available degrees of freedom is of fundamental importance in the study of turbulence and transport in magnetized weakly collisional plasmas, ranging from space settings to fusion devices. In this Letter, we present a theory for the dual cascade found in such plasmas, which predicts a range of new behavior that distinguishes this cascade from that of neutral fluid turbulence. These phenomena are explained in terms of the constrained nature of spectral transfer in nonlinear gyrokinetics. Accompanying this theory are the first observations of these phenomena, obtained via direct numerical simulations using the gyrokinetic code AstroGK. The basic mechanisms that are found provide a framework for understanding the turbulent energy transfer that couples scales both locally and nonlocally.

  16. Energy Transfer and Dual Cascade in Kinetic Magnetized Plasma Turbulence

    Science.gov (United States)

    Plunk, G. G.; Tatsuno, T.

    2011-04-01

    The question of how nonlinear interactions redistribute the energy of fluctuations across available degrees of freedom is of fundamental importance in the study of turbulence and transport in magnetized weakly collisional plasmas, ranging from space settings to fusion devices. In this Letter, we present a theory for the dual cascade found in such plasmas, which predicts a range of new behavior that distinguishes this cascade from that of neutral fluid turbulence. These phenomena are explained in terms of the constrained nature of spectral transfer in nonlinear gyrokinetics. Accompanying this theory are the first observations of these phenomena, obtained via direct numerical simulations using the gyrokinetic code AstroGK. The basic mechanisms that are found provide a framework for understanding the turbulent energy transfer that couples scales both locally and nonlocally.

  17. Kinetic instabilities in relativistic plasmas: the Harris instability revisited

    International Nuclear Information System (INIS)

    Tautz, R.C.

    2008-01-01

    Plasma instabilities that generate aperiodic fluctuations are of outstanding importance in the astrophysical context. Two prominent examples are the electromagnetic Weibel instability and the electrostatic Harris instability, which operate in initially non-magnetized and magnetized plasmas, respectively. In this talk, the original formulation of the Harris instability will be reviewed and generalizations will be presented such as the inclusion of (1) relativistic effects, (2) ion effects, and (3) mode coupling. It will be shown that, with these modifications, a powerful method has been developed for the determination of both the existence and the growth rate of low-frequency instabilities. Applications can be found in astrophysical jets, where the rest frame can be used and so no parallel motion is present. At the end of the talk, how the particle composition of gamma-ray burst jets can be predicted using the Harris technique. (author)

  18. Computer simulation of kinetic properties of plasmas. Final report

    International Nuclear Information System (INIS)

    Denavit, J.

    1982-08-01

    The research was directed toward the development and testing of new numerical methods for particle and hybrid simulation of plasmas, and their application to physical problems of current significance to Magnetic Fusion Energy. This project will terminate on August 31, 1982 and this Final Report describes: (1) the research accomplished since the last renewal on October 1, 1981; and (2) a perspective of the work done since the beginning of the project in February 1972

  19. Hybrid dynamic modeling of Escherichia coli central metabolic network combining Michaelis–Menten and approximate kinetic equations

    DEFF Research Database (Denmark)

    Costa, Rafael S.; Machado, Daniel; Rocha, Isabel

    2010-01-01

    , represent nowadays the limiting factor in the construction of such models. In this study, we compare four alternative modeling approaches based on Michaelis–Menten kinetics for the bi-molecular reactions and different types of simplified rate equations for the remaining reactions (generalized mass action......The construction of dynamic metabolic models at reaction network level requires the use of mechanistic enzymatic rate equations that comprise a large number of parameters. The lack of knowledge on these equations and the difficulty in the experimental identification of their associated parameters...

  20. Non-thermal plasma destruction of allyl alcohol in waste gas: kinetics and modelling

    Science.gov (United States)

    DeVisscher, A.; Dewulf, J.; Van Durme, J.; Leys, C.; Morent, R.; Van Langenhove, H.

    2008-02-01

    Non-thermal plasma treatment is a promising technique for the destruction of volatile organic compounds in waste gas. A relatively unexplored technique is the atmospheric negative dc multi-pin-to-plate glow discharge. This paper reports experimental results of allyl alcohol degradation and ozone production in this type of plasma. A new model was developed to describe these processes quantitatively. The model contains a detailed chemical degradation scheme, and describes the physics of the plasma by assuming that the fraction of electrons that takes part in chemical reactions is an exponential function of the reduced field. The model captured the experimental kinetic data to less than 2 ppm standard deviation.

  1. Non-thermal plasma destruction of allyl alcohol in waste gas: kinetics and modelling

    International Nuclear Information System (INIS)

    Visscher, A de; Dewulf, J; Durme, J van; Leys, C; Morent, R; Langenhove, H Van

    2008-01-01

    Non-thermal plasma treatment is a promising technique for the destruction of volatile organic compounds in waste gas. A relatively unexplored technique is the atmospheric negative dc multi-pin-to-plate glow discharge. This paper reports experimental results of allyl alcohol degradation and ozone production in this type of plasma. A new model was developed to describe these processes quantitatively. The model contains a detailed chemical degradation scheme, and describes the physics of the plasma by assuming that the fraction of electrons that takes part in chemical reactions is an exponential function of the reduced field. The model captured the experimental kinetic data to less than 2 ppm standard deviation

  2. Review and limitations of 3D plasma blob modeling with reduced collisional fluid equations

    Energy Technology Data Exchange (ETDEWEB)

    Angus, Justin R., E-mail: jangus@ucsd.edu [University of California, San Diego, La Jolla, CA (United States); Umansky, Maxim V. [Lawrence Livermore National Laboratory, Livermore, CA (United States); Krashenninikov, Sergei I. [University of California, San Diego, La Jolla, CA (United States)

    2013-07-15

    Recent 3D studies on plasma blobs (coherent structures found in the edge region of magnetic confinement devices) have demonstrated that the drift wave instability can strongly limit the blob’s coherency and cross field convective nature that is predicted by 2D theory. However, the dominant unstable drift wave modes that effect plasma blobs were found to exist in parameter regimes that only marginally satisfied several of the major assumptions considered for the validity of the reduced collisional fluid equations used in the study. Namely, the neglect of electron heat flow, finite electron mean free path effects, and thermal ions. A follow up study demonstrated how the drift wave instability might change if a set of equations that does not suffer from the limitations mentioned above were considered. In the present paper, the results of this later work are used to discuss the limitations on using the collisional fluid equations for 3D studies of plasma blobs.

  3. A Derivation of Source-based Kinetics Equation with Time Dependent Fission Kernel for Reactor Transient Analyses

    International Nuclear Information System (INIS)

    Kim, Song Hyun; Woo, Myeong Hyun; Shin, Chang Ho; Pyeon, Cheol Ho

    2015-01-01

    In this study, a new balance equation to overcome the problems generated by the previous methods is proposed using source-based balance equation. And then, a simple problem is analyzed with the proposed method. In this study, a source-based balance equation with the time dependent fission kernel was derived to simplify the kinetics equation. To analyze the partial variations of reactor characteristics, two representative methods were introduced in previous studies; (1) quasi-statics method and (2) multipoint technique. The main idea of quasistatics method is to use a low-order approximation for large integration times. To realize the quasi-statics method, first, time dependent flux is separated into the shape and amplitude functions, and shape function is calculated. It is noted that the method has a good accuracy; however, it can be expensive as a calculation cost aspect because the shape function should be fully recalculated to obtain accurate results. To improve the calculation efficiency, multipoint method was proposed. The multipoint method is based on the classic kinetics equation with using Green's function to analyze the flight probability from region r' to r. Those previous methods have been used to analyze the reactor kinetics analysis; however, the previous methods can have some limitations. First, three group variables (r g , E g , t g ) should be considered to solve the time dependent balance equation. This leads a big limitation to apply large system problem with good accuracy. Second, the energy group neutrons should be used to analyze reactor kinetics problems. In time dependent problem, neutron energy distribution can be changed at different time. It can affect the change of the group cross section; therefore, it can lead the accuracy problem. Third, the neutrons in a space-time region continually affect the other space-time regions; however, it is not properly considered in the previous method. Using birth history of the neutron sources

  4. A Derivation of Source-based Kinetics Equation with Time Dependent Fission Kernel for Reactor Transient Analyses

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Song Hyun; Woo, Myeong Hyun; Shin, Chang Ho [Hanyang University, Seoul (Korea, Republic of); Pyeon, Cheol Ho [Kyoto University, Osaka (Japan)

    2015-10-15

    In this study, a new balance equation to overcome the problems generated by the previous methods is proposed using source-based balance equation. And then, a simple problem is analyzed with the proposed method. In this study, a source-based balance equation with the time dependent fission kernel was derived to simplify the kinetics equation. To analyze the partial variations of reactor characteristics, two representative methods were introduced in previous studies; (1) quasi-statics method and (2) multipoint technique. The main idea of quasistatics method is to use a low-order approximation for large integration times. To realize the quasi-statics method, first, time dependent flux is separated into the shape and amplitude functions, and shape function is calculated. It is noted that the method has a good accuracy; however, it can be expensive as a calculation cost aspect because the shape function should be fully recalculated to obtain accurate results. To improve the calculation efficiency, multipoint method was proposed. The multipoint method is based on the classic kinetics equation with using Green's function to analyze the flight probability from region r' to r. Those previous methods have been used to analyze the reactor kinetics analysis; however, the previous methods can have some limitations. First, three group variables (r{sub g}, E{sub g}, t{sub g}) should be considered to solve the time dependent balance equation. This leads a big limitation to apply large system problem with good accuracy. Second, the energy group neutrons should be used to analyze reactor kinetics problems. In time dependent problem, neutron energy distribution can be changed at different time. It can affect the change of the group cross section; therefore, it can lead the accuracy problem. Third, the neutrons in a space-time region continually affect the other space-time regions; however, it is not properly considered in the previous method. Using birth history of the

  5. A symbiotic approach to fluid equations and non-linear flux-driven simulations of plasma dynamics

    Science.gov (United States)

    Halpern, Federico

    2017-10-01

    The fluid framework is ubiquitous in studies of plasma transport and stability. Typical forms of the fluid equations are motivated by analytical work dating several decades ago, before computer simulations were indispensable, and can be, therefore, not optimal for numerical computation. We demonstrate a new first-principles approach to obtaining manifestly consistent, skew-symmetric fluid models, ensuring internal consistency and conservation properties even in discrete form. Mass, kinetic, and internal energy become quadratic (and always positive) invariants of the system. The model lends itself to a robust, straightforward discretization scheme with inherent non-linear stability. A simpler, drift-ordered form of the equations is obtained, and first results of their numerical implementation as a binary framework for bulk-fluid global plasma simulations are demonstrated. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, Theory Program, under Award No. DE-FG02-95ER54309.

  6. Regular and chaotic behaviors of plasma oscillations modeled by a modified Duffing equation

    International Nuclear Information System (INIS)

    Enjieu Kadji, H.G.; Chabi Orou, J.B.; Woafo, P.; Abdus Salam International Centre for Theoretical Physics, Trieste

    2005-07-01

    The regular and chaotic behavior of plasma oscillations governed by a modified Duffing equation is studied. The plasma oscillations are described by a nonlinear differential equation of the form x + w 0 2 x + βx 2 + αx 3 = 0 which is similar to a Duffing equation. By focusing on the quadratic term, which is mainly the term modifying the Duffing equation, the harmonic balance method and the fourth order Runge-Kutta algorithm are used to derive regular and chaotic motions respectively. A strong chaotic behavior exhibited by the system in that event when the system is subjected to an external periodic forcing oscillation is reported as β varies. (author)

  7. Transition from gas to plasma kinetic equilibria in gravitating axisymmetric structures

    International Nuclear Information System (INIS)

    Cremaschini, Claudio; Stuchlík, Zdeněk

    2014-01-01

    The problem of the transition from gas to plasma in gravitating axisymmetric structures is addressed under the assumption of having initial and final states realized by kinetic Maxwellian-like equilibria. In astrophysics, the theory applies to accretion-disc scenarios around compact objects. A formulation based on non-relativistic kinetic theory for collisionless systems is adopted. Equilibrium solutions for the kinetic distribution functions describing the initial neutral matter and the resulting plasma state are constructed in terms of single-particle invariants and expressed by generalized Maxwellian distributions. The final plasma configuration is related to the initial gas distribution by the introduction of appropriate functional constraints. Qualitative aspects of the solution are investigated and physical properties of the system are pointed out. In particular, the admitted functional dependences of the fluid fields carried by the corresponding equilibrium distributions are determined. Then, the plasma is proved to violate the condition of quasi-neutrality, implying a net charge separation between ions and electrons. This result is shown to be independent of the precise realization of the plasma distribution function, while a physical mechanism able to support a non-neutral equilibrium state is proposed

  8. Transition from gas to plasma kinetic equilibria in gravitating axisymmetric structures

    Energy Technology Data Exchange (ETDEWEB)

    Cremaschini, Claudio; Stuchlík, Zdeněk [Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám.13, CZ-74601 Opava (Czech Republic)

    2014-04-15

    The problem of the transition from gas to plasma in gravitating axisymmetric structures is addressed under the assumption of having initial and final states realized by kinetic Maxwellian-like equilibria. In astrophysics, the theory applies to accretion-disc scenarios around compact objects. A formulation based on non-relativistic kinetic theory for collisionless systems is adopted. Equilibrium solutions for the kinetic distribution functions describing the initial neutral matter and the resulting plasma state are constructed in terms of single-particle invariants and expressed by generalized Maxwellian distributions. The final plasma configuration is related to the initial gas distribution by the introduction of appropriate functional constraints. Qualitative aspects of the solution are investigated and physical properties of the system are pointed out. In particular, the admitted functional dependences of the fluid fields carried by the corresponding equilibrium distributions are determined. Then, the plasma is proved to violate the condition of quasi-neutrality, implying a net charge separation between ions and electrons. This result is shown to be independent of the precise realization of the plasma distribution function, while a physical mechanism able to support a non-neutral equilibrium state is proposed.

  9. Collaborative Research: A Model of Partially Ionized Plasma Flows with Kinetic Treatment of Neutral Atoms and Nonthermal Ions

    International Nuclear Information System (INIS)

    Pogorelov, Nikolai; Zhang, Ming

    2016-01-01

    Interactions of flows of partially ionized, magnetized plasma are frequently accompanied by the presence of both thermal and non-thermal (pickup) ion components. Such interactions cannot be modeled using traditional MHD equations and require more advanced approaches to treat them. If a nonthermal component of ions is formed due to charge exchange and collisions between the thermal (core) ions and neutrals, it experiences the action of magnetic field, its distribution function is isotropized, and it soon acquires the velocity of the ambient plasma without being thermodynamically equilibrated. This situation, e. g., takes place in the outer heliosphere -- the part of interstellar space beyond the solar system whose properties are determined by the solar wind interaction with the local interstellar medium. This is also possible in laboratory, at million degrees and above, when plasma is conducting electricity far too well, which makes Ohmic heating ineffective. To attain the target temperatures one needs additional heating eventually playing a dominant role. Among such sources is a so-called neutral particle beam heating. This is a wide-spread technique (Joint European Torus and International Thermonuclear Experimental Reactor experiments) based on the injection of powerful beams of neutral atoms into ohmically preheated plasma. In this project we have investigated the energy and density separation between the thermal and nonthermal components in the solar wind and interstellar plasmas. A new model has been developed in which we solve the ideal MHD equations for mixture of all ions and the kinetic Boltzmann equation to describe the transport of neutral atoms. As a separate capability, we can treat the flow of neutral atoms in a multi-component fashion, where neutral atoms born in each thermodynamically distinct region are governed by the Euler gas dynamic equations. We also describe the behavior of pickup ions either kinetically, using the Fokker--Planck equation, or

  10. Collaborative Research: A Model of Partially Ionized Plasma Flows with Kinetic Treatment of Neutral Atoms and Nonthermal Ions

    Energy Technology Data Exchange (ETDEWEB)

    Pogorelov, Nikolai [Univ. of Alabama, Huntsville, AL (United States); Zhang, Ming [Florida Inst. of Technology, Melbourne, FL (United States)

    2016-07-31

    Interactions of flows of partially ionized, magnetized plasma are frequently accompanied by the presence of both thermal and non-thermal (pickup) ion components. Such interactions cannot be modeled using traditional MHD equations and require more advanced approaches to treat them. If a nonthermal component of ions is formed due to charge exchange and collisions between the thermal (core) ions and neutrals, it experiences the action of magnetic field, its distribution function is isotropized, and it soon acquires the velocity of the ambient plasma without being thermodynamically equilibrated. This situation, e. g., takes place in the outer heliosphere –- the part of interstellar space beyond the solar system whose properties are determined by the solar wind interaction with the local interstellar medium. This is also possible in laboratory, at million degrees and above, when plasma is conducting electricity far too well, which makes Ohmic heating ineffective. To attain the target temperatures one needs additional heating eventually playing a dominant role. Among such sources is a so-called neutral particle beam heating. This is a wide-spread technique (Joint European Torus and International Thermonuclear Experimental Reactor experiments) based on the injection of powerful beams of neutral atoms into ohmically preheated plasma. In this project we have investigated the energy and density separation between the thermal and nonthermal components in the solar wind and interstellar plasmas. A new model has been developed in which we solve the ideal MHD equations for mixture of all ions and the kinetic Boltzmann equation to describe the transport of neutral atoms. As a separate capability, we can treat the flow of neutral atoms in a multi-component fashion, where neutral atoms born in each thermodynamically distinct region are governed by the Euler gas dynamic equations. We also describe the behavior of pickup ions either kinetically, using the Fokker--Planck equation

  11. Collaborative Research: A Model of Partially Ionized Plasma Flows with Kinetic Treatment of Neutral Atoms and Nonthermal Ions

    Energy Technology Data Exchange (ETDEWEB)

    Pogorelov, Nikolai [Univ. of Alabama, Huntsville, AL (United States). Dept. of Space Science. Center for Space Plasma and; Zhang, Ming [Florida Inst. of Technology, Melbourne, FL (United States). Physics and Space Sciences Dept.; Borovikov, Sergey [Univ. of Alabama, Huntsville, AL (United States). Dept. of Space Science. Center for Space Plasma and Aeronomic Research; Heerikhuisen, Jacob [Univ. of Alabama, Huntsville, AL (United States). Dept. of Space Science. Center for Space Plasma and Aeronomic Research; Zank, Gary [Univ. of Alabama, Huntsville, AL (United States). Dept. of Space Science. Center for Space Plasma and Aeronomic Research; Gamayunov, Konstantin [Florida Inst. of Technology, Melbourne, FL (United States). Physics and Space Sciences Dept.; Colella, Phillip [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

    2016-07-31

    Interactions of flows of partially ionized, magnetized plasma are frequently accompanied by the presence of both thermal and non-thermal (pickup) ion components. Such interactions cannot be modeled using traditional MHD equations and require more advanced approaches to treat them. If a nonthermal component of ions is formed due to charge exchange and collisions between the thermal (core) ions and neutrals, it experiences the action of magnetic field, its distribution function is isotropized, and it soon acquires the velocity of the ambient plasma without being thermodynamically equilibrated. This situation, e. g., takes place in the outer heliosphere - the part of interstellar space beyond the solar system whose properties are determined by the solar wind interaction with the local interstellar medium. This is also possible in laboratory, at million degrees and above, when plasma is conducting electricity far too well, which makes Ohmic heating ineffective. To attain the target temperatures one needs additional heating eventually playing a dominant role. Among such sources is a so-called neutral particle beam heating. This is a wide-spread technique (Joint European Torus and International Thermonuclear Experimental Reactor experiments) based on the injection of powerful beams of neutral atoms into ohmically preheated plasma. In this project we have investigated the energy and density separation between the thermal and nonthermal components in the solar wind and interstellar plasmas. A new model has been developed in which we solve the ideal MHD equations for mixture of all ions and the kinetic Boltzmann equation to describe the transport of neutral atoms. As a separate capability, we can treat the flow of neutral atoms in a multi-component fashion, where neutral atoms born in each thermodynamically distinct regions are governed by the Euler gas dynamic equations. We also describe the behavior of pickup ions either kinetically, using the Fokker–Planck equation, or

  12. Stochastic substitute for coupled rate equations in the modeling of highly ionized transient plasmas

    International Nuclear Information System (INIS)

    Eliezer, S.; Falquina, R.; Minguez, E.

    1994-01-01

    Plasmas produced by intense laser pulses incident on solid targets often do not satisfy the conditions for local thermodynamic equilibrium, and so cannot be modeled by transport equations relying on equations of state. A proper description involves an excessively large number of coupled rate equations connecting many quantum states of numerous species having different degrees of ionization. Here we pursue a recent suggestion to model the plasma by a few dominant states perturbed by a stochastic driving force. The driving force is taken to be a Poisson impulse process, giving a Langevin equation which is equivalent to a Fokker-Planck equation for the probability density governing the distribution of electron density. An approximate solution to the Langevin equation permits calculation of the characteristic relaxation rate. An exact stationary solution to the Fokker-Planck equation is given as a function of the strength of the stochastic driving force. This stationary solution is used, along with a Laplace transform, to convert the Fokker-Planck equation to one of Schroedinger type. We consider using the classical Hamiltonian formalism and the WKB method to obtain the time-dependent solution

  13. Vlasov equation for photons and quasi-particles in a plasma

    International Nuclear Information System (INIS)

    Mendonca, J.T.

    2014-01-01

    We show that, in quite general conditions, a Vlasov equation can be derived for photons in a medium. The same is true for other quasi-particles, such as plasmons, phonons or driftons, associated with other wave modes in a plasma. The range of validity of this equation is discussed. We also discuss the Landau resonance, and its relation with photon acceleration. Exact and approximate expressions for photon and quasi-particle Landau damping are stated. Photon and quasi-particle acceleration and trapping is also discussed. Specific applications to laser-plasma interaction, and to magnetic fusion turbulence, are considered as illustrations of the general approach. (author)

  14. Plasma kinetic effects on atomistic mix in one dimension and at structured interfaces (II)

    Science.gov (United States)

    Albright, Brian; Yin, Lin; Cooley, James; Haack, Jeffrey; Douglas, Melissa

    2017-10-01

    The Marble campaign seeks to develop a platform for studying mix evolution in turbulent, inhomogeneous, high-energy-density plasmas at the NIF. Marble capsules contain engineered CD foams, the pores of which are filled with hydrogen and tritium. During implosion, hydrodynamic stirring and plasma diffusivity mix tritium fuel into the surrounding CD plasma, leading to both DD and DT fusion neutron production. In this presentation, building upon prior work, kinetic particle-in-cell simulations using the VPIC code are used to examine kinetic effects on thermonuclear burn in Marble-like settings. Departures from Maxwellian distributions are observed near the interface and TN burn rates and inferred temperatures from synthetic neutron time of flight diagnostics are compared with those from treating the background species as Maxwellian. Work performed under the auspices of the U.S. DOE by the Los Alamos National Security, LLC Los Alamos National Laboratory and supported by the ASC and Science programs.

  15. Tracer kinetics: Modelling by partial differential equations of inhomogeneous compartments with age-dependent elimination rates. Pt. 1

    International Nuclear Information System (INIS)

    Winkler, E.

    1991-01-01

    Mathematical models in tracer kinetics are usually based on ordinary differential equations which correspond to a system of kinetically homogeneous compartments (standard compartments). A generalization is possible by the admission of inhomogeneities in the behaviour of the elements belonging to a compartment. The important special case of the age-dependence of elimination rates is treated in its deterministic version. It leads to partial different equations (i.e., systems with distributed coefficients) with the 'age' or the 'residence time' of an element of the compartment as a variable additional to 'time'. The basic equations for one generalized compartment and for systems of such compartments are given together with their general solutions. (orig.) [de

  16. Evaluation of Lagergren Kinetics Equation by Using Novel Kinetics Expression of Sorption of Zn2+ onto Horse Dung Humic Acid (HD-HA

    Directory of Open Access Journals (Sweden)

    Bambang Rusdiarso

    2016-12-01

    Full Text Available Extraction and purification of humic acid from dry horse dung powder (HD-HA was performed successfully and the purified HD-HA was then applied as sorbent to adsorb Zn2+. Extraction and purification were performed based on procedure of Stevenson (1994 under atmospheric air. Parameters investigated in this work consist of effect of medium sorption acidity, sorption rate (ka and desorption rate constant (kd, Langmuir (monolayer and Freundlich (multilayer sorption capacities, and energy (E of sorption. The ka and kd were determined according to the kinetic model of second order sorption reaching equilibrium, monolayer sorption capacity (b and energy (E were determined according to Langmuir isotherm model, and multilayer sorption capacity (B was determined based on Freundlich isotherm model. Sorption of Zn2+ on purified HD-HA was maximum at pH 5.0. The novel kinetic expression resulted from proposed kinetic model has been shown to be more applicable than the commonly known Lagergren equation obtained from the pseudo-first order sorption model. The application of the equation revealed that the intercept of Lagergren equation, ln qe was more complex function of initial concentration of Zn2+ (a, Langmuir sorption capacity (b, and sorbed Zn2+ at equilibrium (xe.

  17. Derivation of stochastic differential equations for scrape-off layer plasma fluctuations from experimentally measured statistics

    Energy Technology Data Exchange (ETDEWEB)

    Mekkaoui, Abdessamad [IEK-4 Forschungszentrum Juelich 52428 (Germany)

    2013-07-01

    A method to derive stochastic differential equations for intermittent plasma density dynamics in magnetic fusion edge plasma is presented. It uses a measured first four moments (mean, variance, Skewness and Kurtosis) and the correlation time of turbulence to write a Pearson equation for the probability distribution function of fluctuations. The Fokker-Planck equation is then used to derive a Langevin equation for the plasma density fluctuations. A theoretical expectations are used as a constraints to fix the nonlinearity structure of the stochastic differential equation. In particular when the quadratically nonlinear dynamics is assumed, then it is shown that the plasma density is driven by a multiplicative Wiener process and evolves on the turbulence correlation time scale, while the linear growth is quadratically damped by the fluctuation level. Strong criteria for statistical discrimination of experimental time series are proposed as an alternative to the Kurtosis-Skewness scaling. This scaling is broadly used in contemporary literature to characterize edge turbulence, but it is inappropriate because a large family of distributions could share this scaling. Strong criteria allow us to focus on the relevant candidate distribution and approach a nonlinear structure of edge turbulence model.

  18. Thermodynamic derivation of Saha's equation for a multi-temperature plasma

    International Nuclear Information System (INIS)

    Morro, Angelo; Romeo, Maurizio

    1988-01-01

    The ionization equilibrium between the constituents of a multi-temperature plasma is investigated within the thermodynamics of fluid mixtures. As a result, a law of mass action is derived that, in the approximation of ideal gases for the constituents, leads to a direct generalization of Saha's equation. The main properties of this generalization are discussed, and contrasted with those of other equations which have appeared in the literature. (author)

  19. Kinetics in Gas Mixtures for Problem of Plasma Assisted Combustion

    Science.gov (United States)

    2010-05-01

    precautions: in the case of relatively low elec- tron density, as it is realized for N2 or for O2, non–zero background due to accumulation of residual electron...and Lave L B 2003 Evaluating automobile fuel/propulsion system technologies Progress in Energy and Combustion Science 29 (2003) 1--69 [11] Polak L S...43 79—110 [41] Janev R K and Reiter D 2004 Collision processes of C2,3Hy and C2,3H + y hydrocarbons with electrons and protons Phys. Plasmas 11 780—829

  20. Two dimensional kinetic analysis of electrostatic harmonic plasma waves

    Energy Technology Data Exchange (ETDEWEB)

    Fonseca-Pongutá, E. C.; Ziebell, L. F.; Gaelzer, R. [Instituto de Física, UFRGS, 91501-970 Porto Alegre, RS (Brazil); Yoon, P. H. [IPST, University of Maryland, College Park, Maryland 20742 (United States); SSR, Kyung Hee University, Yongin, Gyeonggi 446-701 (Korea, Republic of)

    2016-06-15

    Electrostatic harmonic Langmuir waves are virtual modes excited in weakly turbulent plasmas, first observed in early laboratory beam-plasma experiments as well as in rocket-borne active experiments in space. However, their unequivocal presence was confirmed through computer simulated experiments and subsequently theoretically explained. The peculiarity of harmonic Langmuir waves is that while their existence requires nonlinear response, their excitation mechanism and subsequent early time evolution are governed by essentially linear process. One of the unresolved theoretical issues regards the role of nonlinear wave-particle interaction process over longer evolution time period. Another outstanding issue is that existing theories for these modes are limited to one-dimensional space. The present paper carries out two dimensional theoretical analysis of fundamental and (first) harmonic Langmuir waves for the first time. The result shows that harmonic Langmuir wave is essentially governed by (quasi)linear process and that nonlinear wave-particle interaction plays no significant role in the time evolution of the wave spectrum. The numerical solutions of the two-dimensional wave spectra for fundamental and harmonic Langmuir waves are also found to be consistent with those obtained by direct particle-in-cell simulation method reported in the literature.

  1. Analytic method study of point-reactor kinetic equation when cold start-up

    International Nuclear Information System (INIS)

    Zhang Fan; Chen Wenzhen; Gui Xuewen

    2008-01-01

    The reactor cold start-up is a process of inserting reactivity by lifting control rod discontinuously. Inserting too much reactivity will cause short-period and may cause an overpressure accident in the primary loop. It is therefore very important to understand the rule of neutron density variation and to find out the relationships among the speed of lifting control rod, and the duration and speed of neutron density response. It is also helpful for the operators to grasp the rule in order to avoid a start-up accident. This paper starts with one-group delayed neutron point-reactor kinetics equations and provides their analytic solution when reactivity is introduced by lifting control rods discontinuously. The analytic expression is validated by comparison with practical data. It is shown that the analytic solution agrees well with numerical solution. Using this analytical solution, the relationships among neutron density response with the speed of lifting control rod and its duration are also studied. By comparing the results with those under the condition of step inserted reactivity, useful conclusions are drawn

  2. Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation

    Science.gov (United States)

    Yang, Jaw-Yen; Yan, Chin-Yuan; Huang, Juan-Chen; Li, Zhihui

    2014-01-01

    Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidal-statistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied. PMID:25104904

  3. Equations for the non linear evolution of the resistive tearing modes in toroidal plasmas

    International Nuclear Information System (INIS)

    Edery, D.; Pellat, R.; Soule, J.L.

    1979-09-01

    Following the tokamak ordering, we simplify the resistive MHD equations in toroidal geometry. We obtain a closed system of non linear equations for two scalar potentials of the magnetic and velocity fields and for plasma density and temperature. If we expand these equations in the inverse of aspect ratio they are exact to the two first orders. Our formalism should correctly describe the mode coupling by curvature effects /1/ and the toroidal displacement of magnetic surfaces /2/. It provides a natural extension of the well known cylindrical model /3/ and is now being solved on computer

  4. Effects of feeding on the plasma disposition kinetics of the anthelmintic albendazole in laying hens.

    Science.gov (United States)

    Bistoletti, M; Alvarez, L; Lanusse, C; Moreno, L

    2014-01-01

    1. To optimise the use of albendazole (ABZ) as an anthelmintic in hens, the effects of fasting and type of diet on the plasma kinetics of ABZ and its metabolites were evaluated. 2. Twenty-four hens were distributed into 4 groups: In experiment I the Fed group were fed ad libitum, while the Fasted group was fasted over a 12-h period. In experiment II the Pelleted group was fed with pelleted commercial food, while the Grain group was fed with cereal grains. All the groups were treated with ABZ by oral route. Blood samples were taken and plasma analysed by HPLC. 3. ABZ and its metabolites albendazole-sulphoxide (ABZSO) and albendazole-sulphone (ABZSO2) were recovered in plasma in all the groups. The 12-h fasting period did not modify the disposition kinetics of ABZ in hens. The type of feed affected ABZ kinetics. ABZSO concentration profile was higher and detected for longer in the Grain group compared to the Pelleted group. Statistical differences were not found for AUC0-∞ values, whereas the T1/2for and T1/2el were different between groups. 4. Factors affecting ABZ kinetic behaviour should be taken into account to optimise its use to ensure the sustainability of the limited available anthelmintic therapeutic tools in avian parasite control.

  5. Kinetic mechanism of plasma-assisted ignition of hydrocarbons

    International Nuclear Information System (INIS)

    Kosarev, I N; Aleksandrov, N L; Kindysheva, S V; Starikovskaia, S M; Starikovskii, A Yu

    2008-01-01

    Ignition of hydrocarbon-containing gaseous mixtures has been studied experimentally and numerically under the action of a high-voltage nanosecond discharge at elevated temperatures. Ignition delay times were measured behind a reflected shock wave in stoichiometric C n H 2n+2 : O 2 mixtures (10%) diluted with Ar (90%) for n = 1-5. It was shown that the application of the gas discharge leads to more than an order of magnitude decrease in ignition delay time for all hydrocarbons under consideration. The measured values of ignition delay time agree well with the results of a numerical simulation of the ignition based on the calculation of atom and radical production during the discharge and in its afterglow. The analysis of simulation results showed that a non-equilibrium plasma favours the ignition mainly due to O atoms produced in the active phase of the discharge. (fast track communication)

  6. Nonlinear particle-wave kinetics in weakly unstable plasmas

    International Nuclear Information System (INIS)

    Breizman, B.N.; Berk, H.L.; Pekker, M.S.

    1996-01-01

    With the motivation to address the behavior of the fusion produced alpha particles in a thermonuclear reactor, a theory is developed for predicting the wave saturation levels and particle transport in weakly unstable systems with a discrete number of modes in the presence of energetic particle sources and sinks. Conditions are established for either steady state or bursting nonlinear scenarios when several modes are excited for cases where there is and there is not resonance overlap. Depending on parameters, the particles can undergo benign relaxation, with only a small fraction of the available free energy released to waves and with no global transport, or the particles can experience rapid global transport caused by a substantial conversion of their free energy into wave energy. When the resonance condition of the particle-wave interaction is varied adiabatically, the particles trapped in a wave are found to form phase space holes or clumps that enhance the particle-wave energy exchange. This mechanism, which has been experimentally observed when there is frequency chirping, causes increased saturation levels of instabilities. If resonance sweeping is imposed externally, the particle free energy can even be tapped in stable systems where background dissipation suppresses linear instability. Externally applied resonance sweeping can be important for alpha particle energy channeling, as well as for understanding fishbone and some Alfven wave instability experiments. Near instability threshold, that is when the destabilizing drive just exceeds the background dissipation, a more sophisticated analysis is developed to predict the correct saturation. To leading order, this problem reduces to an integral equation for the wave amplitude with a temporally non local cubic term. This equation has a self-similar solution that blows-up in a finite time

  7. A high-order method for the integration of the Galerkin semi-discretized nuclear reactor kinetics equations

    International Nuclear Information System (INIS)

    Vargas, L.

    1988-01-01

    The numerical approximate solution of the space-time nuclear reactor kinetics equation is investigated using a finite-element discretization of the space variable and a high order integration scheme for the resulting semi-discretized parabolic equation. The Galerkin method with spatial piecewise polynomial Lagrange basis functions are used to obtained a continuous time semi-discretized form of the space-time reactor kinetics equation. A temporal discretization is then carried out with a numerical scheme based on the Iterated Defect Correction (IDC) method using piecewise quadratic polynomials or exponential functions. The kinetics equations are thus solved with in a general finite element framework with respect to space as well as time variables in which the order of convergence of the spatial and temporal discretizations is consistently high. A computer code GALFEM/IDC is developed, to implement the numerical schemes described above. This issued to solve a one space dimensional benchmark problem. The results of the numerical experiments confirm the theoretical arguments and show that the convergence is very fast and the overall procedure is quite efficient. This is due to the good asymptotic properties of the numerical scheme which is of third order in the time interval

  8. (KP) equation in warm dusty plasma with variable dust charge, two ...

    Indian Academy of Sciences (India)

    In this work, the propagation of nonlinear waves in warm dusty plasmas with variable dust charge, two-temperature ion and nonthermal electron is studied. By using the reductive perturbation theory, the Kadomstev–Petviashvili (KP) equation is derived. The energy of the soliton and the linear dispersion relation are obtained ...

  9. Study of scattering cross section of a plasma column using Green's function volume integral equation method

    Science.gov (United States)

    Soltanmoradi, Elmira; Shokri, Babak

    2017-05-01

    In this article, the electromagnetic wave scattering from plasma columns with inhomogeneous electron density distribution is studied by the Green's function volume integral equation method. Due to the ready production of such plasmas in the laboratories and their practical application in various technological fields, this study tries to find the effects of plasma parameters such as the electron density, radius, and pressure on the scattering cross-section of a plasma column. Moreover, the incident wave frequency influence of the scattering pattern is demonstrated. Furthermore, the scattering cross-section of a plasma column with an inhomogeneous collision frequency profile is calculated and the effect of this inhomogeneity is discussed first in this article. These results are especially used to determine the appropriate conditions for radar cross-section reduction purposes. It is shown that the radar cross-section of a plasma column reduces more for a larger collision frequency, for a relatively lower plasma frequency, and also for a smaller radius. Furthermore, it is found that the effect of the electron density on the scattering cross-section is more obvious in comparison with the effect of other plasma parameters. Also, the plasma column with homogenous collision frequency can be used as a better shielding in contrast to its inhomogeneous counterpart.

  10. A conservative finite difference method for the numerical solution of plasma fluid equations

    International Nuclear Information System (INIS)

    Colella, P.; Dorr, M.R.; Wake, D.D.

    1999-01-01

    This paper describes a numerical method for the solution of a system of plasma fluid equations. The fluid model is similar to those employed in the simulation of high-density, low-pressure plasmas used in semiconductor processing. The governing equations consist of a drift-diffusion model of the electrons, together with an internal energy equation, coupled via Poisson's equation to a system of Euler equations for each ion species augmented with electrostatic force, collisional, and source/sink terms. The time integration of the full system is performed using an operator splitting that conserves space charge and avoids dielectric relaxation timestep restrictions. The integration of the individual ion species and electrons within the time-split advancement is achieved using a second-order Godunov discretization of the hyperbolic terms, modified to account for the significant role of the electric field in the propagation of acoustic waves, combined with a backward Euler discretization of the parabolic terms. Discrete boundary conditions are employed to accommodate the plasma sheath boundary layer on underresolved grids. The algorithm is described for the case of a single Cartesian grid as the first step toward an implementation on a locally refined grid hierarchy in which the method presented here may be applied on each refinement level

  11. Electromagnetic theory of plasma light scattering

    International Nuclear Information System (INIS)

    Bobin, J.L.

    1969-01-01

    The theory of light scattering by a plasma is formulated using Klimontovich's microscopic distribution functions and Landau method to solve linear kinetic equations. First, Salpeter's derivation and results are given for the spectrum of light scattered by a collisionless plasma. Then, the influence of collision is investigated through B.G.K. kinetic equation. (author) [fr

  12. A simplified model for computing equation of state of argon plasma

    International Nuclear Information System (INIS)

    Wang Caixia; Tian Yangmeng

    2006-01-01

    The paper present a simplified new model of computing equation of state and ionization degree of Argon plasma, which based on Thomas-Fermi (TF) statistical model: the authors fitted the numerical results of the ionization potential calculated by Thomas-Fermi statistical model and gained the analytical function of the potential versus the degree of ionization, then calculated the ionization potential and the average degree of ionization for Argon versus temperature and density in local thermal equilibrium case at 10-1000 eV. The results calculated of this simplified model are basically in agreement with several sets of theory data and experimental data. This simplified model can be used to calculation of the equation of state of plasmas mixture and is expected to have a more wide use in the field of EML technology involving the strongly ionized plasmas. (authors)

  13. Plasma surface functionalization and dyeing kinetics of Pan-Pmma copolymers

    Science.gov (United States)

    Labay, C.; Canal, C.; Rodríguez, C.; Caballero, G.; Canal, J. M.

    2013-10-01

    Fiber surface modification with air corona plasma has been studied through dyeing kinetics under isothermal conditions at 30 °C on an acrylic-fiber fabric with a cationic dye (CI Basic Blue 3) analyzing the absorption, desorption and fixing on the surface of molecules having defined cationic character. The initial dyeing rate in the first 60 s indicates an increase of 58.3% in the dyeing rate due to the effect of corona plasma on the acrylic fiber surface. At the end of the dyeing process, the plasma-treated fabrics absorb 24.7% more dye, and the K/S value of the acrylic fabric increases by 8.8%. With selected dyestuff molecules, new techniques can be designed to amplify the knowledge about plasma-treated surface modifications of macromolecules.

  14. Kinetic Simulations of Plasma Energization and Particle Acceleration in Interacting Magnetic Flux Ropes

    Science.gov (United States)

    Du, S.; Guo, F.; Zank, G. P.; Li, X.; Stanier, A.

    2017-12-01

    The interaction between magnetic flux ropes has been suggested as a process that leads to efficient plasma energization and particle acceleration (e.g., Drake et al. 2013; Zank et al. 2014). However, the underlying plasma dynamics and acceleration mechanisms are subject to examination of numerical simulations. As a first step of this effort, we carry out 2D fully kinetic simulations using the VPIC code to study the plasma energization and particle acceleration during coalescence of two magnetic flux ropes. Our analysis shows that the reconnection electric field and compression effect are important in plasma energization. The results may help understand the energization process associated with magnetic flux ropes frequently observed in the solar wind near the heliospheric current sheet.

  15. Numerical study of drift-kinetic evolution of collisional plasmas in tori

    International Nuclear Information System (INIS)

    Beasley, C.O. Jr.; Meier, H.K.; van Rij, W.I.; McCune, J.E.

    1976-03-01

    Preliminary numerical results for the dynamics of toroidally confined plasmas in the drift-kinetic, Fokker--Planck description are discussed. These solutions were obtained by using the techniques inherent to the collisional plasma model (CPM) described in detail elsewhere. An initial value problem is solved in the local approximation in which collisions and particle dynamics compete in a given magnetic field to set up a quasi-equilibrium. Both the plasma (guiding center) distribution function and many macroscopic quantities of interest are monitored. Good agreement with corresponding but more approximate theories is obtained over a wide range of collisionality, particularly with regard to the neoclassical particle flux. Encouraging confirmation of earlier results for the distribution function is achieved when due account is taken of the differing collisionality of particles with differing energies. These initial results indicate the potential importance of certain non-local effects as well as inclusion of self-consistency between fields and plasma currents and densities

  16. Kinetic models of partially ionized complex plasmas in the low frequency regime

    International Nuclear Information System (INIS)

    Tolias, P.; Ratynskaia, S.; Angelis, U. de

    2011-01-01

    The results from three kinetic models of complex plasmas taking into account collisions with neutrals are compared in the low-frequency regime: The ''full'' model which considers the absorption of plasma fluxes on dust particles and dust charge fluctuations, the ''multi-component'' model where both these effects are neglected, and the ''standard'' model which takes into account the dust charge perturbations but not the absorption of fluxes. We derive and numerically evaluate expressions of the low frequency responses of these models, also taking into account the modification of the capture cross-sections due to the effect of neutrals. The role of plasma sources and collisions with neutrals is assessed by computing the plasma permittivities and static permittivities for all the three models.

  17. Plasma adrenaline kinetics in type 1 (insulin-dependent) diabetic patients with and without autonomic neuropathy

    DEFF Research Database (Denmark)

    Dejgaard, A; Hilsted, J; Henriksen, Jens Henrik Sahl

    1989-01-01

    Plasma adrenaline kinetics (clearance, extraction across the forearm, initial plasma disappearance rate, mean sojourn time, volume of distribution) were studied in sixteen Type 1 (insulin-dependent) diabetic patients during constant i.v. infusion of tritium labelled adrenaline. In patients with (n...... = 8) and without (n = 8) neuropathy forearm venous plasma noradrenaline and adrenaline concentrations as well as plasma clearance of adrenaline based on arterial sampling (1.7 vs 2.1 l/min) were not significantly different. The initial disappearance time (T 1/2) after the infusion of the tritium...... labelled adrenaline had been stopped was significantly prolonged in Type 1 diabetic patients with neuropathy compared to those without (after 20 min infusion 2.7 vs 2.2 min, p less than 0.02, after 75 min infusion 3.7 vs 2.9 min, p less than 0.05). The corresponding values for the mean sojourn time...

  18. An asymptotic preserving unified gas kinetic scheme for frequency-dependent radiative transfer equations

    Energy Technology Data Exchange (ETDEWEB)

    Sun, Wenjun, E-mail: sun_wenjun@iapcm.ac.cn [Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088 (China); Jiang, Song, E-mail: jiang@iapcm.ac.cn [Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088 (China); Xu, Kun, E-mail: makxu@ust.hk [Department of Mathematics and Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Hong Kong (China); Li, Shu, E-mail: li_shu@iapcm.ac.cn [Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088 (China)

    2015-12-01

    This paper presents an extension of previous work (Sun et al., 2015 [22]) of the unified gas kinetic scheme (UGKS) for the gray radiative transfer equations to the frequency-dependent (multi-group) radiative transfer system. Different from the gray radiative transfer equations, where the optical opacity is only a function of local material temperature, the simulation of frequency-dependent radiative transfer is associated with additional difficulties from the frequency-dependent opacity. For the multiple frequency radiation, the opacity depends on both the spatial location and the frequency. For example, the opacity is typically a decreasing function of frequency. At the same spatial region the transport physics can be optically thick for the low frequency photons, and optically thin for high frequency ones. Therefore, the optical thickness is not a simple function of space location. In this paper, the UGKS for frequency-dependent radiative system is developed. The UGKS is a finite volume method and the transport physics is modeled according to the ratio of the cell size to the photon's frequency-dependent mean free path. When the cell size is much larger than the photon's mean free path, a diffusion solution for such a frequency radiation will be obtained. On the other hand, when the cell size is much smaller than the photon's mean free path, a free transport mechanism will be recovered. In the regime between the above two limits, with the variation of the ratio between the local cell size and photon's mean free path, the UGKS provides a smooth transition in the physical and frequency space to capture the corresponding transport physics accurately. The seemingly straightforward extension of the UGKS from the gray to multiple frequency radiation system is due to its intrinsic consistent multiple scale transport modeling, but it still involves lots of work to properly discretize the multiple groups in order to design an asymptotic preserving (AP

  19. Kinetic and Diagnostic Studies of Molecular Plasmas Using Laser Absorption Techniques

    International Nuclear Information System (INIS)

    Welzel, S; Rousseau, A; Davies, P B; Roepcke, J

    2007-01-01

    Within the last decade mid infrared absorption spectroscopy between 3 and 20 μm, known as Infrared Laser Absorption Spectroscopy (IRLAS) and based on tuneable semiconductor lasers, namely lead salt diode lasers, often called tuneable diode lasers (TDL), and quantum cascade lasers (QCL) has progressed considerably as a powerful diagnostic technique for in situ studies of the fundamental physics and chemistry of molecular plasmas. The increasing interest in processing plasmas containing hydrocarbons, fluorocarbons, organo-silicon and boron compounds has lead to further applications of IRLAS because most of these compounds and their decomposition products are infrared active. IRLAS provides a means of determining the absolute concentrations of the ground states of stable and transient molecular species, which is of particular importance for the investigation of reaction kinetics. Information about gas temperature and population densities can also be derived from IRLAS measurements. A variety of free radicals and molecular ions have been detected, especially using TDLs. Since plasmas with molecular feed gases are used in many applications such as thin film deposition, semiconductor processing, surface activation and cleaning, and materials and waste treatment, this has stimulated the adaptation of infrared spectroscopic techniques to industrial requirements. The recent development of QCLs offers an attractive new option for the monitoring and control of industrial plasma processes as well as for highly time-resolved studies on the kinetics of plasma processes. The aim of the present article is threefold: (i) to review recent achievements in our understanding of molecular phenomena in plasmas (ii) to report on selected studies of the spectroscopic properties and kinetic behaviour of radicals, and (iii) to describe the current status of advanced instrumentation for TDLAS in the mid infrared

  20. Transformation kinetics in plasma-sprayed barium- and strontium-doped aluminosilicate (BSAS)

    International Nuclear Information System (INIS)

    Harder, B.J.; Faber, K.T.

    2010-01-01

    The hexacelsian-to-celsian phase transformation in Ba 1-x Sr x Al 2 Si 2 O 8 is of interest for environmental barrier coating applications. Plasma-sprayed microstructures were heat treated above 1100 o C and the kinetics of the hexacelsian-to-celsian transformation were quantified. Activation energies for bulk and crushed materials were determined to be ∼340 and ∼500 kJ mol -1 , respectively. X-ray diffraction and electron backscattered diffraction were used to establish how plasma spraying barium- and strontium-doped aluminosilicate effectively reduces the energy required for its transformation.

  1. Plasma surface functionalization and dyeing kinetics of Pan-Pmma copolymers

    OpenAIRE

    Labay, C.; Canal, C.; Rodríguez, C.; Caballero, G.; Canal, J.M.

    2013-01-01

    Fiber surface modification with air corona plasma has been studied through dyeing kinetics under isothermal conditions at 30 °C on an acrylic-fiber fabric with a cationic dye (CI Basic Blue 3) analyzing the absorption, desorption and fixing on the surface of molecules having defined cationic character. The initial dyeing rate in the first 60 s indicates an increase of 58.3% in the dyeing rate due to the effect of corona plasma on the acrylic fiber surface. At the end of the dyeing process...

  2. Plasma waves

    CERN Document Server

    Swanson, DG

    1989-01-01

    Plasma Waves discusses the basic development and equations for the many aspects of plasma waves. The book is organized into two major parts, examining both linear and nonlinear plasma waves in the eight chapters it encompasses. After briefly discussing the properties and applications of plasma wave, the book goes on examining the wave types in a cold, magnetized plasma and the general forms of the dispersion relation that characterize the waves and label the various types of solutions. Chapters 3 and 4 analyze the acoustic phenomena through the fluid model of plasma and the kinetic effects. Th

  3. Response to Comment on 'On Higher-Order Corrections to Gyrokinetic Vlasov-Poisson Equations in the Long Wavelength Limit [Phys. Plasmas 16,044506 (2009)]'

    International Nuclear Information System (INIS)

    Lee, W.W.; Kolesnikov, R.A.

    2009-01-01

    We show in this Response that the nonlinear Poisson's equation in our original paper derived from the drift kinetic approach can be verified by using the nonlinear gyrokinetic Poisson's equation of Dubin et al. (Phys. Fluids 26, 3524 (1983)). This nonlinear contribution in φ 2 is indeed of the order of k # perpendicular# 4 in the long wavelength limit and remains finite for zero ion temperature, in contrast to the nonlinear term by Parra and Catto (Plasma Phys. Control. Fusion 50, 065014 (2008)), which is of the order of k # perpendicular# 2 and diverges for T i → 0. For comparison, the leading term for the gyrokinetic Poisson's equation in this limit is of the order of k # perpendicular# 2 φ.

  4. Analytical solution of point kinetics equations for linear reactivity variation during the start-up of a nuclear reactor

    Energy Technology Data Exchange (ETDEWEB)

    Palma, Daniel A.P. [CEFET QUIMICA de Nilopolis/RJ, 21941-914 Rio de Janeiro (Brazil)], E-mail: agoncalves@con.ufrj.br; Martinez, Aquilino S.; Goncalves, Alessandro C. [COPPE/UFRJ - Programa de Engenharia Nuclear, Rio de Janeiro (Brazil)

    2009-09-15

    The analytical solution of point kinetics equations with a group of delayed neutrons is useful in predicting the variation of neutron density during the start-up of a nuclear reactor. In the practical case of an increase of nuclear reactor power resulting from the linear insertion of reactivity, the exact analytical solution cannot be obtained. Approximate solutions have been obtained in previous articles, based on considerations that need to be verifiable in practice. In the present article, an alternative analytic solution is presented for point kinetics equations in which the only approximation consists of disregarding the term of the second derivative for neutron density in relation to time. The results proved satisfactory when applied to practical situations in the start-up of a nuclear reactor through the control rods withdraw.

  5. Analytical solution of point kinetics equations for linear reactivity variation during the start-up of a nuclear reactor

    International Nuclear Information System (INIS)

    Palma, Daniel A.P.; Martinez, Aquilino S.; Goncalves, Alessandro C.

    2009-01-01

    The analytical solution of point kinetics equations with a group of delayed neutrons is useful in predicting the variation of neutron density during the start-up of a nuclear reactor. In the practical case of an increase of nuclear reactor power resulting from the linear insertion of reactivity, the exact analytical solution cannot be obtained. Approximate solutions have been obtained in previous articles, based on considerations that need to be verifiable in practice. In the present article, an alternative analytic solution is presented for point kinetics equations in which the only approximation consists of disregarding the term of the second derivative for neutron density in relation to time. The results proved satisfactory when applied to practical situations in the start-up of a nuclear reactor through the control rods withdraw.

  6. Analysis of atmospheric flow over a surface protrusion using the turbulence kinetic energy equation with reference to aeronautical operating systems

    Science.gov (United States)

    Frost, W.; Harper, W. L.

    1975-01-01

    Flow over surface obstructions can produce significantly large wind shears such that adverse flying conditions can occur for aeronautical systems (helicopters, STOL vehicles, etc.). Atmospheric flow fields resulting from a semi-elliptical surface obstruction in an otherwise horizontally homogeneous statistically stationary flow are modelled with the boundary-layer/Boussinesq-approximation of the governing equation of fluid mechanics. The turbulence kinetic energy equation is used to determine the dissipative effects of turbulent shear on the mean flow. Iso-lines of turbulence kinetic energy and turbulence intensity are plotted in the plane of the flow and highlight regions of high turbulence intensity in the stagnation zone and sharp gradients in intensity along the transition from adverse to favourable pressure gradient. Discussion of the effects of the disturbed wind field in CTOL and STOL aircraft flight path and obstruction clearance standards is given. The results indicate that closer inspection of these presently recommended standards as influenced by wind over irregular terrains is required.

  7. Solution of the two-dimensional space-time reactor kinetics equation by a locally one-dimensional method

    International Nuclear Information System (INIS)

    Chen, G.S.; Christenson, J.M.

    1985-01-01

    In this paper, the authors present some initial results from an investigation of the application of a locally one-dimensional (LOD) finite difference method to the solution of the two-dimensional, two-group reactor kinetics equations. Although the LOD method is relatively well known, it apparently has not been previously applied to the space-time kinetics equations. In this investigation, the LOD results were benchmarked against similar computational results (using the same computing environment, the same programming structure, and the same sample problems) obtained by the TWIGL program. For all of the problems considered, the LOD method provided accurate results in one-half to one-eight of the time required by the TWIGL program

  8. Application of Hill's equation for estimating area under the concentration-time curve (AUC) and use of time to AUC 90% for expressing kinetics of drug disposition.

    Science.gov (United States)

    Cheng, Hsien C

    2009-01-01

    Half life and its derived pharmacokinetic parameters are calculated on an assumption that the terminal phase of drug disposition follows a constant rate of disposition. In reality, this assumption may not necessarily be the case. A new method is needed for analyzing PK parameters if the disposition does not follow a first order PK kinetic. Cumulative area under the concentration-time curve (AUC) is plotted against time to yield a hyperbolic (or sigmoidal) AUC-time relationship curve which is then analyzed by Hill's equation to yield AUC(inf), time to achieving AUC50% (T(AUC50%)) or AUC90% (T(AUC90%)), and the Hill's slope. From these parameters, an AUC-time relationship curve can be reconstructed. Projected plasma concentration can be calculated for any time point. Time at which cumulative AUC reaches 90% (T(AUC90%)) can be used as an indicator for expressing how fast a drug is cleared. Clearance is calculated in a traditional manner (i.v. dose/AUC(inf)), and the volume of distribution is proposed to be calculated at T(AUC50%) (0.5 i.v. dose/plasma concentration at T(AUC50%)). This method of estimating AUC is applicable for both i.v. and oral data. It is concluded that the Hill's equation can be used as an alternative method for estimating AUC and analysis of PK parameters if the disposition does not follow a first order kinetic. T(AUC90%) is proposed to be used as an indicator for expressing how fast a drug is cleared from the system.

  9. Kinetic theory for radiation interacting with sound waves in ultrarelativistic pair plasmas

    International Nuclear Information System (INIS)

    Marklund, Mattias; Shukla, Padma K.; Stenflo, Lennart

    2006-01-01

    A kinetic theory for radiation interacting with sound waves in an ultrarelativistic electron-positron plasma is developed. It is shown that the effect of a spatial spectral broadening of the electromagnetic pulse is to introduce a reduction of the growth rates for the decay and modulational instabilities. Such spectral broadening could be due to a finite pulse coherence length, or through the use of random phase filters, and would stabilize the propagation of electromagnetic pulses

  10. Verification of a three-dimensional neutronics model based on multi-point kinetics equations for transient problems

    Energy Technology Data Exchange (ETDEWEB)

    Park, Kyung Seok; Kim, Hyun Dae; Yeom, Choong Sub [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

    1995-07-01

    A computer code for solving the three-dimensional reactor neutronic transient problems utilizing multi-point reactor kinetics equations recently developed has been developed. For evaluating its applicability, the code has been tested with typical 3-D LWR and CANDU reactor transient problems. The performance of the method and code has been compared with the results by fine and coarse meshes computer codes employing the direct methods.

  11. Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas

    International Nuclear Information System (INIS)

    Zawaideh, E.; Najmabadi, F.; Conn, R.W.

    1986-01-01

    A new set of two-fluid equations that are valid from collisional to weakly collisional limits is derived. Starting from gyrokinetic equations in flux coordinates with no zero-order drifts, a set of moment equations describing plasma transport along the field lines of a space- and time-dependent magnetic field is derived. No restriction on the anisotropy of the ion distribution function is imposed. In the highly collisional limit, these equations reduce to those of Braginskii, while in the weakly collisional limit they are similar to the double adiabatic or Chew, Goldberger, and Low (CGL) equations [Proc. R. Soc. London, Ser. A 236, 112 (1956)]. The new set of equations also exhibits a physical singularity at the sound speed. This singularity is used to derive and compute the sound speed. Numerical examples comparing these equations with conventional transport equations show that in the limit where the ratio of the mean free path lambda to the scale length of the magnetic field gradient L/sub B/ approaches zero, there is no significant difference between the solution of the new and conventional transport equations. However, conventional fluid equations, ordinarily expected to be correct to the order (lambda/L/sub B/) 2 , are found to have errors of order (lambda/L/sub u/) 2 = (lambda/L/sub B/) 2 /(1-M 2 ) 2 , where L/sub u/ is the scale length of the flow velocity gradient and M is the Mach number. As such, the conventional equations may contain large errors near the sound speed (Mroughly-equal1)

  12. The quark gluon plasma equation of state and the expansion of the early Universe

    International Nuclear Information System (INIS)

    Sanches, S.M.; Navarra, F.S.; Fogaça, D.A.

    2015-01-01

    Our knowledge of the equation of state of the quark gluon plasma has been continuously growing due to the experimental results from heavy ion collisions, due to recent astrophysical measurements and also due to the advances in lattice QCD calculations. The new findings about this state may have consequences on the time evolution of the early Universe, which can be estimated by solving the Friedmann equations. The solutions of these equations give the time evolution of the energy density and also of the temperature in the beginning of the Universe. In this work we compute the time evolution of the QGP in the early Universe, comparing several equations of state, some of them based on the MIT bag model (and on its variants) and some of them based on lattice QCD calculations. Among other things, we investigate the effects of a finite baryon chemical potential in the evolution of the early Universe

  13. Asymptotic solution of the Vlasov and Poisson equations for an inhomogeneous plasma

    International Nuclear Information System (INIS)

    Croci, R.

    1991-01-01

    The asymptotic solutions to a class of inhomogeneous integral equations that reduce to algebraic equations when a parameter η goes to zero (the kernel becoming proportional to a Dirac δ function) are derived. This class includes the integral equations obtained from the system of Vlasov and Poisson equations for the Fourier transform in space and the Laplace transform in time of the electrostatic potential, when the equilibrium magnetic field is uniform and the equilibrium plasma density depends on ηx, with the co-ordinate z being the direction of the magnetic field. In this case the inhomogeneous term is given by the initial conditions and possibly by sources, and the Laplace-transform variable ω is the eigenvalue parameter. (Author)

  14. A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Chang, E-mail: cliuaa@ust.hk [Department of Mathematics and Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong); Xu, Kun, E-mail: makxu@ust.hk [Department of Mathematics and Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon (Hong Kong); Sun, Quanhua, E-mail: qsun@imech.ac.cn [State Key Laboratory of High-temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, No. 15 Beisihuan Xi Rd, Beijing 100190 (China); Cai, Qingdong, E-mail: caiqd@mech.pku.edu.cn [Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871 (China)

    2016-06-01

    Fluid dynamic equations are valid in their respective modeling scales, such as the particle mean free path scale of the Boltzmann equation and the hydrodynamic scale of the Navier–Stokes (NS) equations. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. Even though the Boltzmann equation is claimed to be valid in all scales, many Boltzmann solvers, including direct simulation Monte Carlo method, require the cell resolution to the order of particle mean free path scale. Therefore, they are still single scale methods. In order to study multiscale flow evolution efficiently, the dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. Even though the UGKS is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time, it still has space to develop more accurate flow solver in the region, where the time step is comparable with the local particle mean free time. In such a scale, there is dynamic difference from the full Boltzmann collision term and the model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region

  15. The analysis of the derivation principles of kinetic equations based on exactly solvable models of the bulk reaction A + B → Product

    International Nuclear Information System (INIS)

    Kipriyanov, A.A.; Doktorov, A.B.

    2005-01-01

    We have considered two many-particle models of the irreversible reaction A + B → Product for which closed kinetic equations for the mean concentration N A (t) of A species can be exactly obtained. These equations are identically recast into a unified form of integro-differential equation of general kinetic theory. It is shown that the memory functions for both models under consideration can be represented as a sum of the Markovian and non-Markovian parts. It is essential that the Markovian part of the Laplace transform of any kernel can be obtained using the Laplace transform of the kernel itself, and is the root of the non-Markovian part of the Laplace transform of the kernel. The properties established allowed us to perform correct approximation of the memory functions at small concentrations [B] of B species and derive the binary non-Markovian integro-differential equation. Within the binary theory accuracy this equation has been rewritten in a regular frame of a familiar rate equation satisfying general principles of binary kinetic equations. Thus using particular exactly solvable many-particle models, we have reproduced the most essential steps of the known general way for the derivation of the binary kinetic equation avoiding the sophisticated many-particle technique and the corresponding approximations. Besides, the results obtained can serve as an additional evidence of the approximations made in a general many-particle approach to the derivation of the binary kinetic equation

  16. The Role of Kinetic Alfven Waves in Plasma Transport in an Ion-scale Flux Rope

    Science.gov (United States)

    Tang, B.; Li, W.; Wang, C.; Dai, L.

    2017-12-01

    Magnetic flux ropes, if generated by multiply X-line reconnections, would be born as a crater type one, meaning the plasma density within is relatively high. They will then evolve into typical flux ropes as plasma are transported away along the magnetic field lines [Zhang et al., 2010]. In this study, we report an ion-scale flux rope observed by MMS on November 28, 2016, which is accompanied by strong kinetic Alfven waves (KAW). The related wave parallel electric field can effectively accelerate electrons inside the flux rope by Landau resonance, resulting into a significant decrease of the electron at 90° pitch angle. The change of electron pitch angle distribution would cause the rapid plasma transport along the magnetic field lines, and help the flux rope evolve into a strong magnetic core in a short time. This wave-particle interaction would be a candidate mechanism to explain the rareness of crater flux ropes in reality.

  17. Characterization of electron states in dense plasmas and its use in atomic kinetics modeling

    International Nuclear Information System (INIS)

    Fisher, D.V.; Maron, Y.

    2003-01-01

    We describe a self-consistent statistical approach to account for plasma density effects in collisional-radiative kinetics. The approach is based on the characterization of three distinct types of electron states, namely, bound, collectivized, and free, and on the formalism of the effective statistical weights (ESW) of the bound states. The present approach accounts for individual and collective effects of the surrounding electrons and ions on atomic (ionic) electron states. High-accuracy expressions for the ESWs of bound states have been derived. The notions of ionization stage population, free electron density, and rate coefficient are redefined in accordance with the present characterization scheme. The modified expressions for the probabilities of electron-impact induced transitions as well as spontaneous and induced radiative transitions are then obtained. The influence of collectivized states on a dense plasma ionization composition is demonstrated to be strong. Examples of calculated ESWs and populations of ionic quantum states for steady state and transient plasmas are given

  18. Classical kinetic equations for orientational effects with account for the two-particle correlation function of a crystal

    International Nuclear Information System (INIS)

    Ol'khovskij, I.I.; Sadykov, N.M.

    1980-01-01

    The paper deals with the development of classical-statistical approach to the orientational effect theory with account of the influence of the two-particle correlation function of a crystal on diffusion processes. Peculiarities of fast particle movement in the crystal moving at small angles to crystallographic axes and planes are caused by a great number of correlated collisions of the beam particle with the crystal atoms during which the particle slightly deviates in each collision from the direction of its movement before the collision. Obtained is the kinetic equation for the distribution function over coordinates and velocities describing the movement of these particles in the crystal. Lacking the particle deceleration the equation describing movement of the beam particles in the averaged potential and their diffusion by velocities is also obtained. The main peculiarity of these equations is the fact that they take into account strong spatial non-uniformity in the crystal atom distribution [ru

  19. MAKSIMA-CHEMIST: a program for Mass Action Kinetics Simulation by Automatic Chemical Equation Manipulation and Integration using Stiff Techniques

    International Nuclear Information System (INIS)

    Carver, M.B.; Hanley, D.V.; Chaplin, K.R.

    1979-02-01

    MAKSIMA-CHEMIST was written to compute the kinetics of simultaneous chemical reactions. The ordinary differential equations, which are automatically derived from the stated chemical equations, are difficult to integrate, as they are coupled in a highly nonlinear manner and frequently involve a large range in the magnitude of the reaction rates. They form a classic 'stiff' differential equaton set which can be integrated efficiently only by recently developed advanced techniques. The new program also contains provision for higher order chemical reactions, and has a dynamic storage and decision feature. This permits it to accept any number of chemical reactions and species, and choose an integraton scheme which will perform most efficiently within the available memory. Sparse matrix techniques are used when the size and structure of the equation set is suitable. Finally, a number of post-analysis options are available, including printer and Calcomp plots of transient response of selected species, and graphical representation of the reaction matrix. (auth)

  20. Enhancing Understanding of Magnetized High Energy Density Plasmas from Solid Liner Implosions Using Fluid Modeling with Kinetic Closures

    Science.gov (United States)

    Masti, Robert; Srinivasan, Bhuvana; King, Jacob; Stoltz, Peter; Hansen, David; Held, Eric

    2017-10-01

    Recent results from experiments and simulations of magnetically driven pulsed power liners have explored the role of early-time electrothermal instability in the evolution of the MRT (magneto-Rayleigh-Taylor) instability. Understanding the development of these instabilities can lead to potential stabilization mechanisms; thereby providing a significant role in the success of fusion concepts such as MagLIF (Magnetized Liner Inertial Fusion). For MagLIF the MRT instability is the most detrimental instability toward achieving fusion energy production. Experiments of high-energy density plasmas from wire-array implosions have shown the requirement for more advanced physics modeling than that of ideal magnetohydrodynamics. The overall focus of this project is on using a multi-fluid extended-MHD model with kinetic closures for thermal conductivity, resistivity, and viscosity. The extended-MHD model has been updated to include the SESAME equation-of-state tables and numerical benchmarks with this implementation will be presented. Simulations of MRT growth and evolution for MagLIF-relevant parameters will be presented using this extended-MHD model with the SESAME equation-of-state tables. This work is supported by the Department of Energy Office of Science under Grant Number DE-SC0016515.

  1. On the kinetic theory of QPEMIC instabilities in weakly ionized plasmas placed in non-parallel fields

    International Nuclear Information System (INIS)

    Milic, B.S.; Gajic, D.Z.

    1994-01-01

    Quasi-perpendicular electromagnetic ion-cyclotron (QPEMIC) modes and instabilities are studied, on the ground of linear theory of perturbations and kinetic equations with BGK collision integrals, in weakly ionized, low-β and moderately non-isothermal plasmas placed in non-parallel electric and magnetic fields. The magnetization is assumed to be sufficiently high to cut off the perpendicular steady-state current. Special attention is given to evaluation of magnitudes of the threshold drifts required for the onset of instabilities. It is found that these drifts are smaller than those for the corresponding quasi-perpendicular electrostatic ion-cyclotron (QPESIC) instabilities studied previously for the same type of plasmas. Both QPEMIC and QPESIC threshold drifts exhibit the same behavioural pattern if the order of harmonic, magnetization, non-isothermality or the angle between the fields are varied. An increase of the angle between the fields lowers the threshold drifts, which means that the presence of u perpendicular to (or E perpendicular to ) facilitates the excitation of both QPEMIC and QPESIC instabilities. The QPEMIC threshold drifts are found to depend on the overall gas pressure, and to decrease as the pressure is lowered, which is a feature not found in the QPESIC case. The discrepancies between the QPEMIC and QPESIC threshold drifts increase if the pressure decreases, or if magnetization, degree of ionization or ion charge number increase. (orig.)

  2. Release kinetics of platelet-derived and plasma-derived growth factors from autologous plasma rich in growth factors.

    Science.gov (United States)

    Anitua, Eduardo; Zalduendo, Mari Mar; Alkhraisat, Mohammad Hamdan; Orive, Gorka

    2013-10-01

    Many studies have evaluated the biological effects of platelet rich plasma reporting the final outcomes on cell and tissues. However, few studies have dealt with the kinetics of growth factor delivery by plasma rich in growth factors. Venous blood was obtained from three healthy volunteers and processed with PRGF-Endoret technology to prepare autologous plasma rich in growth factors. The gel-like fibrin scaffolds were then incubated in triplicate, in a cell culture medium to monitor the release of PDGF-AB, VEGF, HGF and IGF-I during 8 days of incubation. A leukocyte-platelet rich plasma was prepared employing the same technology and the concentrations of growth factors and interleukin-1β were determined after 24h of incubation. After each period, the medium was collected, fibrin clot was destroyed and the supernatants were stored at -80°C until analysis. The growth factor delivery is diffusion controlled with a rapid initial release by 30% of the bioactive content after 1h of incubation and a steady state release when almost 70% of the growth factor content has been delivered. Autologous fibrin matrix retained almost 30% of the amount of the growth factors after 8 days of incubation. The addition of leukocytes to the formula of platelet rich plasma did not increase the concentration of the growth factors, while it drastically increased the presence of pro-inflammatory IL-1β. Further studies employing an in vitro inflammatory model would be interesting to study the difference in growth factors and pro-inflammatory cytokines between leukocyte-free and leukocyte-rich platelet rich plasma. Copyright © 2013 Elsevier GmbH. All rights reserved.

  3. Modulation of release kinetics by plasma polymerization of ampicillin-loaded β -TCP ceramics

    International Nuclear Information System (INIS)

    Labay, C; Buxadera-Palomero, J; Avilés, M; Canal, C; Ginebra, M P

    2016-01-01

    Beta-tricalcium phosphate ( β -TCP) bioceramics are employed in bone repair surgery. Their local implantation in bone defects puts them in the limelight as potential materials for local drug delivery. However, obtaining suitable release patterns fitting the required therapeutics is a challenge. Here, plasma polymerization of ampicillin-loaded β -TCP is studied for the design of a novel antibiotic delivery system. Polyethylene glycol-like (PEG-like) coating of β -TCP by low pressure plasma polymerization was performed using diglyme as precursor, and nanometric PEG-like layers were obtained by simple and double plasma polymerization processes. A significant increase in hydrophobicity, and the presence of plasma polymer was visible on the surface by SEM and quantified by XPS. As a main consequence of the plasma polymerisation, the release kinetics were successfully modified, avoiding burst release, and slowing down the initial rate of release leading to a 4.5 h delay in reaching the same antibiotic release percentage, whilst conservation of the activity of the antibiotic was simultaneously maintained. Thus, plasma polymerisation on the surface of bioceramics may be a good strategy to design controlled drug delivery matrices for local bone therapies. (paper)

  4. REFLECT: a program to integrate the wave equation through a plane stratified plasma

    International Nuclear Information System (INIS)

    Greene, J.W.

    1975-01-01

    A program was developed to integrate the wave equation through a plane stratified plasma with a general density distribution. The reflection and transmission of a plane wave are computed as a function of the angle of incidence. The polarization of the electric vector is assumed to be perpendicular to the plane of incidence. The model for absorption by classical inverse bremsstrahlung avoids the improper extrapolation of underdense formulae that are singular at the plasma critical surface. Surprisingly good agreement with the geometric-optics analysis of a linear layer was found. The system of ordinary differential equations is integrated by the variable-step, variable-order Adams method in the Lawrence Livermore Laboratory Gear package. Parametric studies of the absorption are summarized, and some possibilities for further development of the code are discussed. (auth)

  5. Covariant kinetic dispersion theory of linear transverse waves parallel propagating in magnetized plasmas with thermal anisotropy

    International Nuclear Information System (INIS)

    Lazar, M.; Schlickeiser, R.

    2006-01-01

    The properties of transverse waves parallel propagating in magnetized plasmas with arbitrary composition and thermally anisotropic, are investigated on the basis of relativistic Vlasov-Maxwell equations. The transverse dispersion relations for plasmas with arbitrary distribution functions are derived. These dispersion relations describe the linear response of the system to the initial perturbations and thus define all existing linear (transverse) plasma modes in the system. By analytic continuation the dispersion relations in the whole complex frequency plane are constructed. Further analysis is restricted to the important case of anisotropic bi-Maxwellian equilibrium plasma distribution functions. Explicit forms of the relativistically correct transverse dispersion relations are derived that hold for any values of the plasma temperatures and the temperature anisotropy. In the limit of nonrelativistic plasma temperatures the dispersion relations are expressed in terms of plasma dispersion function, however, the dependence on frequency and wave numbers is markedly different from the standard noncovariant nonrelativistic analysis. Only in the strictly unphysical formal limit of an infinitely large speed of light, c→∞, does the nonrelativistic dispersion relations reduce to the standard noncovariant dispersion relations

  6. Modified bag models for the quark–gluon plasma equation of state

    International Nuclear Information System (INIS)

    Begun, V.V.; Gorenstein, M.I.; Mogilevsky, O.A.

    2011-01-01

    The modified versions of the bag model equation of state (EoS) are considered. They are constructed to satisfy the main qualitative features observed for the quark–gluon plasma EoS in the lattice QCD calculations. A quantitative comparison with the lattice results at high temperatures T are done in the SU(3) gluodynamics and in the full QCD with dynamical quarks. Our analysis advocates a negative value of the bag constant B. (author)

  7. Gyrokinetic Electron and Fully Kinetic Ion Particle Simulation of Collisionless Plasma Dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Yu Lin; Xueyi Wang; Liu Chen; Zhihong Lin

    2009-08-11

    Fully kinetic-particle simulations and hybrid simulations have been utilized for decades to investigate various fundamental plasma processes, such as magnetic reconnection, fast compressional waves, and wave-particle interaction. Nevertheless, due to disparate temporal and spatial scales between electrons and ions, existing fully kinetic-particle codes have to employ either unrealistically high electron-to-ion mass ratio, me/mi, or simulation domain limited to a few or a few ten's of the ion Larmor radii, or/and time much less than the global Alfven time scale in order to accommodate available computing resources. On the other hand, in the hybrid simulation, the ions are treated as fully kinetic particles but the electrons are treated as a massless fluid. The electron kinetic effects, e.g., wave-particle resonances and finite electron Larmor radius effects, are completely missing. Important physics, such as the electron transit time damping of fast compressional waves or the triggering mechanism of magnetic reconnection in collisionless plasmas is absent in the hybrid codes. Motivated by these considerations and noting that dynamics of interest to us has frequencies lower than the electron gyrofrequency, we planned to develop an innovative particle simulation model, gyrokinetic (GK) electrons and fully kinetic (FK) ions. In the GK-electron and FK-ion (GKe/FKi) particle simulation model, the rapid electron cyclotron motion is removed, while keeping finite electron Larmor radii, realistic me/mi ratio, wave-particle interactions, and off-diagonal components of electron pressure tensor. The computation power can thus be significantly improved over that of the full-particle codes. As planned in the project DE-FG02-05ER54826, we have finished the development of the new GK-electron and FK-ion scheme, finished its benchmark for a uniform plasma in 1-D, 2-D, and 3-D systems against linear waves obtained from analytical theories, and carried out a further convergence

  8. Gyrokinetic Electron and Fully Kinetic Ion Particle Simulation of Collisionless Plasma Dynamics

    International Nuclear Information System (INIS)

    Lin, Yu; Wang, Xueyi; Chen, Liu; Lin, Zhihong

    2009-01-01

    Fully kinetic-particle simulations and hybrid simulations have been utilized for decades to investigate various fundamental plasma processes, such as magnetic reconnection, fast compressional waves, and wave-particle interaction. Nevertheless, due to disparate temporal and spatial scales between electrons and ions, existing fully kinetic-particle codes have to employ either unrealistically high electron-to-ion mass ratio, me/mi, or simulation domain limited to a few or a few ten's of the ion Larmor radii, or/and time much less than the global Alfven time scale in order to accommodate available computing resources. On the other hand, in the hybrid simulation, the ions are treated as fully kinetic particles but the electrons are treated as a massless fluid. The electron kinetic effects, e.g., wave-particle resonances and finite electron Larmor radius effects, are completely missing. Important physics, such as the electron transit time damping of fast compressional waves or the triggering mechanism of magnetic reconnection in collisionless plasmas is absent in the hybrid codes. Motivated by these considerations and noting that dynamics of interest to us has frequencies lower than the electron gyrofrequency, we planned to develop an innovative particle simulation model, gyrokinetic (GK) electrons and fully kinetic (FK) ions. In the GK-electron and FK-ion (GKe/FKi) particle simulation model, the rapid electron cyclotron motion is removed, while keeping finite electron Larmor radii, realistic me/mi ratio, wave-particle interactions, and off-diagonal components of electron pressure tensor. The computation power can thus be significantly improved over that of the full-particle codes. As planned in the project DE-FG02-05ER54826, we have finished the development of the new GK-electron and FK-ion scheme, finished its benchmark for a uniform plasma in 1-D, 2-D, and 3-D systems against linear waves obtained from analytical theories, and carried out a further convergence test

  9. Rarefied gas flow simulations using high-order gas-kinetic unified algorithms for Boltzmann model equations

    Science.gov (United States)

    Li, Zhi-Hui; Peng, Ao-Ping; Zhang, Han-Xin; Yang, Jaw-Yen

    2015-04-01

    This article reviews rarefied gas flow computations based on nonlinear model Boltzmann equations using deterministic high-order gas-kinetic unified algorithms (GKUA) in phase space. The nonlinear Boltzmann model equations considered include the BGK model, the Shakhov model, the Ellipsoidal Statistical model and the Morse model. Several high-order gas-kinetic unified algorithms, which combine the discrete velocity ordinate method in velocity space and the compact high-order finite-difference schemes in physical space, are developed. The parallel strategies implemented with the accompanying algorithms are of equal importance. Accurate computations of rarefied gas flow problems using various kinetic models over wide ranges of Mach numbers 1.2-20 and Knudsen numbers 0.0001-5 are reported. The effects of different high resolution schemes on the flow resolution under the same discrete velocity ordinate method are studied. A conservative discrete velocity ordinate method to ensure the kinetic compatibility condition is also implemented. The present algorithms are tested for the one-dimensional unsteady shock-tube problems with various Knudsen numbers, the steady normal shock wave structures for different Mach numbers, the two-dimensional flows past a circular cylinder and a NACA 0012 airfoil to verify the present methodology and to simulate gas transport phenomena covering various flow regimes. Illustrations of large scale parallel computations of three-dimensional hypersonic rarefied flows over the reusable sphere-cone satellite and the re-entry spacecraft using almost the largest computer systems available in China are also reported. The present computed results are compared with the theoretical prediction from gas dynamics, related DSMC results, slip N-S solutions and experimental data, and good agreement can be found. The numerical experience indicates that although the direct model Boltzmann equation solver in phase space can be computationally expensive

  10. Kinetic transport in a magnetically confined and flux-constrained fusion plasma

    International Nuclear Information System (INIS)

    Darmet, G.

    2007-11-01

    This work deals with the kinetic transport in a fusion plasma magnetically confined and flux-constrained. The author proposes a new interpretation of the dynamics of zonal flows. The model that has been studied is a gyrokinetic model reduced to the transport of trapped ions. The inter-change stability that is generated allows the study of the kinetic transport of trapped ions. This model has a threshold instability and can be simulated over a few tens confining time for either thermal bath constraint or flux constraint. For thermal baths constraint, the simulation shows a metastable state where zonal flows are prevailing while turbulence is non-existent. In the case of a flux-constraint, zonal flows appear and relax by exchanging energy with system's kinetic energy and turbulence energy. The competition between zonal flows and turbulence can be then simulated by a predator-prey model. 2 regimes can be featured out: an improved confining regime where zonal flows dominate transport and a turbulent regime where zonal flows and turbulent transport are of the same magnitude order. We show that flux as well as the Reynolds tensor play an important role in the dynamics of the zonal flows and that the gyrokinetic description is relevant for all plasma regions. (A.C.)

  11. Kinetic theory of twisted waves: Application to space plasmas having superthermal population of species

    Science.gov (United States)

    Arshad, Kashif; Poedts, Stefaan; Lazar, Marian

    2017-04-01

    ring shape morphology of a beam with orbital angular momentum (OAM) is ideal for the observation of solar corona around the sun where the intensity of the beam is minimum at the center, in solar experiments, and Earth's ionosphere. The twisted plasma modes carrying OAM are mostly studied either by the fluid theory or Maxwellian distributed Kinetic Theory. But most of the space plasmas and some laboratory plasmas have non-thermal distributions due to super-thermal population of the plasma particles. Therefore the Kinetic Theory of twisted plasma modes carrying OAM are recently studied using non-thermal (kappa) distribution of the super-thermal particles in the presence of the helical electric field and significant change in the damping rates are observed by tuning appropriate parameters.

  12. Kinetic Alfven wave in the presence of kappa distribution function in plasma sheet boundary layer

    Energy Technology Data Exchange (ETDEWEB)

    Shrivastava, G., E-mail: geetphy9@gmail.com; Ahirwar, G. [School of Studies in Physics, Vikram University, Ujjain India (India); Shrivastava, J., E-mail: jayashrivastava2007@gmail.com [Dronacharya Group of Institutions, Greater Noida-India (India)

    2015-07-31

    The particle aspect approach is adopted to investigate the trajectories of charged particles in the electromagnetic field of kinetic Alfven wave. Expressions are found for the dispersion relation, damping/growth rate and associated currents in the presence of kappa distribution function. Kinetic effect of electrons and ions are included to study kinetic Alfven wave because both are important in the transition region. It is found that the ratio β of electron thermal energy density to magnetic field energy density and the ratio of ion to electron thermal temperature (T{sub i}/T{sub e}), and kappa distribution function affect the dispersion relation, damping/growth rate and associated currents in both cases(warm and cold electron limit).The treatment of kinetic Alfven wave instability is based on assumption that the plasma consist of resonant and non resonant particles. The resonant particles participate in an energy exchange process, whereas the non resonant particles support the oscillatory motion of the wave.

  13. A PICKSC Science Gateway for enabling the common plasma physicist to run kinetic software

    Science.gov (United States)

    Hu, Q.; Winjum, B. J.; Zonca, A.; Youn, C.; Tsung, F. S.; Mori, W. B.

    2017-10-01

    Computer simulations offer tremendous opportunities for studying plasmas, ranging from simulations for students that illuminate fundamental educational concepts to research-level simulations that advance scientific knowledge. Nevertheless, there is a significant hurdle to using simulation tools. Users must navigate codes and software libraries, determine how to wrangle output into meaningful plots, and oftentimes confront a significant cyberinfrastructure with powerful computational resources. Science gateways offer a Web-based environment to run simulations without needing to learn or manage the underlying software and computing cyberinfrastructure. We discuss our progress on creating a Science Gateway for the Particle-in-Cell and Kinetic Simulation Software Center that enables users to easily run and analyze kinetic simulations with our software. We envision that this technology could benefit a wide range of plasma physicists, both in the use of our simulation tools as well as in its adaptation for running other plasma simulation software. Supported by NSF under Grant ACI-1339893 and by the UCLA Institute for Digital Research and Education.

  14. Advanced 3-dimensional electron kinetic calculations for the current drive problem in magnetically confined thermonuclear plasmas

    International Nuclear Information System (INIS)

    Peysson, Y.; Decker, J.; Bers, A.; Ram, A.; Harvey, R.

    2004-01-01

    Accurate and fast electron kinetic calculations is a challenging issue for realistic simulations of thermonuclear tokamak plasmas. Relativistic corrections and electron trajectory effects must be fully taken into account for high temperature burning plasmas, while codes should also consistently describe wave-particle resonant interactions in presence of locally large gradients close to internal transport barrier. In that case, neoclassical effects may come into play and self-consistent evaluation of both the radio-frequency and bootstrap currents must be performed. In addition, a complex interplay between momentum and radial electron dynamics may take place, in presence of a possible energy dependent radial transport. Besides the physics needs, there are considerable numerical issues to solve, in order to reduce computer time consumption and memory requirements at an acceptable level, so that kinetic calculations may be valuably incorporated in a chain of codes which determines plasma equilibrium and wave propagation. So far, fully implicit 3-dimensional calculations based on a finite difference scheme and an incomplete L and U matrices factorization have been found to be so most effective method to reach this goal. A review of the present status in this active field of physics is presented, with an emphasis on possible future improvements. (authors)

  15. On an analytical formulation for the mono-energetic neutron space-kinetic equation in full cylinder symmetry

    International Nuclear Information System (INIS)

    Oliveira, F.R.; Bodmann, B.E.J.; Vilhena, M.T.; Carvalho, F.

    2017-01-01

    Highlights: • The present work presents an exact solution to neutron spatial kinetic equation. • It is an exact solution in a heterogeneous cylinder with temporal dependence. • The solution was constructed through the separation of variables method. - Abstract: In the present work we discuss a system of partial differential equations that model neutron space-kinetics in cylindrical geometry and are defined by two sectionally homogeneous cylinder cells, mono-energetic neutrons and one group of delayed neutron precursors. The solution is determined using the technique of variable separation. The associated complete spectra with respect to each variable separation are analysed and truncated such as to allow a parameterized global solution. For the obtained solution we present some numerical results for the scalar neutron flux and its time dependence and projection on the cylinder axis z and the radial and cylinder axis projection. As a case study we consider an insertion of an absorbing medium in the upper cylinder cell. Continuity of the scalar flux at the interface between the two cylinder elements and conserved current density is explained and related to scale invariance of the partial differential equation system together with the initial and boundary conditions. Some numerical results for the scalar angular neutron flux and associated current densities are shown.

  16. A third-order gas-kinetic CPR method for the Euler and Navier-Stokes equations on triangular meshes

    Science.gov (United States)

    Zhang, Chao; Li, Qibing; Fu, Song; Wang, Z. J.

    2018-06-01

    A third-order accurate gas-kinetic scheme based on the correction procedure via reconstruction (CPR) framework is developed for the Euler and Navier-Stokes equations on triangular meshes. The scheme combines the accuracy and efficiency of the CPR formulation with the multidimensional characteristics and robustness of the gas-kinetic flux solver. Comparing with high-order finite volume gas-kinetic methods, the current scheme is more compact and efficient by avoiding wide stencils on unstructured meshes. Unlike the traditional CPR method where the inviscid and viscous terms are treated differently, the inviscid and viscous fluxes in the current scheme are coupled and computed uniformly through the kinetic evolution model. In addition, the present scheme adopts a fully coupled spatial and temporal gas distribution function for the flux evaluation, achieving high-order accuracy in both space and time within a single step. Numerical tests with a wide range of flow problems, from nearly incompressible to supersonic flows with strong shocks, for both inviscid and viscous problems, demonstrate the high accuracy and efficiency of the present scheme.

  17. Ion beam generation at the plasma sheet boundary layer by kinetic Alfven waves

    International Nuclear Information System (INIS)

    Moghaddam-Taaheri, E.; Goertz, C.K.; Smith, R.A.

    1989-01-01

    The kinetic Alfven wave, an Alfven wave with a perpendicular wavelength comparable to the ion gyroradius, can diffuse ions both in velocity and coordinate spaces with comparable transport rates. This may lead to the generation of ion beams in the plasma sheet boundary layer (PSBL). To investigate the ion beam generation process numerically, a two-dimensional quasi-linear code was constructed. Assuming that the plasma β (the ratio of plasma pressure to the magnetic pressure) varies from β = 1 to β << 1 across the magnetic field, the dynamics of the ion beam generation in the PSBL was studied. It was found that if your start with an ion distribution function which monotonically decreases with velocity along the magnetic field and a density gradient across the magnetic field, ions diffuse in velocity-coordinate space until nearly a plateau is established along the diffusion path. Depending on the topology of the magnetic field at the lobe side of the simulation system, i.e., open or closed field lines, the ion distribution function may or may not reach a steady state. If the field lines are open there, i.e., if the diffusion extends into the lobe, the double diffusion process may provide a mechanism for continuously transferring the ions from the central plasma sheet to the lobe. The authors comment on the effect of the particle loss on the establishment of the pressure balance in the plasma sheet

  18. Thermal fluctuation levels of magnetic and electric fields in unmagnetized plasma: The rigorous relativistic kinetic theory

    International Nuclear Information System (INIS)

    Yoon, P. H.; Schlickeiser, R.; Kolberg, U.

    2014-01-01

    Any fully ionized collisionless plasma with finite random particle velocities contains electric and magnetic field fluctuations. The fluctuations can be of three different types: weakly damped, weakly propagating, or aperiodic. The kinetics of these fluctuations in general unmagnetized plasmas, governed by the competition of spontaneous emission, absorption, and stimulated emission processes, is investigated, extending the well-known results for weakly damped fluctuations. The generalized Kirchhoff radiation law for both collective and noncollective fluctuations is derived, which in stationary plasmas provides the equilibrium energy densities of electromagnetic fluctuations by the ratio of the respective spontaneous emission coefficient and the true absorption coefficient. As an illustrative example, the equilibrium energy densities of aperiodic transverse collective electric and magnetic fluctuations in an isotropic thermal electron-proton plasmas of density n e are calculated as |δB|=√((δB) 2 )=2.8(n e m e c 2 ) 1/2 g 1/2 β e 7/4 and |δE|=√((δE) 2 )=3.2(n e m e c 2 ) 1/2 g 1/3 β e 2 , where g and β e denote the plasma parameter and the thermal electron velocity in units of the speed of light, respectively. For densities and temperatures of the reionized early intergalactic medium, |δB|=6·10 −18 G and |δE|=2·10 −16 G result

  19. Kinetic theory of beam-induced plasmas generalised to sophisticated atomic structures

    International Nuclear Information System (INIS)

    Peyraud-Cuenca, Nelly

    1987-01-01

    We present an analytic kinetic model available for all particle-beam-induced atomic plasmas, without any restriction on the distribution of electronic levels. The method is an iteration of the already known solution available only for the distribution of atomic levels as in the rare gases. We recall a universal atomic kinetic model which, independently of its applications to the study of efficient laser systems, might be a first step in the analytic investigation of molecular problems. Then, the iteration is systematically applied to all possible atomic structures whose number is increased by the non-local character of inelastic processes. We deduce a general analytic representation of the 'tail' of the electron distribution function as a ratio between non-local source terms and a combination of inelastic cross sections, from which we exhibit a physical interpretation and essential scaling laws. The theory is applied to sodium which is an important element in the research of efficient laser systems. (author)

  20. The relative importance of fluid and kinetic frequency shifts of an electron plasma wave

    International Nuclear Information System (INIS)

    Winjum, B. J.; Fahlen, J.; Mori, W. B.

    2007-01-01

    The total nonlinear frequency shift of a plasma wave including both fluid and kinetic effects is estimated when the phase velocity of the wave is much less than the speed of light. Using a waterbag or fluid model, the nonlinear frequency shift due to harmonic generation is calculated for an arbitrary shift in the wavenumber. In the limit where the wavenumber does not shift, the result is in agreement with previously published work [R. L. Dewar and J. Lindl, Phys. Fluids 15, 820 (1972); T. P. Coffey, ibid. 14, 1402 (1971)]. This shift is compared to the kinetic shift of Morales and O'Neil [G. J. Morales and T. M. O'Neil, Phys. Rev. Lett. 28, 417 (1972)] for wave amplitudes and values of kλ D of interest to Raman backscatter of a laser driver in inertial confinement fusion

  1. The relative importance of fluid and kinetic frequency shifts of an electron plasma wave

    Science.gov (United States)

    Winjum, B. J.; Fahlen, J.; Mori, W. B.

    2007-10-01

    The total nonlinear frequency shift of a plasma wave including both fluid and kinetic effects is estimated when the phase velocity of the wave is much less than the speed of light. Using a waterbag or fluid model, the nonlinear frequency shift due to harmonic generation is calculated for an arbitrary shift in the wavenumber. In the limit where the wavenumber does not shift, the result is in agreement with previously published work [R. L. Dewar and J. Lindl, Phys. Fluids 15, 820 (1972); T. P. Coffey, Phys. Fluids 14, 1402 (1971)]. This shift is compared to the kinetic shift of Morales and O'Neil [G. J. Morales and T. M. O'Neil, Phys. Rev. Lett. 28, 417 (1972)] for wave amplitudes and values of kλD of interest to Raman backscatter of a laser driver in inertial confinement fusion.

  2. Start broadened profiles with self-consistent radiation transfer and atomic kinetics in plasmas produced by high intensity lasers

    International Nuclear Information System (INIS)

    Olson, G.L.; Comly, J.C.; La Gattuta, J.K.; Kilcrease, D.P.

    1993-01-01

    Spectral line shapes and line strengths have long been used to diagnose plasma temperatures and densities. In dense plasmas, the additional broadening due to Stark effects give additional information about the plasma density. We present calculations that are self-consistent in that the radiation fields of the line transitions and the atomic kinetics are iterated to convergence. Examples are given for simple plasmas with temperature gradients, density gradients, and velocity fields. Then a more complex example of a laser produced plasma is presented

  3. Kinetic theory and simulation of multi-species plasmas in tokamaks excited with ICRF microwaves

    International Nuclear Information System (INIS)

    Kerbel, G.D.; McCoy, M.G.

    1984-01-01

    This paper presents a description of a bounce-averaged Fokker-Planck quasilinear model for the kinetic description of tokamak plasmas. The non-linear collision and quasilinear resonant diffusion operators are represented in a form conducive to numerical solution with specific attention to the treatment of the boundary layer separating trapped and passing orbit regions of velocity space. The numerical techniques employed are detailed in so far as they constitute significant departure from those used in the conventional uniform magnetic field case. Examples are given to illustrate the combined effects of collisional and resonant diffusion

  4. Some kinetic properties of plasma lecithin-cholesterol acyltransferase in hyper-alphalipoproteinemia in man

    International Nuclear Information System (INIS)

    Nikiforova, A.A.; Alksnis, E.G.; Ivanova, E.M.

    1985-01-01

    The aim of this investigation was to study some kinetic properties of lecithin-cholesterol acyltransferase (LCAT) in the blood plasma of patients with hyper-alpha-lipoproteinemia, enabling the presence of LCAT isozymes in the blood to be detected. The velocity of the LCAT reaction was judged by determining labeled CHE formed from 14 C-nonesterified CH and lecithin of HDL on incubation of the latter with the enzyme. Dependence of the velocity of the LCAT reaction on concentration of substrate (nonesterified HDL cholesterol) in four subjects with hyper-alpha-lipoproteinemia is shown

  5. The Pade approximate method for solving problems in plasma kinetic theory

    International Nuclear Information System (INIS)

    Jasperse, J.R.; Basu, B.

    1992-01-01

    The method of Pade Approximates has been a powerful tool in solving for the time dependent propagator (Green function) in model quantum field theories. We have developed a modified Pade method which we feel has promise for solving linearized collisional and weakly nonlinear problems in plasma kinetic theory. In order to illustrate the general applicability of the method, in this paper we discuss Pade solutions for the linearized collisional propagator and the collisional dielectric function for a model collisional problem. (author) 3 refs., 2 tabs

  6. Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis

    International Nuclear Information System (INIS)

    Fillion-Gourdeau, F.; Lorin, E.; Bandrauk, A.D.

    2016-01-01

    A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron–molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic balanced basis, which allows for an efficient and accurate determination of the Dirac spectrum and eigenfunctions. B-spline basis functions are used to obtain high accuracy. This numerical method is used to compute the energy spectrum of the two-center problem and then the evolution of eigenstate wavefunctions in an external electromagnetic field.

  7. Kinetics of two-dimensional electron plasma, interacting with fluctuating potential

    International Nuclear Information System (INIS)

    Boiko, I.I.; Sirenko, Y.M.

    1990-01-01

    In this paper, from the first principles, after the fashion of Klimontovich, the authors derive quantum kinetic equation for electron gas, inhomogeneous in z-direction and homogeneous in XY-plane. Special attention is given to the systems with quasi-two-dimensional electron gas (2 DEG), which are widely explored now. Both interaction between the particles of 2 DEG (in general, of several sorts), and interaction with an external system (phonons, impurities, after change carries etc.) are considered. General theory is used to obtain energy and momentum balance equations and relaxation frequencies for 2 DEG in the basis of plane waves. The case of crossed electric and magnetic fields is also treated. As an illustration the problems of 2 DEG scattering on semibounded three-dimensional electron gas and on two-dimensional hole gas are considered; transverse conductivity of nondegenerate 2 DEG, scattered by impurities in ultraquantum magnetic field, is calculated

  8. A Gas-Kinetic Method for Hyperbolic-Elliptic Equations and Its Application in Two-Phase Fluid Flow

    Science.gov (United States)

    Xu, Kun

    1999-01-01

    A gas-kinetic method for the hyperbolic-elliptic equations is presented in this paper. In the mixed type system, the co-existence and the phase transition between liquid and gas are described by the van der Waals-type equation of state (EOS). Due to the unstable mechanism for a fluid in the elliptic region, interface between the liquid and gas can be kept sharp through the condensation and evaporation process to remove the "averaged" numerical fluid away from the elliptic region, and the interface thickness depends on the numerical diffusion and stiffness of the phase change. A few examples are presented in this paper for both phase transition and multifluid interface problems.

  9. Observations on the properties of second and general-order kinetics equations describing the thermoluminescence processes

    International Nuclear Information System (INIS)

    Kitis, G.; Furetta, C.; Azorin, J.

    2003-01-01

    Synthetic thermoluminescent (Tl) glow peaks, following a second and general kinetics order have been generated by computer. The general properties of the so generated peaks have been investigated over several order of magnitude of simulated doses. Some non usual results which, at the best knowledge of the authors, are not reported in the literature, are obtained and discussed. (Author)

  10. Euler and Navier endash Stokes limits of the Uehling endash Uhlenbeck quantum kinetic equations

    International Nuclear Information System (INIS)

    Arlotti, L.; Lachowicz, M.

    1997-01-01

    The Uehling endash Uhlenbeck evolution equations for gases of identical quantum particles either fermions or bosons, in the case in which the collision kernel does not depend on the distribution function, are considered. The existence of solutions and their asymptotic relations with solutions of the hydrodynamic equations both at the level of the Euler system and at the level of the Navier endash Stokes system are proved. copyright 1997 American Institute of Physics

  11. Boltzmann-equation simulations of radio-frequency-driven, low-temperature plasmas

    International Nuclear Information System (INIS)

    Drallos, P.J.; Riley, M.E.

    1995-01-01

    We present a method for the numerical solution of the Boltzmann equation (BE) describing plasma electrons. We apply the method to a capacitively-coupled, radio-frequency-driven He discharge in parallel-plate (quasi-1D) geometry which contains time scales for physical processes spanning six orders of magnitude. Our BE solution procedure uses the method of characteristics for the Vlasov operator with interpolation in phase space at early time, allowing storage of the distribution function on a fixed phase-space grid. By alternating this BE method with a fluid description of the electrons, or with a novel time-cycle-average equation method, we compute the periodic steady state of a He plasma by time evolution from startup conditions. We find that the results compare favorably with measured current-voltage, plasma density, and ''cited state densities in the ''GEC'' Reference Cell. Our atomic He model includes five levels (some are summed composites), 15 electronic transitions, radiation trapping, and metastable-metastable collisions

  12. Dispersion equations for field-aligned cyclotron waves in axisymmetric magnetospheric plasmas

    Directory of Open Access Journals (Sweden)

    N. I. Grishanov

    2006-03-01

    Full Text Available In this paper, we derive the dispersion equations for field-aligned cyclotron waves in two-dimensional (2-D magnetospheric plasmas with anisotropic temperature. Two magnetic field configurations are considered with dipole and circular magnetic field lines. The main contribution of the trapped particles to the transverse dielectric permittivity is estimated by solving the linearized Vlasov equation for their perturbed distribution functions, accounting for the cyclotron and bounce resonances, neglecting the drift effects, and assuming the weak connection of the left-hand and right-hand polarized waves. Both the bi-Maxwellian and bi-Lorentzian distribution functions are considered to model the ring current ions and electrons in the dipole magnetosphere. A numerical code has been developed to analyze the dispersion characteristics of electromagnetic ion-cyclotron waves in an electron-proton magnetospheric plasma with circular magnetic field lines, assuming that the steady-state distribution function of the energetic protons is bi-Maxwellian. As in the uniform magnetic field case, the growth rate of the proton-cyclotron instability (PCI in the 2-D magnetospheric plasmas is defined by the contribution of the energetic ions/protons to the imaginary part of the transverse permittivity elements. We demonstrate that the PCI growth rate in the 2-D axisymmetric plasmasphere can be significantly smaller than that for the straight magnetic field case with the same macroscopic bulk parameters.

  13. Boltzmann-equation simulations of radio-frequency-driven, low-temperature plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Drallos, P.J.; Riley, M.E.

    1995-01-01

    We present a method for the numerical solution of the Boltzmann equation (BE) describing plasma electrons. We apply the method to a capacitively-coupled, radio-frequency-driven He discharge in parallel-plate (quasi-1D) geometry which contains time scales for physical processes spanning six orders of magnitude. Our BE solution procedure uses the method of characteristics for the Vlasov operator with interpolation in phase space at early time, allowing storage of the distribution function on a fixed phase-space grid. By alternating this BE method with a fluid description of the electrons, or with a novel time-cycle-average equation method, we compute the periodic steady state of a He plasma by time evolution from startup conditions. We find that the results compare favorably with measured current-voltage, plasma density, and ``cited state densities in the ``GEC`` Reference Cell. Our atomic He model includes five levels (some are summed composites), 15 electronic transitions, radiation trapping, and metastable-metastable collisions.

  14. Measurements of the equations of state and spectrum of nonideal xenon plasma under shock compression

    International Nuclear Information System (INIS)

    Zheng, J.; Gu, Y. J.; Chen, Z. Y.; Chen, Q. F.

    2010-01-01

    Experimental equations of state on generation of nonideal xenon plasma by intense shock wave compression was presented in the ranges of pressure of 2-16 GPa and temperature of 31-50 kK, and the xenon plasma with the nonideal coupling parameter Γ range from 0.6-2.1 was generated. The shock wave was produced using the flyer plate impact and accelerated up to ∼6 km/s with a two-stage light gas gun. Gaseous specimens were shocked from two initial pressures of 0.80 and 4.72 MPa at room temperature. Time-resolved spectral radiation histories were recorded by using a multiwavelength channel pyrometer. The transient spectra with the wavelength range of 460-700 nm were recorded by using a spectrometer to evaluate the shock temperature. Shock velocity was measured and particle velocity was determined by the impedance matching methods. The equations of state of xenon plasma and ionization degree have been discussed in terms of the self-consistent fluid variational theory.

  15. Measurements of the equations of state and spectrum of nonideal xenon plasma under shock compression

    Science.gov (United States)

    Zheng, J.; Gu, Y. J.; Chen, Z. Y.; Chen, Q. F.

    2010-08-01

    Experimental equations of state on generation of nonideal xenon plasma by intense shock wave compression was presented in the ranges of pressure of 2-16 GPa and temperature of 31-50 kK, and the xenon plasma with the nonideal coupling parameter Γ range from 0.6-2.1 was generated. The shock wave was produced using the flyer plate impact and accelerated up to ˜6km/s with a two-stage light gas gun. Gaseous specimens were shocked from two initial pressures of 0.80 and 4.72 MPa at room temperature. Time-resolved spectral radiation histories were recorded by using a multiwavelength channel pyrometer. The transient spectra with the wavelength range of 460-700 nm were recorded by using a spectrometer to evaluate the shock temperature. Shock velocity was measured and particle velocity was determined by the impedance matching methods. The equations of state of xenon plasma and ionization degree have been discussed in terms of the self-consistent fluid variational theory.

  16. Is the classical two-term approximation of electron kinetic theory satisfactory for swarms and plasmas?

    International Nuclear Information System (INIS)

    White, R D; Robson, R E; Schmidt, B; Morrison, Michael A

    2003-01-01

    The 'two-term' approximation (representation of the electron distribution by the first two terms of an expansion in spherical harmonics in velocity space) continues to occupy a central role in the low-temperature plasma physics literature, in spite of the mass of evidence illustrating its inadequacy in the swarm (free diffusion) limit for many molecular gases. Part of the problem lies in the failure of many authors to specify quantitatively what they mean when they say that the two-term approximation is 'acceptable'. Thus for example, an error of 10% in transport coefficients may well be acceptable in many plasma applications, but for analysis of highly accurate swarm experiments to compare with ab initio and beam-derived cross-sections, 0.1% or less is required, making 'multi-term' analysis mandatory. While reconciliation of the swarm and plasma literature along the lines of two different accuracy regimes may thus be possible, we dispute claims that the two-term approximation is generally satisfactory for inversion of swarm experiment data to obtain electron impact cross-sections. The unsatisfactory nature of other assumptions implicit in much of the modern plasma kinetic theory literature is also discussed

  17. Merging for Particle-Mesh Complex Particle Kinetic Modeling of the Multiple Plasma Beams

    Science.gov (United States)

    Lipatov, Alexander S.

    2011-01-01

    We suggest a merging procedure for the Particle-Mesh Complex Particle Kinetic (PMCPK) method in case of inter-penetrating flow (multiple plasma beams). We examine the standard particle-in-cell (PIC) and the PMCPK methods in the case of particle acceleration by shock surfing for a wide range of the control numerical parameters. The plasma dynamics is described by a hybrid (particle-ion-fluid-electron) model. Note that one may need a mesh if modeling with the computation of an electromagnetic field. Our calculations use specified, time-independent electromagnetic fields for the shock, rather than self-consistently generated fields. While a particle-mesh method is a well-verified approach, the CPK method seems to be a good approach for multiscale modeling that includes multiple regions with various particle/fluid plasma behavior. However, the CPK method is still in need of a verification for studying the basic plasma phenomena: particle heating and acceleration by collisionless shocks, magnetic field reconnection, beam dynamics, etc.

  18. Analytical representation of the solution of the space kinetic diffusion equation in a one-dimensional and homogeneous domain

    Energy Technology Data Exchange (ETDEWEB)

    Tumelero, Fernanda; Bodmann, Bardo E. J.; Vilhena, Marco T. [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos Graduacao em Engenharia Mecanica; Lapa, Celso M.F., E-mail: fernanda.tumelero@yahoo.com.br, E-mail: bardo.bodmann@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: lapa@ien.gov.br [Instituto de Engenharia Nuclear (IEN/CNEN-RJ), Rio de Janeiro, RJ (Brazil)

    2017-07-01

    In this work we solve the space kinetic diffusion equation in a one-dimensional geometry considering a homogeneous domain, for two energy groups and six groups of delayed neutron precursors. The proposed methodology makes use of a Taylor expansion in the space variable of the scalar neutron flux (fast and thermal) and the concentration of delayed neutron precursors, allocating the time dependence to the coefficients. Upon truncating the Taylor series at quadratic order, one obtains a set of recursive systems of ordinary differential equations, where a modified decomposition method is applied. The coefficient matrix is split into two, one constant diagonal matrix and the second one with the remaining time dependent and off-diagonal terms. Moreover, the equation system is reorganized such that the terms containing the latter matrix are treated as source terms. Note, that the homogeneous equation system has a well known solution, since the matrix is diagonal and constant. This solution plays the role of the recursion initialization of the decomposition method. The recursion scheme is set up in a fashion where the solutions of the previous recursion steps determine the source terms of the subsequent steps. A second feature of the method is the choice of the initial and boundary conditions, which are satisfied by the recursion initialization, while from the rst recursion step onward the initial and boundary conditions are homogeneous. The recursion depth is then governed by a prescribed accuracy for the solution. (author)

  19. Analytical solution of the multigroup neutron diffusion kinetic equation in one-dimensional cartesian geometry by the integral transform technique

    International Nuclear Information System (INIS)

    Ceolin, Celina

    2010-01-01

    The objective of this work is to obtain an analytical solution of the neutron diffusion kinetic equation in one-dimensional cartesian geometry, to monoenergetic and multigroup problems. These equations are of the type stiff, due to large differences in the orders of magnitude of the time scales of the physical phenomena involved, which make them difficult to solve. The basic idea of the proposed method is applying the spectral expansion in the scalar flux and in the precursor concentration, taking moments and solving the resulting matrix problem by the Laplace transform technique. Bearing in mind that the equation for the precursor concentration is a first order linear differential equation in the time variable, to enable the application of the spectral method we introduce a fictitious diffusion term multiplied by a positive value which tends to zero. This procedure opened the possibility to find an analytical solution to the problem studied. We report numerical simulations and analysis of the results obtained with the precision controlled by the truncation order of the series. (author)

  20. The kinetic theory and stability of a stochastic plasma with respect to low frequency perturbations and magnetospheric convection

    International Nuclear Information System (INIS)

    Hurricane, O.A.

    1994-09-01

    In this dissertation, a new linear Vlasov kinetic theory is developed for calculating the plasma response to perturbing electromagnetic fields in cases where the particle dynamics are stochastic; for modes with frequencies less than the typical particle bounce frequency. A variational form is arrived at which allows one to properly perform a stability analysis for a stochastic plasma. In the case of stochastic dynamics, the authors demonstrate that the plasma responds to the flux tube volume average of the perturbing potentials as opposed to the usual case of adiabatic dynamics where plasma responds to the bounce average of the perturbed potentials. They show that for the stochastic plasma, the kinetic variational form maps into the Bernstein energy principle if the perturbation frequency is large compared to all drift frequencies, the perpendicular wavelength is large compared to the Larmor radius, and vanishing of the potentials associated with the parallel electric field are all assumed. By explicit minimization of the energy principle, it is established that the stochastic plasma is always less stable than an adiabatic plasma. Lastly, the effect of strictly enforcing the quasi-neutrality (QN) condition upon a gyro-kinetic type stability analysis is explored. From simple mathematical considerations, it is shown that when the QN condition is imposed convective type modes that are equipotentials along magnetic field lines are created that alter the stability properties of the plasma. The pertinent modifications to the Bernstein energy principle are given

  1. Experimental study of the efficiency of transformation of the dense plasma hypersonic flow kinetic energy into a radiation

    International Nuclear Information System (INIS)

    Kamrukov, A.S.; Kozlov, N.P.; Myshelov, E.P.; Protasov, Yu.S.

    1981-01-01

    Analysis of physical specific features of radiator where plasma heating is performed with tbermalization of directed kinetic energy of dense plasma flows accelerated electrodynamically up to hypersonic velocities during its shock deceleration, is given. It is shown that the plasma heating method considered has a number of principle advantages as compared with methods most disseminated now for generation of dense intensively radiating plasma (current heating exploding method) and suggests new possibilities for construction of selective high brightness radiat.ion sources of ultraviolet and far vacuum ultraviolet ranges of spectrum. Radiation gas dynamic processes of hypersonic plasma flow deceleration formed with magnetoplasma compressors have been experimentally investigated on their interaction with condenced matters in vacuum and basic thermodynamic parameters of shock compressed plasma have been determined. It is shown that the conversion process of kinetic energy of high-velocity plasma flows to radiation is accomplished at very high efficiency-integral luminescence of shock compressed plasma can reach approximately 90% of initial kinetic energy of flow [ru

  2. Simulation studies of plasma waves in the electron foreshock: The transition from reactive to kinetic instability

    International Nuclear Information System (INIS)

    Dum, C.T.

    1990-01-01

    The electron beam-plasma instability is analyzed in particle simulation experiments, starting with a beam of small velocity spread. The dispersion relation is solved for snapshots of the actual evolving electron distribution function, rather than for the usual models consisting of Maxwellians. As the beam broadens, the analysis shows a transition from reactive beam modes, with frequencies extending much below the plasma frequency ω e , to kinetic instability of Langmuir waves, ω∼ω e , which is in agreement with the frequencies and growth rates observed in the simulation. Beam evolution is also in agreement with quasi-linear theory, except at the end of the reactive phase when trapping of beam electrons is seen. Although the spectrum temporarily narrows at this stage, there are, in contrast to previous simulations, still many modes present. the system then can proceed to a kinetic phase in which quasi-linear theory is again applicable. This stage is identical with the evolution starting from a gentle broad beam, except that wave levels are several times higher. With higher wave levels, mode coupling effects are also more prominent, but are still unable to prevent plateau formation. In contrast to the Langmuir wave regime, the reactive broadband wave regime lasts only for a relatively short period. In the electron foreshock it could only persist if a narrow beam or a sharp cutoff feature were maintained by continued beam injection and the time-of-flight mechanism

  3. Benchmark of the local drift-kinetic models for neoclassical transport simulation in helical plasmas

    Science.gov (United States)

    Huang, B.; Satake, S.; Kanno, R.; Sugama, H.; Matsuoka, S.

    2017-02-01

    The benchmarks of the neoclassical transport codes based on the several local drift-kinetic models are reported here. Here, the drift-kinetic models are zero orbit width (ZOW), zero magnetic drift, DKES-like, and global, as classified in Matsuoka et al. [Phys. Plasmas 22, 072511 (2015)]. The magnetic geometries of Helically Symmetric Experiment, Large Helical Device (LHD), and Wendelstein 7-X are employed in the benchmarks. It is found that the assumption of E ×B incompressibility causes discrepancy of neoclassical radial flux and parallel flow among the models when E ×B is sufficiently large compared to the magnetic drift velocities. For example, Mp≤0.4 where Mp is the poloidal Mach number. On the other hand, when E ×B and the magnetic drift velocities are comparable, the tangential magnetic drift, which is included in both the global and ZOW models, fills the role of suppressing unphysical peaking of neoclassical radial-fluxes found in the other local models at Er≃0 . In low collisionality plasmas, in particular, the tangential drift effect works well to suppress such unphysical behavior of the radial transport caused in the simulations. It is demonstrated that the ZOW model has the advantage of mitigating the unphysical behavior in the several magnetic geometries, and that it also implements the evaluation of bootstrap current in LHD with the low computation cost compared to the global model.

  4. Species Entropies in the Kinetic Range of Collisionless Plasma Turbulence: Particle-in-cell Simulations

    Science.gov (United States)

    Gary, S. Peter; Zhao, Yinjian; Hughes, R. Scott; Wang, Joseph; Parashar, Tulasi N.

    2018-06-01

    Three-dimensional particle-in-cell simulations of the forward cascade of decaying turbulence in the relatively short-wavelength kinetic range have been carried out as initial-value problems on collisionless, homogeneous, magnetized electron-ion plasma models. The simulations have addressed both whistler turbulence at β i = β e = 0.25 and kinetic Alfvén turbulence at β i = β e = 0.50, computing the species energy dissipation rates as well as the increase of the Boltzmann entropies for both ions and electrons as functions of the initial dimensionless fluctuating magnetic field energy density ε o in the range 0 ≤ ε o ≤ 0.50. This study shows that electron and ion entropies display similar rates of increase and that all four entropy rates increase approximately as ε o , consistent with the assumption that the quasilinear premise is valid for the initial conditions assumed for these simulations. The simulations further predict that the time rates of ion entropy increase should be substantially greater for kinetic Alfvén turbulence than for whistler turbulence.

  5. Continuum Kinetic Plasma Modeling Using a Conservative 4th-Order Method with AMR

    Science.gov (United States)

    Vogman, Genia; Colella, Phillip

    2012-10-01

    When the number of particles in a Debye sphere is large, a plasma can be accurately represented by a distribution function, which can be treated as a continuous incompressible fluid in phase space. In the most general case the evolution of such a distribution function is described by the 6D Boltzmann-Maxwell partial differential equation system. To address the challenges associated with solving a 6D hyperbolic governing equation, a simpler 3D Vlasov-Poisson system is considered. A 4th-order accurate Vlasov-Poisson model has been developed in one spatial and two velocity dimensions. The governing equation is cast in conservation law form and is solved with a finite volume representation. Adaptive mesh refinement (AMR) is used to allow for efficient use of computational resources while maintaining desired levels of resolution. The model employs a flux limiter to remedy non-physical effects such as numerical dispersion. The model is tested on the two-stream, beam-plasma, and Dory-Guest-Harris instabilities. All results are compared with linear theory.

  6. Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Izacard, Olivier, E-mail: izacard@llnl.gov [Lawrence Livermore National Laboratory, 7000 East Avenue, L-637, Livermore, California 94550 (United States)

    2016-08-15

    In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, called kinetic effects, are required to be taken into account especially for fusion reactor plasmas. Generally, because the perturbation theory is not consistent with observed steady-state non-Maxwellians, these kinetic effects are numerically evaluated by very central processing unit (CPU)-expensive codes, avoiding the analytic complexity of velocity phase space integrals. We develop here a new method based on analytic non-Maxwellian distribution functions constructed from non-orthogonal basis sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental non-Maxwellians, (iii) help to understand unsolved problems such as diagnostics discrepancies from the physical interpretation of the parameters, and (iv) obtain analytic corrections due to kinetic effects given by a small number of terms and removing the numerical error of the evaluation of velocity phase space integrals. This work does not attempt to derive new physical effects even if it could be possible to discover one from the better understandings of some unsolved problems, but here we focus on the analytic prediction of kinetic corrections from analytic non-Maxwellians. As applications, examples of analytic kinetic corrections are shown for the secondary electron emission, the Langmuir probe characteristic curve, and the entropy. This is done by using three analytic representations of the distribution function: the Kappa distribution function, the bi-modal or a new interpreted non-Maxwellian distribution function (INMDF). The existence of INMDFs is proved by new understandings of the experimental discrepancy of the measured electron temperature between two diagnostics in JET. As main results, it

  7. Kinetics of electron-positron pair plasmas using an adaptive Monte Carlo method

    International Nuclear Information System (INIS)

    Pilla, R.P.; Shaham, J.

    1997-01-01

    A new algorithm for implementing the adaptive Monte Carlo method is given. It is used to solve the Boltzmann equations that describe the time evolution of a nonequilibrium electron-positron pair plasma containing high-energy photons. These are coupled nonlinear integro-differential equations. The collision kernels for the photons as well as pairs are evaluated for Compton scattering, pair annihilation and creation, bremsstrahlung, and Coulomb collisions. They are given as multidimensional integrals which are valid for all energies. For an homogeneous and isotropic plasma with no particle escape, the equilibrium solution is expressed analytically in terms of the initial conditions. For two specific cases, for which the photon and the pair spectra are initially constant or have a power-law distribution within the given limits, the time evolution of the plasma is analyzed using the new method. The final spectra are found to be in a good agreement with the analytical solutions. The new algorithm is faster than the Monte Carlo scheme based on uniform sampling and more flexible than the numerical methods used in the past, which do not involve Monte Carlo sampling. It is also found to be very stable. Some astrophysical applications of this technique are discussed. copyright 1997 The American Astronomical Society

  8. Local energy equation for two-electron atoms and relation between kinetic energy and electron densities

    International Nuclear Information System (INIS)

    March, N.H.

    2002-08-01

    In early work, Dawson and March [J. Chem. Phys. 81, 5850 (1984)] proposed a local energy method for treating both Hartree-Fock and correlated electron theory. Here, an exactly solvable model two-electron atom with pure harmonic interactions is treated in its ground state in the above context. A functional relation between the kinetic energy density t(r) at the origin r=0 and the electron density p(r) at the same point then emerges. The same approach is applied to the Hookean atom; in which the two electrons repel with Coulombic energy e 2 /r 12 , with r 12 the interelectronic separation, but are still harmonically confined. Again the kinetic energy density t(r) is the focal point, but now generalization away from r=0 is also effected. Finally, brief comments are added about He-like atomic ions in the limit of large atomic number. (author)

  9. 3D-full wave and kinetics numerical modelling of electron cyclotron resonance ion sources plasma: steps towards self-consistency

    International Nuclear Information System (INIS)

    Mascali, D.; Neri, L.; Castro, G.; Celona, L.; Gammino, S.; Torrisi, G.; Sorbello, G.

    2015-01-01

    Electron Cyclotron Resonance (ECR) ion Sources are the most performing machines for the production of intense beams of multi-charged ions in fundamental science, applied physics and industry. Investigation of plasma dynamics in ECRIS still remains a challenge. A better comprehension of electron heating, ionization and diffusion processes, ion confinement and ion beam formation is mandatory in order to increase ECRIS performances both in terms of output beams currents, charge states, beam quality (emittance minimization, beam halos suppression, etc.). Numerical solution of Vlasov equation via kinetic codes coupled to FEM solvers is ongoing at INFN-LNS, based on a PIC strategy. Preliminary results of the modeling will be shown about wave-plasma interaction and electron-ion confinement: the obtained results are very helpful to better understand the influence of the different parameters (especially RF frequency and power) on the ion beam formation mechanism. The most important clues coming out from the simulations are that although vacuum field RF field distribution (that is a cavity, modal field distribution) is perturbed by the plasma medium, the non-uniformity in the electric field amplitude still persists in the plasma filled cavity. This non-uniformity can be correlated with non-uniform plasma distribution, explaining a number of experimental observations

  10. An analysis of the 'semi-dissipative' terms in the plasma-dynamical equations

    Energy Technology Data Exchange (ETDEWEB)

    Story, L

    1979-01-01

    Consideration is given to the terms arising from collision corrections to the pressures and convective energy flows in the equation of state for the total and electrokinetic pressures and the convective part of the total and relative energy flows obtained by applying hydrodynamical projection techniques to a weakly coupled collisionless plasma near equilibrium. It is shown that the unusual semidissipative contributions to the total pressure deviation from equilibrium and to the convective portion of the total and relative energy flows are zero. The semidissipative contributions in the electrokinetic pressure deviation from equilibrium still remain, however, due to the inclusion of terms usually appearing in the friction vector.

  11. Simulation of laser propagation in a plasma with a frequency wave equation

    International Nuclear Information System (INIS)

    Desroziers, S.; Nataf, F.; Sentis, R.

    2008-01-01

    The aim of this work is to perform numerical simulations of the propagation of a laser in a plasma. At each time step, one has to solve a Helmholtz equation in a domain which consists in some hundreds of millions of cells. To solve this huge linear system, we use an iterative Krylov method preconditioned by a separable matrix. The corresponding linear system is solved with a block cyclic reduction method. Some enlightenments on the parallel implementation are also given. Lastly, numerical results are presented including some features concerning the scalability of the numerical method on a parallel architecture. (authors)

  12. Analysis of nonlinear parabolic equations modeling plasma diffusion across a magnetic field

    International Nuclear Information System (INIS)

    Hyman, J.M.; Rosenau, P.

    1984-01-01

    We analyse the evolutionary behavior of the solution of a pair of coupled quasilinear parabolic equations modeling the diffusion of heat and mass of a magnetically confined plasma. The solutions's behavior, due to the nonlinear diffusion coefficients, exhibits many new phenomena. In short time, the solution converges into a highly organized symmetric pattern that is almost completely independent of initial data. The asymptotic dynamics then become very simple and take place in a finite dimensional space. These conclusions are backed by extensive numerical experimentation

  13. Four-dimensional integral equations for the MHD diffraction waves in plasma

    International Nuclear Information System (INIS)

    Alexandrova, A.A.; Khizhnyak, N.A.

    2000-01-01

    The superficial analysis of the boundary-value nonstationary problem for Alfven wave has shown the principal possibility of using the method of evolutionary integral equations of non-stationary macroscopic electrodynamical in a case of MHD description of waves in plasma. With the importance of strict mathematical solutions obtained for simple model problems that is the diffraction of one separately taken Alfven wave is that it can be the basis for construction of the approximate solutions of more complex boundary-value problems

  14. Solubility of the transport equation in the kinetics of coagulation and fragmentation

    International Nuclear Information System (INIS)

    Dubovskii, P B

    2001-01-01

    We prove a local existence theorem for a continuous solution of the spatially inhomogeneous kinetic coagulation-fragmentation model of Smoluchowski. Then we prove the solubility of the problem in the large in the class of continuous functions. It is important to emphasize that we admit unbounded integral kernels in both cases. The uniqueness of the solution and its continuous dependence on the input data are also demonstrated

  15. Nitric oxide kinetics in the afterglow of a diffuse plasma filament

    International Nuclear Information System (INIS)

    Burnette, D; Montello, A; Adamovich, I V; Lempert, W R

    2014-01-01

    A suite of laser diagnostics is used to study kinetics of vibrational energy transfer and plasma chemical reactions in a nanosecond pulse, diffuse filament electric discharge and afterglow in N 2 and dry air at 100 Torr. Laser-induced fluorescence of NO and two-photon absorption laser-induced fluorescence of O and N atoms are used to measure absolute, time-resolved number densities of these species after the discharge pulse, and picosecond coherent anti-Stokes Raman spectroscopy is used to measure time-resolved rotational temperature and ground electronic state N 2 (v = 0–4) vibrational level populations. The plasma filament diameter, determined from plasma emission and NO planar laser-induced fluorescence images, remains nearly constant after the discharge pulse, over a few hundred microseconds, and does not exhibit expansion on microsecond time scale. Peak temperature in the discharge and the afterglow is low, T ≈ 370 K, in spite of significant vibrational nonequilibrium, with peak N 2 vibrational temperature of T v  ≈ 2000 K. Significant vibrational temperature rise in the afterglow is likely caused by the downward N 2 –N 2 vibration–vibration (V–V) energy transfer. Simple kinetic modeling of time-resolved N, O, and NO number densities in the afterglow, on the time scale longer compared to relaxation and quenching time of excited species generated in the plasma, is in good agreement with the data. In nitrogen, the N atom density after the discharge pulse is controlled by three-body recombination and radial diffusion. In air, N, NO and O concentrations are dominated by the reverse Zel'dovich reaction, N + NO → N 2  + O, and ozone formation reaction, O + O 2  + M → O 3  + M, respectively. The effect of vibrationally excited nitrogen molecules and excited N atoms on NO formation kinetics is estimated to be negligible. The results suggest that NO formation in the nanosecond pulse discharge is dominated by reactions of

  16. Nitric oxide kinetics in the afterglow of a diffuse plasma filament

    Science.gov (United States)

    Burnette, D.; Montello, A.; Adamovich, I. V.; Lempert, W. R.

    2014-08-01

    A suite of laser diagnostics is used to study kinetics of vibrational energy transfer and plasma chemical reactions in a nanosecond pulse, diffuse filament electric discharge and afterglow in N2 and dry air at 100 Torr. Laser-induced fluorescence of NO and two-photon absorption laser-induced fluorescence of O and N atoms are used to measure absolute, time-resolved number densities of these species after the discharge pulse, and picosecond coherent anti-Stokes Raman spectroscopy is used to measure time-resolved rotational temperature and ground electronic state N2(v = 0-4) vibrational level populations. The plasma filament diameter, determined from plasma emission and NO planar laser-induced fluorescence images, remains nearly constant after the discharge pulse, over a few hundred microseconds, and does not exhibit expansion on microsecond time scale. Peak temperature in the discharge and the afterglow is low, T ≈ 370 K, in spite of significant vibrational nonequilibrium, with peak N2 vibrational temperature of Tv ≈ 2000 K. Significant vibrational temperature rise in the afterglow is likely caused by the downward N2-N2 vibration-vibration (V-V) energy transfer. Simple kinetic modeling of time-resolved N, O, and NO number densities in the afterglow, on the time scale longer compared to relaxation and quenching time of excited species generated in the plasma, is in good agreement with the data. In nitrogen, the N atom density after the discharge pulse is controlled by three-body recombination and radial diffusion. In air, N, NO and O concentrations are dominated by the reverse Zel'dovich reaction, N + NO → N2 + O, and ozone formation reaction, O + O2 + M → O3 + M, respectively. The effect of vibrationally excited nitrogen molecules and excited N atoms on NO formation kinetics is estimated to be negligible. The results suggest that NO formation in the nanosecond pulse discharge is dominated by reactions of excited electronic states of nitrogen, occurring on

  17. Interesting features of nonlinear shock equations in dissipative pair-ion-electron plasmas

    International Nuclear Information System (INIS)

    Masood, W.; Rizvi, H.

    2011-01-01

    Two dimensional nonlinear electrostatic waves are studied in unmagnetized, dissipative pair-ion-electron plasmas in the presence of weak transverse perturbation. The dissipation in the system is taken into account by incorporating the kinematic viscosity of both positive and negative ions. In the linear case, a biquadratic dispersion relation is obtained, which yields the fast and slow modes in a pair-ion-electron plasma. It is shown that the limiting cases of electron-ion and pair-ion can be retrieved from the general biquadratic dispersion relation, and the differences in the characters of the waves propagating in both the cases are also highlighted. Using the small amplitude approximation method, the nonlinear Kadomtsev Petviashvili Burgers as well as Burgers-Kadomtsev Petviashvili equations are derived and their applicability for pair-ion-electron plasma is explained in detail. The present study may have relevance to understand the formation of two dimensional electrostatic shocks in laboratory produced pair-ion-electron plasmas.

  18. Kinetic analysis of spin current contribution to spectrum of electromagnetic waves in spin-1/2 plasma. I. Dielectric permeability tensor for magnetized plasmas

    Science.gov (United States)

    Andreev, Pavel A.

    2017-02-01

    The dielectric permeability tensor for spin polarized plasmas is derived in terms of the spin-1/2 quantum kinetic model in six-dimensional phase space. Expressions for the distribution function and spin distribution function are derived in linear approximations on the path of dielectric permeability tensor derivation. The dielectric permeability tensor is derived for the spin-polarized degenerate electron gas. It is also discussed at the finite temperature regime, where the equilibrium distribution function is presented by the spin-polarized Fermi-Dirac distribution. Consideration of the spin-polarized equilibrium states opens possibilities for the kinetic modeling of the thermal spin current contribution in the plasma dynamics.

  19. Kinetic equation of Lagrange particles and turbulence of an incompressible fluid

    International Nuclear Information System (INIS)

    Gordienko, S.N.

    1999-01-01

    Closed equation for the two-point function of the velocity and pressure gradient distribution is obtained. The spectral properties of the turbulent flow are studied on the basis of the analysis of scaling properties of the above equation and the problem on the role of the vorticity distribution in a turbulent flow alternation was considered. It is shown, that alternation is connected with boundary conditions. The geometric picture of the alternation is found. It is established, that distribution of the vorticity and correspondingly the role of alternation in the currents with spirality and without spirality are completely different

  20. A Hartree-Fock-Slater-Boltzmann-Saha method for detailed atomic structure and equation of state of plasmas

    International Nuclear Information System (INIS)

    Jiang Minhao; Meng Xujun

    2005-01-01

    The effect of the free electron background in plasmas is introduced in Hartree-Fock-Slater self-consistent field atomic model to correct the single electron energies for each electron configuration, and to provide accurate atomic data for Boltzmann-Saha equation. In the iteration process chemical potential is adjusted to change the free electron background to satisfy simultaneously the conservation of the free electrons in Saha equation as well as in Hartree-Fock-Slater self-consistent field atomic model. As examples the equations of state of the carbon and aluminum plasmas are calculated to show the applicability of this method. (authors)