Global Vlasov simulation on magnetospheres of astronomical objects

International Nuclear Information System (INIS)

Umeda, Takayuki; Ito, Yosuke; Fukazawa, Keiichiro

2013-01-01

Space plasma is a collisionless, multi-scale, and highly nonlinear medium. There are various types of self-consistent computer simulations that treat space plasma according to various approximations. We develop numerical schemes for solving the Vlasov (collisionless Boltzmann) equation, which is the first-principle kinetic equation for collisionless plasma. The weak-scaling benchmark test shows that our parallel Vlasov code achieves a high performance and a high scalability. Currently, we use more than 1000 cores for parallel computations and apply the present parallel Vlasov code to various cross-scale processes in space plasma, such as a global simulation on the interaction between solar/stellar wind and magnetospheres of astronomical objects

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

Study of the heavy ions (Au+Au at 150 AMeV) collisions with the FOPI detector. Comparison with the Landau-Vlasov model; Etude des collisions d`ions lourds AU+AU a 150 A.MeV avec le detecteur FOPI. Comparaison avec le modele de Landau-Vlasov

Energy Technology Data Exchange (ETDEWEB)

Boussange, S

1995-09-15

In this thesis, heavy ions (Au+Au) collisions experiments are made at 150 AMeV.In the first part, a general study of the nuclear matter equation is presented. Then the used Landau-Vlasov theoretical model is describe. The third part presents the FOPI experience and the details of how to obtain this theoretical predictions (filter, cuts, corrections, possible centrality selections).At the end, experimental results and comparisons with the Landau-Vlasov model are presented. (TEC). 105 refs., 96 figs., 14 tabs.

Cosmology in one dimension: Vlasov dynamics.

Science.gov (United States)

Manfredi, Giovanni; Rouet, Jean-Louis; Miller, Bruce; Shiozawa, Yui

2016-04-01

Numerical simulations of self-gravitating systems are generally based on N-body codes, which solve the equations of motion of a large number of interacting particles. This approach suffers from poor statistical sampling in regions of low density. In contrast, Vlasov codes, by meshing the entire phase space, can reach higher accuracy irrespective of the density. Here, we perform one-dimensional Vlasov simulations of a long-standing cosmological problem, namely, the fractal properties of an expanding Einstein-de Sitter universe in Newtonian gravity. The N-body results are confirmed for high-density regions and extended to regions of low matter density, where the N-body approach usually fails.

The free energy of Maxwell-Vlasov equilibria

International Nuclear Information System (INIS)

Morrison, P.J.; Pfirsch, D.

1989-10-01

A previously derived expression for the energy of arbitrary perturbations about arbitrary Vlasov-Maxwell equilibria is transformed into a very compact form. The new form is also obtained by a canonical transformation method for solving Vlasov's equation, which is based on Lie group theory. This method is simpler than the one used before and provides better physical insight. Finally a procedure is presented for determining the existence of negative-energy modes. In this context the question of why there is an accessibility constraint for the particles, but not for the fields, is discussed. 16 refs

Global well posedness of the relativistic Vlasov-Yukawa system with small data

International Nuclear Information System (INIS)

Ha, Seung-Yeal; Lee, Ho

2007-01-01

In this paper, we present an existence theory and uniform L 1 -stability estimate for classical solutions with small data to the Vlasov-Yukawa system. The Vlasov-Yukawa system corresponds to a short-range correction of the Vlasov-Poisson system appearing in plasma physics and astrophysics. For the existence and stability of classical solutions, we crucially use dispersion estimates due to the smallness of data

Explosions in Landau Vlasov dynamics

International Nuclear Information System (INIS)

Suraud, E.; Cussol, D.; Gregoire, C.; Boilley, D.; Pi, M.; Schuck, P.; Remaud, B.; Sebille, F.

1988-01-01

A microscopic study of the quasi-fusion/explosion transition is presented in the framework of Landau-Vlasov simulations of intermediate energy heavy-ion collisions (bombarding energies between 10 and 100 MeV/A). A detailed analysis in terms of the Equation of State of the system is performed. In agreement with schematic models we find that the composite nuclear system formed in the collision does explode when it stays long enough in the mechanically unstable region (spinodal region). Quantitative estimates of the explosion threshold are given for central symmetric reactions (Ca+Ca and Ar+Ti). The effect of the nuclear matter compressibility modulus is discussed

Connection between hydrodynamic, water bag and Vlasov models

International Nuclear Information System (INIS)

Gros, M.; Bertrand, P.; Feix, M.R.

1978-01-01

The connection between hydrodynamic, water bag and Vlasov models is still under consideration with numerical experiments. For long wavelength, slightly non linear excitations and initial preparations such as the usual adiabatic invariant Pn -3 is space independent, the hydrodynamic model is equivalent to the water bag, and for long wavelengths a nice agreement is found with the full numerical solution of the Vlasov equation. For other initial conditions when the water bag cannot be defined, the hydrodynamic approach does not represent the correct behaviour. (author)

Vlasov modelling of parallel transport in a tokamak scrape-off layer

International Nuclear Information System (INIS)

Manfredi, G; Hirstoaga, S; Devaux, S

2011-01-01

A one-dimensional Vlasov-Poisson model is used to describe the parallel transport in a tokamak scrape-off layer. Thanks to a recently developed 'asymptotic-preserving' numerical scheme, it is possible to lift numerical constraints on the time step and grid spacing, which are no longer limited by, respectively, the electron plasma period and Debye length. The Vlasov approach provides a good velocity-space resolution even in regions of low density. The model is applied to the study of parallel transport during edge-localized modes, with particular emphasis on the particles and energy fluxes on the divertor plates. The numerical results are compared with analytical estimates based on a free-streaming model, with good general agreement. An interesting feature is the observation of an early electron energy flux, due to suprathermal electrons escaping the ions' attraction. In contrast, the long-time evolution is essentially quasi-neutral and dominated by the ion dynamics.

Vlasov modelling of parallel transport in a tokamak scrape-off layer

Energy Technology Data Exchange (ETDEWEB)

Manfredi, G [Institut de Physique et Chimie des Materiaux, CNRS and Universite de Strasbourg, BP 43, F-67034 Strasbourg (France); Hirstoaga, S [INRIA Nancy Grand-Est and Institut de Recherche en Mathematiques Avancees, 7 rue Rene Descartes, F-67084 Strasbourg (France); Devaux, S, E-mail: Giovanni.Manfredi@ipcms.u-strasbg.f, E-mail: hirstoaga@math.unistra.f, E-mail: Stephane.Devaux@ccfe.ac.u [JET-EFDA, Culham Science Centre, Abingdon, OX14 3DB (United Kingdom)

2011-01-15

A one-dimensional Vlasov-Poisson model is used to describe the parallel transport in a tokamak scrape-off layer. Thanks to a recently developed 'asymptotic-preserving' numerical scheme, it is possible to lift numerical constraints on the time step and grid spacing, which are no longer limited by, respectively, the electron plasma period and Debye length. The Vlasov approach provides a good velocity-space resolution even in regions of low density. The model is applied to the study of parallel transport during edge-localized modes, with particular emphasis on the particles and energy fluxes on the divertor plates. The numerical results are compared with analytical estimates based on a free-streaming model, with good general agreement. An interesting feature is the observation of an early electron energy flux, due to suprathermal electrons escaping the ions' attraction. In contrast, the long-time evolution is essentially quasi-neutral and dominated by the ion dynamics.

Modeling Microbunching from Shot Noise Using Vlasov Solvers

International Nuclear Information System (INIS)

Venturini, Marco; Venturini, Marco; Zholents, Alexander

2008-01-01

Unlike macroparticle simulations, which are sensitive to unphysical statistical fluctuations when the number of macroparticles is smaller than the bunch population, direct methods for solving the Vlasov equation are free from sampling noise and are ideally suited for studying microbunching instabilities evolving from shot noise. We review a 2D (longitudinal dynamics) Vlasov solver we have recently developed to study the microbunching instability in the beam delivery systems for x-ray FELs and present an application to FERMI(at)Elettra. We discuss, in particular, the impact of the spreader design on microbunching

Comparison of free-streaming ELM formulae to a Vlasov simulation

Energy Technology Data Exchange (ETDEWEB)

Moulton, D., E-mail: david.moulton@cea.fr [CEA, IRFM, F-13108 Saint-Paul Lez Durance (France); Fundamenski, W. [Imperial College of Science, Technology and Medicine, London (United Kingdom); Manfredi, G. [Institut de Physique et Chimie des Matériaux, CNRS and Université de Strasbourg, BP 43, F-67034 Strasbourg (France); Hirstoaga, S. [INRIA Nancy Grand-Est and Institut de Recherche en Mathématiques Avancées, 7 rue René Descartes, F-67084 Strasbourg (France); Tskhakaya, D. [Association EURATOM-ÖAW, University of Innsbruck, A-6020 Innsbruck (Austria)

2013-07-15

The main drawbacks of the original free-streaming equations for edge localised mode transport in the scrape-off layer [W. Fundamenski, R.A. Pitts, Plasma Phys. Control Fusion 48 (2006) 109] are that the plasma potential is not accounted for and that only solutions for ion quantities are considered. In this work, the equations are modified and augmented in order to address these two issues. The new equations are benchmarked against (and justified by) a numerical simulation which solves the Vlasov equation in 1d1v. When the source function due to an edge localised mode is instantaneous, the modified free-streaming ‘impulse response’ equations agree closely with the Vlasov simulation results. When the source has a finite duration in time, the agreement worsens. However, in all cases the match is encouragingly good, thus justifying the applicability of the free-streaming approach.

Mathematical and numerical methods for Vlasov-Maxwell equations: the contributions of data mining

International Nuclear Information System (INIS)

Assous, F.; Chaskalovic, J.

2014-01-01

There exist a lot of formulations that can model plasma physics or particle accelerators problems as the Vlasov- Maxwell equations. This paper deals with the applications of data mining techniques in the evaluation of numerical solutions of Vlasov-Maxwell models. This is part of the topic of characterizing the model and approximation errors via learning techniques. We give two examples of application. The first one aims at comparing two Vlasov-Maxwell approximate models. In the second one, a scheme based on data mining techniques is proposed to characterize the errors between a P1 and a P2 finite element Particle-In-Cell approach. Beyond these examples, this original approach should operate in all cases where intricate numerical simulations like for the Vlasov-Maxwell equations take a central part. (authors)

Vlasov dynamics of periodically driven systems

Science.gov (United States)

Banerjee, Soumyadip; Shah, Kushal

2018-04-01

Analytical solutions of the Vlasov equation for periodically driven systems are of importance in several areas of plasma physics and dynamical systems and are usually approximated using ponderomotive theory. In this paper, we derive the plasma distribution function predicted by ponderomotive theory using Hamiltonian averaging theory and compare it with solutions obtained by the method of characteristics. Our results show that though ponderomotive theory is relatively much easier to use, its predictions are very restrictive and are likely to be very different from the actual distribution function of the system. We also analyse all possible initial conditions which lead to periodic solutions of the Vlasov equation for periodically driven systems and conjecture that the irreducible polynomial corresponding to the initial condition must only have squares of the spatial and momentum coordinate. The resulting distribution function for other initial conditions is aperiodic and can lead to complex relaxation processes within the plasma.

Simple collision operators for direct Vlasov simulations of laser plasma interaction and transport

International Nuclear Information System (INIS)

Arber, T D; Sircombe, N J

2010-01-01

Non-local electron transport effects have a direct influence on the compression of cryogenic targets in laser driven ICF and target heating in high energy density experiments. There is a growing need for self-consistent models of laser plasma interactions coupled to nonlocal transport. We present a direct Vlasov solver that includes multiple species and a simple collision operator. This BGK model operator - which conserves particle density, energy and momentum - is fully implicit. For collisionless plasmas it has been shown that a double layer may be formed in which an accelerated, kinetic ion population satisfies the zero current condition. Here we extend this result to collisionalities of interest to laser driven ignition to assess the validity of nonlocal electron transport models based on fluid ions.

Vlasov analysis of microbunching instability for magnetized beams

Directory of Open Access Journals (Sweden)

C.-Y. Tsai

2017-05-01

Full Text Available For a high-brightness electron beam with high bunch charge traversing a recirculation beam line, coherent synchrotron radiation and space charge effects may result in microbunching instability (MBI. Both tracking simulation and Vlasov analysis for an early design of a circulator cooler ring (CCR for the Jefferson Lab Electron Ion Collider (JLEIC reveal significant MBI [Ya. Derbenev and Y. Zhang, Proceedings of the Workshop on Beam Cooling and Related Topics, COOL’09, Lanzhou, China, 2009 (2009, FRM2MCCO01]. It is envisioned that the MBI could be substantially suppressed by using a magnetized beam. In this paper we have generalized the existing Vlasov analysis, originally developed for a nonmagnetized beam (or transversely uncoupled beam, to the description of transport of a magnetized beam including relevant collective effects. The new formulation is then employed to confirm prediction of microbunching suppression for a magnetized beam transport in the recirculation arc of a recent JLEIC energy recovery linac (ERL based cooler design for electron cooling. It is found that the smearing effect in the longitudinal beam phase space originates from the large transverse beam size as a nature of the magnetized beams and becomes effective through the x-z correlation when the correlated distance is larger than the microbunched scale. As a comparison, MBI analysis of the early design of JLEIC CCR is also presented in this paper.

Nonlinear gyrokinetic Maxwell-Vlasov equations using magnetic coordinates

International Nuclear Information System (INIS)

Brizard, A.

1988-09-01

A gyrokinetic formalism using magnetic coordinates is used to derive self-consistent, nonlinear Maxwell-Vlasov equations that are suitable for particle simulation studies of finite-β tokamak microturbulence and its associated anomalous transport. The use of magnetic coordinates is an important feature of this work as it introduces the toroidal geometry naturally into our gyrokinetic formalism. The gyrokinetic formalism itself is based on the use of the Action-variational Lie perturbation method of Cary and Littlejohn, and preserves the Hamiltonian structure of the original Maxwell-Vlasov system. Previous nonlinear gyrokinetic sets of equations suitable for particle simulation analysis have considered either electrostatic and shear-Alfven perturbations in slab geometry, or electrostatic perturbations in toroidal geometry. In this present work, fully electromagnetic perturbations in toroidal geometry are considered. 26 refs

Hamiltonian fluid closures of the Vlasov-Ampère equations: From water-bags to N moment models

Energy Technology Data Exchange (ETDEWEB)

Perin, M.; Chandre, C.; Tassi, E. [Aix-Marseille Université, Université de Toulon, CNRS, CPT UMR 7332, 13288 Marseille (France); Morrison, P. J. [Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712-1060 (United States)

2015-09-15

Moment closures of the Vlasov-Ampère system, whereby higher moments are represented as functions of lower moments with the constraint that the resulting fluid system remains Hamiltonian, are investigated by using water-bag theory. The link between the water-bag formalism and fluid models that involve density, fluid velocity, pressure and higher moments is established by introducing suitable thermodynamic variables. The cases of one, two, and three water-bags are treated and their Hamiltonian structures are provided. In each case, we give the associated fluid closures and we discuss their Casimir invariants. We show how the method can be extended to an arbitrary number of fields, i.e., an arbitrary number of water-bags and associated moments. The thermodynamic interpretation of the resulting models is discussed. Finally, a general procedure to derive Hamiltonian N-field fluid models is proposed.

A New Class of Non-Linear, Finite-Volume Methods for Vlasov Simulation

International Nuclear Information System (INIS)

Banks, J.W.; Hittinger, J.A.

2010-01-01

Methods for the numerical discretization of the Vlasov equation should efficiently use the phase space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order, non-linear, finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls oscillations is presented. The method is fourth-order in space and time in well-resolved regions, but smoothly reduces to a third-order upwind scheme as features become poorly resolved. The new scheme is applied to several standard problems for the Vlasov-Poisson system, and the results are compared with those from other finite-volume approaches, including an artificial viscosity scheme and the Piecewise Parabolic Method. It is shown that the new scheme is able to control oscillations while preserving a higher degree of fidelity of the solution than the other approaches.

Turbulence in unmagnetized Vlasov plasmas

International Nuclear Information System (INIS)

Kuo, S.P.

1985-01-01

The classical technique of transformation and characteristics is employed to analyze the problem of strong turbulence in unmagnetized plasmas. The effect of resonance broadening and perturbation expansion are treated simultaneously, without time secularities. The renormalization procedure of Dupree and Tetreault is used in the transformed Vlasov equation to analyze the turbulence and to derive explicitly a diffusion equation. Analyses are extended to inhomogeneous plasmas and the relationship between the transformation and ponderomotive force is obtained. (author)

Continuum Vlasov Simulation in Four Phase-space Dimensions

Science.gov (United States)

Cohen, B. I.; Banks, J. W.; Berger, R. L.; Hittinger, J. A.; Brunner, S.

2010-11-01

In the VALHALLA project, we are developing scalable algorithms for the continuum solution of the Vlasov-Maxwell equations in two spatial and two velocity dimensions. We use fourth-order temporal and spatial discretizations of the conservative form of the equations and a finite-volume representation to enable adaptive mesh refinement and nonlinear oscillation control [1]. The code has been implemented with and without adaptive mesh refinement, and with electromagnetic and electrostatic field solvers. A goal is to study the efficacy of continuum Vlasov simulations in four phase-space dimensions for laser-plasma interactions. We have verified the code in examples such as the two-stream instability, the weak beam-plasma instability, Landau damping, electron plasma waves with electron trapping and nonlinear frequency shifts [2]^ extended from 1D to 2D propagation, and light wave propagation.^ We will report progress on code development, computational methods, and physics applications. This work was performed under the auspices of the U.S. DOE by LLNL under contract no. DE-AC52-07NA27344. This work was funded by the Lab. Dir. Res. and Dev. Prog. at LLNL under project tracking code 08-ERD-031. [1] J.W. Banks and J.A.F. Hittinger, to appear in IEEE Trans. Plas. Sci. (Sept., 2010). [2] G.J. Morales and T.M. O'Neil, Phys. Rev. Lett. 28,417 (1972); R. L. Dewar, Phys. Fluids 15,712 (1972).

An adaptive, implicit, conservative, 1D-2V multi-species Vlasov-Fokker-Planck multi-scale solver in planar geometry

Science.gov (United States)

Taitano, W. T.; Chacón, L.; Simakov, A. N.

2018-07-01

We consider a 1D-2V Vlasov-Fokker-Planck multi-species ionic description coupled to fluid electrons. We address temporal stiffness with implicit time stepping, suitably preconditioned. To address temperature disparity in time and space, we extend the conservative adaptive velocity-space discretization scheme proposed in [Taitano et al., J. Comput. Phys., 318, 391-420, (2016)] to a spatially inhomogeneous system. In this approach, we normalize the velocity-space coordinate to a temporally and spatially varying local characteristic speed per species. We explicitly consider the resulting inertial terms in the Vlasov equation, and derive a discrete formulation that conserves mass, momentum, and energy up to a prescribed nonlinear tolerance upon convergence. Our conservation strategy employs nonlinear constraints to enforce these properties discretely for both the Vlasov operator and the Fokker-Planck collision operator. Numerical examples of varying degrees of complexity, including shock-wave propagation, demonstrate the favorable efficiency and accuracy properties of the scheme.

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.''

Numerical simulation of Vlasov equation with parallel tools

International Nuclear Information System (INIS)

Peyroux, J.

2005-11-01

This project aims to make even more powerful the resolution of Vlasov codes through the various parallelization tools (MPI, OpenMP...). A simplified test case served as a base for constructing the parallel codes for obtaining a data-processing skeleton which, thereafter, could be re-used for increasingly complex models (more than four variables of phase space). This will thus make it possible to treat more realistic situations linked, for example, to the injection of ultra short and ultra intense impulses in inertial fusion plasmas, or the study of the instability of trapped ions now taken as being responsible for the generation of turbulence in tokamak plasmas. (author)

Comparing the line broadened quasilinear model to Vlasov code

International Nuclear Information System (INIS)

Ghantous, K.; Berk, H. L.; Gorelenkov, N. N.

2014-01-01

The Line Broadened Quasilinear (LBQ) model is revisited to study its predicted saturation level as compared with predictions of a Vlasov solver BOT [Lilley et al., Phys. Rev. Lett. 102, 195003 (2009) and M. Lilley, BOT Manual. The parametric dependencies of the model are modified to achieve more accuracy compared to the results of the Vlasov solver both in regards to a mode amplitude's time evolution to a saturated state and its final steady state amplitude in the parameter space of the model's applicability. However, the regions of stability as predicted by LBQ model and BOT are found to significantly differ from each other. The solutions of the BOT simulations are found to have a larger region of instability than the LBQ simulations

Comparing the line broadened quasilinear model to Vlasov code

Energy Technology Data Exchange (ETDEWEB)

Ghantous, K. [Laboratoire de Physique des Plasmas, Ecole Polytechnique, 91128 Palaiseau Cedex (France); Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543-0451 (United States); Berk, H. L. [Institute for Fusion Studies, University of Texas, 2100 San Jacinto Blvd, Austin, Texas 78712-1047 (United States); Gorelenkov, N. N. [Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543-0451 (United States)

2014-03-15

The Line Broadened Quasilinear (LBQ) model is revisited to study its predicted saturation level as compared with predictions of a Vlasov solver BOT [Lilley et al., Phys. Rev. Lett. 102, 195003 (2009) and M. Lilley, BOT Manual. The parametric dependencies of the model are modified to achieve more accuracy compared to the results of the Vlasov solver both in regards to a mode amplitude's time evolution to a saturated state and its final steady state amplitude in the parameter space of the model's applicability. However, the regions of stability as predicted by LBQ model and BOT are found to significantly differ from each other. The solutions of the BOT simulations are found to have a larger region of instability than the LBQ simulations.

Comparing the line broadened quasilinear model to Vlasov code

Science.gov (United States)

Ghantous, K.; Berk, H. L.; Gorelenkov, N. N.

2014-03-01

The Line Broadened Quasilinear (LBQ) model is revisited to study its predicted saturation level as compared with predictions of a Vlasov solver BOT [Lilley et al., Phys. Rev. Lett. 102, 195003 (2009) and M. Lilley, BOT Manual. The parametric dependencies of the model are modified to achieve more accuracy compared to the results of the Vlasov solver both in regards to a mode amplitude's time evolution to a saturated state and its final steady state amplitude in the parameter space of the model's applicability. However, the regions of stability as predicted by LBQ model and BOT are found to significantly differ from each other. The solutions of the BOT simulations are found to have a larger region of instability than the LBQ simulations.

New variational formulation of Maxwell-Vlasov and guiding center theories

International Nuclear Information System (INIS)

Pfirsch, D.

1983-07-01

A new variational formulation of Maxwell-Vlasov and related theories is given in terms of a common Lagrangian density for both the 'Vlasov particles' and the Maxwell fields. This formulation is used to derive in a consistent way, on the one hand, correct charge and current densities and, on the other, corresponding energy and energy flux densities. All of these densities generally show in addition to particle like contributions electric polarization and magnetization terms. By some limiting procedure collisionless guiding center theories with polarization drifts included are also treated. In this way local energy conservation laws are formulated for such theories, which has not been possible up to now. (orig.)

Numerical simulation of Vlasov equation with parallel tools; Simulations numeriques de l'equation de Vlasov a l'aide d'outils paralleles

Energy Technology Data Exchange (ETDEWEB)

Peyroux, J

2005-11-15

This project aims to make even more powerful the resolution of Vlasov codes through the various parallelization tools (MPI, OpenMP...). A simplified test case served as a base for constructing the parallel codes for obtaining a data-processing skeleton which, thereafter, could be re-used for increasingly complex models (more than four variables of phase space). This will thus make it possible to treat more realistic situations linked, for example, to the injection of ultra short and ultra intense impulses in inertial fusion plasmas, or the study of the instability of trapped ions now taken as being responsible for the generation of turbulence in tokamak plasmas. (author)

Resolution of the Vlasov-Maxwell system by PIC discontinuous Galerkin method on GPU with OpenCL

Directory of Open Access Journals (Sweden)

Crestetto Anaïs

2013-01-01

Full Text Available We present an implementation of a Vlasov-Maxwell solver for multicore processors. The Vlasov equation describes the evolution of charged particles in an electromagnetic field, solution of the Maxwell equations. The Vlasov equation is solved by a Particle-In-Cell method (PIC, while the Maxwell system is computed by a Discontinuous Galerkin method. We use the OpenCL framework, which allows our code to run on multicore processors or recent Graphic Processing Units (GPU. We present several numerical applications to two-dimensional test cases.

Non-linear free streaming in Vlasov plasma

Czech Academy of Sciences Publication Activity Database

Sedláček, Zdeněk

2004-01-01

Roč. 54, suppl.C (2004), C82-C88 ISSN 0011-4626. [Symposium on Plasma Physics and Technology/21th./. Prague, 14.06.2004-17.06.2004] Institutional research plan: CEZ:AV0Z2043910 Keywords : plasma oscillations * Vlasov equation Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 0.292, year: 2004

VLASOVIA 2013 - International workshop on the theory and applications of Vlasov equation - Slides of the presentations

International Nuclear Information System (INIS)

Aunai, N.; Belmont, G.; Smets, R.; Chandre, C.; Tassi, E.; Morrison, P.J.; Back, A.; Guillebon, L. de; Qin, H.; Squire, J.; Tang, W.M.; Garbet, X.; Esteve, D.; Sarazin, Y.; Abiteboul, J.; Bourdelle, C.; Dif-Pradalier, G.; Ghendrih, P.; Grandgirard, V.; Latu, G.; Smolyakov, A.; Hervieux, P.A.; Manfredi, G.; Jasiak, R.; Kraus, M.; Mora, P.; Morel, P.; Dreydemy Ghiro, F.; Berionni, V.; Gurcan, O.D.; Morrison, P.J.; Negulescu, C.; Pegoraro, F.; Bulanov, S.V.; Califano, F.; Fedeli, L.; Grassi, A.; Macchi, A.; Petri, J.; Pezzi, O.; Valentini, F.; Perrone, D.; Veltri, P.; Taccogna, F.; Minelli, P.; Thide, B.; Tamburini, F.; Throumoulopoulos, G.; Tasso, H.

2014-01-01

The Vlasov equation is used for the modelling of a wide range of phenomena occurring in natural and man-made plasmas, as well as in other many-particle systems displaying a collective behaviour. The purpose of this workshop is to bring together scientists to discuss the latest results on Vlasov theory and related applications. The topics discussed include: space plasmas, inertial confinement plasmas, magnetic confinement plasmas, quantum effects in collisionless plasmas, gravitational systems, Hamiltonian Vlasov dynamics, and computational and numerical approaches. This document gathers the slides of the presentations.

Transient growth of a Vlasov plasma in a weakly inhomogeneous magnetic field

KAUST Repository

Ratushnaya, Valeria

2016-12-17

We investigate the stability properties of a collisionless Vlasov plasma in a weakly inhomogeneous magnetic field using non-modal stability analysis. This is an important topic in a physics of tokamak plasma rich in various types of instabilities. We consider a thin tokamak plasma in a Maxwellian equilibrium, subjected to a small arbitrary perturbation. Within the framework of kinetic theory, we demonstrate the emergence of short time scale algebraic instabilities evolving in a stable magnetized plasma. We show that the linearized governing operator (Vlasov operator) is non-normal leading to the transient growth of the perturbations on the time scale of several plasma periods that is subsequently followed by Landau damping. We calculate the first-order distribution function and the electric field and study the dependence of the transient growth characteristics on the magnetic field strength and perturbation parameters of the system. We compare our results with uniformly magnetized plasma and field-free Vlasov plasma.

Transient growth of a Vlasov plasma in a weakly inhomogeneous magnetic field

KAUST Repository

Ratushnaya, Valeria; Samtaney, Ravi

2016-01-01

We investigate the stability properties of a collisionless Vlasov plasma in a weakly inhomogeneous magnetic field using non-modal stability analysis. This is an important topic in a physics of tokamak plasma rich in various types of instabilities. We consider a thin tokamak plasma in a Maxwellian equilibrium, subjected to a small arbitrary perturbation. Within the framework of kinetic theory, we demonstrate the emergence of short time scale algebraic instabilities evolving in a stable magnetized plasma. We show that the linearized governing operator (Vlasov operator) is non-normal leading to the transient growth of the perturbations on the time scale of several plasma periods that is subsequently followed by Landau damping. We calculate the first-order distribution function and the electric field and study the dependence of the transient growth characteristics on the magnetic field strength and perturbation parameters of the system. We compare our results with uniformly magnetized plasma and field-free Vlasov plasma.

Study of Vlasov instabilities of a gravitational plasma in realistic cosmology

International Nuclear Information System (INIS)

Baptista, J.P.

1982-11-01

A description is given of the cosmological model in which the perturbations will evolve and a bref survey relating to the evolution of the perturbations such as they have been described in recent works. The role of heavy neutrinos in the evolution of baryon perturbations is recalled. Vlasov's linearized system is established for a gravitational plasma. The classification of the gravitational field according to its components of helicity is given. The method of two timescales is introduced in order to solve Vlasov's linearized system. The standard solutions in helicity modes +-2, +-1, and 0 are studied successively [fr

Instability of the time splitting scheme for the one-dimensional and relativistic Vlasov-Maxwell system

CERN Document Server

Huot, F; Bertrand, P; Sonnendrücker, E; Coulaud, O

2003-01-01

The Time Splitting Scheme (TSS) has been examined within the context of the one-dimensional (1D) relativistic Vlasov-Maxwell model. In the strongly relativistic regime of the laser-plasma interaction, the TSS cannot be applied to solve the Vlasov equation. We propose a new semi-Lagrangian scheme based on a full 2D advection and study its advantages over the classical Splitting procedure. Details of the underlying integration of the Vlasov equation appear to be important in achieving accurate plasma simulations. Examples are given which are related to the relativistic modulational instability and the self-induced transparency of an ultra-intense electromagnetic pulse in the relativistic regime.

Numerical methods and analysis of the nonlinear Vlasov equation on unstructured meshes of phase space

International Nuclear Information System (INIS)

Besse, Nicolas

2003-01-01

This work is dedicated to the mathematical and numerical studies of the Vlasov equation on phase-space unstructured meshes. In the first part, new semi-Lagrangian methods are developed to solve the Vlasov equation on unstructured meshes of phase space. As the Vlasov equation describes multi-scale phenomena, we also propose original methods based on a wavelet multi-resolution analysis. The resulting algorithm leads to an adaptive mesh-refinement strategy. The new massively-parallel computers allow to use these methods with several phase-space dimensions. Particularly, these numerical schemes are applied to plasma physics and charged particle beams in the case of two-, three-, and four-dimensional Vlasov-Poisson systems. In the second part we prove the convergence and give error estimates for several numerical schemes applied to the Vlasov-Poisson system when strong and classical solutions are considered. First we show the convergence of a semi-Lagrangian scheme on an unstructured mesh of phase space, when the regularity hypotheses for the initial data are minimal. Then we demonstrate the convergence of classes of high-order semi-Lagrangian schemes in the framework of the regular classical solution. In order to reconstruct the distribution function, we consider symmetrical Lagrange polynomials, B-Splines and wavelets bases. Finally we prove the convergence of a semi-Lagrangian scheme with propagation of gradients yielding a high-order and stable reconstruction of the solution. (author) [fr

Numerical solution of the Maxwell-Vlasov equations in the periodic regime. Application to the study of isotope separation by ion cyclotron resonance

International Nuclear Information System (INIS)

Omnes, P.

1999-01-01

This work is dedicated to the study of the behaviour of a magnetic confined plasma that is excited by a purely sinusoidal electric current delivered by an antenna. The response of the electrons to the electromagnetic field is considered as linear, whereas the ions of the plasma are represented by a non-relativistic Vlasov equation. In order to avoid transients, the coupled Maxwell-Vlasov equations are solved in a periodic mode and in a bounded domain. An equivalent electric conductivity tensor has been defined, this tensor is a linear operator that links the electric current generated by the movement of the particles to the electromagnetic field. Theoretical considerations can assure the existence and uniqueness of a periodical solution to Vlasov equations and of a solution to Maxwell equations in harmonic mode. The system of equations is periodical and has been solved by using an iterative method. The application of this method to the simulation of a isotopic separation device based on ionic cyclotron resonance has shown that the convergence is reached in a few iterations and that the solution is valid. Furthermore a method based on a finite-volume formulation of Maxwell equations in the time domain is presented. 2 new variables are defined in order to better take into account the Gauss' law and the conservation of the magnetic flux, the new system is still hyperbolic. The parallelization of the process has been successfully realized. (A.C.)

Maxwell-Vlasov equations as a continuous Hamiltonian system

International Nuclear Information System (INIS)

Morrison, P.J.

1980-09-01

The well-known Maxwell-Vlasov equations that describe a collisionless plasma are cast into Hamiltonian form. The dynamical variables are the physical although noncanonical variables E, B and f. We present a Poisson bracket which acts on these variables and the energy functional to produce the equations of motion

From the Hartree dynamics to the Vlasov equation

DEFF Research Database (Denmark)

Benedikter, Niels Patriz; Porta, Marcello; Saffirio, Chiara

2016-01-01

We consider the evolution of quasi-free states describing N fermions in the mean field limit, as governed by the nonlinear Hartree equation. In the limit of large N, we study the convergence towards the classical Vlasov equation. For a class of regular interaction potentials, we establish precise...

Multi-scale approximation of Vlasov equation

International Nuclear Information System (INIS)

Mouton, A.

2009-09-01

One of the most important difficulties of numerical simulation of magnetized plasmas is the existence of multiple time and space scales, which can be very different. In order to produce good simulations of these multi-scale phenomena, it is recommended to develop some models and numerical methods which are adapted to these problems. Nowadays, the two-scale convergence theory introduced by G. Nguetseng and G. Allaire is one of the tools which can be used to rigorously derive multi-scale limits and to obtain new limit models which can be discretized with a usual numerical method: this procedure is so-called a two-scale numerical method. The purpose of this thesis is to develop a two-scale semi-Lagrangian method and to apply it on a gyrokinetic Vlasov-like model in order to simulate a plasma submitted to a large external magnetic field. However, the physical phenomena we have to simulate are quite complex and there are many questions without answers about the behaviour of a two-scale numerical method, especially when such a method is applied on a nonlinear model. In a first part, we develop a two-scale finite volume method and we apply it on the weakly compressible 1D isentropic Euler equations. Even if this mathematical context is far from a Vlasov-like model, it is a relatively simple framework in order to study the behaviour of a two-scale numerical method in front of a nonlinear model. In a second part, we develop a two-scale semi-Lagrangian method for the two-scale model developed by E. Frenod, F. Salvarani et E. Sonnendrucker in order to simulate axisymmetric charged particle beams. Even if the studied physical phenomena are quite different from magnetic fusion experiments, the mathematical context of the one-dimensional paraxial Vlasov-Poisson model is very simple for establishing the basis of a two-scale semi-Lagrangian method. In a third part, we use the two-scale convergence theory in order to improve M. Bostan's weak-* convergence results about the finite

Numerical solution of the Maxwell-Vlasov equations in the periodic regime. Application to the study of isotope separation by ion cyclotron resonance; Resolution numerique des equations de Maxwell-Vlasov en regime periodique. Application a l'etude de la separation isotopique par resonance cyclotron ionique

Energy Technology Data Exchange (ETDEWEB)

Omnes, P

1999-01-25

This work is dedicated to the study of the behaviour of a magnetic confined plasma that is excited by a purely sinusoidal electric current delivered by an antenna. The response of the electrons to the electromagnetic field is considered as linear,whereas the ions of the plasma are represented by a non-relativistic Vlasov equation. In order to avoid transients, the coupled Maxwell-Vlasov equations are solved in a periodic mode and in a bounded domain. An equivalent electric conductivity tensor has been defined, this tensor is a linear operator that links the electric current generated by the movement of the particles to the electromagnetic field. Theoretical considerations can assure the existence and uniqueness of a periodical solution to Vlasov equations and of a solution to Maxwell equations in harmonic mode. The system of equations is periodical and has been solved by using an iterative method. The application of this method to the simulation of a isotopic separation device based on ionic cyclotron resonance has shown that the convergence is reached in a few iterations and that the solution is valid. Furthermore a method based on a finite-volume formulation of Maxwell equations in the time domain is presented. 2 new variables are defined in order to better take into account the Gauss' law and the conservation of the magnetic flux, the new system is still hyperbolic. The parallelization of the process has been successfully realized. (A.C.)

Stability of nonlinear Vlasov-Poisson equilibria through spectral deformation and Fourier-Hermite expansion.

Science.gov (United States)

Siminos, Evangelos; Bénisti, Didier; Gremillet, Laurent

2011-05-01

We study the stability of spatially periodic, nonlinear Vlasov-Poisson equilibria as an eigenproblem in a Fourier-Hermite basis (in the space and velocity variables, respectively) of finite dimension, N. When the advection term in the Vlasov equation is dominant, the convergence with N of the eigenvalues is rather slow, limiting the applicability of the method. We use the method of spectral deformation introduced by Crawford and Hislop [Ann. Phys. (NY) 189, 265 (1989)] to selectively damp the continuum of neutral modes associated with the advection term, thus accelerating convergence. We validate and benchmark the performance of our method by reproducing the kinetic dispersion relation results for linear (spatially homogeneous) equilibria. Finally, we study the stability of a periodic Bernstein-Greene-Kruskal mode with multiple phase-space vortices, compare our results with numerical simulations of the Vlasov-Poisson system, and show that the initial unstable equilibrium may evolve to different asymptotic states depending on the way it was perturbed. © 2011 American Physical Society

application of the galerkin-vlasov method to the flexural analysis

African Journals Online (AJOL)

user

In this research, the Galerkin-Vlasov variational method was used to present a general formulation of the Kirchhoff plate problem with simply supported edges and under distributed ..... analysed for elastic, dynamic and stability behaviour,.

Linear Vlasov plasma oscillations in the Fourier transformed velocity space

Czech Academy of Sciences Publication Activity Database

Sedláček, Zdeněk; Nocera, L.

2002-01-01

Roč. 296, - (2002), s. 117-124 ISSN 0375-9601 Institutional research plan: CEZ:AV0Z2043910 Keywords : linear Vlasov plasma Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 1.483, year: 2002

Numerical simulation of Vlasov equation with parallel tools; Simulations numeriques de l'equation de Vlasov a l'aide d'outils paralleles

Energy Technology Data Exchange (ETDEWEB)

Peyroux, J

2005-11-15

This project aims to make even more powerful the resolution of Vlasov codes through the various parallelization tools (MPI, OpenMP...). A simplified test case served as a base for constructing the parallel codes for obtaining a data-processing skeleton which, thereafter, could be re-used for increasingly complex models (more than four variables of phase space). This will thus make it possible to treat more realistic situations linked, for example, to the injection of ultra short and ultra intense impulses in inertial fusion plasmas, or the study of the instability of trapped ions now taken as being responsible for the generation of turbulence in tokamak plasmas. (author)

Vlasov treatment of coherent synchrotron radiation from arbitrary planar orbits

International Nuclear Information System (INIS)

Warnock, R.; Bassi, G.; Ellison, J.A.

2006-01-01

We study the influence of coherent synchrotron radiation (CSR) on particle bunches traveling on arbitrary planar orbits between parallel conducting plates which represent the vacuum chamber. Our goal is to follow the time evolution of the phase space distribution by solving the Vlasov-Maxwell equations in the time domain. This should provide simulations with lower numerical noise than the macro-particle method, and allow one to study such issues as emittance degradation and microbunching due to CSR in bunch compressors. The fields excited by the bunch are computed in the laboratory frame from a new formula that leads to much simpler computations than usual methods. The nonlinear Vlasov equation, formulated in the interaction picture, is integrated in the beam frame by approximating the Perron-Frobenius operator. For application to a chicane bunch compressor we take steps to deal with energy chirp

One-Dimensional Vlasov-Maxwell Equilibrium for the Force-Free Harris Sheet

International Nuclear Information System (INIS)

Harrison, Michael G.; Neukirch, Thomas

2009-01-01

In this Letter, the first nonlinear force-free Vlasov-Maxwell equilibrium is presented. One component of the equilibrium magnetic field has the same spatial structure as the Harris sheet, but whereas the Harris sheet is kept in force balance by pressure gradients, in the force-free solution presented here force balance is maintained by magnetic shear. Magnetic pressure, plasma pressure and plasma density are constant. The method used to find the equilibrium is based on the analogy of the one-dimensional Vlasov-Maxwell equilibrium problem to the motion of a pseudoparticle in a two-dimensional conservative potential. The force-free solution can be generalized to a complete family of equilibria that describe the transition between the purely pressure-balanced Harris sheet to the force-free Harris sheet

Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations

Science.gov (United States)

Athanassoulis, Agissilaos

2018-03-01

We consider the semiclassical limit of nonlinear Schrödinger equations with initial data that are well localized in both position and momentum (non-parametric wavepackets). We recover the Wigner measure (WM) of the problem, a macroscopic phase-space density which controls the propagation of the physical observables such as mass, energy and momentum. WMs have been used to create effective models for wave propagation in: random media, quantum molecular dynamics, mean field limits, and the propagation of electrons in graphene. In nonlinear settings, the Vlasov-type equations obtained for the WM are often ill-posed on the physically interesting spaces of initial data. In this paper we are able to select the measure-valued solution of the 1  +  1 dimensional Vlasov-Poisson equation which correctly captures the semiclassical limit, thus finally resolving the non-uniqueness in the seminal result of Zhang et al (2012 Comm. Pure Appl. Math. 55 582-632). The same approach is also applied to the Vlasov-Dirac-Benney equation with small wavepacket initial data, extending several known results.

Appearance of eigen modes for the linearized Vlasov-Poisson equation

International Nuclear Information System (INIS)

Degond, P.

1983-01-01

In order to determine the asymptotic behaviour, when the time goes to infinity, of the solution of the linearized Vlasov-Poisson equation, we use eigen modes, associated to continuous linear functionals on a Banach space of analytic functions [fr

On the relativistic Vlasov equation in guiding-center coordinates

International Nuclear Information System (INIS)

Salimullah, M.; Chaudhry, M.B.; Hassan, M.H.A.

1989-11-01

The relativistic Vlasov equation has been expressed in terms of the guiding-center coordinates in a hot magnetized plasma. It is noted that the relativistic effect reduces the cyclotron resonance frequency for electrostatic and electromagnetic waves propagating transverse to the direction of the static magnetic field in the plasma. (author). 4 refs

On invariant measures for the Vlasov equation with a regular potential

International Nuclear Information System (INIS)

Zhidkov, P.E.

2003-01-01

We consider a Vlasov equation with a smooth bounded potential of interaction between particles in a class of measure-valued solutions and construct a measure which is invariant for this problem in a sense

Vlasov simulations of parallel potential drops

Directory of Open Access Journals (Sweden)

H. Gunell

2013-07-01

Full Text Available An auroral flux tube is modelled from the magnetospheric equator to the ionosphere using Vlasov simulations. Starting from an initial state, the evolution of the plasma on the flux tube is followed in time. It is found that when applying a voltage between the ends of the flux tube, about two thirds of the potential drop is concentrated in a thin double layer at approximately one Earth radius altitude. The remaining part is situated in an extended region 1–2 Earth radii above the double layer. Waves on the ion timescale develop above the double layer, and they move toward higher altitude at approximately the ion acoustic speed. These waves are seen both in the electric field and as perturbations of the ion and electron distributions, indicative of an instability. Electrons of magnetospheric origin become trapped between the magnetic mirror and the double layer during its formation. At low altitude, waves on electron timescales appear and are seen to be non-uniformly distributed in space. The temporal evolution of the potential profile and the total voltage affect the double layer altitude, which decreases with an increasing field aligned potential drop. A current–voltage relationship is found by running several simulations with different voltages over the system, and it agrees with the Knight relation reasonably well.

Implications of the Electrostatic Approximation in the Beam Frame on the Nonlinear Vlasov-Maxwell Equations for Intense Beam Propagation

International Nuclear Information System (INIS)

Davidson, Ronald C.; Lee, W. Wei-li; Hong Qin; Startsev, Edward

2001-01-01

This paper develops a clear procedure for solving the nonlinear Vlasov-Maxwell equations for a one-component intense charged particle beam or finite-length charge bunch propagating through a cylindrical conducting pipe (radius r = r(subscript)w = const.), and confined by an applied focusing force. In particular, the nonlinear Vlasov-Maxwell equations are Lorentz-transformed to the beam frame ('primed' variables) moving with axial velocity relative to the laboratory. In the beam frame, the particle motions are nonrelativistic for the applications of practical interest, already a major simplification. Then, in the beam frame, we make the electrostatic approximation which fully incorporates beam space-charge effects, but neglects any fast electromagnetic processes with transverse polarization (e.g., light waves). The resulting Vlasov-Maxwell equations are then Lorentz-transformed back to the laboratory frame, and properties of the self-generated fields and resulting nonlinear Vlasov-Maxwell equations in the laboratory frame are discussed

Gyrokinetic Vlasov code including full three-dimensional geometry of experiments

International Nuclear Information System (INIS)

Nunami, Masanori; Watanabe, Tomohiko; Sugama, Hideo

2010-03-01

A new gyrokinetic Vlasov simulation code, GKV-X, is developed for investigating the turbulent transport in magnetic confinement devices with non-axisymmetric configurations. Effects of the magnetic surface shapes in a three-dimensional equilibrium obtained from the VMEC code are accurately incorporated. Linear simulations of the ion temperature gradient instabilities and the zonal flows in the Large Helical Device (LHD) configuration are carried out by the GKV-X code for a benchmark test against the GKV code. The frequency, the growth rate, and the mode structure of the ion temperature gradient instability are influenced by the VMEC geometrical data such as the metric tensor components of the Boozer coordinates for high poloidal wave numbers, while the difference between the zonal flow responses obtained by the GKV and GKV-X codes is found to be small in the core LHD region. (author)

L2-stability of the Vlasov-Maxwell-Boltzmann system near global Maxwellians

International Nuclear Information System (INIS)

Ha, Seung-Yeal; Xiao, Qinghua; Xiong, Linjie; Zhao, Huijiang

2013-01-01

We present a L 2 -stability theory of the Vlasov-Maxwell-Boltzmann system for the two-species collisional plasma. We show that in a perturbative regime of a global Maxwellian, the L 2 -distance between two strong solutions can be controlled by that between initial data in a Lipschitz manner. Our stability result extends earlier results [Ha, S.-Y. and Xiao, Q.-H., “A revisiting to the L 2 -stability theory of the Boltzmann equation near global Maxwellians,” (submitted) and Ha, S.-Y., Yang, X.-F., and Yun, S.-B., “L 2 stability theory of the Boltzmann equation near a global Maxwellian,” Arch. Ration. Mech. Anal. 197, 657–688 (2010)] on the L 2 -stability of the Boltzmann equation to the Boltzmann equation coupled with self-consistent external forces. As a direct application of our stability result, we show that classical solutions in Duan et al. [“Optimal large-time behavior of the Vlasov-Maxwell-Boltzmann system in the whole space,” Commun. Pure Appl. Math. 24, 1497–1546 (2011)] and Guo [“The Vlasov-Maxwell-Boltzmann system near Maxwellians,” Invent. Math. 153(3), 593–630 (2003)] satisfy a uniform L 2 -stability estimate. This is the first result on the L 2 -stability of the Boltzmann equation coupled with self-consistent field equations in three dimensions

Development of a global toroidal gyrokinetic Vlasov code with new real space field solver

International Nuclear Information System (INIS)

Obrejan, Kevin; Imadera, Kenji; Li, Ji-Quan; Kishimoto, Yasuaki

2015-01-01

This work introduces a new full-f toroidal gyrokinetic (GK) Vlasov simulation code that uses a real space field solver. This solver enables us to compute the gyro-averaging operators in real space to allow proper treatment of finite Larmor radius (FLR) effects without requiring any particular hypothesis and in any magnetic field configuration (X-point, D-shaped etc). The code was well verified through benchmark tests such as toroidal Ion Temperature Gradient (ITG) instability and collisionless damping of zonal flow. (author)

A wavelet-MRA-based adaptive semi-Lagrangian method for the relativistic Vlasov-Maxwell system

International Nuclear Information System (INIS)

Besse, Nicolas; Latu, Guillaume; Ghizzo, Alain; Sonnendruecker, Eric; Bertrand, Pierre

2008-01-01

In this paper we present a new method for the numerical solution of the relativistic Vlasov-Maxwell system on a phase-space grid using an adaptive semi-Lagrangian method. The adaptivity is performed through a wavelet multiresolution analysis, which gives a powerful and natural refinement criterion based on the local measurement of the approximation error and regularity of the distribution function. Therefore, the multiscale expansion of the distribution function allows to get a sparse representation of the data and thus save memory space and CPU time. We apply this numerical scheme to reduced Vlasov-Maxwell systems arising in laser-plasma physics. Interaction of relativistically strong laser pulses with overdense plasma slabs is investigated. These Vlasov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by electromagnetic waves as electron trapping, particle acceleration, and electron plasma wavebreaking. However, the wavelet based adaptive method that we developed here, does not yield significant improvements compared to Vlasov solvers on a uniform mesh due to the substantial overhead that the method introduces. Nonetheless they might be a first step towards more efficient adaptive solvers based on different ideas for the grid refinement or on a more efficient implementation. Here the Vlasov simulations are performed in a two-dimensional phase-space where the development of thin filaments, strongly amplified by relativistic effects requires an important increase of the total number of points of the phase-space grid as they get finer as time goes on. The adaptive method could be more useful in cases where these thin filaments that need to be resolved are a very small fraction of the hyper-volume, which arises in higher dimensions because of the surface-to-volume scaling and the essentially one-dimensional structure of the filaments. Moreover, the main way to improve the efficiency of the adaptive method is to

Regionally Implicit Discontinuous Galerkin Methods for Solving the Relativistic Vlasov-Maxwell System Submitted to Iowa State University

Science.gov (United States)

Guthrey, Pierson Tyler

The relativistic Vlasov-Maxwell system (RVM) models the behavior of collisionless plasma, where electrons and ions interact via the electromagnetic fields they generate. In the RVM system, electrons could accelerate to significant fractions of the speed of light. An idea that is actively being pursued by several research groups around the globe is to accelerate electrons to relativistic speeds by hitting a plasma with an intense laser beam. As the laser beam passes through the plasma it creates plasma wakes, much like a ship passing through water, which can trap electrons and push them to relativistic speeds. Such setups are known as laser wakefield accelerators, and have the potential to yield particle accelerators that are significantly smaller than those currently in use. Ultimately, the goal of such research is to harness the resulting electron beams to generate electromagnetic waves that can be used in medical imaging applications. High-order accurate numerical discretizations of kinetic Vlasov plasma models are very effective at yielding low-noise plasma simulations, but are computationally expensive to solve because of the high dimensionality. In addition to the general difficulties inherent to numerically simulating Vlasov models, the relativistic Vlasov-Maxwell system has unique challenges not present in the non-relativistic case. One such issue is that operator splitting of the phase gradient leads to potential instabilities, thus we require an alternative to operator splitting of the phase. The goal of the current work is to develop a new class of high-order accurate numerical methods for solving kinetic Vlasov models of plasma. The main discretization in configuration space is handled via a high-order finite element method called the discontinuous Galerkin method (DG). One difficulty is that standard explicit time-stepping methods for DG suffer from time-step restrictions that are significantly worse than what a simple Courant-Friedrichs-Lewy (CFL

Solving the Vlasov equation in two spatial dimensions with the Schrödinger method

Science.gov (United States)

Kopp, Michael; Vattis, Kyriakos; Skordis, Constantinos

2017-12-01

We demonstrate that the Vlasov equation describing collisionless self-gravitating matter may be solved with the so-called Schrödinger method (ScM). With the ScM, one solves the Schrödinger-Poisson system of equations for a complex wave function in d dimensions, rather than the Vlasov equation for a 2 d -dimensional phase space density. The ScM also allows calculating the d -dimensional cumulants directly through quasilocal manipulations of the wave function, avoiding the complexity of 2 d -dimensional phase space. We perform for the first time a quantitative comparison of the ScM and a conventional Vlasov solver in d =2 dimensions. Our numerical tests were carried out using two types of cold cosmological initial conditions: the classic collapse of a sine wave and those of a Gaussian random field as commonly used in cosmological cold dark matter N-body simulations. We compare the first three cumulants, that is, the density, velocity and velocity dispersion, to those obtained by solving the Vlasov equation using the publicly available code ColDICE. We find excellent qualitative and quantitative agreement between these codes, demonstrating the feasibility and advantages of the ScM as an alternative to N-body simulations. We discuss, the emergence of effective vorticity in the ScM through the winding number around the points where the wave function vanishes. As an application we evaluate the background pressure induced by the non-linearity of large scale structure formation, thereby estimating the magnitude of cosmological backreaction. We find that it is negligibly small and has time dependence and magnitude compatible with expectations from the effective field theory of large scale structure.

Numerical Integration of the Vlasov Equation of Two Colliding Beams

CERN Document Server

Zorzano-Mier, M P

2000-01-01

In a circular collider the motion of particles of one beam is strongly perturbed at the interaction points by the electro-magnetic field associated with the counter-rotating beam. For any two arbitrary initial particle distributions the time evolution of the two beams can be known by solving the coupled system of two Vlasov equations. This collective description is mandatory when the two beams have similar strengths, as in the case of LEP or LHC. The coherent modes excited by this beam-beam interaction can be a strong limitation for the operation of LHC. In this work, the coupled Vlasov equations of two colliding flat beams are solved numerically using a finite difference scheme. The results suggest that, for the collision of beams with equal tunes, the tune shift between the $\\sigma$- and $\\pi$- coherent dipole mode depends on the unperturbed tune $q$ because of the deformation that the so-called dynamic beta effect induces on the beam distribution. Only when the unperturbed tune $q\\rightarrow 0.25$ this tun...

Fourth-Order Conservative Vlasov-Maxwell Solver for Cartesian and Cylindrical Phase Space Coordinates

Science.gov (United States)

Vogman, Genia

Plasmas are made up of charged particles whose short-range and long-range interactions give rise to complex behavior that can be difficult to fully characterize experimentally. One of the most complete theoretical descriptions of a plasma is that of kinetic theory, which treats each particle species as a probability distribution function in a six-dimensional position-velocity phase space. Drawing on statistical mechanics, these distribution functions mathematically represent a system of interacting particles without tracking individual ions and electrons. The evolution of the distribution function(s) is governed by the Boltzmann equation coupled to Maxwell's equations, which together describe the dynamics of the plasma and the associated electromagnetic fields. When collisions can be neglected, the Boltzmann equation is reduced to the Vlasov equation. High-fidelity simulation of the rich physics in even a subset of the full six-dimensional phase space calls for low-noise high-accuracy numerical methods. To that end, this dissertation investigates a fourth-order finite-volume discretization of the Vlasov-Maxwell equation system, and addresses some of the fundamental challenges associated with applying these types of computationally intensive enhanced-accuracy numerical methods to phase space simulations. The governing equations of kinetic theory are described in detail, and their conservation-law weak form is derived for Cartesian and cylindrical phase space coordinates. This formulation is well known when it comes to Cartesian geometries, as it is used in finite-volume and finite-element discretizations to guarantee local conservation for numerical solutions. By contrast, the conservation-law weak form of the Vlasov equation in cylindrical phase space coordinates is largely unexplored, and to the author's knowledge has never previously been solved numerically. Thereby the methods described in this dissertation for simulating plasmas in cylindrical phase space

The Vlasov-Navier-Stokes System in a 2D Pipe: Existence and Stability of Regular Equilibria

Science.gov (United States)

Glass, Olivier; Han-Kwan, Daniel; Moussa, Ayman

2018-05-01

In this paper, we study the Vlasov-Navier-Stokes system in a 2D pipe with partially absorbing boundary conditions. We show the existence of stationary states for this system near small Poiseuille flows for the fluid phase, for which the kinetic phase is not trivial. We prove the asymptotic stability of these states with respect to appropriately compactly supported perturbations. The analysis relies on geometric control conditions which help to avoid any concentration phenomenon for the kinetic phase.

Yang-Mills-Vlasov system in the temporal gauge

International Nuclear Information System (INIS)

Choquet-Bruhat, Y.; Noutchegueme, N.

1991-01-01

We prove a local in time existence theorem of a solution of the Cauchy problem for the Yang-Mills-Vlasov integrodifferential system. Such equations govern the evolution of plasmas, for instance of quarks and gluons (quagmas), where non abelian gauge fields and Yang-Mills charges replace the usual electromagnetic field and electric charge. We work with the temporal gauge and use functional spaces with appropriate weight on the momenta, but no fall off is required in the space direction [fr

Numerical study of a Vlasov equation for systems with interacting particles

Energy Technology Data Exchange (ETDEWEB)

Herrera, Dianela; Curilef, Sergio [Departamento de Física, Universidad Católica del Norte, Avenida Angamos 0610, Antofagasta (Chile)

2015-03-10

We solve numerically the Vlasov equation for the self-gravitating sheet model. We used the method introduced by Cheng and Knorr [Comput Phys 22, 330-351 (1976)]. We discuss the quasi-stationary state for some thermodynamical observables, specifically the kinetic energy, whose trend is depicted for early evolution.

KEEN Wave Simulations: Comparing various PIC to various fixed grid Vlasov to Phase-Space Adaptive Sparse Tiling & Effective Lagrangian (PASTEL) Techniques

Science.gov (United States)

Afeyan, Bedros; Larson, David; Shadwick, Bradley; Sydora, Richard

2017-10-01

We compare various ways of solving the Vlasov-Poisson and Vlasov-Maxwell equations on rather demanding nonlinear kinetic phenomena associated with KEEN and KEEPN waves. KEEN stands for Kinetic, Electrostatic, Electron Nonlinear, and KEEPN, for electron-positron or pair plasmas analogs. Because these self-organized phase space structures are not steady-state, or single mode, or fluid or low order moment equation limited, typical techniques with low resolution or too much noise will distort the answer too much, too soon, and fail. This will be shown via Penrose criteria triggers for instability at the formation stage as well as particle orbit statistics in fully formed KEEN waves and KEEN-KEEN and KEEN-EPW interacting states. We will argue that PASTEL is a viable alternative to traditional methods with reasonable chances of success in higher dimensions. Work supported by a Grant from AFOSR PEEP.

Lifting particle coordinate changes of magnetic moment type to Vlasov-Maxwell Hamiltonian dynamics

International Nuclear Information System (INIS)

Morrison, P. J.; Vittot, M.; Guillebon, L. de

2013-01-01

Techniques for coordinate changes that depend on both dependent and independent variables are developed and applied to the Maxwell-Vlasov Hamiltonian theory. Particle coordinate changes with a new velocity variable dependent on the magnetic field, with spatial coordinates unchanged, are lifted to the field theoretic level, by transforming the noncanonical Poisson bracket and Hamiltonian structure of the Vlasov-Maxwell dynamics. Several examples are given including magnetic coordinates, where the velocity is decomposed into components parallel and perpendicular to the local magnetic field, and the case of spherical velocity coordinates. An example of the lifting procedure is performed to obtain a simplified version of gyrokinetics, where the magnetic moment is used as a coordinate and the dynamics is reduced by elimination of the electric field energy in the Hamiltonian.

Nonlinear wave evolution in VLASOV plasma: a lie-transform analysis

International Nuclear Information System (INIS)

Cary, J.R.

1979-08-01

Nonlinear wave evolution in Vlasov plasma is analyzed using the Lie transform, a powerful mathematical tool which is applicable to Hamiltonian systems. The first part of this thesis is an exposition of the Lie transform. Dewar's general Lie transform theory is explained and is used to construct Deprit's Lie transform perturbation technique. The basic theory is illustrated by simple examples

Superexponentially damped Vlasov plasma oscillations in the Fourier transformed velocity space

Czech Academy of Sciences Publication Activity Database

Sedláček, Zdeněk; Nocera, L.

2002-01-01

Roč. 52, supplement D (2002), s. 65-69 ISSN 0011-4626. [Symposium on Plasma Physics and Technology/20th./. Prague, 10.06.2002-13.06.2002] Institutional research plan: CEZ:AV0Z2043910 Keywords : Vlasov plasma, oscillator Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 0.311, year: 2002

Vlasov Treatment of Coherent Synchrotron Radiation from Arbitrary Planar Orbits

International Nuclear Information System (INIS)

Warnock, R

2004-01-01

We study the influence of coherent synchrotron radiation (CSR) on particle bunches traveling on arbitrary planar orbits between parallel conducting plates. The plates represent shielding due to the vacuum chamber. The vertical distribution of charge is an arbitrary fixed function. Our goal is to follow the time evolution of the phase space distribution by solving the Vlasov-Maxwell equations in the time domain. This provides simulations with lower numerical noise than the macroparticle method, and allows one to study such issues as emittance degradation and microbunching due to CSR in bunch compressors. The fields excited by the bunch are computed in the laboratory frame from a new formula that leads to much simpler computations than the usual retarded potentials or Lienard-Wiechert potentials. The nonlinear Vlasov equation, formulated in the interaction picture, is integrated in the beam frame by approximating the Perron-Frobenius operator. The distribution function is represented by B-splines, in a scheme preserving positivity and normalization of the distribution. For application to a chicane bunch compressor we take steps to deal with energy chirp, an initial near-perfect correlation of energy with position in the bunch

Numerical solutions of the Vlasov equation

International Nuclear Information System (INIS)

Satofuka, Nobuyuki; Morinishi, Koji; Nishida, Hidetoshi

1985-01-01

A numerical procedure is derived for the solutions of the one- and two-dimensional Vlasov-Poisson system equations. This numerical procedure consists of the phase space discretization and the integration of the resulting set of ordinary differential equations. In the phase space discretization, derivatives with respect to the phase space variable are approximated by a weighted sum of the values of the distribution function at properly chosen neighboring points. Then, the resulting set of ordinary differential equations is solved by using an appropriate time integration scheme. The results for linear Landau damping, nonlinear Landau damping and counter-streaming plasmas are investigated and compared with those of the splitting scheme. The proposed method is found to be very accurate and efficient. (author)

Action principles for the Vlasov equation: Four old, one new

International Nuclear Information System (INIS)

Ye, Huanchun; Morrison, P.J.

1991-01-01

Action principles for the Vlasov equation are presented. Four previously known action principles, which differ by the choice of dynamical variables, are described and the interrelationship between them discussed. A new action principle called the leaf action, which manifestly preserves the Casimir invariants and possess a single function as the dynamical variable, is presented. The relationship to the noncanonical Hamiltonian formalism is also explored. 21 refs

Nonlinear behavior of a monochromatic wave in a one-dimensional Vlasov plasma

International Nuclear Information System (INIS)

Shoucri, M.M.; Gagne, R.R.J.

1978-01-01

The nonlinear evolution of a monochromatic wave in a one-dimensional Vlasov plasma is studied numerically. The numerical results are carried out far enough in time for phase mixing to dominate the asymptotic state of the system. A qualitative comparison with previously reported simulations is given

Superexponentially damped Vlasov plasma oscillations in the Fourier transformed velocity space

International Nuclear Information System (INIS)

Sedlacek, Z.; Nocera, L.

2002-01-01

The Landau (exponentially) damped solutions of the Vlasov-Poisson equation Fourier transformed with respect to velocity are genuine eigenmodes corresponding to complex eigenvalues. In addition there exist solutions decaying faster than exponentially which exhibit no oscillatory behaviour. A new characterization is given of the initial conditions that give rise to these solutions together with a numerical demonstration

The energy-momentum tensor for the linearized Maxwell-Vlasov and kinetic guiding center theories

International Nuclear Information System (INIS)

Pfirsch, D.; Morrison, P.J.; Texas Univ., Austin

1990-02-01

A modified Hamilton-Jacobi formalism is introduced as a tool to obtain the energy-momentum and angular-momentum tensors for any kind of nonlinear or linearized Maxwell-collisionless kinetic theories. The emphasis is on linearized theories, for which these tensors are derived for the first time. The kinetic theories treated - which need not be the same for all particle species in a plasma - are the Vlasov and kinetic guiding center theories. The Hamiltonian for the guiding center motion is taken in the form resulting from Dirac's constraint theory for non-standard Lagrangian systems. As an example of the Maxwell-kinetic guiding center theory, the second-order energy for a perturbed homogeneous magnetized plasma is calculated with initially vanishing field perturbations. The expression obtained is compared with the corresponding one of Maxwell-Vlasov theory. (orig.)

The energy-momentum tensor for the linearized Maxwell-Vlasov and kinetic guiding center theories

International Nuclear Information System (INIS)

Pfirsch, D.; Morrison, P.J.

1990-02-01

A modified Hamilton-Jacobi formalism is introduced as a tool to obtain the energy-momentum and angular-momentum tensors for any king of nonlinear or linearized Maxwell-collisionless kinetic theories. The emphasis is on linearized theories, for which these tensors are derived for the first time. The kinetic theories treated --- which need not be the same for all particle species in a plasma --- are the Vlasov and kinetic guiding center theories. The Hamiltonian for the guiding center motion is taken in the form resulting from Dirac's constraint theory for non-standard Lagrangian systems. As an example of the Maxwell-kinetic guiding center theory, the second-order energy for a perturbed homogeneous magnetized plasma is calculated with initially vanishing field perturbations. The expression obtained is compared with the corresponding one of Maxwell-Vlasov theory. 11 refs

Nonadiabatic quantum Vlasov equation for Schwinger pair production

International Nuclear Information System (INIS)

Kim, Sang Pyo; Schubert, Christian

2011-01-01

Using Lewis-Riesenfeld theory, we derive an exact nonadiabatic master equation describing the time evolution of the QED Schwinger pair-production rate for a general time-varying electric field. This equation can be written equivalently as a first-order matrix equation, as a Vlasov-type integral equation, or as a third-order differential equation. In the last version it relates to the Korteweg-de Vries equation, which allows us to construct an exact solution using the well-known one-soliton solution to that equation. The case of timelike delta function pulse fields is also briefly considered.

Single particle dynamics of many-body systems described by Vlasov-Fokker-Planck equations

International Nuclear Information System (INIS)

Frank, T.D.

2003-01-01

Using Langevin equations we describe the random walk of single particles that belong to particle systems satisfying Vlasov-Fokker-Planck equations. In doing so, we show that Haissinski distributions of bunched particles in electron storage rings can be derived from a particle dynamics model

On classical solutions of the relativistic Vlasov-Klein-Gordon system

Directory of Open Access Journals (Sweden)

Michael Kunzinger

2005-01-01

Full Text Available We consider a collisionless ensemble of classical particles coupled with a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove local-in-time existence of classical solutions and a continuation criterion which says that a solution can blow up only if the particle momenta become large. We also show that classical solutions are global in time in the one-dimensional case.

Non-modal stability analysis and transient growth in a magnetized Vlasov plasma

KAUST Repository

Ratushnaya, V.

2014-12-01

Collisionless plasmas, such as those encountered in tokamaks, exhibit a rich variety of instabilities. The physical origin, triggering mechanisms and fundamental understanding of many plasma instabilities, however, are still open problems. We investigate the stability properties of a 3-dimensional collisionless Vlasov plasma in a stationary homogeneous magnetic field. We narrow the scope of our investigation to the case of Maxwellian plasma and examine its evolution with an electrostatic approximation. For the first time using a fully kinetic approach we show the emergence of the local instability, a transient growth, followed by classical Landau damping in a stable magnetized plasma. We show that the linearized Vlasov operator is non-normal leading to the algebraic growth of the perturbations using non-modal stability theory. The typical time scales of the obtained instabilities are of the order of several plasma periods. The first-order distribution function and the corresponding electric field are calculated and the dependence on the magnetic field and perturbation parameters is studied. Our results offer a new scenario of the emergence and development of plasma instabilities on the kinetic scale.

Non-modal stability analysis and transient growth in a magnetized Vlasov plasma

KAUST Repository

Ratushnaya, V.; Samtaney, Ravi

2014-01-01

Collisionless plasmas, such as those encountered in tokamaks, exhibit a rich variety of instabilities. The physical origin, triggering mechanisms and fundamental understanding of many plasma instabilities, however, are still open problems. We investigate the stability properties of a 3-dimensional collisionless Vlasov plasma in a stationary homogeneous magnetic field. We narrow the scope of our investigation to the case of Maxwellian plasma and examine its evolution with an electrostatic approximation. For the first time using a fully kinetic approach we show the emergence of the local instability, a transient growth, followed by classical Landau damping in a stable magnetized plasma. We show that the linearized Vlasov operator is non-normal leading to the algebraic growth of the perturbations using non-modal stability theory. The typical time scales of the obtained instabilities are of the order of several plasma periods. The first-order distribution function and the corresponding electric field are calculated and the dependence on the magnetic field and perturbation parameters is studied. Our results offer a new scenario of the emergence and development of plasma instabilities on the kinetic scale.

Progress on a Vlasov Treatment of Coherent Synchrotron Radiation from Arbitrary Planar Orbits

CERN Document Server

Bassi, Gabriele; Warnock, Robert L

2005-01-01

We study the influence of coherent synchrotron radiation (CSR) on particle bunches traveling on arbitrary planar orbits between parallel conducting plates (shielding). The time evolution of the phase space distribution is determined by solving the Vlasov-Maxwell equations in the time domain. This provides lower numerical noise than the macroparticle method, and allows the study of emittance degradation and microbunching in bunch compressors. We calculate the fields excited by the bunch in the lab frame using a formula simpler than that based on retarded potentials.* We have developed an algorithm for solving the Vlasov equation in the beam frame using arc length as the independent variable and our method of local characteristics (discretized Perron-Frobenius operator).We integrate in the interaction picture in the hope that we can adopt a fixed grid. The distribution function will be represented by B-splines, in a scheme preserving positivity and normalization of the distribution. The transformation between l...

Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach

Energy Technology Data Exchange (ETDEWEB)

Pham, Huyên, E-mail: pham@math.univ-paris-diderot.fr; Wei, Xiaoli, E-mail: tyswxl@gmail.com [Laboratoire de Probabilités et Modèles Aléatoires, CNRS, UMR 7599, Université Paris Diderot (France)

2016-12-15

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.

Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach

International Nuclear Information System (INIS)

Pham, Huyên; Wei, Xiaoli

2016-01-01

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.

Antisymmetrized molecular dynamics of wave packets with stochastic incorporation of Vlasov equation

International Nuclear Information System (INIS)

Ono, Akira; Horiuchi, Hisashi.

1996-01-01

The first purpose of this report is to present an extended AMD model which can generally describe such minor branching processes by removing the restriction on the one-body distribution function. This is done not by generalizing the wave packets to arbitrary single-particle wave functions but by representing the diffused and/or deformed wave packet as an ensemble of Gaussian wave packets. In other words, stochastic displacements are given to the wave packets in phase space so that the ensemble-average of the time evolution of the one-body distribution function is essentially equivalent to the solution of Vlasov equation which does not have any restriction on the shape of wave packets. This new model is called AMD-V. Although AMD-V is equivalent to Vlasov equation in the instantaneous time evolution of the one-body distribution function for an AMD wave function, AMD-V describes the branching into channels and the fluctuation of the mean field which are caused by the spreading or the splitting of the single-particle wave function. The second purpose of this report is to show the drastic effect of this new stochastic process of wave packet splitting on the dynamics of heavy ion collisions, especially in the fragmentation mechanism. We take the 40 Ca + 40 Ca system at the incident energy 35 MeV/nucleon. It will be shown that the reproduction of data by the AMD-V calculation is surprisingly good. We will see that the effect of the wave packet diffusion is crucially important to remove the spurious binary feature of the AMD calculation and to enable the multi-fragment final state. (J.P.N.)

Large Time Behavior of the Vlasov-Poisson-Boltzmann System

Directory of Open Access Journals (Sweden)

Li Li

2013-01-01

Full Text Available The motion of dilute charged particles can be modeled by Vlasov-Poisson-Boltzmann system. We study the large time stability of the VPB system. To be precise, we prove that when time goes to infinity, the solution of VPB system tends to global Maxwellian state in a rate Ot−∞, by using a method developed for Boltzmann equation without force in the work of Desvillettes and Villani (2005. The improvement of the present paper is the removal of condition on parameter λ as in the work of Li (2008.

Local WKB dispersion relation for the Vlasov-Maxwell equations

International Nuclear Information System (INIS)

Berk, H.L.; Dominguez, R.R.

1982-10-01

A formalism for analyzing systems of integral equations, based on the Wentzel-Kramers-Brillouin (WKB) approximation, is applied to the Vlasov-Maxwell integral equations in an arbitrary-β, spatially inhomogenous plasma model. It is shown that when treating frequencies comparable with and larger than the cyclotron frequency, relevant new terms must be accounted for to treat waves that depend upon local spatial gradients. For a specific model, the response for very short wavelength and high frequency is shown to reduce to the straight-line orbit approximation when the WKB rules are correctly followed

Renormalized perturbation theory: Vlasov-Poisson System, weak turbulence limit and gyrokinetics

International Nuclear Information System (INIS)

Zhang, Y.Z.; Mahajan, S.M.

1987-10-01

The Self-consistency of the renormalized perturbation theory is demonstrated by applying it to the Vlasov-Poisson System and showing that the theory has the correct weak turbulence limit. Energy conservation is proved to arbitrary high order for the electrostatic drift waves. The theory is applied to derive renormalized equations for a low-β gyrokinetic system. Comparison of our theory with other current theories is presented. 22 refs

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

Dielectric energy versus plasma energy, and Hamiltonian action-angle variables for the Vlasov equation

International Nuclear Information System (INIS)

Morrison, P.J.

1992-04-01

Expressions for the energy content of one-dimensional electrostatic perturbations about homogeneous equilibria are revisited. The well-known dielectric energy, var-epsilon D , is compared with the exact plasma free energy expression, δ 2 F, that is conserved by the Vlasov-Poisson system. The former is an expression in terms of the perturbed electric field amplitude, while the latter is determined by a generating function, which describes perturbations of the distribution function that respect the important constraint of dynamical accessibility of the system. Thus the comparison requires solving the Vlasov equation for such a perturbations of the distribution function in terms of the electric field. This is done for neutral modes of oscillation that occur for equilibria with stationary inflection points, and it is seen that for these special modes δ 2 F = var-epsilon D . In the case of unstable and corresponding damped modes it is seen that δ 2 F ≠ var-epsilon D ; in fact δ 2 F ≡ 0. This failure of the dielectric energy expression persists even for arbitrarily small growth and damping rates since var-epsilon D is nonzero in this limit, whereas δ 2 F remains zero. The connection between the new exact energy expression and the at-best approximate var-epsilon D is described. The new expression motivates natural definitions of Hamiltonian action variables and signature. A general linear integral transform is introduced that maps the linear version of the noncanonical Hamiltonian structure, which describes the Vlasov equation, to action-angle (diagonal) form

Kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field based on the nonlinear Vlasov-Maxwell equations

International Nuclear Information System (INIS)

Davidson, R.C.; Chen, C.

1997-08-01

A kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field B sol (rvec x) is developed. The analysis is carried out for a thin beam with characteristic beam radius r b much-lt S, and directed axial momentum γ b mβ b c (in the z-direction) large compared with the transverse momentum and axial momentum spread of the beam particles. Making use of the nonlinear Vlasov-Maxwell equations for general distribution function f b (rvec x,rvec p,t) and self-consistent electrostatic field consistent with the thin-beam approximation, the kinetic model is used to investigate detailed beam equilibrium properties for a variety of distribution functions. Examples are presented both for the case of a uniform solenoidal focusing field B z (z) = B 0 = const. and for the case of a periodic solenoidal focusing field B z (z + S) = B z (z). The nonlinear Vlasov-Maxwell equations are simplified in the thin-beam approximation, and an alternative Hamiltonian formulation is developed that is particularly well-suited to intense beam propagation in periodic focusing systems. Based on the present analysis, the Vlasov-Maxwell description of intense nonneutral beam propagation through a periodic solenoidal focusing field rvec B sol (rvec x) is found to be remarkably tractable and rich in physics content. The Vlasov-Maxwell formalism developed here can be extended in a straightforward manner to investigate detailed stability behavior for perturbations about specific choices of beam equilibria

Hamiltonian field description of the one-dimensional Poisson-Vlasov equations

International Nuclear Information System (INIS)

Morrison, P.J.

1981-07-01

The one-dimensional Poisson-Vlasov equations are cast into Hamiltonian form. A Poisson Bracket in terms of the phase space density, as sole dynamical variable, is presented. This Poisson bracket is not of the usual form, but possesses the commutator properties of antisymmetry, bilinearity, and nonassociativity by virtue of the Jacobi requirement. Clebsch potentials are seen to yield a conventional (canonical) formulation. This formulation is discretized by expansion in terms of an arbitrary complete set of basis functions. In particular, a wave field representation is obtained

Instability of the filtering method for Vlasov's equation

International Nuclear Information System (INIS)

Figua, H.; Bouchut, F.; Fijalkow, E.

1999-01-01

Klimas has introduced a smoothed Fourier-Fourier method. This method consists in convolving the original distribution function with a Gaussian distribution function, and, next, in solving the new system with a transformed splitting algorithm. Unfortunately, a second-order term appears in the new equation. In this work, it is studied how this term affects the numerical equation. In particular it is proven that instability occurs in the linear version of the Vlasov equation obtained by considering only free non-interacting particles. It is proved that the use of Fourier-Fourier transform is a fundamental requirement to solve this new equation. An important property is pointed out concerning the filtered distribution function in the transformed space. (K.A.)

Numerical study of non-ideal Vlasov-BGK plasmas

International Nuclear Information System (INIS)

Levchenko, V.D.; Sigov, Y.S.; Premuda, F.

1995-01-01

A relatively simple quasi-classical description of quantum plasmas using as first approximation the Bhatnagar-Gross-Krook (BGK) collision integral, if combined with the modern numerical simulation methods, might be effective tool of a deep study of non-ideal plasma kinetics in a variety of urgent applications as inertial confinement and cold fusion, transport and collective properties of highly condensed plasmas in liquid metals, semi- and superconductors and others. Consider one-dimensional degenerate plasma consisting of thermal electrons and thermal bosons (deuterons) in the vicinity of the equilibrium Fermi- and Bose-type distributions respectively. In the frame of our rough mixed model we solve Vlasov-BGK-Poisson eqs using simplified version of the SUR code

Expeditious 3D poisson vlasov algorithm applied to ion extraction from a plasma

International Nuclear Information System (INIS)

Whealton, J.H.; McGaffey, R.W.; Meszaros, P.S.

1983-01-01

A new 3D Poisson Vlasov algorithm is under development which differs from a previous algorithm, referenced in this paper, in two respects: the mesh lines are cartesian, and the Poisson equation is solved iteratively. The resulting algorithm has been used to examine the same boundary value problem as considered in the earlier algorithm except that the number of nodes is 2 times greater. The same physical results were obtained except the computational time was reduced by a factor of 60 and the memory requirement was reduced by a factor of 10. This algorithm at present restricts Neumann boundary conditions to orthogonal planes lying along mesh lines. No such restriction applies to Dirichlet boundaries. An emittance diagram is shown below where those points lying on the y = 0 line start on the axis of symmetry and those near the y = 1 line start near the slot end

Vlasov-Fokker-Planck modeling of magnetized plasma

Energy Technology Data Exchange (ETDEWEB)

Thomas, Alexander [Univ. of Michigan, Ann Arbor, MI (United States)

2016-08-01

Understanding the magnetic fields that can develop in high-power-laser interactions with solid-density plasma is important because such fields significantly modify both the magnitude and direction of electron heat fluxes. The dynamics of such fields evidently have consequences for inertial fusion energy applications, as the coupling of the laser beams with the walls or pellet and the development of temperature inhomogeneities are critical to the uniformity of the implosion and potentially the success of, for example, the National Ignition Facility. To study these effects, we used the code Impacta, a two-dimensional, fully implicit, Vlasov-Fokker-Planck code with self-consistent magnetic fields and a hydrodynamic ion model, designed for nanosecond time-scale laser-plasma interactions. Heat-flux effects in Ohm’s law under non-local conditions was investigated; physics that is not well captured by standard numerical models but is nevertheless important in fusion-related scenarios. Under such conditions there are numerous interesting physical effects, such as collisional magnetic instabilities, amplification of magnetic fields, re-emergence of non-locality through magnetic convection, and reconnection of magnetic field lines and redistribution of thermal energy. In this project highlights included the first full-scale kinetic simulations of a magnetized hohlraum and the discovery of a new magnetic reconnection mechanism, as well as a completed PhD thesis and the production of a new code for Inertial Fusion research.

Vlasov-Fokker-Planck modeling of magnetized plasma

International Nuclear Information System (INIS)

Thomas, Alexander

2016-01-01

Understanding the magnetic fields that can develop in high-power-laser interactions with solid-density plasma is important because such fields significantly modify both the magnitude and direction of electron heat fluxes. The dynamics of such fields evidently have consequences for inertial fusion energy applications, as the coupling of the laser beams with the walls or pellet and the development of temperature inhomogeneities are critical to the uniformity of the implosion and potentially the success of, for example, the National Ignition Facility. To study these effects, we used the code Impacta, a two-dimensional, fully implicit, Vlasov-Fokker-Planck code with self-consistent magnetic fields and a hydrodynamic ion model, designed for nanosecond time-scale laser-plasma interactions. Heat-flux effects in Ohm's law under non-local conditions was investigated; physics that is not well captured by standard numerical models but is nevertheless important in fusion-related scenarios. Under such conditions there are numerous interesting physical effects, such as collisional magnetic instabilities, amplification of magnetic fields, re-emergence of non-locality through magnetic convection, and reconnection of magnetic field lines and redistribution of thermal energy. In this project highlights included the first full-scale kinetic simulations of a magnetized hohlraum and the discovery of a new magnetic reconnection mechanism, as well as a completed PhD thesis and the production of a new code for Inertial Fusion research.

Equations of motion of test particles for solving the spin-dependent Boltzmann–Vlasov equation

Energy Technology Data Exchange (ETDEWEB)

Xia, Yin [Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800 (China); University of Chinese Academy of Science, Beijing 100049 (China); Xu, Jun, E-mail: xujun@sinap.ac.cn [Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800 (China); Li, Bao-An [Department of Physics and Astronomy, Texas A& M University-Commerce, Commerce, TX 75429-3011 (United States); Department of Applied Physics, Xi' an Jiao Tong University, Xi' an 710049 (China); Shen, Wen-Qing [Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800 (China)

2016-08-10

A consistent derivation of the equations of motion (EOMs) of test particles for solving the spin-dependent Boltzmann–Vlasov equation is presented. The resulting EOMs in phase space are similar to the canonical equations in Hamiltonian dynamics, and the EOM of spin is the same as that in the Heisenburg picture of quantum mechanics. Considering further the quantum nature of spin and choosing the direction of total angular momentum in heavy-ion reactions as a reference of measuring nucleon spin, the EOMs of spin-up and spin-down nucleons are given separately. The key elements affecting the spin dynamics in heavy-ion collisions are identified. The resulting EOMs provide a solid foundation for using the test-particle approach in studying spin dynamics in heavy-ion collisions at intermediate energies. Future comparisons of model simulations with experimental data will help to constrain the poorly known in-medium nucleon spin–orbit coupling relevant for understanding properties of rare isotopes and their astrophysical impacts.

Vlasov-Maxwell equilibrium solutions for Harris sheet magnetic field with Kappa velocity distribution

International Nuclear Information System (INIS)

Fu, W.-Z.; Hau, L.-N.

2005-01-01

An exact solution of the steady-state, one-dimensional Vlasov-Maxwell equations for a plasma current sheet with oppositely directed magnetic field was found by Harris in 1962. The so-called Harris magnetic field model assumes Maxwellian velocity distributions for oppositely drifting ions and electrons and has been widely used for plasma stability studies. This paper extends Harris solutions by using more general κ distribution functions that incorporate Maxwellian distribution in the limit of κ→∞. A new functional form for the plasma pressure as a function of the magnetic vector potential p(A) is found and the magnetic field is a modified tanh z function. In the extended solutions the effective temperature is no longer spatially uniform like in the Harris model and the thickness of the current layer decreases with decreasing κ

Stability analysis of a Vlasov-Wave system describing particles interacting with their environment

Science.gov (United States)

De Bièvre, Stephan; Goudon, Thierry; Vavasseur, Arthur

2018-06-01

We study a kinetic equation of the Vlasov-Wave type, which arises in the description of the behavior of a large number of particles interacting weakly with an environment, composed of an infinite collection of local vibrational degrees of freedom, modeled by wave equations. We use variational techniques to establish the existence of large families of stationary states for this system, and analyze their stability.

From the nonlinear Fokker-Planck equation to the Vlasov description and back: Confined interacting particles with drag

Science.gov (United States)

Plastino, A. R.; Curado, E. M. F.; Nobre, F. D.; Tsallis, C.

2018-02-01

Nonlinear Fokker-Planck equations endowed with power-law diffusion terms have proven to be valuable tools for the study of diverse complex systems in physics, biology, and other fields. The nonlinearity appearing in these evolution equations can be interpreted as providing an effective description of a system of particles interacting via short-range forces while performing overdamped motion under the effect of an external confining potential. This point of view has been recently applied to the study of thermodynamical features of interacting vortices in type II superconductors. In the present work we explore an embedding of the nonlinear Fokker-Planck equation within a Vlasov equation, thus incorporating inertial effects to the concomitant particle dynamics. Exact time-dependent solutions of the q -Gaussian form (with compact support) are obtained for the Vlasov equation in the case of quadratic confining potentials.

A hybrid-Vlasov model based on the current advance method for the simulation of collisionless magnetized plasma

Czech Academy of Sciences Publication Activity Database

Valentini, F.; Trávníček, Pavel; Califano, F.; Hellinger, Petr; Mangeney, A.

2007-01-01

Roč. 225, č. 1 (2007), s. 753-770 ISSN 0021-9991 Institutional research plan: CEZ:AV0Z30420517 Keywords : numerical simulations * hybrid simulations * Vlasov simulations Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 2.372, year: 2007

Theoretical and numerical study of the equations of Vlasov-Maxwell in the covariant formalism

International Nuclear Information System (INIS)

Back, A.

2011-11-01

A new point of view is proposed for the simulation of plasmas using the kinetic model which links the equations of Vlasov for the distribution of particles and the equations of Maxwell for the electromagnetic contribution of fields. We use the following principle: the equations of Physics are mathematical objects which put in relation geometrical objects. To preserve the geometrical properties of the various objects in an equation, we use, for the theoretical and numerical study, the differential geometry. All the equations of Physics can be written with differential forms and this point of view is not dependent on the choice of coordinates. We propose then a discretization of the differential forms by using B-Splines. To be coherent with the theory, we also propose a discretization of the various operations of the differential geometry. We test our scheme, first on the equations of Maxwell with several boundary conditions and since it does not depend on the system of coordinates, we also test it when we change coordinates. Finally, we apply the same method to the equations of Vlasov-Poisson in one-dimension and we propose several numerical schemes. (author)

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)

Longitudinal traveling waves bifurcating from Vlasov plasma equilibria

International Nuclear Information System (INIS)

Holloway, J.P.

1989-01-01

The kinetic equations governing longitudinal motion along a straight magnetic field in a multi-species collisionless plasma are investigated. A necessary condition for the existence of small amplitude spatially periodic equilibria and traveling waves near a given spatially uniform background equilibrium is derived, and the wavelengths which such solutions must approach as their amplitude decreases to zero are discussed. A sufficient condition for the existence of these small amplitude waves is also established. This is accomplished by studying the nonlinear ODE for the potential which arises when the distribution functions are represented in a BGK form; the arbitrary functions of energy that describe the BGK representation are tested as an infinite dimensional set of parameters in a bifurcation theory for the ODE. The positivity and zero current condition in the wave frame of the BGK distribution functions are maintained. The undamped small amplitude nonlinear waves so constructed can be made to satisfy the Vlasov dispersion relation exactly, but in general they need only satisfy it approximately. Numerical calculations reveal that even a thermal equilibrium electron-proton plasma with equal ion and electron temperatures will support undamped traveling waves with phase speeds greater than 1.3 times the electron velocity; the dispersion relation for this case exhibits both Langmuir and ion-acoustic branches as long wavelength limits, and shows how these branches are in fact connected by short wavelength waves of intermediate frequency. In apparent contradiction to the linear theory of Landau, these exact solutions of the kinetic equations do not damp; this contradiction is explained by observing that the linear theory is, in general, fundamentally incapable of describing undamped traveling waves

Deterministic methods for the relativistic Vlasov-Maxwell equations and the Van Allen belts dynamics

International Nuclear Information System (INIS)

Le Bourdiec, S.

2007-03-01

Artificial satellites operate in an hostile radiation environment, the Van Allen radiation belts, which partly condition their reliability and their lifespan. In order to protect them, it is necessary to characterize the dynamics of the energetic electrons trapped in these radiation belts. This dynamics is essentially determined by the interactions between the energetic electrons and the existing electromagnetic waves. This work consisted in designing a numerical scheme to solve the equations modelling these interactions: the relativistic Vlasov-Maxwell system of equations. Our choice was directed towards methods of direct integration. We propose three new spectral methods for the momentum discretization: a Galerkin method and two collocation methods. All of them are based on scaled Hermite functions. The scaling factor is chosen in order to obtain the proper velocity resolution. We present in this thesis the discretization of the one-dimensional Vlasov-Poisson system and the numerical results obtained. Then we study the possible extensions of the methods to the complete relativistic problem. In order to reduce the computing time, parallelization and optimization of the algorithms were carried out. Finally, we present 1Dx-3Dv (mono-dimensional for x and three-dimensional for velocity) computations of Weibel and whistler instabilities with one or two electrons species. (author)

Trapped Electron Instability of Electron Plasma Waves: Vlasov simulations and theory

Science.gov (United States)

Berger, Richard; Chapman, Thomas; Brunner, Stephan

2013-10-01

The growth of sidebands of a large-amplitude electron plasma wave is studied with Vlasov simulations for a range of amplitudes (. 001 vph = +/-ωbe , where vph =ω0 /k0 and ωbe is the bounce frequency of a deeply trapped electron. In 2D simulations, we find that the instability persists and co-exists with the filamentation instability. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and funded by the Laboratory Research and Development Program at LLNL under project tracking code 12-ERD.

Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme

Energy Technology Data Exchange (ETDEWEB)

Squire, J.; Tang, W. M. [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Qin, H. [Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States); Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China)

2012-08-15

A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of discrete exterior calculus [Desbrun et al., e-print arXiv:math/0508341 (2005)], the field solver, interpolation scheme, and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.

Kinetic instabilities of thin current sheets: Results of two-and-one-half-dimensional Vlasov code simulations

International Nuclear Information System (INIS)

Silin, I.; Buechner, J.

2003-01-01

Nonlinear triggering of the instability of thin current sheets is investigated by two-and-one-half- dimensional Vlasov code simulations. A global drift-resonant instability (DRI) is found, which results from the lower-hybrid-drift waves penetrating from the current sheet edges to the center where they resonantly interact with unmagnetized ions. This resonant nonlinear instability grows faster than a Kelvin-Helmholtz instability obtained in previous studies. The DRI is either asymmetric or symmetric mode or a combination of the two, depending on the relative phase of the lower-hybrid-drift waves at the edges of the current sheet. With increasing particle mass ratio the wavenumber of the fastest-growing mode increases as kL z ∼(m i /m e ) 1/2 /2 and the growth rate of the DRI saturates at a finite level

Deterministic methods for the relativistic Vlasov-Maxwell equations and the Van Allen belts dynamics; Methodes deterministes de resolution des equations de Vlasov-Maxwell relativistes en vue du calcul de la dynamique des ceintures de Van Allen

Energy Technology Data Exchange (ETDEWEB)

Le Bourdiec, S

2007-03-15

Artificial satellites operate in an hostile radiation environment, the Van Allen radiation belts, which partly condition their reliability and their lifespan. In order to protect them, it is necessary to characterize the dynamics of the energetic electrons trapped in these radiation belts. This dynamics is essentially determined by the interactions between the energetic electrons and the existing electromagnetic waves. This work consisted in designing a numerical scheme to solve the equations modelling these interactions: the relativistic Vlasov-Maxwell system of equations. Our choice was directed towards methods of direct integration. We propose three new spectral methods for the momentum discretization: a Galerkin method and two collocation methods. All of them are based on scaled Hermite functions. The scaling factor is chosen in order to obtain the proper velocity resolution. We present in this thesis the discretization of the one-dimensional Vlasov-Poisson system and the numerical results obtained. Then we study the possible extensions of the methods to the complete relativistic problem. In order to reduce the computing time, parallelization and optimization of the algorithms were carried out. Finally, we present 1Dx-3Dv (mono-dimensional for x and three-dimensional for velocity) computations of Weibel and whistler instabilities with one or two electrons species. (author)

Vlasov Simulation of Electrostatic Solitary Structures in Multi-Component Plasmas

Science.gov (United States)

Umeda, Takayuki; Ashour-Abdalla, Maha; Pickett, Jolene S.; Goldstein, Melvyn L.

2012-01-01

Electrostatic solitary structures have been observed in the Earth's magnetosheath by the Cluster spacecraft. Recent theoretical work has suggested that these solitary structures are modeled by electron acoustic solitary waves existing in a four-component plasma system consisting of core electrons, two counter-streaming electron beams, and one species of background ions. In this paper, the excitation of electron acoustic waves and the formation of solitary structures are studied by means of a one-dimensional electrostatic Vlasov simulation. The present result first shows that either electron acoustic solitary waves with negative potential or electron phase-space holes with positive potential are excited in four-component plasma systems. However, these electrostatic solitary structures have longer duration times and higher wave amplitudes than the solitary structures observed in the magnetosheath. The result indicates that a high-speed and small free energy source may be needed as a fifth component. An additional simulation of a five-component plasma consisting of a stable four-component plasma and a weak electron beam shows the generation of small and fast electron phase-space holes by the bump-on-tail instability. The physical properties of the small and fast electron phase-space holes are very similar to those obtained by the previous theoretical analysis. The amplitude and duration time of solitary structures in the simulation are also in agreement with the Cluster observation.

On the Magnetic Shield for a Vlasov-Poisson Plasma

Science.gov (United States)

Caprino, Silvia; Cavallaro, Guido; Marchioro, Carlo

2017-12-01

We study the screening of a bounded body Γ against the effect of a wind of charged particles, by means of a shield produced by a magnetic field which becomes infinite on the border of Γ . The charged wind is modeled by a Vlasov-Poisson plasma, the bounded body by a torus, and the external magnetic field is taken close to the border of Γ . We study two models: a plasma composed by different species with positive or negative charges, and finite total mass of each species, and another made of many species of the same sign, each having infinite mass. We investigate the time evolution of both systems, showing in particular that the plasma particles cannot reach the body. Finally we discuss possible extensions to more general initial data. We show also that when the magnetic lines are straight lines, (that imposes an unbounded body), the previous results can be improved.

Vlasov simulations of kinetic Alfvén waves at proton kinetic scales

Energy Technology Data Exchange (ETDEWEB)

Vásconez, C. L. [Dipartimento di Fisica, Università della Calabria, I-87036 Cosenza (Italy); Observatorio Astronómico de Quito, Escuela Politécnica Nacional, Quito (Ecuador); Valentini, F.; Veltri, P. [Dipartimento di Fisica, Università della Calabria, I-87036 Cosenza (Italy); Camporeale, E. [Centrum Wiskunde and Informatica, Amsterdam (Netherlands)

2014-11-15

Kinetic Alfvén waves represent an important subject in space plasma physics, since they are thought to play a crucial role in the development of the turbulent energy cascade in the solar wind plasma at short wavelengths (of the order of the proton gyro radius ρ{sub p} and/or inertial length d{sub p} and beyond). A full understanding of the physical mechanisms which govern the kinetic plasma dynamics at these scales can provide important clues on the problem of the turbulent dissipation and heating in collisionless systems. In this paper, hybrid Vlasov-Maxwell simulations are employed to analyze in detail the features of the kinetic Alfvén waves at proton kinetic scales, in typical conditions of the solar wind environment (proton plasma beta β{sub p} = 1). In particular, linear and nonlinear regimes of propagation of these fluctuations have been investigated in a single-wave situation, focusing on the physical processes of collisionless Landau damping and wave-particle resonant interaction. Interestingly, since for wavelengths close to d{sub p} and β{sub p} ≃ 1 (for which ρ{sub p} ≃ d{sub p}) the kinetic Alfvén waves have small phase speed compared to the proton thermal velocity, wave-particle interaction processes produce significant deformations in the core of the particle velocity distribution, appearing as phase space vortices and resulting in flat-top velocity profiles. Moreover, as the Eulerian hybrid Vlasov-Maxwell algorithm allows for a clean almost noise-free description of the velocity space, three-dimensional plots of the proton velocity distribution help to emphasize how the plasma departs from the Maxwellian configuration of thermodynamic equilibrium due to nonlinear kinetic effects.

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)

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

Global existence of classical solutions to the Vlasov-Poisson system in a three dimensional, cosmological setting

OpenAIRE

Rein, Gerhard; Rendall, Alan D.

1993-01-01

The initial value problem for the Vlasov-Poisson system is by now well understood in the case of an isolated system where, by definition, the distribution function of the particles as well as the gravitational potential vanish at spatial infinity. Here we start with homogeneous solutions, which have a spatially constant, non-zero mass density and which describe the mass distribution in a Newtonian model of the universe. These homogeneous states can be constructed explicitly, and we consider d...

Formation of large-amplitude dust ion-acoustic shocks in dusty plasmas

International Nuclear Information System (INIS)

Eliasson, B.; Shukla, P.K.

2005-01-01

Theoretical and numerical studies of self-steepening and shock formation of large-amplitude dust ion-acoustic waves in dusty plasmas are presented. A comparison is made between the nondispersive two fluid model, which predicts the formation of large-amplitude compressive and rarefactive dust ion-acoustic shocks, Vlasov simulations, and recent laboratory experiments

Integral propagator solvers for Vlasov-Fokker-Planck equations

International Nuclear Information System (INIS)

Donoso, J M; Rio, E del

2007-01-01

We briefly discuss the use of short-time integral propagators on solving the so-called Vlasov-Fokker-Planck equation for the dynamics of a distribution function. For this equation, the diffusion tensor is singular and the usual Gaussian representation of the short-time propagator is no longer valid. However, we prove that the path-integral approach on solving the equation is, in fact, reliable by means of our generalized propagator, which is obtained through the construction of an auxiliary solvable Fokker-Planck equation. The new representation of the grid-free advancing scheme describes the inherent cross- and self-diffusion processes, in both velocity and configuration spaces, in a natural manner, although these processes are not explicitly depicted in the differential equation. We also show that some splitting methods, as well as some finite-difference schemes, could fail in describing the aforementioned diffusion processes, governed in the whole phase space only by the velocity diffusion tensor. The short-time transition probability offers a stable and robust numerical algorithm that preserves the distribution positiveness and its norm, ensuring the smoothness of the evolving solution at any time step. (fast track communication)

Explicit analytical solution of the nonlinear Vlasov Poisson system

International Nuclear Information System (INIS)

Skarka, V.; Mahajan, S.M.; Fijalkow, E.

1993-10-01

In order to describe the time evolution of an inhomogeneous collisionless plasma the nonlinear Vlasov equation is solved perturbatively, using the subdynamics approach and the diagrammatic techniques. The solution is given in terms of a double perturbation series, one with respect to the nonlinearities and the other with respect to the interaction between particles. The infinite sum of interaction terms can be performed exactly due to the property of dynamical factorization. Following the methodology, the exact solution in each order with respect to nonlinearities is computed. For a choice of initial perturbation the first order exact solution is numerically integrated in order to find the local density excess. The approximate analytical solution is found to be in excellent agreement with exact numerical integration as well as with ab initio numerical simulations. Analytical computation gives a better insight into the problem and it has the advantage to be simpler, and also accessible in some range of parameters where it is difficult to find numerical solutions. (author). 27 refs, 12 figs

Non-Linear Excitation of Ion Acoustic Waves

DEFF Research Database (Denmark)

Michelsen, Poul; Hirsfield, J. L.

1974-01-01

The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation.......The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation....

Energy loss of heavy ion beams in plasma

Energy Technology Data Exchange (ETDEWEB)

Okada, T; Hotta, T [Tokyo Univ. of Agriculture and Technology, Koganei (Japan). Faculty of Technology

1997-12-31

The energy loss of heavy-ion beams (HIB) is studied by means of Vlasov theory and Particle-in-Cell (PIC) simulations in a plasma. The interaction of HIB with a plasma is of central importance for inertial confinement fusion (ICF). A number of studies on the HIB interaction with target plasma have been published. It is important for heavy-ion stopping that the effects of the non-linear interaction of HIB within the Vlasov theory are included. Reported are results of a numerical study of nonlinear effects to the stopping power for HIB in plasma. It is shown that the PIC simulations of collective effects of the stopping power are in a good agreement with the Vlasov theory. (author). 2 tabs., 1 fig., 5 refs.

The Vlasov equation with strong magnetic field and oscillating electric field as a model for isotop resonant separation

Directory of Open Access Journals (Sweden)

Emmanuel Frenod

2002-01-01

Full Text Available We study the qualitative behavior of solutions to the Vlasov equation with strong external magnetic field and oscillating electric field. This model is relevant to the understanding of isotop resonant separation. We show that the effective equation is a kinetic equation with a memory term. This memory term involves a pseudo-differential operator whose kernel is characterized by an integral equation involving Bessel functions. The kernel is explicitly given in some particular cases.

Application of the Modified Vlasov Model to the Free Vibration Analysis of Thick Plates Resting on Elastic Foundations

OpenAIRE

Ozgan, Korhan; Daloglu, Ayse T.

2009-01-01

The Modified Vlasov Model is applied to the free vibration analysis of thick plates resting on elastic foundations. The effects of the subsoil depth, plate dimensions and their ratio, the value of the vertical deformation parameter within the subsoil on the frequency parameters of plates on elastic foundations are investigated. A four-noded, twelve degrees of freedom quadrilateral finite element (PBQ4) is used for plate bending analysis based on Mindlin plate theory which is effectively appli...

Evolution of the phase-space density and the Jeans scale for dark matter derived from the Vlasov-Einstein equation

International Nuclear Information System (INIS)

Piattella, O.F.; Rodrigues, D.C.; Fabris, J.C.; Pacheco, J.A. de Freitas

2013-01-01

We discuss solutions of Vlasov-Einstein equation for collisionless dark matter particles in the context of a flat Friedmann universe. We show that, after decoupling from the primordial plasma, the dark matter phase-space density indicator Q = ρ/(σ 1D 2 ) 3/2 remains constant during the expansion of the universe, prior to structure formation. This well known result is valid for non-relativistic particles and is not ''observer dependent'' as in solutions derived from the Vlasov-Poisson system. In the linear regime, the inclusion of velocity dispersion effects permits to define a physical Jeans length for collisionless matter as function of the primordial phase-space density indicator: λ J = (5π/G) 1/2 Q −1/3 ρ dm −1/6 . The comoving Jeans wavenumber at matter-radiation equality is smaller by a factor of 2-3 than the comoving wavenumber due to free-streaming, contributing to the cut-off of the density fluctuation power spectrum at the lowest scales. We discuss the physical differences between these two scales. For dark matter particles of mass equal to 200 GeV, the derived Jeans mass is 4.3 × 10 −6 M ⊙

Mathematic study and numerical implantation of the Vlasov-Darwin model

International Nuclear Information System (INIS)

Sonnendrucker, E.

1994-12-01

Numerical simulation of some phenomena in plasma physics, or more generally in electromagnetism, can be more easily done using approximate models of Maxwell equations such as the Darwin model in which the transverse part of the displacement current in the Ampere equation is neglected, or such as the static model in which the time derivatives are neglected. In this note, the Darwin model is presented first, and then an asymptotic analysis of Maxwell equations is given with limit conditions of perfect conductor on one part of the side, and Silver-Muller absorbing conditions on the other part. This allows to obtain a variational formulation for the Darwin model which is a good approximation of Maxwell equations. A variational formulation for the quasi-static model is also obtained. In a second part this implantation is described using a 2-D finite element method coupled with a particulate method for the Vlasov equations which leads to numerical results allowing a determination of the different models application. (J.S.). 2 refs

Wigner transformation in curved space-time and the curvature correction of the Vlasov equation for semiclassical gravitating systems

International Nuclear Information System (INIS)

Winter, J.

1985-01-01

A covariant generalization of the Wigner transformation of quantum equations is proposed for gravitating many-particle systems, which modifies the Einstein-Liouville equations for the coupled gravity-matter problem by inclusion of quantum effects of the matter moving in its self-consistent classical gravitational field, in order to extend their realm of validity to higher particle densities. The corrections of the Vlasov equation (Liouville equation in one-particle phase space) are exhibited as combined effects of quantum mechanics and the curvature of space-time arranged in a semiclassical expansion in powers of h 2 , the first-order term of which is explicitly calculated. It is linear in the Riemann tensor and in its gradient; the Riemann tensor occurs in a similar position as the tensor of the Yang-Mills field strength in a corresponding Vlasov equation for systems with local gauge invariance in the purely classical limit. The performance of the Wigner transformation is based on expressing the equation of motion for the two-point function of the Klein-Gordon field, in particular the Beltrami operator, in terms of a midpoint and a distance vector covariantly defined for the two points. This implies the calculation of deviations of the geodesic between these points, the standard concept of which has to be refined to include infinitesimal variations of the second order. A differential equation for the second-order deviation is established

Transition from convective to absolute Raman instability via the longitudinal relativistic effect by using Vlasov-Maxwell simulations

Science.gov (United States)

Wang, Q.; Liu, Z. J.; Zheng, C. Y.; Xiao, C. Z.; Feng, Q. S.; Zhang, H. C.; He, X. T.

2018-01-01

The longitudinal relativistic effect on stimulated Raman backscattering (SRBS) is investigated by using one-dimensional (1D) Vlasov-Maxwell simulations. Using a short backscattered light seed pulse with a very small amplitude, the linear gain spectra of SRBS in the strongly convective regime is presented by combining the relativistic and non-relativistic 1D Vlasov-Maxwell simulations, which is in agreement with the steady-state linear theory. More interestingly, by considering transition from convective to absolute instability due to electron trapping, we successfully predict the critical duration of the seed which can just trigger the kinetic inflation of the excited SRBS after the seed leaves the simulation box. The critical duration in the relativistic case is much shorter than that in the nonrelativistic case, which indicates that the kinetic inflation more easily occurs in the relativistic case than in the nonrelativistic case. In the weakly convective regime, the transition from convective to absolute instability for SRBS can directly occur in the linear regime due to the longitudinal relativistic modification. For the same pump, our simulations first demonstrate that the SRBS excited by a short and small seed pulse is a convective instability in the nonrelativistic case but becomes an absolute instability due to the decrease of the linear Landau damping from the longitudinal relativistic modification in the relativistic case. In more detail, the growth rate of the backscattered light is also in excellent agreement with theoretical prediction.

Fully nonlinear phenomenology of the Berk-Breizman augmentation of the Vlasov-Maxwell system

International Nuclear Information System (INIS)

Vann, R.G.L.; Dendy, R.O.; Rowlands, G.; Arber, T.D.; D'Ambrumenil, N.

2003-01-01

The Berk-Breizman augmentation of the Vlasov-Maxwell system is widely used to model self-consistent resonant excitation and damping of wave fields by evolving energetic particle populations in magnetic fusion plasmas. The key model parameters are the particle annihilation rate ν a , which drives bump-on-tail structure, and the linear wave damping rate γ d . A code, based on the piecewise parabolic method, is used to integrate the fully nonlinear Berk-Breizman system of equations across the whole (ν a ,γ d ) parameter space. The results of this code show that the system's behavior can be classified into one of four types, each of which occurs in a well-defined region of parameter space: chaotic, periodic, steady state, and damped. The corresponding evolution in (x,v) phase space is also examined

Solution of the linearised Vlasov equation for collisionless plasmas evolving in external fields of arbitrary spatial and time dependence: Pt. 2

International Nuclear Information System (INIS)

Skarka, V.; Coveney, P.V.

1990-01-01

We solve perturbatively the linearised Vlasov equation describing inhomogeneous collisionless plasmas evolving in time-dependent external fields. The method employs an explicitly time-dependent formalism and is facilitated by the used of diagrammatic techniques. It leads to a straightforward algorithm for computing the contribution to the solution, order by order in the external field. In the previous paper we provided the solution to first order; higher orders are described in the present paper. (author)

A study of the disintegration of highly excited nuclei with the Vlasov-Uehling-Uhlenbeck equation

International Nuclear Information System (INIS)

Vinet, L.; Gregoire, C.; Schuck, P.; Remaud, B.; Sebille, F.

1987-01-01

The disintegration of hot and/or compressed nuclei is studied using (i) the Vlasov equation (VE) with imposed spherical symmetry, (ii) the VE in three dimensions (3D) and (iii) the VE in three dimensions supplemented by the Uehling-Uhlenbeck collision term (VUU). We find that case (ii) is slightly more unstable with respect to disintegration compared to case (i) whereas (iii) tends to make nuclei more stable. In all cases the thermal energies (15-20 MeV per nucleon) needed to totally disintegrate a nucleus seem to be higher than those found in static and hydrodynamic calculation. On the contrary, compressional energy very much helps disintegration. Some comments on the introduction of fluctuations and corresponding fragmentation are added. (orig.)

Dynamic Analysis of Thick Plates Including Deep Beams on Elastic Foundations Using Modified Vlasov Model

Directory of Open Access Journals (Sweden)

Korhan Ozgan

2013-01-01

Full Text Available Dynamic analysis of foundation plate-beam systems with transverse shear deformation is presented using modified Vlasov foundation model. Finite element formulation of the problem is derived by using an 8-node (PBQ8 finite element based on Mindlin plate theory for the plate and a 2-node Hughes element based on Timoshenko beam theory for the beam. Selective reduced integration technique is used to avoid shear locking problem for the evaluation of the stiffness matrices for both the elements. The effect of beam thickness, the aspect ratio of the plate and subsoil depth on the response of plate-beam-soil system is analyzed. Numerical examples show that the displacement, bending moments and shear forces are changed significantly by adding the beams.

Kinetic stability of field-reversed configurations

International Nuclear Information System (INIS)

Staudenmeier, J.L.; Hsiao, M.-Y.

1991-01-01

The internal tilt mode is considered to be the biggest threat to Field-Reversed Configuration (FRC) global stability. The tilt stability of the FRC is studied using the MHD, Hall MHD, and the Vlasov-fluid (Vlasov ions, cold massless fluid electrons) models. Nonlinear Hall MHD calculations showed that the FRC was stable to the tilt mode when the s value of the FRC was below a critical value that was dependent on plasma length. The critical s value is larger for longer plasma equilibria. The stability of FRC's with toroidal field was studied with a linear initial value MHD code. The calculations showed an axial perturbation wavelength of the most unstable eigenfunction that was consistent with internal probe measurements made on translated FRC's. Linear Vlasov-fluid eigenvalue calculations showed that kinetic ion effects can change both the growth rate and the structure of the eigenfunctions when compared to the corresponding MHD modes. Calculations on short FRC equilibria indicate that MHD is not the appropriate small gyroradius limit of the Vlasov-fluid model because the axial transit time of a thermal ion is approximately equal to an MHD growth time for the tilt mode. Calculations were done using a small number of unstable MHD eigenfunctions as basis functions in order to reduce the dimensionality of the stability problem. The results indicated that this basis set can produce inaccurate growth rates at large value for s for some equilibria

Second order oscillations of a Vlasov-Poisson plasma in the Fourier transformed space

International Nuclear Information System (INIS)

Sedlacek, Z.; Nocera, L.

1991-05-01

The Vlasov-Poisson system of equations in the Fourier-transformed velocity space is studied. At first some results of the linear theory are reformulated: in the new representation the Van Kampen eigenmodes and their adjoint are found to be ordinary functions with convenient piece-wise continuity properties. A transparent derivation is given of the free-streaming temporal echo in terms of the kinematics of wave packets in the Fourier-transformed velocity space. This analysis is further extended to include Coulomb interactions which allows to establish a connection between the echo theory, the second order oscillations of Best and the phenomenon of linear sidebands. The calculation of the time evolution of the global second order electric field is performed in detail in the case of a Maxwellian equilibrium distribution function. It is concluded that the phenomenon of linear sidebands may be properly explained in terms of the intrinsic features of the equilibrium distribution function. (author) 5 figs., 32 refs

Relativistic extension of a charge-conservative finite element solver for time-dependent Maxwell-Vlasov equations

Science.gov (United States)

Na, D.-Y.; Moon, H.; Omelchenko, Y. A.; Teixeira, F. L.

2018-01-01

Accurate modeling of relativistic particle motion is essential for physical predictions in many problems involving vacuum electronic devices, particle accelerators, and relativistic plasmas. A local, explicit, and charge-conserving finite-element time-domain (FETD) particle-in-cell (PIC) algorithm for time-dependent (non-relativistic) Maxwell-Vlasov equations on irregular (unstructured) meshes was recently developed by Moon et al. [Comput. Phys. Commun. 194, 43 (2015); IEEE Trans. Plasma Sci. 44, 1353 (2016)]. Here, we extend this FETD-PIC algorithm to the relativistic regime by implementing and comparing three relativistic particle-pushers: (relativistic) Boris, Vay, and Higuera-Cary. We illustrate the application of the proposed relativistic FETD-PIC algorithm for the analysis of particle cyclotron motion at relativistic speeds, harmonic particle oscillation in the Lorentz-boosted frame, and relativistic Bernstein modes in magnetized charge-neutral (pair) plasmas.

Flows of non-smooth vector fields and degenerate elliptic equations with applications to the Vlasov-Poisson and semigeostrophic systems

CERN Document Server

Colombo, Maria

2017-01-01

The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows.

Vlasov simulation of the relativistic effect on the breaking of large amplitude plasma waves

International Nuclear Information System (INIS)

Xu Hui; Sheng Zhengming; Zhang Jie

2007-01-01

The influence of relativistic and thermal effects on plasma wave breaking has been studied by solving the coupled Vlasov-Poisson equations. When the relativistic effect is not considered, the wave breaking will not occur, provided the initial perturbation is less than certain value as predicted previously, and the largest amplitude of the plasma wave will decrease with the increase of the initial temperature. When the relativistic effect is considered, wave breaking always occurs during the time evolution, irrespective of the initial perturbation amplitude. Yet the smaller the initial perturbation amplitude is, the longer is the time for wave breaking to occur. With large initial perturbations, wave breaking can always occur with the without the relativistic effect. However, the results are significantly different in the two cases. The thermal effects of electrons decrease the threshold value to initial amplitude for wave breaking and large phase velocity makes the nonlinear phenomenon occur more easily. (authors)

Bending analysis of agglomerated carbon nanotube-reinforced beam resting on two parameters modified Vlasov model foundation

Science.gov (United States)

Ghorbanpour Arani, A.; Zamani, M. H.

2018-06-01

The present work deals with bending behavior of nanocomposite beam resting on two parameters modified Vlasov model foundation (MVMF), with consideration of agglomeration and distribution of carbon nanotubes (CNTs) in beam matrix. Equivalent fiber based on Eshelby-Mori-Tanaka approach is employed to determine influence of CNTs aggregation on elastic properties of CNT-reinforced beam. The governing equations are deduced using the principle of minimum potential energy under assumption of the Euler-Bernoulli beam theory. The MVMF required the estimation of γ parameter; to this purpose, unique iterative technique based on variational principles is utilized to compute value of the γ and subsequently fourth-order differential equation is solved analytically. Eventually, the transverse displacements and bending stresses are obtained and compared for different agglomeration parameters, various boundary conditions simultaneously and variant elastic foundation without requirement to instate values for foundation parameters.

Towards a collisionless fluid closure in plasma turbulence

Energy Technology Data Exchange (ETDEWEB)

Dif Pradalier, G

2005-07-01

In this work 2 generic possible descriptions of a plasma have been compared namely the kinetic and the fluid approaches. The latter focuses on the successive moments (n, u, p, q,...) of the distribution function, whereas the former describes the time-evolution in phase space of this distribution function, both being based on the Vlasov equation. The fluid description is attractive for the Vlasov equation is tractable with great difficulties. Nevertheless it rests on a major difficulty: as the set of fluid equations constitute an infinite hierarchy, a closure equation must be chosen. The first chapter details physical characteristics of a fundamental kinetic interaction mechanism between waves and particles. In chapter 2 we propose a fluid closure that allows analytic comparison with a linear fully kinetic result, near an homogeneous, electrostatic, Maxwellian equilibrium. This approach consists in adjusting chosen parameters in order to minimize the discrepancies between fluid and kinetic linear response functions. In chapter 3 we present a general frame for a fluid closure in a magnetized plasma. This is attempted in a linear, simplified model with low dimensionality.

Multilevel and Multi-index Monte Carlo methods for the McKean–Vlasov equation

KAUST Repository

Haji-Ali, Abdul-Lateef

2017-09-12

We address the approximation of functionals depending on a system of particles, described by stochastic differential equations (SDEs), in the mean-field limit when the number of particles approaches infinity. This problem is equivalent to estimating the weak solution of the limiting McKean–Vlasov SDE. To that end, our approach uses systems with finite numbers of particles and a time-stepping scheme. In this case, there are two discretization parameters: the number of time steps and the number of particles. Based on these two parameters, we consider different variants of the Monte Carlo and Multilevel Monte Carlo (MLMC) methods and show that, in the best case, the optimal work complexity of MLMC, to estimate the functional in one typical setting with an error tolerance of $$\\\\mathrm {TOL}$$TOL, is when using the partitioning estimator and the Milstein time-stepping scheme. We also consider a method that uses the recent Multi-index Monte Carlo method and show an improved work complexity in the same typical setting of . Our numerical experiments are carried out on the so-called Kuramoto model, a system of coupled oscillators.

Fully kinetic simulation of ion acoustic and dust-ion acoustic waves

International Nuclear Information System (INIS)

Hosseini Jenab, S. M.; Kourakis, I.; Abbasi, H.

2011-01-01

A series of numerical simulations is presented, based on a recurrence-free Vlasov kinetic model using kinetic phase point trajectories. All plasma components are modeled kinetically via a Vlasov evolution equation, then coupled through Poisson's equation. The dynamics of ion acoustic waves in an electron-ion and in a dusty (electron-ion-dust) plasma configuration are investigated, focusing on wave decay due to Landau damping and, in particular, on the parametric dependence of the damping rate on the dust concentration and on the electron-to-ion temperature ratio. In the absence of dust, the occurrence of damping was observed, as expected, and its dependence to the relative magnitude of the electron vs ion temperature(s) was investigated. When present, the dust component influences the charge balance, enabling dust-ion acoustic waves to survive Landau damping even in the extreme regime where T e ≅ T i . The Landau damping rate is shown to be minimized for a strong dust concentration or/and for a high value of the electron-to-ion temperature ratio. Our results confirm earlier theoretical considerations and contribute to the interpretation of experimental observations of dust-ion acoustic wave characteristics.

Coherent state methods for semi-classical heavy-ion physics

International Nuclear Information System (INIS)

Remaud, B.; Sebille, F.; Raffray, Y.

1985-01-01

A semi-classical model of many fermion systems is developed in view of solving the Vlasov equation; it provides an unified description of both static and dynamic properties of the system. The phase space distribution functions are written as convolution products of generalized coherent state distributions with semi-probabilistic weight functions. The generalized coherent states are defined from the local constants of motion of the dynamical system; they may reduce to the usuel ones (eigen states of the annihilation operator) only at the harmonic limit. Solving the Vlasov equation consists in two steps: (i) search for weight functions which properly describe the initial density distributions (ii) calculation of the evolutions of the coherent state set which acts as a moving basis for the Vlasov equation solutions. Sample applications to statics are analyzed: fermions in a harmonic field, self-consistent nuclear slabs. Outlooks of dynamical applications are discussed with a special attention to the fast nucleon emission in heavy-ion reactions

Semi-classical approaches to the phase space evolutions in intermediate energy heavy ion collisions

Energy Technology Data Exchange (ETDEWEB)

Remaud, B; Sebille, F; Raffray, Y; Gregoire, C; Vinet, L

1986-01-06

The properties of semi-classical phase space evolution equations - as the Vlasov/Boltzmann equations - are discussed in the context of the heavy ion reaction theory at intermediate energies (from 10 to 100 MeV per nucleon). The generalized coherent state set is shown to form a (over) complete basis for the phase space; then every solution of the Vlasov/Boltzmann equations can be defined as a convolution product of the generalized coherent state basis by an appropriate weight function w. The uniform approximation for w is shown to provide an accurate semi-classical description of fermion systems in their ground state: the examples of fermions in a harmonic well and of cold nuclei are discussed. The solution of the Vlasov equation amounts to follow the time evolution of the coherent states which play the role of a moving basis. For the Boltzmann equation, the collision term is taken into account by explicit or implicit variations of the function w. Typical applications are discussed: nuclear response to the giant monopole resonance excitation, fast nucleon emission in heavy-ion reactions. (orig.).

Ion Acoustic Waves in the Presence of Langmuir Oscillations

DEFF Research Database (Denmark)

Pécseli, Hans

1976-01-01

The dielectric function for long-wavelength, low-frequency ion acoustic waves in the presence of short-wavelength, high-frequency electron oscillations is presented, where the ions are described by the collision-free Vlasov equation. The effect of the electron oscillations can be appropriately...

The Arrow of Time in the Collapse of Collisionless Self-gravitating Systems: Non-validity of the Vlasov-Poisson Equation during Violent Relaxation

Science.gov (United States)

Beraldo e Silva, Leandro; de Siqueira Pedra, Walter; Sodré, Laerte; Perico, Eder L. D.; Lima, Marcos

2017-09-01

The collapse of a collisionless self-gravitating system, with the fast achievement of a quasi-stationary state, is driven by violent relaxation, with a typical particle interacting with the time-changing collective potential. It is traditionally assumed that this evolution is governed by the Vlasov-Poisson equation, in which case entropy must be conserved. We run N-body simulations of isolated self-gravitating systems, using three simulation codes, NBODY-6 (direct summation without softening), NBODY-2 (direct summation with softening), and GADGET-2 (tree code with softening), for different numbers of particles and initial conditions. At each snapshot, we estimate the Shannon entropy of the distribution function with three different techniques: Kernel, Nearest Neighbor, and EnBiD. For all simulation codes and estimators, the entropy evolution converges to the same limit as N increases. During violent relaxation, the entropy has a fast increase followed by damping oscillations, indicating that violent relaxation must be described by a kinetic equation other than the Vlasov-Poisson equation, even for N as large as that of astronomical structures. This indicates that violent relaxation cannot be described by a time-reversible equation, shedding some light on the so-called “fundamental paradox of stellar dynamics.” The long-term evolution is well-described by the orbit-averaged Fokker-Planck model, with Coulomb logarithm values in the expected range 10{--}12. By means of NBODY-2, we also study the dependence of the two-body relaxation timescale on the softening length. The approach presented in the current work can potentially provide a general method for testing any kinetic equation intended to describe the macroscopic evolution of N-body systems.

Harmonic effects on ion-bulk waves and simulation of stimulated ion-bulk-wave scattering in CH plasmas

Science.gov (United States)

Feng, Q. S.; Zheng, C. Y.; Liu, Z. J.; Cao, L. H.; Xiao, C. Z.; Wang, Q.; Zhang, H. C.; He, X. T.

2017-08-01

Ion-bulk (IBk) wave, a novel branch with a phase velocity close to the ion’s thermal velocity, discovered by Valentini et al (2011 Plasma Phys. Control. Fusion 53 105017), is recently considered as an important electrostatic activity in solar wind, and thus of great interest to space physics and also inertial confinement fusion. The harmonic effects on IBk waves has been researched by Vlasov simulation for the first time. The condition of excitation of the large-amplitude IBk waves is given. The nature of nonlinear IBk waves in the condition of kFeng scattering (SFS) has been proposed and also verified by Vlasov-Maxwell code. In CH plasmas, in addition to the stimulated Brillouin scattering from multi ion-acoustic waves, there exists SIBS simultaneously. This research gives an insight into the SIBS in the field of laser plasma interaction.

Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems

International Nuclear Information System (INIS)

Xiao, Jianyuan; Liu, Jian; He, Yang; Zhang, Ruili; Qin, Hong; Sun, Yajuan

2015-01-01

Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint http://arxiv.org/abs/arXiv:1505.06076 (2015)], which produces five exactly soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave

Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems

Energy Technology Data Exchange (ETDEWEB)

Xiao, Jianyuan [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Qin, Hong [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA; Liu, Jian [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; He, Yang [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Zhang, Ruili [School of Nuclear Science and Technology and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; Key Laboratory of Geospace Environment, CAS, Hefei, Anhui 230026, China; Sun, Yajuan [LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100190, China

2015-11-01

Explicit high-order non-canonical symplectic particle-in-cell algorithms for classical particle-field systems governed by the Vlasov-Maxwell equations are developed. The algorithms conserve a discrete non-canonical symplectic structure derived from the Lagrangian of the particle-field system, which is naturally discrete in particles. The electromagnetic field is spatially discretized using the method of discrete exterior calculus with high-order interpolating differential forms for a cubic grid. The resulting time-domain Lagrangian assumes a non-canonical symplectic structure. It is also gauge invariant and conserves charge. The system is then solved using a structure-preserving splitting method discovered by He et al. [preprint arXiv: 1505.06076 (2015)], which produces five exactly soluble sub-systems, and high-order structure-preserving algorithms follow by combinations. The explicit, high-order, and conservative nature of the algorithms is especially suitable for long-term simulations of particle-field systems with extremely large number of degrees of freedom on massively parallel supercomputers. The algorithms have been tested and verified by the two physics problems, i.e., the nonlinear Landau damping and the electron Bernstein wave. (C) 2015 AIP Publishing LLC.

Wave Propagation in an Ion Beam-Plasma System

DEFF Research Database (Denmark)

Jensen, T. D.; Michelsen, Poul; Juul Rasmussen, Jens

1979-01-01

The spatial evolution of a velocity- or density-modulated ion beam is calculated for stable and unstable ion beam plasma systems, using the linearized Vlasov-Poisson equations. The propagation properties are found to be strongly dependent on the form of modulation. In the case of velocity...

Ion distributions upstream and downstream of the Earth's bow shock: first results from Vlasiator

Directory of Open Access Journals (Sweden)

D. Pokhotelov

2013-12-01

Full Text Available A novel hybrid-Vlasov code, Vlasiator, is developed for global simulations of magnetospheric plasma kinetics. The code is applied to model the collisionless bow shock on scales of the Earth's magnetosphere in two spatial dimensions and three dimensions in velocity space retrieving ion distribution functions over the entire foreshock and magnetosheath regions with unprecedented detail. The hybrid-Vlasov approach produces noise-free uniformly discretized ion distribution functions comparable to those measured in situ by spacecraft. Vlasiator can reproduce features of the ion foreshock and magnetosheath well known from spacecraft observations, such as compressional magnetosonic waves generated by backstreaming ion populations in the foreshock and mirror modes in the magnetosheath. An overview of ion distributions from various regions of the bow shock is presented, demonstrating the great opportunities for comparison with multi-spacecraft observations.

Weakly Collisional and Collisionless Astrophysical Plasmas

DEFF Research Database (Denmark)

Berlok, Thomas

are used to study weakly collisional, stratified atmospheres which offer a useful model of the intracluster medium of galaxy clusters. Using linear theory and computer simulations, we study instabilities that feed off thermal and compositional gradients. We find that these instabilities lead to vigorous...... investigate helium mixing in the weakly collisional intracluster medium of galaxy clusters using Braginskii MHD. Secondly, we present a newly developed Vlasov-fluid code which can be used for studying fully collisionless plasmas such as the solar wind and hot accretions flows. The equations of Braginskii MHD...... associated with the ions and is thus well suited for studying collisionless plasmas. We have developed a new 2D-3V Vlasov-fluid code which works by evolving the phase-space density distribution of the ions while treating the electrons as an inertialess fluid. The code uses the particle-incell (PIC) method...

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.

Diagnosing collisionless energy transfer using field-particle correlations: Vlasov-Poisson plasmas

Science.gov (United States)

Howes, Gregory G.; Klein, Kristopher G.; Li, Tak Chu

2017-02-01

Turbulence plays a key role in the conversion of the energy of large-scale fields and flows to plasma heat, impacting the macroscopic evolution of the heliosphere and other astrophysical plasma systems. Although we have long been able to make direct spacecraft measurements of all aspects of the electromagnetic field and plasma fluctuations in near-Earth space, our understanding of the physical mechanisms responsible for the damping of the turbulent fluctuations in heliospheric plasmas remains incomplete. Here we propose an innovative field-particle correlation technique that can be used to measure directly the secular energy transfer from fields to particles associated with collisionless damping of the turbulent fluctuations. Furthermore, this novel procedure yields information about the collisionless energy transfer as a function of particle velocity, providing vital new information that can help to identify the dominant collisionless mechanism governing the damping of the turbulent fluctuations. Kinetic plasma theory is used to devise the appropriate correlation to diagnose Landau damping, and the field-particle correlation technique is thoroughly illustrated using the simplified case of the Landau damping of Langmuir waves in a 1D-1V (one dimension in physical space and one dimension in velocity space) Vlasov-Poisson plasma. Generalizations necessary to apply the field-particle correlation technique to diagnose the collisionless damping of turbulent fluctuations in the solar wind are discussed, highlighting several caveats. This novel field-particle correlation technique is intended to be used as a primary analysis tool for measurements from current, upcoming and proposed spacecraft missions that are focused on the kinetic microphysics of weakly collisional heliospheric plasmas, including the Magnetospheric Multiscale (MMS), Solar Probe Plus, Solar Orbiter and Turbulence Heating ObserveR (THOR) missions.

2D accelerator design for SITEX negative ion source

International Nuclear Information System (INIS)

Whealton, J.H.; Raridon, R.J.; McGaffey, R.W.; McCollough, D.H.; Stirling, W.L.; Dagenhart, W.K.

1983-01-01

Solving the Poisson-Vlasov equations where the magnetic field, B, is assumed constant, we optimize the optical system of a SITEX negative ion source in infinite slot geometry. Algorithms designed to solve the above equations were modified to include the curved emitter boundary data appropriate to a negative ion source. Other configurations relevant to negative ion sources are examined

Non-Linear Langmuir Wave Modulation in Collisionless Plasmas

DEFF Research Database (Denmark)

Dysthe, K. B.; Pécseli, Hans

1977-01-01

in the expressions concerning the modulation instability of a plane Langmuir wave. When the Vlasov equation for the ions is applied, a Langmuir wave is modulationally unstable for arbitrary perturbations independent of the unperturbed wave amplitude, in contrast to what is found for fluid ions. A simple analogy...

Application of the Modified Vlasov Model to the Free Vibration Analysis of Thick Plates Resting on Elastic Foundations

Directory of Open Access Journals (Sweden)

Korhan Ozgan

2009-01-01

Full Text Available The Modified Vlasov Model is applied to the free vibration analysis of thick plates resting on elastic foundations. The effects of the subsoil depth, plate dimensions and their ratio, the value of the vertical deformation parameter within the subsoil on the frequency parameters of plates on elastic foundations are investigated. A four-noded, twelve degrees of freedom quadrilateral finite element (PBQ4 is used for plate bending analysis based on Mindlin plate theory which is effectively applied to the analysis of thin and thick plates when selective reduced integration technique is used. The first ten natural frequency parameters are presented in tabular and graphical forms to show the effects of the parameters considered in the study. It is concluded that the effect of the subsoil depth on the frequency parameters of the plates on elastic foundation is generally larger than that of the other parameters considered in the study.

Stability of Nonlinear Wave Patterns to the Bipolar Vlasov-Poisson-Boltzmann System

Science.gov (United States)

Li, Hailiang; Wang, Yi; Yang, Tong; Zhong, Mingying

2018-04-01

The main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction waves for the bipolar Vlasov-Poisson-Boltzmann (VPB) system. To this end, motivated by the micro-macro decomposition to the Boltzmann equation in Liu and Yu (Commun Math Phys 246:133-179, 2004) and Liu et al. (Physica D 188:178-192, 2004), we first set up a new micro-macro decomposition around the local Maxwellian related to the bipolar VPB system and give a unified framework to study the nonlinear stability of the basic wave patterns to the system. Then, as applications of this new decomposition, the time-asymptotic stability of the two typical nonlinear wave patterns, viscous shock waves and rarefaction waves are proved for the 1D bipolar VPB system. More precisely, it is first proved that the linear superposition of two Boltzmann shock profiles in the first and third characteristic fields is nonlinearly stable to the 1D bipolar VPB system up to some suitable shifts without the zero macroscopic mass conditions on the initial perturbations. Then the time-asymptotic stability of the rarefaction wave fan to compressible Euler equations is proved for the 1D bipolar VPB system. These two results are concerned with the nonlinear stability of wave patterns for Boltzmann equation coupled with additional (electric) forces, which together with spectral analysis made in Li et al. (Indiana Univ Math J 65(2):665-725, 2016) sheds light on understanding the complicated dynamic behaviors around the wave patterns in the transportation of charged particles under the binary collisions, mutual interactions, and the effect of the electrostatic potential forces.

Multi-dimensional, fully-implicit, spectral method for the Vlasov-Maxwell equations with exact conservation laws in discrete form

Science.gov (United States)

Delzanno, G. L.

2015-11-01

A spectral method for the numerical solution of the multi-dimensional Vlasov-Maxwell equations is presented. The plasma distribution function is expanded in Fourier (for the spatial part) and Hermite (for the velocity part) basis functions, leading to a truncated system of ordinary differential equations for the expansion coefficients (moments) that is discretized with an implicit, second order accurate Crank-Nicolson time discretization. The discrete non-linear system is solved with a preconditioned Jacobian-Free Newton-Krylov method. It is shown analytically that the Fourier-Hermite method features exact conservation laws for total mass, momentum and energy in discrete form. Standard tests involving plasma waves and the whistler instability confirm the validity of the conservation laws numerically. The whistler instability test also shows that we can step over the fastest time scale in the system without incurring in numerical instabilities. Some preconditioning strategies are presented, showing that the number of linear iterations of the Krylov solver can be drastically reduced and a significant gain in performance can be obtained.

A Modeling of Compressible Droplets in a Fluid

OpenAIRE

Boudin, Laurent; Desvilletter, Laurent; Motte, Renaud

2003-01-01

In this work, we are interested in a complex fluid-kinetic model that aims to take into account the compressibility of the droplets of the spray. The ambient fluid is described by Euler-like equations, in which the transfer of momentum and energy form the droplets is taken into account, while the spray is represented by a probability density function satisfying a Vlasov-like equation. Implicit terms crop up because of the compressibility of the droplets. After having derived...

Tunneling process in heavy-ion fusion and fission

Energy Technology Data Exchange (ETDEWEB)

Iwamoto, Akira [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment; Kondratyev, V.; Bonasera, A.

1998-10-01

We present a model towards the many-body description of sub-barrier fusion and spontaneous fission based on the semiclassical Vlasov equation and the Feynman path integral method. We define suitable collective variables from the Vlasov solution and use the imaginary time technique for the dynamics below the Coulomb barrier. (author)

Dynamical simulation of heavy ion collisions; VUU and QMD method

International Nuclear Information System (INIS)

Niita, Koji

1992-01-01

We review two simulation methods based on the Vlasov-Uehling-Uhlenbeck (VUU) equation and Quantum Molecular Dynamics (QMD), which are the most widely accepted theoretical framework for the description of intermediate-energy heavy-ion reactions. We show some results of the calculations and compare them with the experimental data. (author)

Parasitic excitation of ion Bernstein waves from a Faraday shielded fast wave loop antenna

International Nuclear Information System (INIS)

Skiff, F.; Ono, M.; Colestock, P.; Wong, K.L.

1984-12-01

Parasitic excitation of ion Bernstein waves is observed from a Faraday shielded fast wave loop antenna in the ion cyclotron frequency range. Local analysis of the Vlasov-Maxwell equations demonstrates the role of plasma density gradient in the coupling process. The effects of plasma density and of parallel wave number on the excitation process are investigated

The theory and simulation of relativistic electron beam transport in the ion-focused regime

International Nuclear Information System (INIS)

Swanekamp, S.B.; Holloway, J.P.; Kammash, T.; Gilgenbach, R.M.

1992-01-01

Several recent experiments involving relativistic electron beam (REB) transport in plasma channels show two density regimes for efficient transport; a low-density regime known as the ion-focused regime (IFR) and a high-pressure regime. The results obtained in this paper use three separate models to explain the dependency of REB transport efficiency on the plasma density in the IFR. Conditions for efficient beam transport are determined by examining equilibrium solutions of the Vlasov--Maxwell equations under conditions relevant to IFR transport. The dynamic force balance required for efficient IFR transport is studied using the particle-in-cell (PIC) method. These simulations provide new insight into the transient beam front physics as well as the dynamic approach to IFR equilibrium. Nonlinear solutions to the beam envelope are constructed to explain oscillations in the beam envelope observed in the PIC simulations but not contained in the Vlasov equilibrium analysis. A test particle analysis is also developed as a method to visualize equilibrium solutions of the Vlasov equation. This not only provides further insight into the transport mechanism but also illustrates the connections between the three theories used to describe IFR transport. Separately these models provide valuable information about transverse beam confinement; together they provide a clear physical understanding of REB transport in the IFR

Ion species stratification within strong shocks in two-ion plasmas

Science.gov (United States)

Keenan, Brett D.; Simakov, Andrei N.; Taitano, William T.; Chacón, Luis

2018-03-01

Strong collisional shocks in multi-ion plasmas are featured in many environments, with Inertial Confinement Fusion (ICF) experiments being one prominent example. Recent work [Keenan et al., Phys. Rev. E 96, 053203 (2017)] answered in detail a number of outstanding questions concerning the kinetic structure of steady-state, planar plasma shocks, e.g., the shock width scaling by the Mach number, M. However, it did not discuss shock-driven ion-species stratification (e.g., relative concentration modification and temperature separation). These are important effects since many recent ICF experiments have evaded explanation by standard, single-fluid, radiation-hydrodynamic (rad-hydro) numerical simulations, and shock-driven fuel stratification likely contributes to this discrepancy. Employing the state-of-the-art Vlasov-Fokker-Planck code, iFP, along with multi-ion hydro simulations and semi-analytics, we quantify the ion stratification by planar shocks with the arbitrary Mach number and the relative species concentration for two-ion plasmas in terms of ion mass and charge ratios. In particular, for strong shocks, we find that the structure of the ion temperature separation has a nearly universal character across ion mass and charge ratios. Additionally, we find that the shock fronts are enriched with the lighter ion species and the enrichment scales as M4 for M ≫ 1.

Linear kinetic stability of a field-reversed configuration with two ion components

International Nuclear Information System (INIS)

Staudenmeier, J.L.; Barnes, D.C.; Lewis, H.R.

1990-01-01

It has been suggested that a small fraction of non-axis encircling high energy ions may be sufficient to stabilize the tilt mode in a large s FRC. Experimental alteration of the ion distribution function in this manner might be achieved by rf heating the tail of the distribution function or by neutral beam injection. A linear Vlasov-fluid eigenfunction-eigenfrequency approach was used to investigate possible stabilization of the tilt mode by a high energy component. The ion distribution function is modeled as the sum of two Maxwellians with separate temperatures and no ion flow velocity. The cold component has a thermal s = 7, where s is the approximate number of ion gyroradii contained between the field null and the separatrix. The temperature ratio of the hot component to the cold component (T H /T T ) was varied from 2 to 100. Global hot particle fractions (n H ) up to ∼ .5 were used in the computations

Large-Time Behavior of Solutions to Vlasov-Poisson-Fokker-Planck Equations: From Evanescent Collisions to Diffusive Limit

Science.gov (United States)

Herda, Maxime; Rodrigues, L. Miguel

2018-03-01

The present contribution investigates the dynamics generated by the two-dimensional Vlasov-Poisson-Fokker-Planck equation for charged particles in a steady inhomogeneous background of opposite charges. We provide global in time estimates that are uniform with respect to initial data taken in a bounded set of a weighted L^2 space, and where dependencies on the mean-free path τ and the Debye length δ are made explicit. In our analysis the mean free path covers the full range of possible values: from the regime of evanescent collisions τ → ∞ to the strongly collisional regime τ → 0. As a counterpart, the largeness of the Debye length, that enforces a weakly nonlinear regime, is used to close our nonlinear estimates. Accordingly we pay a special attention to relax as much as possible the τ -dependent constraint on δ ensuring exponential decay with explicit τ -dependent rates towards the stationary solution. In the strongly collisional limit τ → 0, we also examine all possible asymptotic regimes selected by a choice of observation time scale. Here also, our emphasis is on strong convergence, uniformity with respect to time and to initial data in bounded sets of a L^2 space. Our proofs rely on a detailed study of the nonlinear elliptic equation defining stationary solutions and a careful tracking and optimization of parameter dependencies of hypocoercive/hypoelliptic estimates.

Dispersions in Semi-Classical Dynamics

International Nuclear Information System (INIS)

Zielinska-Pfabe, M.; Gregoire, C.

1987-01-01

Dispersions around mean values of one-body observables are obtained by restoring classical many-body correlations in Vlasov and Landau-Vlasov dynamics. The method is applied to the calculation of fluctuations in mass, charge and linear momentum in heavy-ion collisions. Results are compared to those obtained by the Balian-Veneroni variational principle in semi-classical approximation

Study of energy deposition in heavy-ion reactions

International Nuclear Information System (INIS)

Mota, V. De La; Abgrall, P.; Sebille, F.; Haddad, F.

1993-01-01

An investigation of energy deposition mechanisms in heavy-ion reactions at intermediate energies is presented. Theoretical simulations are performed in the framework of the semi-classical Landau-Vlasov model. They emphasize the influence of the initial non-equilibrium conditions, and the connection with the incident energy is discussed. Characteristic times involved in the energy thermalization process and finite size effects are analyzed. (authors) 20 refs., 4 figs

Investigation of Ion Acoustic Waves in Collisionless Plasmas

DEFF Research Database (Denmark)

Christoffersen, G. B.; Jensen, Vagn Orla; Michelsen, Poul

1974-01-01

The Green's functions for the linearized ion Vlasov equation with a given boundary value are derived. The propagation properties of ion acoustic waves are calculated by performing convolution integrals over the Green's functions. For Te/Ti less than about 3 it is concluded that the collective...... interaction is very weak and that the propagation properties are determined almost completely by freely streaming ions. The wave damping, being due to phase mixing, is determined by the width of the perturbed distribution function rather than by the slope of the undisturbed distribution function at the phase...

Equilibrium of field reversed configurations with rotation. I. One space dimension and one type of ion

International Nuclear Information System (INIS)

Rostoker, Norman; Qerushi, Artan

2002-01-01

Self-consistent solutions of the Vlasov-Maxwell equations are obtained. They involve rigid rotor distributions. This selection is justified on physical grounds. For this selection the Vlasov equation can be replaced by moment equations which terminate without any additional assumptions. For one-dimensional equilibria with one type of ion these equations have exact solutions. A complete equilibrium solution appropriate to a field reversed configuration with rotation can be obtained by solving a generalized Grad-Shafranov equation for the flux function. From this solution all other physical quantities can be determined. A Green's function method is developed to solve this equation, which provides a basis for an iterative solution. This method has the advantage that at every iteration the boundary conditions are satisfied. In this paper cylindrical geometry with one space dimension and one type of ion is considered, where analytic solutions are available. The convergence of the Green's function method is established. For this nonlinear problem there is usually more than one solution for completely specified boundary conditions (bifurcation). The present method selects one solution. It is applicable to equilibria with many ion species and to two dimensions

Drift Compression and Final Focus Options for Heavy Ion Fusion

International Nuclear Information System (INIS)

Hong Qin; Davidson, Ronald C.; Barnard, John J.; Lee, Edward P.

2005-01-01

A drift compression and final focus lattice for heavy ion beams should focus the entire beam pulse onto the same focal spot on the target. We show that this requirement implies that the drift compression design needs to satisfy a self-similar symmetry condition. For un-neutralized beams, the Lie symmetry group analysis is applied to the warm-fluid model to systematically derive the self-similar drift compression solutions. For neutralized beams, the 1-D Vlasov equation is solved explicitly, and families of self-similar drift compression solutions are constructed. To compensate for the deviation from the self-similar symmetry condition due to the transverse emittance, four time-dependent magnets are introduced in the upstream of the drift compression such that the entire beam pulse can be focused onto the same focal spot

Semi-classical approach of heavy ion physics at intermediate energies

International Nuclear Information System (INIS)

Vinet, L.

1986-01-01

The study of heavy ion collisions at intermediate energies (10 to 100 MeV/A), can be undertaken by a semi-classical approach: the nuclear Vlasov equation. It is possible to decompose the one body distribution function over a suitable coherent state basis for dynamical studies. This method is applied for colliding slabs, and the results are compared with those of TDHF. With imposed spherical symmetry, the isoscalar monopole resonance, evaporation, formation of bubble nuclei and total evaporation, are obtained. The extension to three dimensions and to the Landau-Vlasov equation through the residual interaction included in the Uehling-Uhlenbeck collision term, permits a general study of the dynamical instability of highly excited nuclei. The application to heavy ion collisions gives a description of both the main mechanisms of reaction, and the ineffective fusion for the system 40 Ar (35 MeV/A) + 27 Al. Alpha particle multiplicities in correlation with evaporated residues in the experience 40 Ar (27 MeV/A) + 27 Al, have been extracted. From theoretical results, different scenari are proposed (entrance channel limitation and exit channel disintegration), in order to explain the disappearance of the fusion component observed for this system at energies above 32 MeV/A [fr

Self-consistent Vlasov-Maxwell description of the longitudinal dynamics of intense charged particle beams

Directory of Open Access Journals (Sweden)

Ronald C. Davidson

2004-02-01

Full Text Available This paper describes a self-consistent kinetic model for the longitudinal dynamics of a long, coasting beam propagating in straight (linear geometry in the z direction in the smooth-focusing approximation. Starting with the three-dimensional Vlasov-Maxwell equations, and integrating over the phase-space (x_{⊥},p_{⊥} transverse to beam propagation, a closed system of equations is obtained for the nonlinear evolution of the longitudinal distribution function F_{b}(z,p_{z},t and average axial electric field ⟨E_{z}^{s}⟩(z,t. The primary assumptions in the present analysis are that the dependence on axial momentum p_{z} of the distribution function f_{b}(x,p,t is factorable, and that the transverse beam dynamics remains relatively quiescent (absence of transverse instability or beam mismatch. The analysis is carried out correct to order k_{z}^{2}r_{w}^{2} assuming slow axial spatial variations with k_{z}^{2}r_{w}^{2}≪1, where k_{z}∼∂/∂z is the inverse length scale of axial variation in the line density λ_{b}(z,t=∫dp_{z}F_{b}(z,p_{z},t, and r_{w} is the radius of the conducting wall (assumed perfectly conducting. A closed expression for the average longitudinal electric field ⟨E_{z}^{s}⟩(z,t in terms of geometric factors, the line density λ_{b}, and its derivatives ∂λ_{b}/∂z,… is obtained for the class of bell-shaped density profiles n_{b}(r,z,t=(λ_{b}/πr_{b}^{2}f(r/r_{b}, where the shape function f(r/r_{b} has the form specified by f(r/r_{b}=(n+1(1-r^{2}/r_{b}^{2}^{n} for 0≤r

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.

Finite Larmor radius effects on the stability properties of internal modes of a z-pinch

International Nuclear Information System (INIS)

Aakerstedt, H.O.

1987-01-01

From the Vlasov-fluid model a set of approximate stability equations describing the stability of a cylindrically symmetric z-pinch is derived. The equations are derived in the limit of small gyroradius and include first order kinetic effects such as finite ion Larmor radius effects and resonant ion effects. Neglecting the resonant ion terms, we explicitly solve this set of equations for a constant current density profile leading to a dispersion relation. FLR effects are shown for the case of m=1 internal mode to be stabilizing and for large wavenumbers k, using a trial function approach, absolute stabilization is found. (author)

Effect of cold plasma on the Kelvin-Helmholtz instability

International Nuclear Information System (INIS)

Melander, B.G.

1978-01-01

The thesis studies the effect of a two-component plasma (hot and cold) on the shear driven Kelvin-Helmholtz instability. An ion distribution with a shear flow parallel to the ambient magnetic field and a density gradient parallel to the shear direction is used. Both the electrostatic and electromagnetic versions of the instability are studied in the limit of hydromagnetic frequencies. The dispersion relation is obtained in the electrostatic case by solving the Vlasov equation for the perturbed ion and electron densities and then using the quasineutrality condition. In the electromagnetic case the coupled Vlasov and Maxwell's equations are solved to obtain the dispersion relation

Hamiltonian closures in fluid models for plasmas

Science.gov (United States)

Tassi, Emanuele

2017-11-01

This article reviews recent activity on the Hamiltonian formulation of fluid models for plasmas in the non-dissipative limit, with emphasis on the relations between the fluid closures adopted for the different models and the Hamiltonian structures. The review focuses on results obtained during the last decade, but a few classical results are also described, in order to illustrate connections with the most recent developments. With the hope of making the review accessible not only to specialists in the field, an introduction to the mathematical tools applied in the Hamiltonian formalism for continuum models is provided. Subsequently, we review the Hamiltonian formulation of models based on the magnetohydrodynamics description, including those based on the adiabatic and double adiabatic closure. It is shown how Dirac's theory of constrained Hamiltonian systems can be applied to impose the incompressibility closure on a magnetohydrodynamic model and how an extended version of barotropic magnetohydrodynamics, accounting for two-fluid effects, is amenable to a Hamiltonian formulation. Hamiltonian reduced fluid models, valid in the presence of a strong magnetic field, are also reviewed. In particular, reduced magnetohydrodynamics and models assuming cold ions and different closures for the electron fluid are discussed. Hamiltonian models relaxing the cold-ion assumption are then introduced. These include models where finite Larmor radius effects are added by means of the gyromap technique, and gyrofluid models. Numerical simulations of Hamiltonian reduced fluid models investigating the phenomenon of magnetic reconnection are illustrated. The last part of the review concerns recent results based on the derivation of closures preserving a Hamiltonian structure, based on the Hamiltonian structure of parent kinetic models. Identification of such closures for fluid models derived from kinetic systems based on the Vlasov and drift-kinetic equations are presented, and

Stimulated ion Compton scattering instability of whistlers in plasmas

International Nuclear Information System (INIS)

Shukla, P. K.; Shukla, Nitin; Stenflo, L.

2006-01-01

The nonlinear interactions between magnetic field-aligned broadband whistler wave packets (hereafter referred to as whistlerons) and ion quasimodes in magnetized plasmas are considered. By treating the whistlerons as quasiparticles, their nonlinear propagation in a slowly varying medium supported by ion quasimode density perturbations is studied. A nonlinear dispersion relation within the framework of the wave-kinetic (for the whistlerons) and Vlasov (for the ion quasimodes) descriptions is derived. The dispersion relation admits a kinetic modulational instability. The growth rate of the latter is presented. The present result can improve our understanding of the nonlinear propagation of incoherent whistlers, which have been frequently observed in the Earth's magnetosphere as well as in laboratory plasmas

Kinetic description of a wiggler pumped ion-channel free electron laser

International Nuclear Information System (INIS)

Mehdian, H; Raghavi, A

2006-01-01

The wiggler pumped ion-channel free electron laser (WPIC-FEL) is treated and the classes of possible single-particle electron trajectories in this configuration are discussed in the paper. A new region of orbital stability is seen in the negative mass regime. A kinetic description of WPIC-FEL is given. Vlasov-Maxwell equations are solved to get the linear gain in a tenuous-beam limit, where the beam plasma frequency is much less than the radiation frequency and the self-field effects can be ignored

Kinetic description of electron-proton instability in high-intensity proton linacs and storage rings based on the Vlasov-Maxwell equations

Directory of Open Access Journals (Sweden)

Ronald C. Davidson

1999-05-01

Full Text Available The present analysis makes use of the Vlasov-Maxwell equations to develop a fully kinetic description of the electrostatic, electron-ion two-stream instability driven by the directed axial motion of a high-intensity ion beam propagating in the z direction with average axial momentum γ_{b}m_{b}β_{b}c through a stationary population of background electrons. The ion beam has characteristic radius r_{b} and is treated as continuous in the z direction, and the applied transverse focusing force on the beam ions is modeled by F_{foc}^{b}=-γ_{b}m_{b}ω_{βb}^{0^{2}}x_{⊥} in the smooth-focusing approximation. Here, ω_{βb}^{0}=const is the effective betatron frequency associated with the applied focusing field, x_{⊥} is the transverse displacement from the beam axis, (γ_{b}-1m_{b}c^{2} is the ion kinetic energy, and V_{b}=β_{b}c is the average axial velocity, where γ_{b}=(1-β_{b}^{2}^{-1/2}. Furthermore, the ion motion in the beam frame is assumed to be nonrelativistic, and the electron motion in the laboratory frame is assumed to be nonrelativistic. The ion charge and number density are denoted by +Z_{b}e and n_{b}, and the electron charge and number density by -e and n_{e}. For Z_{b}n_{b}>n_{e}, the electrons are electrostatically confined in the transverse direction by the space-charge potential φ produced by the excess ion charge. The equilibrium and stability analysis retains the effects of finite radial geometry transverse to the beam propagation direction, including the presence of a perfectly conducting cylindrical wall located at radius r=r_{w}. In addition, the analysis assumes perturbations with long axial wavelength, k_{z}^{2}r_{b}^{2}≪1, and sufficiently high frequency that |ω/k_{z}|≫v_{Tez} and |ω/k_{z}-V_{b}|≫v_{Tbz}, where v_{Tez} and v_{Tbz} are the characteristic axial thermal speeds of the background electrons and beam ions. In this regime, Landau damping (in axial velocity space v_{z} by resonant ions and

Nonlinear localized dust acoustic waves in a charge varying dusty plasma with nonthermal ions

International Nuclear Information System (INIS)

Tribeche, Mouloud; Amour, Rabia

2007-01-01

A numerical investigation is presented to show the existence, formation, and possible realization of large-amplitude dust acoustic (DA) solitary waves in a charge varying dusty plasma with nonthermal ions. These nonlinear localized structures are self-consistent solutions of the collisionless Vlasov equation with a population of fast particles. The spatial patterns of the variable charge DA solitary wave are significantly modified by the nonthermal effects. The results complement and provide new insights into previously published results on this problem

Contributions to mathematical analysis and to numerical approximation in plasma physics

International Nuclear Information System (INIS)

Besse, N.

2009-01-01

The author's scientific works deal with numerical analysis and the simulation of the partial differential equations that intervene in the transport of charged particles and in plasma physics. In the chapters 2 and 3, a reduction of the Vlasov equation is presented, this method is based on the Liouville geometric invariants and it leads to a mathematical model named water-bag model that can be coupled with various equations of the electromagnetic field: the Poisson equation, the quasi-neutral equation or Maxwell equations. In the chapter 3 this reduction method is applied to the Vlasov gyro-kinetic equation to form the gyro-water-bag model. The mathematical analysis of this model produces interesting analytical results such as: threshold instabilities, instability growth rate, transport coefficient and non-linear turbulence mechanisms. Simulations have been performed to study turbulence in magnetized plasmas. In these plasmas occurred numerous instabilities due to the presence of high density and temperature gradients. These instabilities generate turbulence that deteriorates plasma confinement conditions required for thermonuclear fusion. The numerical calculation of turbulent thermal diffusivities is important since confinement time is determined by these transport coefficients. The chapter 4 gathers mathematical analysis issues like convergence or prior knowledge of errors concerning several high-order numerical methods used to solve Vlasov-Poisson or Vlasov-Einstein equation systems as well as the induction equation of an idealistic MHD system. The chapter 5 presents original numerical methods to solve several non-linear Vlasov equations such as Vlasov-Poisswell, Vlasov-Darwin, Vlasov-Maxwell and Vlasov-gyrokinetic that are involved either in inertial fusion or in magnetic confinement fusion

Vlasov simulations of electron hole dynamics in inhomogeneous magnetic field

Science.gov (United States)

Kuzichev, Ilya; Vasko, Ivan; Agapitov, Oleksiy; Mozer, Forrest; Artemyev, Anton

2017-04-01

Electron holes (EHs) or phase space vortices are solitary electrostatic waves existing due to electrons trapped within EH electrostatic potential. Since the first direct observation [1], EHs have been widely observed in the Earth's magnetosphere: in reconnecting current sheets [2], injection fronts [3], auroral region [4], and many other space plasma systems. EHs have typical spatial scales up to tens of Debye lengths, electric field amplitudes up to hundreds of mV/m and propagate along magnetic field lines with velocities of about electron thermal velocity [5]. The role of EHs in energy dissipation and supporting of large-scale potential drops is under active investigation. The accurate interpretation of spacecraft observations requires understanding of EH evolution in inhomogeneous plasma. The critical role of plasma density gradients in EH evolution was demonstrated in [6] using PIC simulations. Interestingly, up to date no studies have addressed a role of magnetic field gradients in EH evolution. In this report, we use 1.5D gyrokinetic Vlasov code to demonstrate the critical role of magnetic field gradients in EH dynamics. We show that EHs propagating into stronger (weaker) magnetic field are decelerated (accelerated) with deceleration (acceleration) rate dependent on the magnetic field gradient. Remarkably, the reflection points of decelerating EHs are independent of the average magnetic field gradient in the system and depend only on the EH parameters. EHs are decelerated (accelerated) faster than would follow from the "quasi-particle" concept assuming that EH is decelerated (accelerated) entirely due to the mirror force acting on electrons trapped within EH. We demonstrate that EH propagation in inhomogeneous magnetic fields results in development of a net potential drop along an EH, which depends on the magnetic field gradient. The revealed features will be helpful for interpreting spacecraft observations and results of advanced particle simulations. In

Nonrelativistic theory of heavy-ion collisions

International Nuclear Information System (INIS)

Bertsch, G.

1984-01-01

A wide range of phenomena is observed in heavy-ion collisions, calling for a comprehensive theory based on fundamental principles of many-particle quantum mechanics. At low energies, the nuclear dynamics is controlled by the mean field, as we know from spectroscopic nuclear physics. We therefore expect the comprehensive theory of collisions to contain mean-field theory at low energies. The mean-field theory is the subject of the first lectures in this chapter. This theory can be studied quantum mechanically, in which form it is called TDHF (time-dependent Hartree-Fock), or classically, where the equation is called the Vlasov equation. 25 references, 14 figures

Low Mach-number collisionless electrostatic shocks and associated ion acceleration

Science.gov (United States)

Pusztai, I.; TenBarge, J. M.; Csapó, A. N.; Juno, J.; Hakim, A.; Yi, L.; Fülöp, T.

2018-03-01

The existence and properties of low Mach-number (M≳ 1) electrostatic collisionless shocks are investigated with a semi-analytical solution for the shock structure. We show that the properties of the shock obtained in the semi-analytical model can be well reproduced in fully kinetic Eulerian Vlasov-Poisson simulations, where the shock is generated by the decay of an initial density discontinuity. Using this semi-analytical model, we study the effect of the electron-to-ion temperature ratio and the presence of impurities on both the maximum shock potential and the Mach number. We find that even a small amount of impurities can influence the shock properties significantly, including the reflected light ion fraction, which can change several orders of magnitude. Electrostatic shocks in heavy ion plasmas reflect most of the hydrogen impurity ions.

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.

Magnetic blocking direct-recovery efficiency

International Nuclear Information System (INIS)

Whealton, J.H.; Wooten, J.H.; McGaffey, R.W.

1981-10-01

The ion recovery efficiency of a transverse magnetic field monochromatic direct recovery device intended for intense neutral beams is examined theoretically by solving a Poisson-Vlasov equation. An optimum in recovery efficiency is obtained for finite ion current density and excess initial speed

Magnetic fusion with high energy self-colliding ion beams

International Nuclear Information System (INIS)

Restoker, N.; Wessel, F.; Maglich, B.; Fisher, A.

1993-01-01

Field-reversed configurations of energetic large orbit ions with neutralizing electrons have been proposed as the basis of a fusion reactor. Vlasov equilibria consisting of a ring or an annulus have been investigated. A stability analysis has been carried out for a long thin layer of energetic ions in a low density background plasma. There is a growing body of experimental evidence from tokamaks that energetic ions slow down and diffuse in accordance with classical theory in the presence of large non-thermal fluctuations and anomalous transport of low energy (10 keV) ions. Provided that major instabilities are under control, it seems likely that the design of a reactor featuring energetic self-colliding ion beams can be based on classical theory. In this case a confinement system that is much better than a tokamak is possible. Several methods are described for creating field reversed configurations with intense neutralized ion beams

Magnetic fusion with high energy self-colliding ion beams

International Nuclear Information System (INIS)

Rostoker, N.; Wessel, F.; Maglich, B.; Fisher, A.

1992-06-01

Field-reversed configurations of energetic large orbit ions with neutralizing electrons have been proposed as the basis of a fusion reactor. Vlasov equilibria consisting of a ring or an annulus have been investigated. A stability analysis has been carried out for a long thin layer of energetic ions in a low density background plasma. There is a growing body of experimental evidence from tokamaks that energetic ions slow down and diffuse in accordance with classical theory in the presence of large non-thermal fluctuations and anomalous transport of low energy (10 keV) ions. Provided that major instabilities are under control, it seems likely that the design of a reactor featuring energetic self-colliding ion beams can be based on classical theory. In this case a confinement system that is much better than a tokamak is possible. Several methods are described for creating field reversed configurations with intense neutralized ion beams

The dynamics of electron and ion holes in a collisionless plasma

Directory of Open Access Journals (Sweden)

B. Eliasson

2005-01-01

Full Text Available We present a review of recent analytical and numerical studies of the dynamics of electron and ion holes in a collisionless plasma. The new results are based on the class of analytic solutions which were found by Schamel more than three decades ago, and which here work as initial conditions to numerical simulations of the dynamics of ion and electron holes and their interaction with radiation and the background plasma. Our analytic and numerical studies reveal that ion holes in an electron-ion plasma can trap Langmuir waves, due the local electron density depletion associated with the negative ion hole potential. Since the scale-length of the ion holes are on a relatively small Debye scale, the trapped Langmuir waves are Landau damped. We also find that colliding ion holes accelerate electron streams by the negative ion hole potentials, and that these streams of electrons excite Langmuir waves due to a streaming instability. In our Vlasov simulation of two colliding ion holes, the holes survive the collision and after the collision, the electron distribution becomes flat-topped between the two ion holes due to the ion hole potentials which work as potential barriers for low-energy electrons. Our study of the dynamics between electron holes and the ion background reveals that standing electron holes can be accelerated by the self-created ion cavity owing to the positive electron hole potential. Vlasov simulations show that electron holes are repelled by ion density minima and attracted by ion density maxima. We also present an extension of Schamel's theory to relativistically hot plasmas, where the relativistic mass increase of the accelerated electrons have a dramatic effect on the electron hole, with an increase in the electron hole potential and in the width of the electron hole. A study of the interaction between electromagnetic waves with relativistic electron holes shows that electromagnetic waves can be both linearly and nonlinearly

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)

Scaling of the distribution function and the critical exponents near the point of a marginal stability under the Vlasov-Poisson equations

International Nuclear Information System (INIS)

Ivanov, Alexei

2000-08-01

A model system, described by the consistent Vlasov-Poisson equations under periodical boundary conditions, has been studied numerically near the point of a marginal stability. The power laws, typical for a system, undergoing a second-order phase transition, hold in a vicinity of the critical point: (i) A ∝ -θ β , β=1.907±0.006 for θ ≤ 0, where A is the saturated amplitude of the marginally-stable mode; (ii) χ ∝ θ -γ as θ → 0, γ=γ - =1.020±0.008 for θ + =0.995±0.020 for θ > 0, where χ=∂A/∂F 1 at F 1 → 0 is the susceptibility to external drive of the strain F 1 ; (iii) at θ=0 the system responds to external drive as A ∝ F 1 1/δ , and δ=1.544±0.002. θ=( 2 >- cr 2 >)/ cr 2 > is the dimensionless reduced velocity dispersion. Within the error of computation these critical exponents satisfy to equality γ=β(δ-1), known in thermodynamics as the Widom equality, which is direct consequence of scaling invariance of the Fourier components f m of the distribution function f at |θ| m (λ at t, λ av v, λ aθ θ, λ aA0 A 0 , λ aF F 1 )=λf m (t, v, θ, A 0 , F 1 ) at θ approx. = 0. On the contrary to thermodynamics these critical indices indicate to a very wide critical area. In turn, it means that critical phenomena may determine macroscopic dynamics of a large fraction of systems. (author)

Effect of pion mean-field on properties of pions and kaons from heavy-ion collisions

International Nuclear Information System (INIS)

Zheng Yuming; Chu Zili; Wang Hui; Sa Benhao

1996-01-01

The Relativistic Vlasov-Uehling-Uhlenbeck (RVUU) model is used to study the properties of pions and kaons produced in heavy ion collisions. We include the nuclear medium effect on kaon and pion in the model, and simulate pion production and subthreshold kaon production in Kr + Zr reactions at 1 GeV/u. The calculated results show that the attractive pion optical potential changes the final-state pion momentum spectrum, enhancing the yield of pions with low transverse momenta. At the same time it also increases the kaon abundance and modifies the kaon momentum distribution

Some aspects of nuclear dynamics

International Nuclear Information System (INIS)

Gregoire, C.

1987-01-01

First the BBGKY hierarchy of equations is presented; the method developed here lies on a reduction procedure of a many body density distribution function. From the equations, Hartree and Hartree-Fock approximations are deduced, and time dependent Hartree-Fock equation. Then two derivations of a nuclear reaction kinetic equation are presented: the Woldmann-Snider equation and the Botermans-Malfliet equation. The Wigner transformation is used and the Landau-Vlasov equation is studied. (Or Vlasov-Uehling-Uhlenbeck or Boltzmann-Uehling-Uhlenbeck equation). Keypoints of approximate solutions are mentioned. Simulation calculations of phenomenological collisions are shown. Then dynamics of heavy ion reactions is studied from results presented

Numerical study of the evolution of a magnetized plasma by means of a hybrid model

Energy Technology Data Exchange (ETDEWEB)

Dinu, L [Institutul de Matematica, Bucharest (Romania); Vlad, M [Institutul de Fizica si Tehnologia Aparatelor cu Radiatii, Bucharest (Romania)

1979-01-01

A numerical solution of the Vlasov-fluid model describing a time and space plasma evolution is presented. This should be compared with J.P. Frjedberg's analysis (1), (2) which provides growth rates for instabilities and some stability criteria.

Stability of the magnetosonic wave in a cometary multi-ion plasma

Science.gov (United States)

Sreekala, G.; Varghese, Anu; Jayakumar, Neethu; Michael, Manesh; Sebastian, Sijo; Venugopal, Chandu

2017-05-01

A generalized dispersion relation of the magnetosonic wave in a four component plasma consisting of electrons and hydrogen ions of solar origin and positively and negatively charged oxygen ions of cometary origin has been derived by using the Vlasov-Maxwell kinetic model. Parallel to the magnetic field, the hydrogen and electron components are modeled by a drifting Maxwellian distribution; perpendicular to the magnetic field, we use a loss cone type distribution obtained by the subtraction of two Maxwellian distributions having different temperatures. The effect of change in the drift velocity of streaming components and number densities and temperatures of each species in driving the instability has been analyzed both analytically and numerically. For typical parameters at comet Halley, we find that both positively and negatively charged oxygen ions can drive the wave unstable.

On Landau Vlasov simulations of giant resonances

International Nuclear Information System (INIS)

Pi, M.; Schuck, P.; Suraud, E.; Gregoire, C.; Remaud, B.; Sebille, F.

1987-05-01

We present VUU calculations of giant resonances obtained in energetic heavy ion collisions. Also is considered the case of the giant dipole in 40 Ca and the possibility of studying the effects of rotation on such collective modes

Adsorption of chromium species from industrial effluent using magnesium-bentonite clay composite: kinetics, equilibrium and risk assessment study

CSIR Research Space (South Africa)

Tjia, FH

2017-07-01

Full Text Available technologies have been developed and implemented for removal of chromium from wastewaters. These include: adsorption, precipitation, ion exchange, reverse osmosis, electroplating, phytoremediation and wetlands (Vlasov and D'Yakonov, 1965, Tan et al., 1993, Qu...

Scaling of the distribution function and the critical exponents near the point of a marginal stability under the Vlasov-Poisson equations

Energy Technology Data Exchange (ETDEWEB)

Lvanov, Alexei [Theory and Computer Simulation Center, National Inst. for Fusion Science, Toki, Gifu (Japan)

2000-08-01

A model system, described by the consistent Vlasov-Poisson equations under periodical boundary conditions, has been studied numerically near the point of a marginal stability. The power laws, typical for a system, undergoing a second-order phase transition, hold in a vicinity of the critical point: (i) A {proportional_to} -{theta}{sup {beta}}, {beta}=1.907{+-}0.006 for {theta} {<=} 0, where A is the saturated amplitude of the marginally-stable mode; (ii) {chi} {proportional_to} {theta}{sup -{gamma}} as {theta} {yields} 0, {gamma}={gamma}{sub -}=1.020{+-}0.008 for {theta} < 0, and {gamma}={gamma}{sub +}=0.995{+-}0.020 for {theta} > 0, where {chi}={partial_derivative}A/{partial_derivative}F{sub 1} at F{sub 1} {yields} 0 is the susceptibility to external drive of the strain F{sub 1}; (iii) at {theta}=0 the system responds to external drive as A {proportional_to} F{sub 1}{sup 1/{delta}}, and {delta}=1.544{+-}0.002. {theta}=(-)/ is the dimensionless reduced velocity dispersion. Within the error of computation these critical exponents satisfy to equality {gamma}={beta}({delta}-1), known in thermodynamics as the Widom equality, which is direct consequence of scaling invariance of the Fourier components f{sub m} of the distribution function f at |{theta}| << 1, i.e. f{sub m}({lambda}{sup at}t, {lambda}{sup av}v, {lambda}{sup a{theta}}{theta}, {lambda}{sup aA0}A{sub 0}, {lambda}{sup aF}F{sub 1})={lambda}f{sub m}(t, v, {theta}, A{sub 0}, F{sub 1}) at {theta} approx. = 0. On the contrary to thermodynamics these critical indices indicate to a very wide critical area. In turn, it means that critical phenomena may determine macroscopic dynamics of a large fraction of systems. (author)

A general theory for gauge-free lifting

International Nuclear Information System (INIS)

Morrison, P. J.

2013-01-01

A theory for lifting equations of motion for charged particle dynamics, subject to given electromagnetic like forces, up to a gauge-free system of coupled Hamiltonian Vlasov-Maxwell like equations is given. The theory provides very general expressions for the polarization and magnetization vector fields in terms of the particle dynamics description of matter. Thus, as is common in plasma physics, the particle dynamics replaces conventional constitutive relations for matter. Several examples are considered including the usual Vlasov-Maxwell theory, a guiding center kinetic theory, Vlasov-Maxwell theory with the inclusion of spin, and a Vlasov-Maxwell theory with the inclusion of Dirac's magnetic monopoles. All are shown to be Hamiltonian field theories and the Jacobi identity is proven directly.

Theoretical models for describing longitudinal bunch compression in the neutralized drift compression experiment

Directory of Open Access Journals (Sweden)

Adam B. Sefkow

2006-09-01

Full Text Available Heavy ion drivers for warm dense matter and heavy ion fusion applications use intense charge bunches which must undergo transverse and longitudinal compression in order to meet the requisite high current densities and short pulse durations desired at the target. The neutralized drift compression experiment (NDCX at the Lawrence Berkeley National Laboratory is used to study the longitudinal neutralized drift compression of a space-charge-dominated ion beam, which occurs due to an imposed longitudinal velocity tilt and subsequent neutralization of the beam’s space charge by background plasma. Reduced theoretical models have been used in order to describe the realistic propagation of an intense charge bunch through the NDCX device. A warm-fluid model is presented as a tractable computational tool for investigating the nonideal effects associated with the experimental acceleration gap geometry and voltage waveform of the induction module, which acts as a means to pulse shape both the velocity and line density profiles. Self-similar drift compression solutions can be realized in order to transversely focus the entire charge bunch to the same focal plane in upcoming simultaneous transverse and longitudinal focusing experiments. A kinetic formalism based on the Vlasov equation has been employed in order to show that the peaks in the experimental current profiles are a result of the fact that only the central portion of the beam contributes effectively to the main compressed pulse. Significant portions of the charge bunch reside in the nonlinearly compressing part of the ion beam because of deviations between the experimental and ideal velocity tilts. Those regions form a pedestal of current around the central peak, thereby decreasing the amount of achievable longitudinal compression and increasing the pulse durations achieved at the focal plane. A hybrid fluid-Vlasov model which retains the advantages of both the fluid and kinetic approaches has been

Direct measurement of the plasma response to electrostatic ion waves

International Nuclear Information System (INIS)

Sarfaty, M.; DeSouza-Machado, S.; Skiff, F.

1995-01-01

Plasma wave-wave and wave-particle interactions are studied in a linear magnetized plasma. The relatively quiet plasma is produced by an argon gas-discharge. The plasma density is n e ≅ 10 9 cm -3 and the electron/ion temperatures are T e ≅ 5eV and T i = 0.05eV. A grid and a four ring antenna, both mounted on a scanning carriage, are used to launch electrostatic ion waves in the plasma. Laser Induced Fluorescence measurements of both the linear and the nonlinear plasma response to the wave fields are presented. The Vlasov-Poisson equations are used to explain the measured zero, first and second order terms of the ion distribution function in the presence of wave fields. In addition to the broadening (heating) of the ion distribution as the authors increase the wave amplitudes, induced plasma flows are observed both along and across the magnetic field

Giant dipole modes in heavy-ion reactions

International Nuclear Information System (INIS)

Suraud, E.; Schuck, P.

1988-07-01

A detailed study of the excitation of giant dipole modes (GDR) in intermediate energy heavy-ion collisions is presented in the framework of a full (non linearized) Landau-Vlasov equation. After having recalled the basic inputs of this dynamical formalism, within insisting upon the limitations of the Uehling-Uhlenbeck collision integral and upon the introduction of a realistic (isospin dependant) effective interaction, we present our tools for analysing the GDR in the simple case of isolated nuclei. We then pass on to simulations of collisions and discuss in some detail isospin modes in the model 12 Be + 12 C reaction. Results obtained for the energy of the excited dipole mode are in agreement with what is expected for excited, rotating, giant dipole oscillations in deformed nuclei

Linear Plasma Oscillation Described by Superposition of Normal Modes

DEFF Research Database (Denmark)

Pécseli, Hans

1974-01-01

The existence of steady‐state solutions to the linearized ion and electron Vlasov equation is demonstrated for longitudinal waves in an initially stable plasma. The evolution of an arbitrary initial perturbation can be described by superposition of these solutions. Some common approximations...

Electron kinetics in a laser plasma with increased collisionality

Czech Academy of Sciences Publication Activity Database

Mašek, Jan; Rohlena, Karel

2010-01-01

Roč. 165, 6-10 (2010), s. 405-411 ISSN 1042-0150 Institutional research plan: CEZ:AV0Z10100523 Keywords : ion sources * stimulated Raman scattering * Vlasov-Maxwell model * Raman cascading Subject RIV: BH - Optics, Masers, Lasers Impact factor: 0.660, year: 2010

Fully-kinetic Ion Simulation of Global Electrostatic Turbulent Transport in C-2U

Science.gov (United States)

Fulton, Daniel; Lau, Calvin; Bao, Jian; Lin, Zhihong; Tajima, Toshiki; TAE Team

2017-10-01

Understanding the nature of particle and energy transport in field-reversed configuration (FRC) plasmas is a crucial step towards an FRC-based fusion reactor. The C-2U device at Tri Alpha Energy (TAE) achieved macroscopically stable plasmas and electron energy confinement time which scaled favorably with electron temperature. This success led to experimental and theoretical investigation of turbulence in C-2U, including gyrokinetic ion simulations with the Gyrokinetic Toroidal Code (GTC). A primary objective of TAE's new C-2W device is to explore transport scaling in an extended parameter regime. In concert with the C-2W experimental campaign, numerical efforts have also been extended in A New Code (ANC) to use fully-kinetic (FK) ions and a Vlasov-Poisson field solver. Global FK ion simulations are presented. Future code development is also discussed.

Continuum kinetic methods for analyzing wave physics and distribution function dynamics in the turbulence dissipation challenge

Science.gov (United States)

Juno, J.; Hakim, A.; TenBarge, J.; Dorland, W.

2015-12-01

We present for the first time results for the turbulence dissipation challenge, with specific focus on the linear wave portion of the challenge, using a variety of continuum kinetic models: hybrid Vlasov-Maxwell, gyrokinetic, and full Vlasov-Maxwell. As one of the goals of the wave problem as it is outlined is to identify how well various models capture linear physics, we compare our results to linear Vlasov and gyrokinetic theory. Preliminary gyrokinetic results match linear theory extremely well due to the geometry of the problem, which eliminates the dominant nonlinearity. With the non-reduced models, we explore how the subdominant nonlinearities manifest and affect the evolution of the turbulence and the energy budget. We also take advantage of employing continuum methods to study the dynamics of the distribution function, with particular emphasis on the full Vlasov results where a basic collision operator has been implemented. As the community prepares for the next stage of the turbulence dissipation challenge, where we hope to do large 3D simulations to inform the next generation of observational missions such as THOR (Turbulence Heating ObserveR), we argue for the consideration of hybrid Vlasov and full Vlasov as candidate models for these critical simulations. With the use of modern numerical algorithms, we demonstrate the competitiveness of our code with traditional particle-in-cell algorithms, with a clear plan for continued improvements and optimizations to further strengthen the code's viability as an option for the next stage of the challenge.

Resolution of unsteady Maxwell equations with charges in non convex domains

International Nuclear Information System (INIS)

Garcia, Emmanuelle

2002-01-01

This research thesis deals with the modelling and numerical resolution of problems related to plasma physics. The interaction of charged particles (electrons and ions) with electromagnetic fields is modelled with the system of unsteady Vlasov-Maxwell coupled equations (the Vlasov system describes the transport of charged particles and the Maxwell equations describe the wave propagation). The author presents definitions related to singular domains, establishes a Helmholtz decomposition in a space of electro-magnetostatic solutions. He reports a mathematical analysis of decompositions into a regular and a singular part of general functional spaces intervening in the investigation of the Maxwell system in complex geometries. The method is then implemented for bi-dimensional domains. A last part addressed the study and the numerical resolution of three-dimensional problems

On the stability of pick-up ion ring distributions in the outer heliosheath

International Nuclear Information System (INIS)

Summerlin, Errol J.; Viñas, Adolfo F.; Moore, Thomas E.; Christian, Eric R.; Cooper, John F.

2014-01-01

The 'secondary energetic neutral atom (ENA)' hypothesis for the ribbon feature observed by the Interstellar Boundary Explorer (IBEX) posits that the neutral component of the solar wind continues beyond the heliopause and charge exchanges with interstellar ions in the Outer Heliosheath (OHS). This creates pick-up ions that gyrate about the draped interstellar magnetic field (ISMF) lines at pitch angles near 90° on the locus where the ISMF lies tangential to the heliopause and perpendicular to the heliocentric radial direction. This location closely coincides with the location of the ribbon feature according to the prevailing inferences of the ISMF orientation and draping. The locally gyrating ions undergo additional charge exchange and escape as free-flying neutral atoms, many of which travel back toward the inner solar system and are imaged by IBEX as a ribbon tracing out the locus described above. For this mechanism to succeed, the pick-up ions must diffuse in pitch angle slowly enough to permit secondary charge exchange before their pitch angle distribution substantially broadens away from 90°. Previous work using linear Vlasov dispersion analysis of parallel propagating waves has suggested that the ring distribution in the OHS is highly unstable, which, if true, would make the secondary ENA hypothesis incapable of rendering the observed ribbon. In this paper, we extend this earlier work to more realistic ring distribution functions. We find that, at the low densities necessary to produce the observed IBEX ribbon via the secondary ENA hypothesis, growth rates are highly sensitive to the temperature of the beam and that even very modest temperatures of the ring beam corresponding to beam widths of <1° are sufficient to damp the self-generated waves associated with the ring beam. Thus, at least from the perspective of linear Vlasov dispersion analysis of parallel propagating waves, there is no reason to expect that the ring distributions necessary to

Langmuir turbulence in space plasmas

Energy Technology Data Exchange (ETDEWEB)

Goldman, M.V. [Colorado Univ., Boulder, CO (United States); Newman, D.L. [Colorado Univ., Boulder, CO (United States); Wang, J.G. [Colorado Univ., Boulder, CO (United States); Muschietti, L. [California Univ., Berkeley (United States). Space Sciences Lab.

1996-11-01

Recent developments in theoretical and numerical modeling of Langmuir turbulence in space and laboratory plasmas are addressed. Kinetic effects, which have been missing from (fluid) traditional Zakharov equation models are explored using Vlasov code simulations. These studies are motivated by beam-driven Langmuir waves and particle distributions measured in earth`s foreshock region, and by beam-driven Langmuir waves and beams that underlie type III solar radio emission in the solar wind. The nonlinear physical processes studied in these 1-D Vlasov simulations include both wave-wave interactions and acceleration of particles by waves-leading to electron-beam flattening. We study bump-on-tail instabilities as boundary value problems, and determine the interplay in space and time between beam plateau formation, stimulated wave-wave backscatter cascades, and strong turbulence wave-packet collapse. (orig.).

Effect of continuous eigenvalue spectrum on plasma transport in toroidal systems

International Nuclear Information System (INIS)

Yamagishi, Tomejiro

1993-03-01

The effect of the continuous eigenvalue of the Vlasov equation on the cross field ion thermal flux is investigated. The continuum contribution due to the toroidal drift resonance is found to play an important role in ion transport particularly near the edge, which may apply to the interpretation of the sharp increase of ion heat conductivity near the periphery observed in large tokamaks. (author)

Waves in unmagnetized plasma

International Nuclear Information System (INIS)

Lambert, A.J.D.

1979-01-01

A review of linear and weakly non-linear theory of electron waves, ion waves and electromagnetic waves in plasmas is presented. The author restricts the discussion to an infinitely extended, homogeneous and isotropic plasma, not affected by external fields and described by Vlasov's and Maxwell's equations. (Auth.)

DICE/ColDICE: 6D collisionless phase space hydrodynamics using a lagrangian tesselation

Science.gov (United States)

Sousbie, Thierry

2018-01-01

DICE is a C++ template library designed to solve collisionless fluid dynamics in 6D phase space using massively parallel supercomputers via an hybrid OpenMP/MPI parallelization. ColDICE, based on DICE, implements a cosmological and physical VLASOV-POISSON solver for cold systems such as dark matter (CDM) dynamics.

Conservation of energy and momentum in nonrelativistic plasmas

International Nuclear Information System (INIS)

Sugama, H.; Watanabe, T.-H.; Nunami, M.

2013-01-01

Conservation laws of energy and momentum for nonrelativistic plasmas are derived from applying Noether's theorem to the action integral for the Vlasov-Poisson-Ampère system [Sugama, Phys. Plasmas 7, 466 (2000)]. The symmetric pressure tensor is obtained from modifying the asymmetric canonical pressure tensor with using the rotational symmetry of the action integral. Differences between the resultant conservation laws and those for the Vlasov-Maxwell system including the Maxwell displacement current are clarified. These results provide a useful basis for gyrokinetic conservation laws because gyrokinetic equations are derived as an approximation of the Vlasov-Poisson-Ampère system.

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.

Semi-classical approaches for the proton emission in intermediate energy heavy ion reactions

International Nuclear Information System (INIS)

Gregoire, C.; Scheuter, F.; Remaud, B.; Sebille, F.

1984-05-01

Semi-classical approaches are proposed to study the transition between the one- and two-body processes in intermediate energy heavy ion collisions. The Landau-Vlasov equation is used as a transport equation for nucleons in the nuclear matter. We apply our formalism to the fast proton ejection. On the one hand, the effects of the nucleon-nucleon collisions are studied for the particles which travel through the nucleus cores. On the other hand, the inertial emission turns out to be an important proton emission mechanism. Our results conflict the interpretation of the proton spectra in terms of moving sources. Reasonable agreements with the experimental data are found without reference to any thermal equilibrium

Evidence for transient, local ion foreshocks caused by dayside magnetopause reconnection

Directory of Open Access Journals (Sweden)

Y. Pfau-Kempf

2016-11-01

Full Text Available We present a scenario resulting in time-dependent behaviour of the bow shock and transient, local ion reflection under unchanging solar wind conditions. Dayside magnetopause reconnection produces flux transfer events driving fast-mode wave fronts in the magnetosheath. These fronts push out the bow shock surface due to their increased downstream pressure. The resulting bow shock deformations lead to a configuration favourable to localized ion reflection and thus the formation of transient, travelling foreshock-like field-aligned ion beams. This is identified in two-dimensional global magnetospheric hybrid-Vlasov simulations of the Earth's magnetosphere performed using the Vlasiator model (http://vlasiator.fmi.fi. We also present observational data showing the occurrence of dayside reconnection and flux transfer events at the same time as Geotail observations of transient foreshock-like field-aligned ion beams. The spacecraft is located well upstream of the foreshock edge and the bow shock, during a steady southward interplanetary magnetic field and in the absence of any solar wind or interplanetary magnetic field perturbations. This indicates the formation of such localized ion foreshocks.

Plasma simulation with the Differential Algebraic Cubic Interpolated Propagation scheme

Energy Technology Data Exchange (ETDEWEB)

Utsumi, Takayuki [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment

1998-03-01

A computer code based on the Differential Algebraic Cubic Interpolated Propagation scheme has been developed for the numerical solution of the Boltzmann equation for a one-dimensional plasma with immobile ions. The scheme advects the distribution function and its first derivatives in the phase space for one time step by using a numerical integration method for ordinary differential equations, and reconstructs the profile in phase space by using a cubic polynomial within a grid cell. The method gives stable and accurate results, and is efficient. It is successfully applied to a number of equations; the Vlasov equation, the Boltzmann equation with the Fokker-Planck or the Bhatnagar-Gross-Krook (BGK) collision term and the relativistic Vlasov equation. The method can be generalized in a straightforward way to treat cases such as problems with nonperiodic boundary conditions and higher dimensional problems. (author)

Plasma physics on the TI-85 calculator or Down with supercomputers

International Nuclear Information System (INIS)

Sedlacek, Z.

1998-10-01

In the Fourier transformed velocity space the Vlasov plasma oscillations may be interpreted as a wave propagation process corresponding to an imperfectly trapped (leaking) wave. The Landau damped solutions of the Vlasov-Poisson equation then become genuine Eigenmodes corresponding to complex eigenvalues. To illustrate this new interpretation we solve numerically the Fourier transformed Vlasov-Poisson equation, essentially a perturbed advective equation, on the TI-85 pocket graphics calculator. A program is described, based on the method of lines: A finite-difference scheme is utilized to discretize the transformed equation and the resulting set of ordinary differential equations is then solved in time. The user can choose from several possible finite-difference differentiation schemes differing in the total number of points and the number of downwind points. The resulting evolution of the electric field showing the Landau damped plasma oscillations is displayed on the screen of the calculator. In addition, calculation of the eigenvalues of the Fourier transformed Vlasov-Poisson operator is possible. The user can also experiment with the numerical solution of the advective equation which describes free streaming. (author)

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.

Fluid dynamics of giant resonances on high spin states

International Nuclear Information System (INIS)

Di Nardo, M.; Di Toro, M.; Giansiracusa, G.; Lombardo, U.; Russo, G.

1983-01-01

We describe giant resonances built on high spin states along the yrast line as scaling solutions of a linearized Vlasov equation in a rotating frame obtained from a TDHF theory in phase space. For oblate cranked solutions we get a shift and a splitting of the isoscalar giant resonances in terms of the angular velocity. Results are shown for 40 Ca and 168 Er. The relative CM strengths are also calculated. (orig.)

Central collisions of heavy ion physics

International Nuclear Information System (INIS)

Fung, S.Y.

1985-09-01

The research program concentrates on correlation studies in central collisions. The investigation includes: multi-pion production, total event structure, application of the Vlasov-Uehling-Uhlenbeck model (VUU) to the data and energy dependence of thermalization and nuclear stopping power. The initial analysis on the Uranium-Uranium exposure at 960 MeV/nucleon is completed. In place of the conventional sphericity analysis, global transverse momentum as a function of rapidity and azimuthal angle is a more appropriate parameter for these data in the total event analysis. This transverse momentum analysis is extended to other projectile/target systems with initial results for Ar on KCl, BaI 2 , Pb, and U on U. In the area of pion production, results for Kr on RbBr at the Darmstadt Heavy Ion Study are reported. Early findings that the source size is related to the emitted pion momentum is confirmed. 17 refs

Mathematical study and numerical simulations of bi-kinetic plasma sheaths

International Nuclear Information System (INIS)

Badsi, Mehdi

2016-01-01

This thesis focuses on the construction and the numerical simulation theoretical models of plasmas in interaction with an absorbing wall. These models are based on two species Vlasov-Poisson or Vlasov-Ampere systems in the presence of boundary conditions. The expected stationary solutions must verify the balance of the flux of charges in the orthogonal direction to the wall. This feature is called the ambi-polarity. Through the study of a non linear Poisson equation, we prove the well-posedness of 1d-1v stationary Vlasov-Poisson system, for which we determine incoming particles distributions and a wall potential that induces the ambi-polarity as well as a non negative charge density hold. We also give a quantitative estimates of the thickness of the boundary layer that develops at the wall. These results are illustrated numerically. We prove the linear stability of the electronic stationary solution for a non-stationary Vlasov-Ampere system. Finally, we study a 1d-3v stationary Vlasov-Poisson system in the presence of a constant and parallel to the wall magnetic field. We determine incoming particles distributions and a wall potential so that the ambi-polarity holds. We study a non linear Poisson equation through a non linear functional energy that admits minimizers. We established some bounds on the numerical parameters inside which, our model is relevant and we propose an interpretation of the results. (author)

Proton and heavy ion acceleration by stochastic fluctuations in the Earth's magnetotail

Directory of Open Access Journals (Sweden)

F. Catapano

2016-10-01

Full Text Available Spacecraft observations show that energetic ions are found in the Earth's magnetotail, with energies ranging from tens of keV to a few hundreds of keV. In this paper we carry out test particle simulations in which protons and other ion species are injected in the Vlasov magnetic field configurations obtained by Catapano et al. (2015. These configurations represent solutions of a generalized Harris model, which well describes the observed profiles in the magnetotail. In addition, three-dimensional time-dependent stochastic electromagnetic perturbations are included in the simulation box, so that the ion acceleration process is studied while varying the equilibrium magnetic field profile and the ion species. We find that proton energies of the order of 100 keV are reached with simulation parameters typical of the Earth's magnetotail. By changing the ion mass and charge, we can study the acceleration of heavy ions such as He+ +  and O+, and it is found that energies of the order of 100–200 keV are reached in a few seconds for He+ + , and about 100 keV for O+.

CSR Effects in a Bunch Compressor influence of the Beam Frame Transverse Force

CERN Document Server

Bassi, G

2005-01-01

We study the influence of coherent synchrotron radiation (CSR) on particle bunches traveling on arbitrary planar orbits between parallel conducting plates (shielding) with a Vlasov approach. [1] The fields excited by the bunch are computed in the lab frame using a formula simpler than that based on retarded potentials. The Vlasov equation is solved in the beam frame interaction picture. In recent numerical investigations we solved the Vlasov equation for a bunch compressor using the Liouville-Maxwell approximation (LMA), where the bunch density is evolved under the fields produced by the unperturbed density (subject to external fields only), neglecting the beam frame transverse force. [2] Here we report on the influence of the beam frame transverse force on the equations of motion.

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)

Extended MHD modeling of nonlinear instabilities in fusion and space plasmas

Energy Technology Data Exchange (ETDEWEB)

Germaschewski, Kai [Univ. of New Hampshire, Durham, NH (United States)

2017-11-15

A number of different sub-projects where pursued within this DOE early career project. The primary focus was on using fully nonlinear, curvilinear, extended MHD simulations of instabilities with applications to fusion and space plasmas. In particular, we performed comprehensive studies of the dynamics of the double tearing mode in different regimes and confi gurations, using Cartesian and cyclindrical geometry and investigating both linear and non-linear dynamics. In addition to traditional extended MHD involving Hall term and electron pressure gradient, we also employed a new multi-fluid moment model, which shows great promise to incorporate kinetic effects, in particular off-diagonal elements of the pressure tensor, in a fluid model, which is naturally computationally much cheaper than fully kinetic particle or Vlasov simulations. We used our Vlasov code for detailed studies of how weak collisions effect plasma echos. In addition, we have played an important supporting role working with the PPPL theory group around Will Fox and Amitava Bhattacharjee on providing simulation support for HED plasma experiments performed at high-powered laser facilities like OMEGA-EP in Rochester, NY. This project has support a great number of computational advances in our fluid and kinetic plasma models, and has been crucial to winning multiple INCITE computer time awards that supported our computational modeling.

MHD-Vlasov simulation of the toroidal Alfven eigenmode

International Nuclear Information System (INIS)

Todo, Y.; Sato, T.; Watanabe, K.; Watanabe, T.H.; Horiuchi, R.

1994-11-01

A new simulation method has been developed to investigate the excitation and saturation processes of toroidal Alfven eigenmodes (TAE modes). The background plasma is described by a full-MHD fluid model, while the kinetic evolution of energetic alpha particles is followed by the drift kinetic equation. The magnetic fluctuation of n = 2 mode develops and saturates at the level of 1.8x10 -3 of the equilibrium field when the initial beta of alpha particles is 2% at the magnetic axis. After saturation, the TAE mode amplitude shows an oscillatory behavior with a frequency corresponding to the bounce frequency of the alpha particles trapped by the TEA mode. The decrease of the power transfer rate from the alpha particles to the TAE mode, which is due to the trapped particle effect of a finite-amplitude wave, causes the saturation. From the linear growth rate the saturation level can be estimated. (author)

Proton and heavy ion acceleration by stochastic fluctuations in the Earth's magnetotail

Energy Technology Data Exchange (ETDEWEB)

Catapano, Filomena; Zimbardo, Gaetano; Perri, Silvia; Greco, Antonella [Calabria Univ., Rende (Italy). Dept. of Physics; Artemyev, Anton V. [Russian Academy of Science, Moscow (Russian Federation). Space Research Inst.; California Univ., Los Angeles, CA (United States). Dept. of Earth, Planetary, and Space Science and Inst. of Geophysics and Planetary Physics

2016-07-01

Spacecraft observations show that energetic ions are found in the Earth's magnetotail, with energies ranging from tens of keV to a few hundreds of keV. In this paper we carry out test particle simulations in which protons and other ion species are injected in the Vlasov magnetic field configurations obtained by Catapano et al. (2015). These configurations represent solutions of a generalized Harris model, which well describes the observed profiles in the magnetotail. In addition, three-dimensional time-dependent stochastic electromagnetic perturbations are included in the simulation box, so that the ion acceleration process is studied while varying the equilibrium magnetic field profile and the ion species. We find that proton energies of the order of 100 keV are reached with simulation parameters typical of the Earth's magnetotail. By changing the ion mass and charge, we can study the acceleration of heavy ions such as He{sup ++} and O{sup +}, and it is found that energies of the order of 100-200 keV are reached in a few seconds for He{sup ++}, and about 100 keV for O{sup +}.

Modelling RF-plasma interaction in ECR ion sources

Directory of Open Access Journals (Sweden)

Mascali David

2017-01-01

Full Text Available This paper describes three-dimensional self-consistent numerical simulations of wave propagation in magnetoplasmas of Electron cyclotron resonance ion sources (ECRIS. Numerical results can give useful information on the distribution of the absorbed RF power and/or efficiency of RF heating, especially in the case of alternative schemes such as mode-conversion based heating scenarios. Ray-tracing approximation is allowed only for small wavelength compared to the system scale lengths: as a consequence, full-wave solutions of Maxwell-Vlasov equation must be taken into account in compact and strongly inhomogeneous ECRIS plasmas. This contribution presents a multi-scale temporal domains approach for simultaneously including RF dynamics and plasma kinetics in a “cold-plasma”, and some perspectives for “hot-plasma” implementation. The presented results rely with the attempt to establish a modal-conversion scenario of OXB-type in double frequency heating inside an ECRIS testbench.

Stability of the field-reversed mirror

International Nuclear Information System (INIS)

Morse, E.C.

1979-01-01

The stability of a field reversed mirror plasma configuration is studied with an energy principle derived from the Vlasov equation. Because of finite orbit effects, the stability properties of a field-reversed mirror are different from the stability properties of similar magnetohydrodynamic equilibria. The Vlasov energy principle developed here is applied to a computer simulation of an axisymmetric field-reversed mirror state. It has been possible to prove that the l = 0 modes, called tearing modes, satisfy a sufficient condition for stability. Precessional modes, with l = 1, 2, are found to be unstable at low growth rate. This suggests possible turbulent behavior (Bohm confinement) in the experimental devices aiming at field reversal. Techniques for suppressing these instabilities are outlined, and the applicability of the Vlasov energy principle to more complicated equilibrium models is shown

Dynamics of unstable systems

International Nuclear Information System (INIS)

Posch, H.A.; Narnhofer, H.; Thirring, W.

1990-01-01

We study the dynamics of classical particles interacting with attractive Gaussian potentials. This system is thermodynamically not stable and exhibits negative specific heat. The results of the computer simulation of the dynamics are discussed in comparison with various theories. In particular, we find that the condensed phase is a stationary solution of the Vlasov equation, but the Vlasov dynamics cannot describe the collapse. 14 refs., 1 tab., 11 figs. (Authors)

Condition for a single bunch high frequency fast blow-up

International Nuclear Information System (INIS)

Wang, J.M.; Pellegrini, C.

1980-01-01

We study the longitudinal stability of a single particle bunch in a storage ring using Vlasov equation. We show that the Vlasov equation has solutions corresponding to a fast, microwave instability if a condition on the beam current, qualitatively similar to the stability condition for a coasting beam, is satisfied. This condition can be used to define a threshold current, and to discuss its dependence on the longitudinal coupling impedance

1. contribution of the dynamics on the reactions mechanisms in the heavy ions collisions at the intermediary energies (20-100 MeV/A) for the light systems. 2. management of radioactive wastes by new options: nuclear data measurement programme between 20 and 150 MeV; 1. role de la dynamique sur les mecanismes de reactions dans les collisions d'ions lourds aux energies intermediaires (20-100 MeV/A) pour des systemes legers. 2. gestion des dechets radioactifs par des options nouvelles: programme de mesures de donnees nucleaires entre 20 et 150 MeV

Energy Technology Data Exchange (ETDEWEB)

Eudes, Ph

2000-09-22

The first part concerns the features of emitted charged particles in heavy ions reactions that have been studied in the framework of the semi classical Landau-Vlasov approach for the light system Ar + Al at 65 MeV/nucleon incident energy. The second part is devoted to the radioactive waste management (transmutation), but it was necessary to increase the data banks evaluated in neutrons up to 150-200 MeV and to create a data bank in protons. In the European framework it was decide to focus on three representative elements: lead (spallation target), iron (structure material) and uranium (actinide). (N.C.)

1. contribution of the dynamics on the reactions mechanisms in the heavy ions collisions at the intermediary energies (20-100 MeV/A) for the light systems. 2. management of radioactive wastes by new options: nuclear data measurement programme between 20 and 150 MeV; 1. role de la dynamique sur les mecanismes de reactions dans les collisions d'ions lourds aux energies intermediaires (20-100 MeV/A) pour des systemes legers. 2. gestion des dechets radioactifs par des options nouvelles: programme de mesures de donnees nucleaires entre 20 et 150 MeV

Energy Technology Data Exchange (ETDEWEB)

Eudes, Ph

2000-09-22

The first part concerns the features of emitted charged particles in heavy ions reactions that have been studied in the framework of the semi classical Landau-Vlasov approach for the light system Ar + Al at 65 MeV/nucleon incident energy. The second part is devoted to the radioactive waste management (transmutation), but it was necessary to increase the data banks evaluated in neutrons up to 150-200 MeV and to create a data bank in protons. In the European framework it was decide to focus on three representative elements: lead (spallation target), iron (structure material) and uranium (actinide). (N.C.)

Nonlinear turbulence theory and simulation of Buneman instability

International Nuclear Information System (INIS)

Yoon, P. H.; Umeda, T.

2010-01-01

In the present paper, the weak turbulence theory for reactive instabilities, formulated in a companion paper [P. H. Yoon, Phys. Plasmas 17, 112316 (2010)], is applied to the strong electron-ion two-stream (or Buneman) instability. The self-consistent theory involves quasilinear velocity space diffusion equation for the particles and nonlinear wave kinetic equation that includes quasilinear (or induced emission) term as well as nonlinear wave-particle interaction term (or a term that represents an induced scattering off ions). We have also performed one-dimensional electrostatic Vlasov simulation in order to benchmark the theoretical analysis. Under the assumption of self-similar drifting Gaussian distribution function for the electrons it is shown that the current reduction and the accompanying electron heating as well as electric field turbulence generation can be discussed in a self-consistent manner. Upon comparison with the Vlasov simulation result it is found that quasilinear wave kinetic equation alone is insufficient to account for the final saturation amplitude. Upon including the nonlinear scattering term in the wave kinetic equation, however, we find that a qualitative agreement with the simulation is recovered. From this, we conclude that the combined quasilinear particle diffusion plus induced emission and scattering (off ions) processes adequately account for the nonlinear development of the Buneman instability.

Fast-ion stabilization of tokamak plasma turbulence

Science.gov (United States)

Di Siena, A.; Görler, T.; Doerk, H.; Poli, E.; Bilato, R.

2018-05-01

A significant reduction of the turbulence-induced anomalous heat transport has been observed in recent studies of magnetically confined plasmas in the presence of a significant fast-ion fractions. Therefore, the control of fast-ion populations with external heating might open the way to more optimistic scenarios for future fusion devices. However, little is known about the parameter range of relevance of these fast-ion effects which are often only highlighted in correlation with substantial electromagnetic fluctuations. Here, a significant fast ion induced stabilization is also found in both linear and nonlinear electrostatic gyrokinetic simulations which cannot be explained with the conventional assumptions based on pressure profile and dilution effects. Strong wave-fast particle resonant interactions are observed for realistic parameters where the fast particle trace approximation clearly failed and explained with the help of a reduced Vlasov model. In contrast to previous interpretations, fast particles can actively modify the Poisson field equation—even at low fast particle densities where dilution tends to be negligible and at relatively high temperatures, i.e. T  <  30T e . Further key parameters controlling the role of the fast ions are identified in the following and various ways of further optimizing their beneficial impact are explored. Finally, possible extensions into the electromagnetic regime are briefly discussed and the relevance of these findings for ITER standard scenarios is highlighted.

Theoretical models of non-Maxwellian equilibria for one-dimensional collisionless plasmas

Science.gov (United States)

Allanson, O.; Neukirch, T.; Wilson, F.; Troscheit, S.

2016-12-01

It is ideal to use exact equilibrium solutions of the steady state Vlasov-Maxwell system to intialise collsionless simulations. However, exact equilibrium distribution functions (DFs) for a given macroscopic configuration are typically unknown, and it is common to resort to using `flow-shifted' Maxwellian DFs in their stead. These DFs may be consistent with a macrosopic system with the target number density and current density, but could well have inaccurate higher order moments. We present recent theoretical work on the `inverse problem in Vlasov-Maxwell equilibria', namely calculating an exact solution of the Vlasov equation for a specific given magnetic field. In particular, we focus on one-dimensional geometries in Cartesian (current sheets) coordinates.1. From 1D fields to Vlasov equilibria: Theory and application of Hermite Polynomials: (O. Allanson, T. Neukirch, S. Troscheit and F. Wilson, Journal of Plasma Physics, 82, 905820306 (2016) [28 pages, Open Access] )2. An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta: (O. Allanson, T. Neukirch, F. Wilson and S. Troscheit, Physics of Plasmas, 22, 102116 (2015) [11 pages, Open Access])3. Neutral and non-neutral collisionless plasma equilibria for twisted flux tubes: The Gold-Hoyle model in a background field (O. Allanson, F. Wilson and T. Neukirch, (2016)) (accepted, Physics of Plasmas)

1. contribution of the dynamics on the reactions mechanisms in the heavy ions collisions at the intermediary energies (20-100 MeV/A) for the light systems. 2. management of radioactive wastes by new options: nuclear data measurement programme between 20 and 150 MeV

International Nuclear Information System (INIS)

Eudes, Ph.

2000-01-01

The first part concerns the features of emitted charged particles in heavy ions reactions that have been studied in the framework of the semi classical Landau-Vlasov approach for the light system Ar + Al at 65 MeV/nucleon incident energy. The second part is devoted to the radioactive waste management (transmutation), but it was necessary to increase the data banks evaluated in neutrons up to 150-200 MeV and to create a data bank in protons. In the European framework it was decide to focus on three representative elements: lead (spallation target), iron (structure material) and uranium (actinide). (N.C.)

Fast Advection of Magnetic Fields by Hot Electrons

International Nuclear Information System (INIS)

Willingale, L.; Thomas, A. G. R.; Krushelnick, K.; Nilson, P. M.; Kaluza, M. C.; Dangor, A. E.; Evans, R. G.; Fernandes, P.; Haines, M. G.; Kamperidis, C.; Kingham, R. J.; Ridgers, C. P.; Sherlock, M.; Wei, M. S.; Najmudin, Z.; Bandyopadhyay, S.; Notley, M.; Minardi, S.; Tatarakis, M.; Rozmus, W.

2010-01-01

Experiments where a laser-generated proton beam is used to probe the megagauss strength self-generated magnetic fields from a nanosecond laser interaction with an aluminum target are presented. At intensities of 10 15 W cm -2 and under conditions of significant fast electron production and strong heat fluxes, the electron mean-free-path is long compared with the temperature gradient scale length and hence nonlocal transport is important for the dynamics of the magnetic field in the plasma. The hot electron flux transports self-generated magnetic fields away from the focal region through the Nernst effect [A. Nishiguchi et al., Phys. Rev. Lett. 53, 262 (1984)] at significantly higher velocities than the fluid velocity. Two-dimensional implicit Vlasov-Fokker-Planck modeling shows that the Nernst effect allows advection and self-generation transports magnetic fields at significantly faster than the ion fluid velocity, v N /c s ≅10.

Space charge effects and coherent stability limits in barrier buckets

Directory of Open Access Journals (Sweden)

Oliver Boine-Frankenheim

2003-03-01

Full Text Available A large-scale Vlasov simulation study of the microwave instability below transition energy in a beam confined between two barrier pulses is performed. Starting from a matched distribution function for the confined ion beam including the space charge impedance the stability threshold in the longitudinal impedance plane is obtained. A simple stability criterium is found to be in good agreement with the simulation results.

Physical mechanism of parametric instabilities near the lower-hybrid frequency in inhomogeneous plasma

International Nuclear Information System (INIS)

Porkolab, M.

1974-10-01

The dispersion relation for parametric instabilities near the lower-hybrid frequency is obtained from model fluid equations. The following instabilities are discussed: for rf pump frequencies ω 0 greater than or equal to 3ω/sub LH/, ω/sub pe/ approximately equal to Ω/sub e/, resonant decay into ion sound (ion cyclotron) modes (previously predicted) is found. In the regime of 1 less than or equal to ω 0 /ω/sub LH/ less than or equal to 3, ω/sub pe/ approximately equal to Ω/sub e/, decay into ion quasi-modes is found. In strong magnetic fields decay into quasi-modes is also found for 3 less than or equal to ω 0 /ω/sub LH/. This mechanism is similar to nonlinear Landau damping in weak turbulence theory. In addition, decay into the purely growing mode and fluid-quasi modes may also occur. The results are compared with recent calculations from the Vlasov equation. The effects of plasma-inhomogeneities are considered, including effective thresholds due to density gradients and finite pump extent. The implications of these results to rf heating of tokamaks near the lower-hybrid frequency are discussed. (auth)

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.

From particle to kinetic and hydrodynamic descriptions of flocking

OpenAIRE

Ha, Seung-Yeal; Tadmor, Eitan

2008-01-01

We discuss the Cucker-Smale's (C-S) particle model for flocking, deriving precise conditions for flocking to occur when pairwise interactions are sufficiently strong long range. We then derive a Vlasov-type kinetic model for the C-S particle model and prove it exhibits time-asymptotic flocking behavior for arbitrary compactly supported initial data. Finally, we introduce a hydrodynamic description of flocking based on the C-S Vlasov-type kinetic model and prove flocking behavior \\emph{without...

COMBINATION OF DENSITY AND ENERGY MODULATION IN MICROBUNCHING ANALYSIS

Energy Technology Data Exchange (ETDEWEB)

Tsai, Cheng Ying [Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); Li, Rui [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

2016-05-01

Microbunching instability (MBI) has been one of the most challenging issues in the transport of high-brightness electron beams for modern recirculating or energy recovery linac machines. Recently we have developed and implemented a Vlasov solver [1] to calculate the microbunching gain for an arbitrary beamline lattice, based on the extension of existing theoretical formulation [2-4] for the microbunching amplification from an initial density perturbation to the final density modulation. For more thorough analyses, in addition to the case of (initial) density to (final) density amplification, we extend in this paper the previous formulation to more general cases, including energy to density, density to energy and energy to energy amplifications for a recirculation machine. Such semi-analytical formulae are then incorporated into our Vlasov solver, and qualitative agreement is obtained when the semi-analytical Vlasov results are compared with particle tracking simulation using ELEGANT [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.

Nuclear dynamics with the (finite range) Gogny force: flow effects

International Nuclear Information System (INIS)

Sebille, F.; Royer, G.; Schuck, P.; Gregoire, C.

1988-01-01

We introduce for the first time the effective finite range interaction of Gogny in the semi-classical description of heavy ion reactions based on the Landau-Vlasov equation. The characteristics of the flow for heavy ion collisions are studied as functions of the incident energy, the impact parameter and the mass number. The momentum dependence in the mean field together with the non linearities in the collision kernel decrease the flow in contradiction with other calculations; the origins of this discrepancy are studied in details

Gyrokinetic water-bag modeling of a plasma column: Magnetic moment distribution and finite Larmor radius effects

Science.gov (United States)

Klein, R.; Gravier, E.; Morel, P.; Besse, N.; Bertrand, P.

2009-08-01

Describing turbulent transport in fusion plasmas is a major concern in magnetic confinement fusion. It is now widely known that kinetic and fluid descriptions can lead to significantly different properties. Although more accurate, the kinetic calculation of turbulent transport is much more demanding of computer resources than fluid simulations. An alternative approach is based on a water-bag representation of the distribution function that is not an approximation but rather a special class of initial conditions, allowing one to reduce the full kinetic Vlasov equation into a set of hydrodynamics equations while keeping its kinetic character [P. Morel, E. Gravier, N. Besse et al., Phys. Plasmas 14, 112109 (2007)]. In this paper, the water-bag concept is used in a gyrokinetic context to study finite Larmor radius effects with the possibility of using the full Larmor radius distribution instead of an averaged Larmor radius. The resulting model is used to study the ion temperature gradient (ITG) instability.

Kinetic Scale Structure of Low-frequency Waves and Fluctuations

Energy Technology Data Exchange (ETDEWEB)

López, Rodrigo A.; Yoon, Peter H. [Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742 (United States); Viñas, Adolfo F. [NASA Goddard Space Flight Center, Heliophysics Science Division, Geospace Physics Laboratory, Mail Code 673, Greenbelt, MD 20771 (United States); Araneda, Jaime A., E-mail: rlopezh@umd.edu, E-mail: yoonp@umd.edu [Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Concepción (Chile)

2017-08-10

The dissipation of solar wind turbulence at kinetic scales is believed to be important for the heating of the corona and for accelerating the wind. The linear Vlasov kinetic theory is a useful tool for identifying various wave modes, including kinetic Alfvén, fast magnetosonic/whistler, and ion-acoustic (or kinetic slow), and their possible roles in the dissipation. However, the kinetic mode structure in the vicinity of ion-cyclotron modes is not clearly understood. The present paper aims to further elucidate the structure of these low-frequency waves by introducing discrete particle effects through hybrid simulations and Klimontovich formalism of spontaneous emission theory. The theory and simulation of spontaneously emitted low-frequency fluctuations are employed to identify and distinguish the detailed mode structures associated with ion-Bernstein modes versus quasi-modes. The spontaneous emission theory and simulation also confirm the findings of the Vlasov theory in that the kinetic Alfvén waves can be defined over a wide range of frequencies, including the proton cyclotron frequency and its harmonics, especially for high-beta plasmas. This implies that these low-frequency modes may play predominant roles even in the fully kinetic description of kinetic scale turbulence and dissipation despite the fact that cyclotron harmonic and Bernstein modes may also play important roles in wave–particle interactions.

On Landau Scenario of Chaotization for Beam Distribution

International Nuclear Information System (INIS)

Parsa, Z.; Zadorozhny, V.

1999-01-01

We examine a problem in nonlinear dynamics in which both regular and chaotic motions are possible. Thus we deal with some of the fundamental theoretical problem of accelerator physics, mathematics theory of dynamical systems, and other fields of physics. The focus is on the appearance of chaos in a beam distribution. A study of the problem is based on two observations. The First observation is that using Lyapunov method and its extension we obtain solutions of partial differential equations. Using this approach we discuss the problem of finding a solution of Vlasov-Poisson equation, i.e., some stationary solution where we consider magnetic field as some disturbance with a small parameter. Thus the solution of Vlasov equation yields an asymptotic series such that the solution of Vlasov-Poisson equation is the basis solution for one. The second observation is that physical chaos is weakly limit of, well known, the Landau bifurcation's. This fact we have proved using ideas on the Nature of Turbulence

A new model for the collective beam-beam interaction

Energy Technology Data Exchange (ETDEWEB)

Ellison, J.A.; Sobol, A.V. [New Mexico Univ., Albuquerque, NM (United States); Vogt, M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2006-09-15

The Collective Beam-Beam interaction is studied in the framework of maps with a ''kick-lattice'' model in 4-D phase space. A novel approach to the classical method of averaging is used to derive an approximate map which is equivalent to a flow within the averaging approximation. The flow equation is a continuous-time Vlasov equation which we call the averaged Vlasov equation, the new model of this paper. The power of this approach is evidenced by the fact that the averaged Vlasov equation has exact equilibria and the associated lineralized equations have uncoupled azimuthal Fourier modes. The equation for the Fourier modes leads to a Fredholm integral equation of the third kind and the setting is ready-made for the development of a weakly nonlinear theory to study the coupling of the {pi} and {sigma} modes. The {pi} and {sigma} modes are calculated from the third kind integral equation and results are compared with the kick-lattice model. (orig.)

Case Studies in Space Charge and Plasma Acceleration of Charged Beams

CERN Document Server

Bazzani, A; Londrillo, P; Sinigardi, S; Turchetti, G

2014-01-01

Plasma acceleration with electron or proton driver beams is a challenging opportunity for high energy physics. An energy doubling experiment with electron drivers was successfully performed at SLAC and a key experiment AWAKE with proton drivers is on schedule at CERN. Simulations play an important role in choosing the best experimental conditions and in interpreting the results. The Vlasov equation is the theoretical tool to describe the interaction of a driver particle beam or a driver laser pulse with a plasma. Collective effects, such as tune shift and mismatch instabilities, appear in high intensity standard accelerators and are described by the Poisson-Vlasov equation. In the paper we review the Vlasov equation in electrostatic and fully electromagnetic case. The general framework of variational principles is used to derive the equation, the local form of the balance equations and related conservation laws. In the electrostatic case we remind the analytic Kapchinskij-Vladimirskij (K-V) model and we propo...

A new model for the collective beam-beam interaction

International Nuclear Information System (INIS)

Ellison, J.A.; Sobol, A.V.; Vogt, M.

2006-09-01

The Collective Beam-Beam interaction is studied in the framework of maps with a ''kick-lattice'' model in 4-D phase space. A novel approach to the classical method of averaging is used to derive an approximate map which is equivalent to a flow within the averaging approximation. The flow equation is a continuous-time Vlasov equation which we call the averaged Vlasov equation, the new model of this paper. The power of this approach is evidenced by the fact that the averaged Vlasov equation has exact equilibria and the associated lineralized equations have uncoupled azimuthal Fourier modes. The equation for the Fourier modes leads to a Fredholm integral equation of the third kind and the setting is ready-made for the development of a weakly nonlinear theory to study the coupling of the π and σ modes. The π and σ modes are calculated from the third kind integral equation and results are compared with the kick-lattice model. (orig.)

Noncanonical Hamiltonian methods in plasma dynamics

International Nuclear Information System (INIS)

Kaufman, A.N.

1982-01-01

A Hamiltonian approach to plasma dynamics is described. The Poisson bracket of two observables g 1 and g 2 is given by using an antisymmetric tensor J, and must satisfy the Jacobi condition. The J can be obtained by elementary tensor analysis. The evolution in time of an observable g is given in terms of the Poisson bracket and a Hamiltonian H(Z). The guiding-center description of particle motion was presented by Littlejohn. The ponderomotive drift and force, the wave-induced oscillation-center velocity, and the gyrofrequency shift are obtained. The Lie transform yields the wave-induced increment to the gyromomentum. In the coulomb model for a Vlasov system, the dynamical variable is the Vlasov distribution f(z). The Hamiltonian functional and the Poisson bracket are obtained. The coupling of f(z) to the Maxwell field appears in the Poisson bracket. The evolution equation yields the Vlasov-Maxwell system. (Kato, T.)

Verification of gyrokinetic microstability codes with an LHD configuration

Energy Technology Data Exchange (ETDEWEB)

Mikkelsen, D. R. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Nunami, M. [National Inst. for Fusion Science (Japan); Watanabe, T. -H. [Nagoya Univ. (Japan); Sugama, H. [National Inst. for Fusion Science (Japan); Tanaka, K. [National Inst. for Fusion Science (Japan)

2014-11-01

We extend previous benchmarks of the GS2 and GKV-X codes to verify their algorithms for solving the gyrokinetic Vlasov-Poisson equations for plasma microturbulence. Code benchmarks are the most complete way of verifying the correctness of implementations for the solution of mathematical models for complex physical processes such as those studied here. The linear stability calculations reported here are based on the plasma conditions of an ion-ITB plasma in the LHD configuration. The plasma parameters and the magnetic geometry differ from previous benchmarks involving these codes. We find excellent agreement between the independently written pre-processors that calculate the geometrical coefficients used in the gyrokinetic equations. Grid convergence tests are used to establish the resolution and domain size needed to obtain converged linear stability results. The agreement of the frequencies, growth rates and eigenfunctions in the benchmarks reported here provides additional verification that the algorithms used by the GS2 and GKV-X codes are correctly finding the linear eigenvalues and eigenfunctions of the gyrokinetic Vlasov-Poisson equations.

The role of collision terms for nucleon emission in intermediate energy heavy ion reactions

International Nuclear Information System (INIS)

Gregoire, C.; Scheuter, F.; Remaud, B.; Sebille, F.

1984-01-01

A semi-classical description of heavy ion collisions is developed with a particular attention to the nucleon flux from one partner through the other one. The phase-space extension of the nucleons is explicitly treated by means of the Wigner transform of the density matrix. Its dynamical evolution is obtained by solving the Landau-Vlasov equation, where collision terms are explicitely introduced. As a matter of fact, the experimental nucleon spectra usually described by a thermal source with an intermediate velocity (around vsub(beam)/2) are interpreted in our framework by the coexistence of one-and two-body dissipation. Multi-differential cross-sections d 2 σ/dEdΩ are computed for the 12 C(86MeV/u) + 12 C system and are compared with the experimental data. Comparisons are also given for the 16 O (20 MeV/u) + 197 Au system

Landau fluid model for weakly nonlinear dispersive magnetohydrodynamics

International Nuclear Information System (INIS)

Passot, T.; Sulem, P. L.

2005-01-01

In may astrophysical plasmas such as the solar wind, the terrestrial magnetosphere, or in the interstellar medium at small enough scales, collisions are negligible. When interested in the large-scale dynamics, a hydrodynamic approach is advantageous not only because its numerical simulations is easier than of the full Vlasov-Maxwell equations, but also because it provides a deep understanding of cross-scale nonlinear couplings. It is thus of great interest to construct fluid models that extended the classical magnetohydrodynamic (MHD) equations to collisionless situations. Two ingredients need to be included in such a model to capture the main kinetic effects: finite Larmor radius (FLR) corrections and Landau damping, the only fluid-particle resonance that can affect large scales and can be modeled in a relatively simple way. The Modelization of Landau damping in a fluid formalism is hardly possible in the framework of a systematic asymptotic expansion and was addressed mainly by means of parameter fitting in a linearized setting. We introduced a similar Landau fluid model but, that has the advantage of taking dispersive effects into account. This model properly describes dispersive MHD waves in quasi-parallel propagation. Since, by construction, the system correctly reproduces their linear dynamics, appropriate tests should address the nonlinear regime. In a first case, we show analytically that the weakly nonlinear modulational dynamics of quasi-parallel propagating Alfven waves is well captured. As a second test we consider the parametric decay instability of parallel Alfven waves and show that numerical simulations of the dispersive Landau fluid model lead to results that closely match the outcome of hybrid simulations. (Author)

Macroscopic plasma properties and stability theory

International Nuclear Information System (INIS)

Sakanaka, P.H.

1981-01-01

1. Two-fluid equations: (a) Boltzmann equation: complete set of equations; collision models - Vlasov, BGK, Fokker-Planck-Landau, Boltzmann. (b) Moments of the Boltzmann equation: problem of closure. (c) Two-fluid equations. 2. One-fluid equation: (a) One-fluid variables. (b) One-fluid equations: quasi-neutrality. (c) Resistive MHD equations. (d) Ideal MHD equations: one-adiabatic approximation; double-adiabatic approximation - CGL. 3. MHD stability problem - energy principle: (a) Linearized ideal MHD equations: force-operator equation. (b) Boundary conditions. (c) Self-adjointness of force operator. (d) The energy principle. 4. Stability problems: application of the energy principle; stability of sharp-boundary plasmas. 5. Thermodynamic approach for stability of plasmas: Newcomb and Rosenbluth's stability criteria. (author)

Kinetic Alfven wave with density variation and loss-cone distribution function of multi-ions in PSBL region

Science.gov (United States)

Tamrakar, Radha; Varma, P.; Tiwari, M. S.

2018-05-01

Kinetic Alfven wave (KAW) generation due to variation of loss-cone index J and density of multi-ions (H+, He+ and O+) in the plasma sheet boundary layer region (PSBL) is investigated. Kinetic approach is used to derive dispersion relation of wave using Vlasov equation. Variation of frequency with respect to wide range of k⊥ρi (where k⊥ is wave vector across the magnetic field, ρi is gyroradius of ions and i denotes H+, He+ and O+ ions) is analyzed. It is found that each ion gyroradius and number density shows different effect on wave generation with varying width of loss-cone. KAW is generated with multi-ions (H+, He+ and O+) over wide regime for J=1 and shows dissimilar effect for J=2. Frequency is reduced with increasing density of gyrating He+ and O+ ions. Wave frequency is obtained within the reported range which strongly supports generation of kinetic Alfven waves. A sudden drop of frequency is also observed for H+ and He+ ion which may be due to heavy penetration of these ions through the loss-cone. The parameters of PSBL region are used for numerical calculation. The application of these results are in understanding the effect of gyrating multi-ions in transfer of energy and Poynting flux losses from PSBL region towards ionosphere and also describing the generation of aurora.

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

Disintegration of nuclei and formation of composite systems in intermediate energy heavy ion reactions

International Nuclear Information System (INIS)

Gregoire, C.; Jacquet, D.; Sebille, F.; Vinet, L.; Pi, M.; Suraud, E.; Schuck, P.

1987-04-01

In a first part, the Landau-Vlasov dynamical instabilities found in the expansion of an excited nucleus are discussed with their dependence on the initial preparation. In a second part, we show the absence of fusion window when residual interactions are involved. We describe also onset and properties of ineffectual and incomplete fusion for systems like 40 Ar + 27 Al and 238 U near the Fermi energy and 12 C + 139 La at 50 MeV/u

Resonant effects on the low frequency vlasov stability of axisymmetric field reversed configurations

International Nuclear Information System (INIS)

Finn, J.M.; Sudan, R.N.

We investigate the effect of particle resonances on low frequency MHD modes in field-reversed geometries, e.g., an ion ring. It is shown that, for sufficiently high field reversal, modes which are hydromagnetically stable can be driven unstable by ion resonances. The stabilizing effect of a toroidal magnetic field is discussed

A comparison of non-local electron transport models relevant to inertial confinement fusion

Science.gov (United States)

Sherlock, Mark; Brodrick, Jonathan; Ridgers, Christopher

2017-10-01

We compare the reduced non-local electron transport model developed by Schurtz et al. to Vlasov-Fokker-Planck simulations. Two new test cases are considered: the propagation of a heat wave through a high density region into a lower density gas, and a 1-dimensional hohlraum ablation problem. We find the reduced model reproduces the peak heat flux well in the ablation region but significantly over-predicts the coronal preheat. The suitability of the reduced model for computing non-local transport effects other than thermal conductivity is considered by comparing the computed distribution function to the Vlasov-Fokker-Planck distribution function. It is shown that even when the reduced model reproduces the correct heat flux, the distribution function is significantly different to the Vlasov-Fokker-Planck prediction. Two simple modifications are considered which improve agreement between models in the coronal region. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Kinetic description of linear theta-pinch equilibria

International Nuclear Information System (INIS)

Batchelor, D.B.; Davidson, R.C.

1975-01-01

Equilibrium properties of linear theta-pinch plasmas are studied within the framework of the steady-state (o/x=0) Vlasov-Maxwell equations. The analysis is carried out for an infinitely long plasma column aligned parallel to an externally applied axial magnetic field Bsub(z)sup(ext)esub(z). Equilibrium properties are calculated for the class of rigid-rotor Vlasov equilibria, in which the th component distribution function (Hsub(perpendicular), Psub(theta), upsilonsub(z) depends on perpendicular energy H and canonical angular momentum Psub(theta), exclusively through the linear combination Hsub(perpendicular)-ωsub(j)Psub(theta), where ω;=const.=angular velocity of mean rotation. General equilibrium relations that pertain to the entire class of rigid-rotor Vlasov equilibria are discussed; and specific examples of sharp- and diffuse-boundary equilibrium configurations are considered. Rigid-rotor density and magnetic field profiles are compared with experimentally observed profiles. A general prescription is given for determining the functional dependence of the equilibrium distribution function on Hsub(perpendicular)-ωsub(j)Psub(theta) in circumstances, where the density profile or magnetic field profile is specified. (author)

Self-similar expansion of dusts in a plasma

International Nuclear Information System (INIS)

Luo, H.; Yu, M.Y.

1992-01-01

The self-similar expansion of two species of dust particles in an equilibrium plasma is investigated by means of fluid as well as Vlasov theories. It is found that under certain conditions the density of the dust with the smaller charge-to-mass ratio can vanish at a finite value of the self-similar variable, while the density of the remaining dust species attains a plateau. The kinetic theory predicts a secondary decay in which the latter density eventually also vanishes

Installation and operation of the 400 kW 140 GHz gyrotron on the MTX experiment

International Nuclear Information System (INIS)

Ferguson, S.W.; Felker, B.; Jackson, M.C.; Petersen, D.E.; Sewall, N.R.; Stever, R.D.

1991-09-01

This paper describes the installation and operation of the 400 kW 140 GHz gyrotron used for plasma heating on the Microwave Tokamak Experiment (MTX) at Lawrence Livermore National Laboratory (LLNL). The Varian VGT-8140 gyrotron has operated at a power level of 400 kW for 100 ms in conjunction with MTX plasma shots. The gyrotron system is comprised of a high voltage (-80 kV) modulated power supply, a multistation CAMAC computer control, a 5-tesla superconducting magnet, a series of conventional copper magnets, a circulating fluorinert (FC75) window cooling system, a circulating oil cooling system, a water cooling system, and microwave frequency and power diagnostics. Additionally, a Vlasov launcher is used to convert the gyrotron TE 15,2 mode to a Gaussian beam. Two versions of the Vlasov launcher have been used on the gyrotron, one version designed by LLNL and one version designed by the Japan Atomic Energy Research Institute (JAERI). The Gaussian beam from the Vlasov launcher is transported to the MTX tokamak by a series of 5 mirrors in a 35-meter-long, high-efficiency, quasioptical beam transport system. A twist polarizer is built into one of the mirrors to adjust for horizontal polarization in the tokamak. No windows are used between the Vlasov reflector and the MTX tokamak. A laser alignment system is used to perform the initial system alignment. A summary of the design and operating characteristics of each of these systems is included. Also included is a summary of the system operation and performance

Two-ion hybrid resonances and ion cyclotron absorption in tokamak plasmas

International Nuclear Information System (INIS)

Brambilla, M.; Ottaviani, M.

1983-11-01

The behaviour of IC waves near resonances in tokamak geometry is investigated in details. For this purpose, a one-dimensional model is proposed, which takes into account the orientation of the incident wavefronts with respect both to the singular layer and to the magnetic surfaces. The differential equations describing the waves are derived again from Vlasov-Maxwell equations in the finite Larmor radius approximation; they are shown to conserve the wave power flux in the absence of dissipation, and to reproduce the local dispersion relation in the WKB limit. These equations are solved exactly in some important situations, and with the Green-function technique in the general case. The amount of power coupled to Bernstein waves and absorbed by cyclotron damping is explicitly evaluated. (orig.)

Nonresonant decay of lower hybrid waves

International Nuclear Information System (INIS)

Brambilla, M.; Liberman, B.; Pesic, S.S.; Moreau, D.

1979-01-01

Parametric decay of Lower Hybrid waves has been extensively studied since a few years. To derive the dispersion relation of the decay waves, two different approaches have been used in the literature. In the first the pump electric field is assumed to be homogeneous in space (dipole approximation) and Vlasov Equation is integrated in the Oscillating Center Coordinates (OCC). In the second approach the parametric decay process is considered as the linear stage of a three wave interaction (pump, sideband and beat wave) and the dispersion relation is obtained from a recursive solution of Vlasov equation

Fully Electromagnetic Nonlinear Gyrokinetic Equations for Tokamak Edge Turbulence

International Nuclear Information System (INIS)

Hahm, T.S.; Wang, Lu; Madsen, J.

2008-01-01

An energy conserving set of the fully electromagnetic nonlinear gyrokinetic Vlasov equation and Maxwell's equations, which is applicable to both L-mode turbulence with large amplitude and H-mode turbulence in the presence of high E x B shear has been derived. The phase-space action variational Lie perturbation method ensures the preservation of the conservation laws of the underlying Vlasov-Maxwell system. Our generalized ordering takes ρ i θi ∼ L E ∼ L p i is the thermal ion Larmor radius and ρ θi = B/B θ ρ i ), as typically observed in the tokamak H-mode edge, with L E and L p being the radial electric field and pressure gradient lengths. We take k # perpendicular# ρ i ∼ 1 for generality, and keep the relative fluctuation amplitudes e(delta)φ/T i ∼ (delta)B/B up to the second order. Extending the electrostatic theory in the presence of high E x B shear [Hahm, Phys. Plasmas 3, 4658 (1996)], contributions of electromagnetic fluctuations to the particle charge density and current are explicitly evaluated via pull-back transformation from the gyrocenter distribution function in the gyrokinetic Maxwell's equation

Numerical aspects of drift kinetic turbulence: Ill-posedness, regularization and a priori estimates of sub-grid-scale terms

KAUST Repository

Samtaney, Ravi

2012-01-01

We present a numerical method based on an Eulerian approach to solve the Vlasov-Poisson system for 4D drift kinetic turbulence. Our numerical approach uses a conservative formulation with high-order (fourth and higher) evaluation of the numerical fluxes coupled with a fourth-order accurate Poisson solver. The fluxes are computed using a low-dissipation high-order upwind differencing method or a tuned high-resolution finite difference method with no numerical dissipation. Numerical results are presented for the case of imposed ion temperature and density gradients. Different forms of controlled regularization to achieve a well-posed system are used to obtain convergent resolved simulations. The regularization of the equations is achieved by means of a simple collisional model, by inclusion of an ad-hoc hyperviscosity or artificial viscosity term or by implicit dissipation in upwind schemes. Comparisons between the various methods and regularizations are presented. We apply a filtering formalism to the Vlasov equation and derive sub-grid-scale (SGS) terms analogous to the Reynolds stress terms in hydrodynamic turbulence. We present a priori quantifications of these SGS terms in resolved simulations of drift-kinetic turbulence by applying a sharp filter. © 2012 IOP Publishing Ltd.

Numerical aspects of drift kinetic turbulence: ill-posedness, regularization and a priori estimates of sub-grid-scale terms

International Nuclear Information System (INIS)

Samtaney, Ravi

2012-01-01

We present a numerical method based on an Eulerian approach to solve the Vlasov-Poisson system for 4D drift kinetic turbulence. Our numerical approach uses a conservative formulation with high-order (fourth and higher) evaluation of the numerical fluxes coupled with a fourth-order accurate Poisson solver. The fluxes are computed using a low-dissipation high-order upwind differencing method or a tuned high-resolution finite difference method with no numerical dissipation. Numerical results are presented for the case of imposed ion temperature and density gradients. Different forms of controlled regularization to achieve a well-posed system are used to obtain convergent resolved simulations. The regularization of the equations is achieved by means of a simple collisional model, by inclusion of an ad-hoc hyperviscosity or artificial viscosity term or by implicit dissipation in upwind schemes. Comparisons between the various methods and regularizations are presented. We apply a filtering formalism to the Vlasov equation and derive sub-grid-scale (SGS) terms analogous to the Reynolds stress terms in hydrodynamic turbulence. We present a priori quantifications of these SGS terms in resolved simulations of drift-kinetic turbulence by applying a sharp filter.

Semiclassical and phase space approaches to dynamic and collisional problems of nuclei

International Nuclear Information System (INIS)

Hasse, R.W.; Gregoire, C.; Remaud, B.; Jaenicke, J.; Schuck, P.

1988-09-01

This article summarises recent work on the semiclassical (Thomas-Fermi like) treatment of nuclear correlations and dynamical problems. After a short outline of hte general technique the nucleon-nucleus optical potential in the doorway approximation (2p-1h and 2h-1p intermediate states) is treated. The imaginary part serves to calculate the energy dependent correction to the real part. The level density parameter, occupation numbers, and the mean free path are discussed. The semiclassical treatment of the nuclear response function is given in detail. Applications to inelastic electron scattering in the quasi-elastic peak region are presented. Analogously, inelastic proton scattering is calculated. Because of the surface absorption this reaction excites the surface response. The imaginary part of the single-particle (hole) potential in the evaluation of the response function introduces a 2p-2h spreading. The missing charge in the longitudinal response is reduced but not all experimental puzzles can be explained. The experience gained in the description of phenomena close to equilibrium serves to construct solutions of the Landau-Vlasov (alias Vlasov-Uehling-Uhlenbeck) equation for the description of non-equilibrium processes encountered in heavy ion reactions

Speedy motions of a body immersed in an infinitely extended medium

OpenAIRE

Buttà, P.; Ferrari, G.; Marchioro, C.

2009-01-01

We study the motion of a classical point body of mass M, moving under the action of a constant force of intensity E and immersed in a Vlasov fluid of free particles, interacting with the body via a bounded short range potential Psi. We prove that if its initial velocity is large enough then the body escapes to infinity increasing its speed without any bound "runaway effect". Moreover, the body asymptotically reaches a uniformly accelerated motion with acceleration E/M. We then discuss at a he...

Longitudinal motion in high current ion beams: a self-consistent phase space distribution with an envelope equation

International Nuclear Information System (INIS)

Neuffer, D.

1979-03-01

Many applications of particle acceleration, such as heavy ion fusion, require longitudinal bunching of a high intensity particle beam to extremely high particle currents with correspondingly high space charge forces. This requires a precise analysis of longitudinal motion including stability analysis. Previous papers have treated the longitudinal space charge force as strictly linear, and have not been self-consistent; that is, they have not displayed a phase space distribution consistent with this linear force so that the transport of the phase space distribution could be followed, and departures from linearity could be analyzed. This is unlike the situation for transverse phase space where the Kapchinskij--Vladimirskij (K--V) distribution can be used as the basis of an analysis of transverse motion. In this paper a self-consistent particle distribution in longitudinal phase space is derived which is a solution of the Vlasov equation and an envelope equation for this solution is derived

Discrete Kinetic Eigenmode Spectra of Electron Plasma Oscillations in Weakly Collisional Plasma: A Numerical Study

Science.gov (United States)

Black, Carrie; Germaschewski, Kai; Bhattacharjee, Amitava; Ng, C. S.

2013-01-01

It has been demonstrated that in the presence of weak collisions, described by the Lenard-Bernstein collision operator, the Landau-damped solutions become true eigenmodes of the system and constitute a complete set. We present numerical results from an Eulerian Vlasov code that incorporates the Lenard-Bernstein collision operator. The effect of the collisions on the numerical recursion phenomenon seen in Vlasov codes is discussed. The code is benchmarked against exact linear eigenmode solutions in the presence of weak collisions, and a spectrum of Landau-damped solutions is determined within the limits of numerical resolution. Tests of the orthogonality and the completeness relation are presented.

Charged particle emission: the Child-Langmuir model

International Nuclear Information System (INIS)

Degond, P.; Raviart, P.A.

1993-01-01

The recent mathematical results concerning boundary emission modelling are reviewed with a synthetical view. The plane diode case is first studied; the Child-Langmuir model is then characterized as the limit to an absolutely non standard singular perturbation problem and is associated with approximate models (constrained and penalized models) which may be easily generalized in more realistic cases; an iterative solution method for the penalized problem is studied. The derived Child-Langmuir model is extended to the cylindrical diode case and to an arbitrary geometry case: constrained and penalized models related to the stationary Vlasov-Poisson equations are studied and extended to the Vlasov-Maxwell evolution equation general case

An algorithm for the calculation of 3-D ICRF [Ion Cyclotron Range of Frequencies] fields in tokamak geometry

International Nuclear Information System (INIS)

Smithe, D.N.; Colestock, P.L.; Kashuba, R.J.; Kammash, T.

1987-04-01

A computational scheme is developed which permits tractable calculation of three-dimensional full-wave solutions to the Maxwell-Vlasov equations under typical Ion Cyclotron Range of Frequencies (ICRF) experimental conditions. The method is unique in that power deposition to the plasma is determined via the anti-Hermitian part of a truncated warm-plasma dielectric operator, rather than as the result of an assumed phenomenological collision frequency. The resulting computer code allows arbitrary variation of density, temperature, magnetic field, and minority concentration in the poloidal plane by performing a convolution of poloidal modes to produce a coupled system of differential equations in the radial variable. By assuming no inhomogeneity along the toroidal axis, an inverse transform over k/sub parallel/ is performed to yield the full three-dimensional field solutions. The application of the code to TFTR-like plasmas shows a mild resonance structure in antenna loading related to the changing number of wavelengths between antenna and the resonance layer. 48 figs

Dust-lower-hybrid waves in a magnetized self-gravitating dusty plasma

International Nuclear Information System (INIS)

Salimullah, M.; Roy Chowdhury, A.; Dasgupta, B.

1997-11-01

General dispersion relation for a self-gravitating magnetized and finite temperature dusty plasma has been derived using the Vlasov-kinetic theory in guiding center technique. Results of earlier studies in unmagnetized situations turn out to be special cases of our general dispersion relation. In addition to the usual dust-acoustic waves in unmagnetized plasmas, we find an ultra-low-frequency mode in the frequency range between cyclotron frequencies of ions and charged dust particles and the Jean's instability of the self-gravitating dusty plasma systems. (author)

Macroscopic dynamics of thermal nuclear excitations

International Nuclear Information System (INIS)

Bastrukov, S.I.; Deak, F.; Kiss, A.; Seres, Z.

1989-11-01

The concept of kinetic temperature as a local dynamical variable of thermal nuclear collective motion is formulated using long-mean-free-path approach based on the Landau-Vlasov kinetic equation. In the Fermi drop model the thermal fluid dynamics of the spherical nucleus is analyzed. It is shown that in a compressible Fermi liquid the temperature pulses propagate in the form of spherical wave in phase with the acoustic wave. The thermal and compressional excitations are caused by the isotropic harmonic oscillations of the Fermi sphere in momentum space. (author) 25 refs.; 2 figs

Comparison of multi-fluid moment models with particle-in-cell simulations of collisionless magnetic reconnection

International Nuclear Information System (INIS)

Wang, Liang; Germaschewski, K.; Hakim, Ammar H.; Bhattacharjee, A.

2015-01-01

We introduce an extensible multi-fluid moment model in the context of collisionless magnetic reconnection. This model evolves full Maxwell equations and simultaneously moments of the Vlasov-Maxwell equation for each species in the plasma. Effects like electron inertia and pressure gradient are self-consistently embedded in the resulting multi-fluid moment equations, without the need to explicitly solving a generalized Ohm's law. Two limits of the multi-fluid moment model are discussed, namely, the five-moment limit that evolves a scalar pressures for each species and the ten-moment limit that evolves the full anisotropic, non-gyrotropic pressure tensor for each species. We first demonstrate analytically and numerically that the five-moment model reduces to the widely used Hall magnetohydrodynamics (Hall MHD) model under the assumptions of vanishing electron inertia, infinite speed of light, and quasi-neutrality. Then, we compare ten-moment and fully kinetic particle-in-cell (PIC) simulations of a large scale Harris sheet reconnection problem, where the ten-moment equations are closed with a local linear collisionless approximation for the heat flux. The ten-moment simulation gives reasonable agreement with the PIC results regarding the structures and magnitudes of the electron flows, the polarities and magnitudes of elements of the electron pressure tensor, and the decomposition of the generalized Ohm's law. Possible ways to improve the simple local closure towards a nonlocal fully three-dimensional closure are also discussed

Turbulent transport of energetic ions

International Nuclear Information System (INIS)

Dannert, Tilman; Hauff, Thilo; Jenko, Frank; Guenter, Sibylle

2006-01-01

Approaching ITER operation, the issue of anomalous transport of fast particles becomes more and more important. This is partly because the ITER heating and current drive system relies heavily on neutral beam injection. Moreover burning plasmas are heated by fast fusion α particles.Fusion α particles are characterised by a fixed energy and an isotropic velocity distribution. Therefore they have gyroradii one magnitude larger than the thermal ions. The dependency of the particle diffusion of α test particles on the Kubo number K = VExBτc/λc (VExB mean E x B velocity, τc, λc correlation time and length of the turbulent potential) is presented. For different turbulent regimes, different dependency of the diffusion on the gyroradius is found. For large Kubo numbers, the transport is found to remain constant for gyroradii up to the correlation length of the potential, whereas it is drastically reduced in the small Kubo number regime.In the second part, a model for beam ions injected along the equilibrium magnetic field is described. The beam ions are treated gyrokinetically in a self-consistent way with the equilibrium distribution function taken as a shifted Maxwellian. The implications of such a model for the Vlasov equation, the field equations, and the calculation of moments and fluxes are discussed. Linear and nonlinear results, obtained with the gyrokinetic flux tube code GENE show the existence of a new instability driven by fast beam ions. The instability has a maximum growth rate at perpendicular wave numbers of kyρs ∼ 0.15 and depends mainly on the beam velocity and the density gradient of the beam ions. This instability leads to a replacement of bulk ion particle transport by fast ion particle transport, connected to a strongly enhanced heat flux. In the presence of this instability, the turbulent particle and heat transport is dominated by fast ions

On improved confinement in mirror plasmas by a radial electric field

Science.gov (United States)

Ågren, O.; Moiseenko, V. E.

2017-11-01

A weak radial electric field can suppress radial excursions of a guiding center from its mean magnetic surface. The physical origin of this effect is the smearing action by a poloidal E × B rotation, which tend to cancel out the inward and outward radial drifts. A use of this phenomenon may provide larger margins for magnetic field shaping with radial confinement of particles maintained in the collision free idealization. Mirror fields, stabilized by a quadrupolar field component, are of particular interest for their MHD stability and the possibility to control the quasi neutral radial electric field by biased potential plates outside the confinement region. Flux surface footprints on the end tank wall have to be traced to avoid short-circuiting between biased plates. Assuming a robust biasing procedure, moderate voltage demands for the biased plates seems adequate to cure even the radial excursions of Yushmanov ions which could be locally trapped near the mirrors. Analytical expressions are obtained for a magnetic quadrupolar mirror configuration which possesses minimal radial magnetic drifts in the central confinement region. By adding a weak controlled radial quasi-neutral electric field, the majority of gyro centers are predicted to be forced to move even closer to their respective mean magnetic surface. The gyro center radial coordinate is in such a case an accurate approximation for a constant of motion. By using this constant of motion, the analysis is in a Vlasov description extended to finite β. A correspondence between that Vlasov system and a fluid description with a scalar pressure and an electric potential is verified. The minimum B criterion is considered and implications for flute mode stability in the considered magnetic field is analyzed. By carrying out a long-thin expansion to a higher order, the validity of the calculations are extended to shorter and more compact device designs.

Evolution of longitudinal equilibrium distribution in the adiabatic regime

International Nuclear Information System (INIS)

Wei, J.; Lee, S.Y.; Ruggiero, A.G.

1990-01-01

Evolution of longitudinal equilibrium distribution of a hadron bunch under the beam-environment interaction is investigated based on a self-consistent solution of the Vlasov equation. The effect of this interaction on the distribution can be characterized by a dimensionless quantity in analogy to the one describing the microwave-instability criterion. In the case that the coupling impedance (Z/n) is reactive and frequency independent, the change in the distribution results in a stabilization that keeps the bunch below the instability threshold; microwave instability is thus eliminated. Monte Carlo simulation for the microwave instability agrees with analytic solution of the Vlasov equation provided that bunch shape distortion due to the coupling is taken into account

Hermite Polynomials and the Inverse Problem for Collisionless Equilibria

Science.gov (United States)

Allanson, O.; Neukirch, T.; Troscheit, S.; Wilson, F.

2017-12-01

It is long established that Hermite polynomial expansions in either velocity or momentum space can elegantly encode the non-Maxwellian velocity-space structure of a collisionless plasma distribution function (DF). In particular, Hermite polynomials in the canonical momenta naturally arise in the consideration of the 'inverse problem in collisionless equilibria' (IPCE): "for a given macroscopic/fluid equilibrium, what are the self-consistent Vlasov-Maxwell equilibrium DFs?". This question is of particular interest for the equilibrium and stability properties of a given macroscopic configuration, e.g. a current sheet. It can be relatively straightforward to construct a formal solution to IPCE by a Hermite expansion method, but several important questions remain regarding the use of this method. We present recent work that considers the necessary conditions of non-negativity, convergence, and the existence of all moments of an equilibrium DF solution found for IPCE. We also establish meaningful analogies between the equations that link the microscopic and macrosopic descriptions of the Vlasov-Maxwell equilibrium, and those that solve the initial value problem for the heat equation. In the language of the heat equation, IPCE poses the pressure tensor as the 'present' heat distribution over an infinite domain, and the non-Maxwellian features of the DF as the 'past' distribution. We find sufficient conditions for the convergence of the Hermite series representation of the DF, and prove that the non-negativity of the DF can be dependent on the magnetisation of the plasma. For DFs that decay at least as quickly as exp(-v^2/4), we show non-negativity is guaranteed for at least a finite range of magnetisation values, as parameterised by the ratio of the Larmor radius to the gradient length scale. 1. O. Allanson, T. Neukirch, S. Troscheit & F. Wilson: From one-dimensional fields to Vlasov equilibria: theory and application of Hermite polynomials, Journal of Plasma Physics, 82

Stimulated brillouin scattering of electromagnetic waves in a dusty plasma

International Nuclear Information System (INIS)

Salimullah, M.; Sen, A.

1991-08-01

The stimulated Brilluoin scattering of electromagnetic waves in a homogeneous, unmagnetized and collisionless dusty plasma has been investigated theoretically. The Vlasov equation has been solved perturbatively to find the nonlinear response of the plasma particles. The presence of the dust particles introduces a background inhomogeneous electric field which significantly influences the dispersive properties of the plasma. At the ion acoustic branch we find the usual scattering slightly modified by the charged dust grains. However, at the frequency lower than the ion acoustic branch we find a new mode of the plasma arising from the oscillations of the ions in the static structure of the dust distribution. This low frequency branch causes enhanced stimulated Brillouin scattering of electromagnetic waves in a dusty plasma. (author). 15 refs

High-power microwave transmission and mode conversion program. Progress report, June 15, 1993--June 15, 1994

International Nuclear Information System (INIS)

Vernon, R.J.; Lorbeck, J.A.

1994-06-01

This report briefly discusses the following topics: (1) Quasi-optical converter design for Varian gyrotron SN 4.1; (2) Quasi-optical converter cold-test measurement; (3) Modification of geometrical-optics synthesized surfaces; (4)Diffraction synthesis; (5) Tapered dimpled launcher; (6) Work on Vlasov converter system for Varian gyrotron SN 4.1R; (7) Analysis of gyrotron spurious modes; (8) MIT code benchmarking; (9) Development of low-power efficiency test for Vlasov converters; (10) Investigation of optimal beam waist size and mode content for injection into a circular and rectangular corrugated waveguides; (11) The effect of corrugations on reduction of the fields at the wall of waveguides; (12) Shipping of a microwave scanner to Varian and further microwave scanner development; and (13) Code transferred to Varian

Velocity space ring-plasma instability, magnetized, Part I: Theory

International Nuclear Information System (INIS)

Lee, J.K.; Birdsall, C.K.

1979-01-01

The interaction of magnetized monoenergetic ions (a ring in velocity space) with a homogeneous Maxwellian target plasma is studied numerically using linear Vlasov theory. The ring may be produced when an energetic beam is injected perpendicular to a uniform magnetic field. In addition to yielding the previously known results, the present study classifies this flute-like instability into three distinct regimes based on the beam density relative to the plasma density, where many features such as physical mechanisms, dispersion diagrams, and maximum growth rates are quite different. The effects of electron dynamics, plasma or ring thermal spread, the ratio of ω/sub p//ω/sub c/ for plasma ions, and electromagnetic modifications are also considered

2.5-dimensional numerical modeling of the formation of a plasma channel due to ion redistribution during the propagation of a finite sequence of relativistic electron bunches through high-density and low-density plasmas

International Nuclear Information System (INIS)

Karas, V.I.; Karas, I.V.; Levchenko, V.D.; Sigov, Yu.S.; Fainberg, Ya.B.

1997-01-01

Results of numerical simulations of the excitation of wake fields in high- and low-density plasmas are presented. The propagation of relativistic electron bunches in a plasma is described by a closed set of relativistic Vlasov equations for two spatial coordinates and three velocity coordinates for each plasma component and the nonlinear Maxwell equations for self-consistent electromagnetic fields. Numerical modeling shows that, under ordinary experimental conditions (when the length and radius of the bunch are much less than the skin depth), the radius of the bunches propagating in a plasma varies over a wide range. In this case, the dynamics of both the plasma and the bunches is nonlinear. The radial redistribution of the plasma ions in self-consistent fields leads to the formation of a plasma channel. Incorporating this phenomenon is important for studying the propagation of relativistic electron bunches in a plasma

Experimental program based on a High Beta Q Machine. Final report, 1 May 1978-30 September 1980

International Nuclear Information System (INIS)

Ribe, F.L.

1980-07-01

This report summarizes work done in designing and constructing the High Beta Q Machine from the inception of the work in May 1978 until the present time. It is a 3-m long, low-compression theta pinch with a 22-cm-diameter segmented compression coil with a minimum axial periodicity length of 10 cm. This capability of driving the machine as a simple, low-density theta pinch, and also of independently applying periodic magnetic fields before or after formation of the plasma column, gives the device considerable flexibility. Reported here is the construction and testing of the machine, development of its diagnostics and initial measurements of the plasma at early times in the duration of the crowbarred magnetic field. The experimental effort has been paralleled by theoretical work to model the diffuse profile, collisionless plasma in its response to the periodic RF magnetic fields. The model chosen is the Freidberg-Pearlstein Vlasov-fluid model which provides an MHD-like description but with accounting of ion kinetic effects over diffuse equilibrium profiles. A computer code has been developed to accurately calculate the resistive response of the plasma column, giving the power absorption by ion Landau damping and more recently, ion-cyclotron damping

Renormalized plasma turbulence theory: A quasiparticle picture

International Nuclear Information System (INIS)

DuBois, D.F.

1981-01-01

A general renormalized statistical theory of Vlasov turbulence is given which proceeds directly from the Vlasov equation and does not assume prior knowledge of sophisticated field-theoretic techniques. Quasiparticles are the linear excitations of the turbulent system away from its instantaneous mean (ensemble-averaged) state or background; the properties of this background state ''dress'' or renormalize the quasiparticle responses. It is shown that all two-point responses (including the dielectric) and all two-point correlation functions can be completely described by the mean distribution function and three fundamental quantities. Two of these are the quasiparticle responses: the propagator and the potential source: which measure, respectively, the separate responses of the mean distribution function and the mean electrostatic potential to functional changes in an external phase-space source added to Vlasov's equation. The third quantity is the two-point correlation function of the incoherent part of the phase-space density which acts as a self-consistent source of quasiparticle and potential fluctuations. This theory explicitly takes into account the self-consistent nature of the electrostatic-field fluctuations which introduces new effects not found in the usual ''test-particle'' theories. Explicit equations for the fundamental quantities are derived in the direct interaction approximation. Special attention is paid to the two-point correlations and the relation to theories of phase-space granulation

Performance of particle in cell methods on highly concurrent computational architectures

International Nuclear Information System (INIS)

Adams, M.F.; Ethier, S.; Wichmann, N.

2009-01-01

Particle in cell (PIC) methods are effective in computing Vlasov-Poisson system of equations used in simulations of magnetic fusion plasmas. PIC methods use grid based computations, for solving Poisson's equation or more generally Maxwell's equations, as well as Monte-Carlo type methods to sample the Vlasov equation. The presence of two types of discretizations, deterministic field solves and Monte-Carlo methods for the Vlasov equation, pose challenges in understanding and optimizing performance on today large scale computers which require high levels of concurrency. These challenges arises from the need to optimize two very different types of processes and the interactions between them. Modern cache based high-end computers have very deep memory hierarchies and high degrees of concurrency which must be utilized effectively to achieve good performance. The effective use of these machines requires maximizing concurrency by eliminating serial or redundant work and minimizing global communication. A related issue is minimizing the memory traffic between levels of the memory hierarchy because performance is often limited by the bandwidths and latencies of the memory system. This paper discusses some of the performance issues, particularly in regard to parallelism, of PIC methods. The gyrokinetic toroidal code (GTC) is used for these studies and a new radial grid decomposition is presented and evaluated. Scaling of the code is demonstrated on ITER sized plasmas with up to 16K Cray XT3/4 cores.

Performance of particle in cell methods on highly concurrent computational architectures

International Nuclear Information System (INIS)

Adams, M F; Ethier, S; Wichmann, N

2007-01-01

Particle in cell (PIC) methods are effective in computing Vlasov-Poisson system of equations used in simulations of magnetic fusion plasmas. PIC methods use grid based computations, for solving Poisson's equation or more generally Maxwell's equations, as well as Monte-Carlo type methods to sample the Vlasov equation. The presence of two types of discretizations, deterministic field solves and Monte-Carlo methods for the Vlasov equation, pose challenges in understanding and optimizing performance on today large scale computers which require high levels of concurrency. These challenges arises from the need to optimize two very different types of processes and the interactions between them. Modern cache based high-end computers have very deep memory hierarchies and high degrees of concurrency which must be utilized effectively to achieve good performance. The effective use of these machines requires maximizing concurrency by eliminating serial or redundant work and minimizing global communication. A related issue is minimizing the memory traffic between levels of the memory hierarchy because performance is often limited by the bandwidths and latencies of the memory system. This paper discusses some of the performance issues, particularly in regard to parallelism, of PIC methods. The gyrokinetic toroidal code (GTC) is used for these studies and a new radial grid decomposition is presented and evaluated. Scaling of the code is demonstrated on ITER sized plasmas with up to 16K Cray XT3/4 cores

Annual progress report

International Nuclear Information System (INIS)

Simon, A.

1975-01-01

Considerable success has been achieved this year in research aimed at extending the asymptotic threshold nonlinear theory to plasmas governed by the Vlasov equation and in a group of linear studies concerned with drift instabilities in sheared magnetic fields. The nonlinear results are general and have been applied to the bump-on-tail instability and to the collisionless drift and the dissipative trapped electron instability in unsheared fields. The linear studies have dealt with the effects of resonant electrons, finite collisionality, finite-beta, neoclassical modifications and ion gyro-motion on trapped electron instabilities in sheared magnetic fields

Instabilities in strongly coupled plasmas

CERN Document Server

Kalman, G J

2003-01-01

The conventional Vlasov treatment of beam-plasma instabilities is inappropriate when the plasma is strongly coupled. In the strongly coupled liquid state, the strong correlations between the dust grains fundamentally affect the conditions for instability. In the crystalline state, the inherent anisotropy couples the longitudinal and transverse polarizations, and results in unstable excitations in both polarizations. We summarize analyses of resonant and non-resonant, as well as resistive instabilities. We consider both ion-dust streaming and dust beam-plasma instabilities. Strong coupling, in general, leads to an enhancement of the growth rates. In the crystalline phase, a resonant transverse instability can be excited.

STABILITY OF AXIALLY COMPRESSED SINGLE-CELL MONO ...

African Journals Online (AJOL)

. I : Warping constant ω: ... using generalized strain fields on Vlasov's equation, the number of kinematic unknowns can be drastically reduced. ... OF EQUIUBRlUM: NIGERIAN JOURNAL OF TECHNOLOGY, VOL. 28 NO.2, SEPTEMBER 2009 ...

Research and design of quasi-optical mode converter

International Nuclear Information System (INIS)

Liu Jianwei; Zhao Qing

2013-01-01

This paper presents a quasi-optical mode converter which can convert the output mode of gyrotrons and other high-power microwave oscillators into quasi-Gaussian beam, aiming to achieve transverse output of quasi-Gaussian beam TEM 00 mode. First, we analyze mode propagation in the waveguide and the working mechanism of the Vlasov launcher. Then the radiation fields are calculated using vector diffraction theory. At last a quasi-optical mode converter is designed to convert the 94 GHz, TE 62 mode millimeter wave into quasi-Gaussian beam with programming method. The results prove that quasi-Gaussian mode can be obtained at the output window with a simple Vlasov launcher and two mirrors, and the power transmission efficiency of the quasi-optical mode converter reaches to 87.5%. (authors)

A unified approach to the Darwin approximation

International Nuclear Information System (INIS)

Krause, Todd B.; Apte, A.; Morrison, P. J.

2007-01-01

There are two basic approaches to the Darwin approximation. The first involves solving the Maxwell equations in Coulomb gauge and then approximating the vector potential to remove retardation effects. The second approach approximates the Coulomb gauge equations themselves, then solves these exactly for the vector potential. There is no a priori reason that these should result in the same approximation. Here, the equivalence of these two approaches is investigated and a unified framework is provided in which to view the Darwin approximation. Darwin's original treatment is variational in nature, but subsequent applications of his ideas in the context of Vlasov's theory are not. We present here action principles for the Darwin approximation in the Vlasov context, and this serves as a consistency check on the use of the approximation in this setting

Electrostatic effect for the collisionless tearing mode

International Nuclear Information System (INIS)

Hoshino, M.

1987-01-01

Electron dynamics has not been self-consistently considered in collisionless tearing mode theories to date because of the mathematical complexity of the Vlasov-Maxwell equations. We have found using computer simulations that electrostatic fields play an important role in the tearing mode. Vlasov theory, including the electrostatic field, is investigated for topologies with both antiparallel and nonantiparallel magnetic field lines. The electrostatic field influences the resonant current in the neutral sheet which is a non-MHD effect, and modifies the linear growth rate. At the magnetopause, where the field lines are not antiparallel, the electrostatic effect acts to raise the linear growth rate of the tearing mode. On the other hand, in the magnetotail, where magnetic field lines are antiparallel, the electrostatic effect reduces the tearing mode growth rate. copyright American Geophysical Union 1987

Kinetic stability analyses in a bumpy cylinder

International Nuclear Information System (INIS)

Dominguez, R.R.; Berk, H.L.

1981-01-01

Recent interest in the ELMO Bumpy Torus (EBT) has prompted a number of stability analyses of both the hot electron rings and the toroidal plasma. Typically these works employ the local approximation, neglecting radial eigenmode structure and ballooning effects to perform the stability analysis. In the present work we develop a fully kinetic formalism for performing nonlocal stability analyses in a bumpy cylinder. We show that the Vlasov-Maxwell integral equations (with one ignorable coordinate) are self-adjoint and hence amenable to analysis using numerical techniques developed for self-adjoint systems of equations. The representation we obtain for the kernel of the Vlasov-Maxwell equations is a differential operator of arbitrarily high order. This form leads to a manifestly self-adjoint system of differential equations for long wavelength modes

Theory of neutron spectra from d-d-reactions in the linear z-pinch and the plasma focus

International Nuclear Information System (INIS)

Deutsch, R.; Kaeppeler, H.J.

1982-05-01

Because of a finite gyroradius effect, the equilibrium probability density function of the ions in the azimuthal magnetic field of a linear z-pinch becomes anisotropic. This density function was derived by solving the Vlasov equation and used to determine the neutron spectra produced in the deuterium plasma of a z-pinch. The neutron spectra were calculated for two models, differing in the energy distribution of the fast ions. A background plasma with 'slow' ions was also considered. The interactions of the fast ions with the slow ions and 'beam-beam' interactions between fast ions were considered. Typical spectra for arbitrary directions to the cylindrical axis are given. The anisotropy factors were calculated. Considering the influence of the azimuthal magnetic field on the equilibrium density function of the deuterons, the well known particularities of the neutron spectra are obtained without any of the contradictions typical of the traditional models. (orig.)

Vlasov equilibrium and nonlocal stability properties of an inhomogeneous plasma column

International Nuclear Information System (INIS)

Davidson, R.C.

1976-01-01

A fully kinetic, nonlocal, matrix dispersion equation is derived for electrostatic perturbations about a spatially nonuniform cylindrical plasma equilibrium. The analysis is carried out for the class of radially confined rigid-rotor equilibria described by f 0 /subj/(x,v) = (n/subj/m/subj//2πT/subj/) F (H/sub perpendicular//T/subj/- ω/subj/P/sub theta//T/subj/,v/subz/), where P/sub theta/ is the canonical angular momentum, v/subz/ is the axial velocity, H/sub perpendicular/ is the perpendicular energy, and n/subj/, T/subj/, and ω/subj/ are constants. Assuming equilibrium charge neutrality and negligible spatial variation in the axial magnetic field B 0 e/subz/, it is shown that the particle trajectories (in the equilibrium electric and magnetic fields) and the orbit integrals required in the stability analysis can be evaluated in closed form. Expanding the perturbed electrostatic potential in terms of the vacuum eigenfunctions ]J/subl/(lambda/subn/r) closing-brace for the conducting cylinder leads to a matrix dispersion equation of the form det[delta/subn//sub prime//subn+ Σ/subj/chi/subj//subn//sub prime//subn(ω)]=0, where the susceptibility chi/subj//subn//sub prime//subn(ω) is expressed as a phase-space integral over f 0 /subj/(x,v) and known functions of ω, r lambda/subn/, etc. The limiting case of strongly magnetized electrons and unmagnetized ions is considered together with a preliminary application to the lower-hyprid-drift instability

The non-resonant decay of the fast magnetosonic wave during ICRH of a tokamak plasma

International Nuclear Information System (INIS)

Avinash, K.; Core, W.G.; Hellsten, T.; Farrell, C.M.

1988-01-01

The non-resonant decay of the fast magnetosonic wave into an Ion Bernstein wave and a quasi-mode is investigated from the point of view of assessing the importance of this process for the observed direct heating of the edge plasma during ion-cyclotron resonance heating (ICRH). Starting from the Maxwell-Vlasov equations, expressions for the threshold electric field and the growth rates of the decay process are obtained. For JET like parameters, the thresholds for the decay are easily exceeded and the growth time for typical fast wave electric field strengths is of the order of a microsecond. The parametric dependence of the threshold on magnetic field, temperature, the density of the various ion species, and electron-ion collisions is studied. Finally the relevance of this process to the heating of plasma edge during ICRH is discussed. (author)

Equilibrium and stability properties of relativistic electron rings and E-layers

International Nuclear Information System (INIS)

Uhm, H.

1976-01-01

Equilibrium and stability properties of magnetically confined partially-neutralized thin electron ring and E-layer are investigated using the Vlasov-Maxwell equations. The analysis is carried out within the context of the assumption that the minor dimensions (a,b) of the system are much less than the collisionless skin depth (c/antiω/sub p/). The equilibrium configuration of the E-layer is assumed to be an infinitely long, azimuthally symmetric hollow electron beam which is aligned parallel to a uniform axial magnetic field. On the other hand, the electron ring is located at the midplane of an externally imposed mirror field which acts to confine the ring both axially and radially. The equilibrium properties of the E-layer and electron ring are obtained self-consistently for several choices of equilibrium electron distribution function. The negative-mass instability analysis is carried out for the relativistic E-layer equilibrium in which all of the electrons have the same transverse energy and a spread in canonical angular momentum, assuming a fixed ion background. The ion resonance instability properties are investigated for a relativistic nonneutral E-layer aligned parallel to a uniform magnetic field and located between two ground coaxial cylindrical conductors. The stability properties of a nonrelativistic electron ring is investigated within the framework of the linearized Vlasov-Poisson equations. The dispersion relation is obtained for the self-consistent electron distribution function in which all electrons have the same value of energy an the same value of canonical angular momentum. The positive ions in the electron ring are assumed to form an immobile partially neutralizing background. The stability criteria as well as the instability growth rates are derived and discussed including the effect of geometrical configuration of the system. Equilibrium space-charge effects play a significant role in stability behavior

Finite Larmor radius stabilization of ballooning modes in tokamaks

International Nuclear Information System (INIS)

Tsang, K.T.

1980-07-01

A ballooning mode equation that includes full finite Larmor radius effects has been derived from the Vlasov equation for a circular tokamak equilibrium. Numerical solution of this equation shows that finite Larmor radius effects are stabilizing

Classical limit for semirelativistic Hartree systems

KAUST Repository

Aki, Gonca L.; Markowich, Peter A.; Sparber, Christof

2008-01-01

Wigner transformation techniques that its classical limit yields the well known relativistic Vlasov-Poisson system. The result holds for the case of attractive and repulsive mean-field interactions, with an additional size constraint in the attractive

Isospin and angular momentum effects in the peripheral heavy ion reactions; Effets d`isospin et de moment angulaire dans les reactions d`ions lourds peripheriques

Energy Technology Data Exchange (ETDEWEB)

Jouault, B.; De La Mota, V.; Sebille, F.; Royer, G. [Laboratoire de Physique Subatomique et des Technologies Associees - SUBATECH, Centre National de la Recherche Scientifique, 44 - Nantes (France); Lecolley, J. F. [Lab. de Physique Corpusculaire, Caen Univ., 14 (France)

1997-10-01

The semi-classical Landau Vlasov model has been used to investigate the decay modes of peripheral Pb + Au reactions at 29 MeV/n. Statics and dynamics of these very massive nuclei are analyzed especially through the isospin dependence of the effective nuclear force. The degree of dissipation of the collisions is studied for different bins of impact parameter pointing out the influence of the nucleon-nucleon cross section. The appearance of intermediate mass fragments from neck-like structures is evidenced and the effects of angular momentum transfers are shown to play a fundamental role in this phenomenon. The theoretical results are compared with experimental data, showing the importance of the dynamical and out of equilibrium effects on the observables. (authors) 7 refs.

Transient Plasma Photonic Crystals for High-Power Lasers.

Science.gov (United States)

Lehmann, G; Spatschek, K H

2016-06-03

A new type of transient photonic crystals for high-power lasers is presented. The crystal is produced by counterpropagating laser beams in plasma. Trapped electrons and electrically forced ions generate a strong density grating. The lifetime of the transient photonic crystal is determined by the ballistic motion of ions. The robustness of the photonic crystal allows one to manipulate high-intensity laser pulses. The scheme of the crystal is analyzed here by 1D Vlasov simulations. Reflection or transmission of high-power laser pulses are predicted by particle-in-cell simulations. It is shown that a transient plasma photonic crystal may act as a tunable mirror for intense laser pulses. Generalizations to 2D and 3D configurations are possible.

New Insight into Short-Wavelength Solar Wind Fluctuations from Vlasov Theory

Science.gov (United States)

Sahraoui, Fouad; Belmont, G.; Goldstein, M. L.

2012-01-01

The nature of solar wind (SW) turbulence below the proton gyroscale is a topic that is being investigated extensively nowadays, both theoretically and observationally. Although recent observations gave evidence of the dominance of kinetic Alfven waves (KAWs) at sub-ion scales with omega omega (sub ci)) is more relevant. Here, we study key properties of the short-wavelength plasma modes under limited, but realistic, SW conditions, Typically Beta(sub i) approx. > Beta (sub e) 1 and for high oblique angles of propagation 80 deg theory, we discuss the relevance of each plasma mode (fast, Bernstein, KAW, whistler) in carrying the energy cascade down to electron scales. We show, in particular, that the shear Alfven mode (known in the magnetohydrodynamic limit) extends at scales kappa rho (sub i) approx. > 1 to frequencies either larger or smaller than omega (sub ci), depending on the anisotropy kappa (parallel )/ kappa(perpendicular). This extension into small scales is more readily called whistler (omega > omega (sub ci)) or KAW (omega < omega (sub ci)) although the mode is essentially the same. This contrasts with the well-accepted idea that the whistler branch always develops as a continuation at high frequencies of the fast magnetosonic mode. We show, furthermore, that the whistler branch is more damped than the KAW one, which makes the latter the more relevant candidate to carry the energy cascade down to electron scales. We discuss how these new findings may facilitate resolution of the controversy concerning the nature of the small-scale turbulence, and we discuss the implications for present and future spacecraft wave measurements in the SW.

Linear response theory for long-range interacting systems in quasistationary states.

Science.gov (United States)

Patelli, Aurelio; Gupta, Shamik; Nardini, Cesare; Ruffo, Stefano

2012-02-01

Long-range interacting systems, while relaxing to equilibrium, often get trapped in long-lived quasistationary states which have lifetimes that diverge with the system size. In this work, we address the question of how a long-range system in a quasistationary state (QSS) responds to an external perturbation. We consider a long-range system that evolves under deterministic Hamilton dynamics. The perturbation is taken to couple to the canonical coordinates of the individual constituents. Our study is based on analyzing the Vlasov equation for the single-particle phase-space distribution. The QSS represents a stable stationary solution of the Vlasov equation in the absence of the external perturbation. In the presence of small perturbation, we linearize the perturbed Vlasov equation about the QSS to obtain a formal expression for the response observed in a single-particle dynamical quantity. For a QSS that is homogeneous in the coordinate, we obtain an explicit formula for the response. We apply our analysis to a paradigmatic model, the Hamiltonian mean-field model, which involves particles moving on a circle under Hamiltonian dynamics. Our prediction for the response of three representative QSSs in this model (the water-bag QSS, the Fermi-Dirac QSS, and the Gaussian QSS) is found to be in good agreement with N-particle simulations for large N. We also show the long-time relaxation of the water-bag QSS to the Boltzmann-Gibbs equilibrium state. © 2012 American Physical Society

Fourier–Hermite spectral representation for the Vlasov–Poisson system in the weakly collisional limit

KAUST Repository

Parker, Joseph T.; Dellar, Paul J.

2015-01-01

Copyright © Cambridge University Press 2015. We study Landau damping in the 1+1D Vlasov-Poisson system using a Fourier-Hermite spectral representation. We describe the propagation of free energy in Fourier-Hermite phase space using forwards

[Plasma properties: Annual report

International Nuclear Information System (INIS)

1987-01-01

The Magneto-Fluid Dynamics Division of the Courant Institute is engaged in a broad program of basic research in the theoretical aspects of plasma physics and magneto-fluid dynamics with emphasis on those areas which are relevant to the fusion energy program. The total research program in the division includes efforts in the areas of plasma containment, stability, equilibrium, transport, wave propagation (including shock waves), heating, orbit theory, as well as numerical experiments and the development of practical numerical methods in all plasma problems. Applications are made to the following project areas: Tokamaks, Mirrors, Stellarators, and Alternate Concepts. Developments include the whole spectrum of models from macroscopic MHD and guiding center to Vlasov, drift kinetic Fokker-Planck, and Boltzmann. This document describes research completed as well as programs in progress

Isospin and angular momentum effects in the peripheral heavy ion reactions

International Nuclear Information System (INIS)

Jouault, B.; De La Mota, V.; Sebille, F.; Royer, G.; Lecolley, J. F.

1997-01-01

The semi-classical Landau Vlasov model has been used to investigate the decay modes of peripheral Pb + Au reactions at 29 MeV/n. Statics and dynamics of these very massive nuclei are analyzed especially through the isospin dependence of the effective nuclear force. The degree of dissipation of the collisions is studied for different bins of impact parameter pointing out the influence of the nucleon-nucleon cross section. The appearance of intermediate mass fragments from neck-like structures is evidenced and the effects of angular momentum transfers are shown to play a fundamental role in this phenomenon. The theoretical results are compared with experimental data, showing the importance of the dynamical and out of equilibrium effects on the observables. (authors)

Risk-sensitive mean-field games

KAUST Repository

Tembine, Hamidou

2014-04-01

In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a Hamilton -Jacobi- Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics. © 1963-2012 IEEE.

Risk-sensitive mean-field games

KAUST Repository

Tembine, Hamidou; Zhu, Quanyan; Başar, Tamer

2014-01-01

In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a Hamilton -Jacobi- Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics. © 1963-2012 IEEE.

Cucker-Smale model with normalized communication weights and time delay

KAUST Repository

Choi, Young-Pil

2017-03-06

We study a Cucker-Smale-type system with time delay in which agents interact with each other through normalized communication weights. We construct a Lyapunov functional for the system and provide sufficient conditions for asymptotic flocking, i.e., convergence to a common velocity vector. We also carry out a rigorous limit passage to the mean-field limit of the particle system as the number of particles tends to infinity. For the resulting Vlasov-type equation we prove the existence, stability and large-time behavior of measure-valued solutions. This is, to our best knowledge, the first such result for a Vlasov-type equation with time delay. We also present numerical simulations of the discrete system with few particles that provide further insights into the flocking and oscillatory behaviors of the particle velocities depending on the size of the time delay.

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.

A Boltzmann equation approach to the damping of giant resonances in nuclei

International Nuclear Information System (INIS)

Schuck, P.; Winter, J.

1983-01-01

The Vlasov equation plus collision term (Boltzmann equation) represents an appropriate frame for the treatment of giant resonances (zero sound modes) in nuclei. With no adjustable parameters we obtain correct positions and widths for the giant quadrupole resonances. (author)

Ion acoustic eigenmodes in a collisionless bounded plasma:

International Nuclear Information System (INIS)

Kuhn, S.; Schupfer, N.; Santiago, M.A.M.; Assis, A.S. de

1990-01-01

This paper is based on an integral-equation method developed for solving the general linearized perturbation problem for a one-dimensional, uniform collisionless plasma with thin sheats, bounded by two planar electrodes. The underlying system of equations consists of a) the Vlasov equations for all particle species involved; b) Poisson's equation; c) the equation of total-current conservation; d) the particle boundary conditions at the left and right hand electrodes and e) the external-circuit equation. The method allows for very general equilibrium, boundary and external-circuit conditions. Using Laplace transformations in both time and space, it is set up to handle the complete initial value problem but also yields, as a by-product, the solution to the eigenmode problem. The only application to date of this method was to the Pierce Diode with a non-trivial external circuit, in which case the equation determining the complex eigenfrequencies ω n was found in analytic form. The said method is applied to ion-acoustic eigenmodes in a one-dimensional, collisionless bounded plasma consisting of non-drifting thermal electrons and a cold ion beam propagating through them. In this case, which is of relevance in the context of both Q- and DP-machines, the eigenfrequencies can no longer be obtained as solutions of an analytically explicit homogeneous system of linear integral equations. Via appropriate basis- set expansions of all perturbation functions involved, this system is transformed into a system of linear algebraic equations for the ω-dependent expansion coefficients, from which the eigenfrequencies can be obtained as the zeros of the'system determinant'. The results include studies on how the eigenfrequencies depend on plasma, boundary, as well as a comparison between these bounded-system ion-acoustic eigenmodes and their infinite-plasma counter-parts. (Author)

Double layer -- a particle accelerator in the magnetosphere

Energy Technology Data Exchange (ETDEWEB)

Fu, Xiangrong [Los Alamos National Laboratory

2015-07-16

Slides present the material under the following topics: Introduction (What is a double layer (DL)? Why is it important? Key unsolved problems); Theory -- time-independent solutions of 1D Vlasov--Poisson system; Particle-in-cell simulations (Current-driven DLs); and Electron acceleration by DL (Betatron acceleration). Key problems include the generation mechanism, stability, and electron acceleration. In summary, recent observations by Van Allen Probes show large number of DLs in the outer radiation belt, associated with enhanced flux of relativistic electrons. Simulations show that ion acoustic double layers can be generated by field-aligned currents. Thermal electrons can gain energy via betatron acceleration in a dipole magnetic field.

Dynamical aspects of particle emission in binary dissipative collisions -effects on hot-nuclei formation

International Nuclear Information System (INIS)

Eudes, Ph.; Basrak, Z.; Sebille, F.

1997-01-01

Characteristics of charged-particle emission in heavy-ion reactions have been studied in the framework of the semiclassical Landau-Vlasov approach for the 40 Ar + 27 Al collisions at 65 MeV/u. The reaction mechanism is dominated by binary dissipative collisions. After an abundant prompt emission coming from the overlapping region between the target and the projectile, two excited nuclei, the quasi-target and the quasi-projectile, emerge from the collision. To shed some light on the role played by dynamical effects, light-charged particle observables, which are currently used as an experimental signature a of hot equilibrated nucleus, have been carefully investigated. (K.A.)

Equilibrium structure of the plasma sheet boundary layer-lobe interface

Science.gov (United States)

Romero, H.; Ganguli, G.; Palmadesso, P.; Dusenbery, P. B.

1990-01-01

Observations are presented which show that plasma parameters vary on a scale length smaller than the ion gyroradius at the interface between the plasma sheet boundary layer and the lobe. The Vlasov equation is used to investigate the properties of such a boundary layer. The existence, at the interface, of a density gradient whose scale length is smaller than the ion gyroradius implies that an electrostatic potential is established in order to maintain quasi-neutrality. Strongly sheared (scale lengths smaller than the ion gyroradius) perpendicular and parallel (to the ambient magnetic field) electron flows develop whose peak velocities are on the order of the electron thermal speed and which carry a net current. The free energy of the sheared flows can give rise to a broadband spectrum of electrostatic instabilities starting near the electron plasma frequency and extending below the lower hybrid frequency.

Multifragmentation: Surface instabilities or statistical decay

International Nuclear Information System (INIS)

Moretto, L.G.; Tso, K.; Delis, D.; Colonna, N.; Wozniak, G.J.

1992-11-01

Boltzmann-Nordheim-Vlasov calculations show multifragmentation that seems to originate from surface instabilities. These instabilities are traced to a sheet instability caused by the proximity interaction. Experimental data, on the other hand, suggest that multifragmentation may be dominated by phase space

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.

Multifragmentation: surface instabilities or statistical decay?

International Nuclear Information System (INIS)

Moretto, L.G.; Tso, K.; Delis, D.; Colonna, N.; Wozniak, G.J.

1993-01-01

Boltzmann-Nordheim-Vlasov calculations show multifragmentation that seems to originate from surface instabilities. These instabilities are traced to a sheet instability caused by the proximity interaction. Experimental data, on the other hand, suggest that multifragmentation may be dominated by phase space. (author)

Nuclear dynamics in phase space

International Nuclear Information System (INIS)

Di Toro, M.

1984-07-01

We present a unified semiclassical picture of nuclear dynamics, from collective states to heavy ion physics, based on a study of the time evolution of the Wigner distribution function. We discuss in particular the mean field dynamics, in this ''quantal'' phase space, which is ruled by the nuclear Vlasov equation. Simple approximate solutions are worked out for rotational and vibrational collective motions. Giant resonances are shown to be quite well described as scaling modes, which are equivalent to a lowest multipole (up to 1sub(max)=2) distortions of the momentum distribution. Applications are shown to heavy ion physics to study giant resonances on high spin states and dynamical collective effects in subthreshold π-production. Several possible extensions and in particular the inclusion of two-body collision terms are finally discussed

Kinetic equilibrium of space charge dominated beams in a misaligned quadrupole focusing channel

International Nuclear Information System (INIS)

Goswami, A.; Sing Babu, P.; Pandit, V. S.

2013-01-01

The dynamics of intense beam propagation through the misaligned quadrupole focusing channel has been studied in a self-consistent manner using nonlinear Vlasov-Maxwell equations. The equations of motion of the beam centroid have been developed and found to be independent of any specific beam distribution. A Vlasov equilibrium distribution and beam envelope equations have been obtained, which provide us a theoretical tool to investigate the dynamics of intense beam propagating in a misaligned quadrupole focusing channel. It is shown that the displaced quadrupoles only cause the centroid of the beam to wander off axis. The beam envelope around the centroid obeys the familiar Kapchinskij-Vladimirskij envelope equation that is independent of the centroid motion. However, the rotation of the quadrupole about its optical axis affects the beam envelope and causes an increase in the projected emittances in the two transverse planes due to the inter-plane coupling

Identification of low-frequency kinetic wave modes in the Earth's ion foreshock

Directory of Open Access Journals (Sweden)

X. Blanco-Cano

1997-03-01

Full Text Available In this work we use ion and magnetic field data from the AMPTE-UKS mission to study the characteristics of low frequency (ωr « Ωp waves observed upstream of the Earth's bow shock. We test the application of various plasma-field correlations and magnetic ratios derived from linear Vlasov theory to identify the modes in this region. We evaluate (for a parameter space consistent with the ion foreshock the Alfvén ratio, the parallel compressibility, the cross-helicity, the noncoplanar ratio, the magnetic compression and the polarization for the two kinetic instabilities that can be generated in the foreshock by the interaction of hot diffuse ions with the solar wind: the left-hand resonant and the right-hand resonant ion beam instabilities. Comparison of these quantities with the observed plasma-field correlations and various magnetic properties of the waves observed during 10 intervals on 30 October 1984, where the waves are associated with diffuse ions, allows us to identify regions with Alfvénic waves and regions where the predominant mode is the right-hand resonant instability. In all the cases the waves are transverse, propagating at angles ≤ 33° and are elliptically polarized. Our results suggest that while the observed Alfvén waves are generated locally by hot diffuse ions, the right-handed waves may result from the superposition of waves generated by two different types of beam distribution (i.e. cold beam and diffuse ions. Even when there was good agreement between the values of observed transport ratios and the values given by the theory, some discrepancies were found. This shows that the observed waves are different from the theoretical modes and that mode identification based only on polarization quantities does not give a complete picture of the waves' characteristics and can lead to mode identification of waves whose polarization may agree with theoretical predictions even when other properties can diverge from those of the

Guiding-center models for edge plasmas and numerical simulations of isolated plasma filaments

International Nuclear Information System (INIS)

Madsen, Jens

2010-09-01

The work presented in this thesis falls into two categories: development of reduced dynamical models applicable to edge turbulence in magnetically confined fusion plasmas and numerical simulations of isolated plasma filaments in the scrape-off layer region investigating the influence of finite Larmor radius effects on the radial plasma transport. The coexistence of low-frequency fluctuations, having length scales comparable to the ion gyroradius, steep pressure gradients and strong E x B flows in the edge region of fusion plasmas violates the standard gyrokinetic ordering. In this thesis two models are presented that overcome some of the difficulties associated with the development of reduced dynamical models applicable to the edge. Second order guiding-center coordinates are derived using the phasespace Lie transform method. Using a variational principle the corresponding Vlasov-Maxwell equations expressed in guiding-center coordinates are derived including a local energy theorem. The second order terms describe lowest order finite Larmor radius effects. This set of equations might be relevant for edge plasmas due to the capability of capturing strong E x B flows and lowest order finite Larmor radius effects self-consistently. Next, an extension of the existing gyrokinetic formalism with strong flows is presented. In this work the background electric fields is dynamical, whereas earlier contributions did only incorporate a stationary electric field. In an ordering relevant for edge plasma turbulence, fully electromagnetic second order gyrokinetic coordinates and the corresponding gyrokinetic Vlasov-Maxwell equations are derived, including a local energy theorem. By taking the polarization and magnetization densities in the drift kinetic limit, we present the gyrokinetic Vlasov-Maxwell equations in a more tractable form, which could be relevant for direct numerical simulations of edge plasma turbulence. Finally, an investigation of the influence of finite Larmor

Guiding-center models for edge plasmas and numerical simulations of isolated plasma filaments

Energy Technology Data Exchange (ETDEWEB)

Madsen, Jens

2010-09-15

The work presented in this thesis falls into two categories: development of reduced dynamical models applicable to edge turbulence in magnetically confined fusion plasmas and numerical simulations of isolated plasma filaments in the scrape-off layer region investigating the influence of finite Larmor radius effects on the radial plasma transport. The coexistence of low-frequency fluctuations, having length scales comparable to the ion gyroradius, steep pressure gradients and strong E x B flows in the edge region of fusion plasmas violates the standard gyrokinetic ordering. In this thesis two models are presented that overcome some of the difficulties associated with the development of reduced dynamical models applicable to the edge. Second order guiding-center coordinates are derived using the phasespace Lie transform method. Using a variational principle the corresponding Vlasov-Maxwell equations expressed in guiding-center coordinates are derived including a local energy theorem. The second order terms describe lowest order finite Larmor radius effects. This set of equations might be relevant for edge plasmas due to the capability of capturing strong E x B flows and lowest order finite Larmor radius effects self-consistently. Next, an extension of the existing gyrokinetic formalism with strong flows is presented. In this work the background electric fields is dynamical, whereas earlier contributions did only incorporate a stationary electric field. In an ordering relevant for edge plasma turbulence, fully electromagnetic second order gyrokinetic coordinates and the corresponding gyrokinetic Vlasov-Maxwell equations are derived, including a local energy theorem. By taking the polarization and magnetization densities in the drift kinetic limit, we present the gyrokinetic Vlasov-Maxwell equations in a more tractable form, which could be relevant for direct numerical simulations of edge plasma turbulence. Finally, an investigation of the influence of finite Larmor

On the Stability of Pick-up Ion Ring Distributions in the Outer Heliosheath

Science.gov (United States)

Summerlin, Errol J.; Viñas, Adolfo F.; Moore, Thomas E.; Christian, Eric R.; Cooper, John F.

2014-10-01

The "secondary energetic neutral atom (ENA)" hypothesis for the ribbon feature observed by the Interstellar Boundary Explorer (IBEX) posits that the neutral component of the solar wind continues beyond the heliopause and charge exchanges with interstellar ions in the Outer Heliosheath (OHS). This creates pick-up ions that gyrate about the draped interstellar magnetic field (ISMF) lines at pitch angles near 90° on the locus where the ISMF lies tangential to the heliopause and perpendicular to the heliocentric radial direction. This location closely coincides with the location of the ribbon feature according to the prevailing inferences of the ISMF orientation and draping. The locally gyrating ions undergo additional charge exchange and escape as free-flying neutral atoms, many of which travel back toward the inner solar system and are imaged by IBEX as a ribbon tracing out the locus described above. For this mechanism to succeed, the pick-up ions must diffuse in pitch angle slowly enough to permit secondary charge exchange before their pitch angle distribution substantially broadens away from 90°. Previous work using linear Vlasov dispersion analysis of parallel propagating waves has suggested that the ring distribution in the OHS is highly unstable, which, if true, would make the secondary ENA hypothesis incapable of rendering the observed ribbon. In this paper, we extend this earlier work to more realistic ring distribution functions. We find that, at the low densities necessary to produce the observed IBEX ribbon via the secondary ENA hypothesis, growth rates are highly sensitive to the temperature of the beam and that even very modest temperatures of the ring beam corresponding to beam widths of distributions necessary to produce the observed IBEX ENA flux via the secondary ENA hypothesis will be unstable to their own self-generated turbulence.

An analytic method for agent-based modeling of spatially inhomogeneous disease dynamics

NARCIS (Netherlands)

Bock, W.; Fattler, T.; Rodiah, I.; Tse, O.T.C.; Villagonzalo, C.D.; Esguerra, J.P.H.; Soriano, M.N.; Bornales, J.B.; Carpio-Bernido, M.V.; Bernido, C.C.

2017-01-01

In this article we set up a microscopic model for the spread of an infectious disease based on configuration space analysis. Using the so-called Vlasov scaling we obtained the corresponding mesoscopic (kinetic) equations, describing the density of susceptible and infected individuals (particles) in

Collective excitations of harmonically trapped ideal gases

NARCIS (Netherlands)

Van Schaeybroeck, B.; Lazarides, A.

2009-01-01

We theoretically study the collective excitations of an ideal gas confined in an isotropic harmonic trap. We give an exact solution to the Boltzmann-Vlasov equation; as expected for a single-component system, the associated mode frequencies are integer multiples of the trapping frequency. We show

Pramana – Journal of Physics | Indian Academy of Sciences

Indian Academy of Sciences (India)

We derive relativistic fluid set of equations for neutrinos and electrons from relativistic Vlasov equations with Fermi weak interaction force. Using these fluid equations, we obtain a dispersion relation describing neutrino beam plasma instability, which is little different from normal dispersion relation of streaming instability.

Ultra-low-frequency electrostatic modes in a magnetized dusty plasma

International Nuclear Information System (INIS)

Salimullah, M.; Amin, M.R.; Roy Chowdhury, A.R.; Salahuddin, M.

1997-11-01

A study on the extremely low-frequency possible electrostatic modes in a finite temperature magnetized dusty plasma taking the charged dust grains as the third component has been carried out using the appropriate Vlasov-kinetic theory for the dynamics of the electrons, ions and the dust particles. It is found that the inequalities of charge and number density of plasma species, and the finite-Larmor-radius thermal kinetic effects of the mobile charged dust grains, introduce the existence of very low-frequency electrostatic eigenmodes in the three-component homogeneous magnetized dusty plasma. The relevance of the present investigation to space and astrophysical situations as well as laboratory experiments for dust Coulomb crystallization has been pointed out. (author)

Uncertainty quantification for mean field games in social interactions

KAUST Repository

Dia, Ben Mansour

2016-01-09

We present an overview of mean field games formulation. A comparative analysis of the optimality for a stochastic McKean-Vlasov process with time-dependent probability is presented. Then we examine mean-field games for social interactions and we show that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize couple (marriage). However , if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. Finally we introduce the Wiener chaos expansion for the construction of solution of stochastic differential equations of Mckean-Vlasov type. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and allow to quantify the uncertainty in the optimality system.

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

Nonlinear Delta-f Particle Simulations of Collective Effects in High-Intensity Bunched Beams

CERN Document Server

Qin, Hong; Hudson, Stuart R; Startsev, Edward

2005-01-01

The collective effects in high-intensity 3D bunched beams are described self-consistently by the nonlinear Vlasov-Maxwell equations.* The nonlinear delta-f method,** a particle simulation method for solving the nonlinear Vlasov-Maxwell equations, is being used to study the collective effects in high-intensity 3D bunched beams. The delta-f method, as a nonlinear perturbative scheme, splits the distribution function into equilibrium and perturbed parts. The perturbed distribution function is represented as a weighted summation over discrete particles, where the particle orbits are advanced by equations of motion in the focusing field and self-consistent fields, and the particle weights are advanced by the coupling between the perturbed fields and the zero-order distribution function. The nonlinear delta-f method exhibits minimal noise and accuracy problems in comparison with standard particle-in-cell simulations. A self-consistent 3D kinetic equilibrium is first established for high intensity bunched beams. The...

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

Uncertainty quantification for mean field games in social interactions

KAUST Repository

Dia, Ben Mansour

2016-01-01

We present an overview of mean field games formulation. A comparative analysis of the optimality for a stochastic McKean-Vlasov process with time-dependent probability is presented. Then we examine mean-field games for social interactions and we show that optimizing the long-term well-being through effort and social feeling state distribution (mean-field) will help to stabilize couple (marriage). However , if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. Finally we introduce the Wiener chaos expansion for the construction of solution of stochastic differential equations of Mckean-Vlasov type. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and allow to quantify the uncertainty in the optimality system.

Identification of low-frequency kinetic wave modes in the Earth's ion foreshock

Directory of Open Access Journals (Sweden)

X. Blanco-Cano

Full Text Available In this work we use ion and magnetic field data from the AMPTE-UKS mission to study the characteristics of low frequency (ω_r « Ω_p waves observed upstream of the Earth's bow shock. We test the application of various plasma-field correlations and magnetic ratios derived from linear Vlasov theory to identify the modes in this region. We evaluate (for a parameter space consistent with the ion foreshock the Alfvén ratio, the parallel compressibility, the cross-helicity, the noncoplanar ratio, the magnetic compression and the polarization for the two kinetic instabilities that can be generated in the foreshock by the interaction of hot diffuse ions with the solar wind: the left-hand resonant and the right-hand resonant ion beam instabilities. Comparison of these quantities with the observed plasma-field correlations and various magnetic properties of the waves observed during 10 intervals on 30 October 1984, where the waves are associated with diffuse ions, allows us to identify regions with Alfvénic waves and regions where the predominant mode is the right-hand resonant instability. In all the cases the waves are transverse, propagating at angles ≤ 33° and are elliptically polarized. Our results suggest that while the observed Alfvén waves are generated locally by hot diffuse ions, the right-handed waves may result from the superposition of waves generated by two different types of beam distribution (i.e. cold beam and diffuse ions. Even when there was good agreement between the values of observed transport ratios and the values given by the theory, some discrepancies were found. This shows that the observed waves are different from the theoretical modes and that mode identification based only on polarization quantities does not give a complete picture of the waves' characteristics and can lead to mode identification of waves whose polarization may agree with theoretical predictions even when

Selective chelation-supercritical fluid extraction of metal ions from waste materials

International Nuclear Information System (INIS)

Wai, C.N.; Laintz, K.E.; Yonker, C.R.

1993-01-01

The removal of toxic organics, metals, and radioisotopes from solids or liquids is a major concern in the treatment of industrial and nuclear wastes. For this reason, developing methods for selective separation of toxic metals and radioactive materials from solutions of complex matrix is an important problem in environmental research. Recent developments indicate supercritical fluids are good solvents for organic compounds. Many gases become supercritical fluids under moderate temperatures and pressures. For example, the critical temperature and pressure of carbon dioxide are 31 degrees C and 73 atm, respectively. The high diffusivity, low viscosity, and T-P dependence of solvent strength are some attractive properties of supercritical fluid extraction (SFE). Since CO 2 offers the additional benefits of stability and non-toxicity, the SFE technique avoids generation of organic liquid waste and exposure of personnel to toxic solvents. While direct extraction of metal ions by supercritical fluids is highly inefficient, these ions when complexed with organic ligands become quite soluble in supercritical fluids. Specific ligands can be used to achieve selective extraction of metal ions in this process. After SFE, the fluid phase can be depressurized for precipitation of the metal chelates and recycled. The ligand can also be regenerated for repeated use. The success of this selective chelation-supercritical fluid extraction (SC-SFE) process depends on a number of factors including the efficiencies of the selective chelating agents, solubilities of metal chelates in supercritical fluids, rate of extraction, ease of regeneration of the ligands, etc. In this report, the authors present recent results on the studies of the solubilities of metal chelates in supercritical CO 2 , experimental ions from aqueous solution, and the development of selective chelating agents (ionizable crown ethers) for the extraction of lanthanides and actinides

Nuclear de-excitation processes following medium energy heavy ion collisions

International Nuclear Information System (INIS)

Blann, M.

1986-09-01

As heavy ion reaction studies have progressed from beam energies below 10 MeV/nucleon to higher energies, many non-equilibrium reaction phenomena have been observed. Among these are nucleon emission with velocities in excess of the beam velocity, incomplete momentum transfer to evaporation residue and fission-like fragments, γ-rays with energies in excess of 100 MeV, and π 0 production when beam energies are below the threshold for production by the nucleon-nucleon collision mechanism. Additionally, prefission neutrons have been observed in excess of numbers expected from equilibrium models. A few of the approaches which have been applied to these phenomena are as follows: Intranuclear cascade: two body collisions are assumed to mediate the equilibration. The geometry and momentum space is followed semiclassically. The approach has many successes though it may suffer in a few applications is not following holes; TDHF considers one body processes only; in the energy regime of interest, two body processes are important so that this may not be a viable approach; Boltzmann-Uehling-Uhlenbeck or Vlasov-Uehling-Uhlenbeck (BUU/VUU) equations combine both one body and two body dynamics. The spatial and momentum evolution of the reactions are followed in a mean field. These should be the Cadillacs of the models. They are computationally tedious, and sometimes significant approximations are made in order to achieve computational tract ability; models of collective deceleration. A very simple model approach is discussed to interpret these phenomena, the Boltzmann master equation (BME). The hybrid model was the first to be applied to the question of heavy ion precompound decay, and the BME second. 26 refs., 5 figs., 2 tabs

Radiation phenomena of plasma waves, 1

International Nuclear Information System (INIS)

Ohnuma, Toshiro.

1978-06-01

The fundamental radiation theories on radiation phenomena of plasma waves are presented. As the fundamental concepts of propagating waves, phase, group and ray velocities are explained, and phase velocity surface, group velocity surface, ray velocity surface and refractive index surface are considered. These concepts are important in anisotropic plasma. Fundamental equations for electron plasma waves in a fluid model and fundamental equations for ion plasma waves can be expressed with the above mentioned concepts. Kuehl derived the formulas for general radiation fields of electromagnetic and electrostatic waves which are radiated from an arbitrary current source. Fundamental equations for kinetic model are the Vlasov equation and Maxwell equations. By investigating electromagnetic radiation in cold anisotropic plasma, Kuehl found the important behavior that the fields radiated from a source become very large in certain directions for some ranges of plasma parameters. The fact is the so-called high frequency resonance cone. A fundamental formula for quasi-static radiation from an oscillating point source in warm anisotropic plasma includes the near field of electromagnetic mode and the field of electrostatic mode, which are radiated from the source. This paper presents the formula in a generalized form. (Kato, T.)

Generalized reduced fluid model with finite ion-gyroradius effects

International Nuclear Information System (INIS)

Hsu, C.T.; Hazeltine, R.D.; Morrison, P.J.

1985-04-01

Reduced fluid models have become important tools for studying the nonlinear dynamics of plasma in a large aspect-ratio tokamak. A self-consistent nonlinear reduced fluid model, with finite ion-gyroradius effects is presented. The model is distinctive in allowing for arbitrary beta and in satisfying an exact, relatively simple energy conservation law

Generation of fast electrons in the external corona of laser plasma by the Raman scattering

Czech Academy of Sciences Publication Activity Database

Mašek, Martin; Rohlena, Karel

2008-01-01

Roč. 163, 4-6 (2008), 551-558 ISSN 1042-0150 R&D Projects: GA ČR GA202/05/2475 Institutional research plan: CEZ:AV0Z10100523 Keywords : Vlasov equation * stimulated Raman scattering * Raman cascade Subject RIV: BH - Optics, Masers, Lasers Impact factor: 0.415, year: 2008

Effects of the mean-field dynamics and the phase-space geometry on the cluster formation

International Nuclear Information System (INIS)

Basrak, Z.; Eudes, P.; Abgrall, P.; Haddad, F.; Sebille, F.

1997-01-01

A model allowing to simulate the production of clusters is developed and applied to heavy-ion reactions at intermediate energies. The model investigates the geometrical properties of the dynamically generated one-body phase space. The collision process is entirely governed by the Landau-Vlasov model, which provides the time evolution of the one-body phase-space distribution. Particles emitted during successive time intervals of the dynamics are gathered together into subensembles to which a clusterization procedure is applied. Comparison with the experimental data for the Ar(65 MeV/nucleon) + Al reaction shows that the average behaviour of particle-dependent global observables is correctly reproduced within this framework. These results point out that the studied global properties of heavy-ion collisions greatly rely on the dynamical effects of the primary non-steady stage of the nuclear reaction. (orig.)

Measurement of the electron beam mode in earth's foreshock

Science.gov (United States)

Onsager, T. G.; Holzworth, R. H.

1990-01-01

High frequency electric field measurements from the AMPTE IRM plasma wave receiver are used to identify three simultaneously excited electrostatic wave modes in the earth's foreshock region: the electron beam mode, the Langmuir mode, and the ion acoustic mode. A technique is developed which allows the rest frame frequecy and wave number of the electron beam waves to be determined. It is shown that the experimentally determined rest frame frequency and wave number agree well with the most unstable frequency and wave number predicted by linear homogeneous Vlasov theory for a plasma with Maxwellian background electrons and a Lorentzian electron beam. From a comparison of the experimentally determined and theoretical values, approximate limits are put on the electron foreshock beam temperatures. A possible generation mechanism for ion acoustic waves involving mode coupling between the electron beam and Langmuir modes is also discussed.

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

Integration of Extended MHD and Kinetic Effects in Global Magnetosphere Models

Science.gov (United States)

Germaschewski, K.; Wang, L.; Maynard, K. R. M.; Raeder, J.; Bhattacharjee, A.

2015-12-01

Computational models of Earth's geospace environment are an important tool to investigate the science of the coupled solar-wind -- magnetosphere -- ionosphere system, complementing satellite and ground observations with a global perspective. They are also crucial in understanding and predicting space weather, in particular under extreme conditions. Traditionally, global models have employed the one-fluid MHD approximation, which captures large-scale dynamics quite well. However, in Earth's nearly collisionless plasma environment it breaks down on small scales, where ion and electron dynamics and kinetic effects become important, and greatly change the reconnection dynamics. A number of approaches have recently been taken to advance global modeling, e.g., including multiple ion species, adding Hall physics in a Generalized Ohm's Law, embedding local PIC simulations into a larger fluid domain and also some work on simulating the entire system with hybrid or fully kinetic models, the latter however being to computationally expensive to be run at realistic parameters. We will present an alternate approach, ie., a multi-fluid moment model that is derived rigorously from the Vlasov-Maxwell system. The advantage is that the computational cost remains managable, as we are still solving fluid equations. While the evolution equation for each moment is exact, it depends on the next higher-order moment, so that truncating the hiearchy and closing the system to capture the essential kinetic physics is crucial. We implement 5-moment (density, momentum, scalar pressure) and 10-moment (includes pressure tensor) versions of the model, and use local approximations for the heat flux to close the system. We test these closures by local simulations where we can compare directly to PIC / hybrid codes, and employ them in global simulations using the next-generation OpenGGCM to contrast them to MHD / Hall-MHD results and compare with observations.

Dissipation of Alfven Waves at Fluid Scale through Parametric Decay Instabilities in Low-beta Turbulent Plasma

Science.gov (United States)

Fu, X.; Li, H.; Guo, F.; Li, X.; Roytershteyn, V.

2017-12-01

The solar wind is a turbulent magnetized plasma extending from the upper atmosphere of the sun to the edge of the heliosphere. It carries charged particles and magnetic fields originated from the Sun, which have great impact on the geomagnetic environment and human activities in space. In such a magnetized plasma, Alfven waves play a crucial role in carrying energy from the surface of the Sun, injecting into the solar wind and establishing power-law spectra through turbulent energy cascades. On the other hand, in compressible plasmas large amplitude Alfven waves are subject to a parametric decay instability (PDI) which converts an Alfven wave to another counter-propagating Alfven wave and an ion acoustic wave (slow mode). The counter-propagating Alfven wave provides an important ingredient for turbulent cascade, and the slow-mode wave provides a channel for solar wind heating in a spatial scale much larger than ion kinetic scales. Growth and saturation of PDI in quiet plasma have been intensively studied using linear theory and nonlinear simulations in the past. Here using 3D hybrid simulations, we show that PDI is still effective in turbulent low-beta plasmas, generating slow modes and causing ion heating. Selected events in WIND data are analyzed to identify slow modes in the solar wind and the role of PDI, and compared with our simulation results. We also investigate the validity of linear Vlasov theory regarding PDI growth and slow mode damping in turbulent plasmas. Since PDI favors low plasma beta, we expect to see more evidence of PDI in the solar wind close to the Sun, especially from the upcoming NASA's Parker Solar Probe mission which will provide unprecedented wave and plasma data as close as 8.5 solar radii from the Sun.

Simplified Model of Nonlinear Landau Damping

International Nuclear Information System (INIS)

Yampolsky, N.A.; Fisch, N.J.

2009-01-01

The nonlinear interaction of a plasma wave with resonant electrons results in a plateau in the electron distribution function close to the phase velocity of the plasma wave. As a result, Landau damping of the plasma wave vanishes and the resonant frequency of the plasma wave downshifts. However, this simple picture is invalid when the external driving force changes the plasma wave fast enough so that the plateau cannot be fully developed. A new model to describe amplification of the plasma wave including the saturation of Landau damping and the nonlinear frequency shift is proposed. The proposed model takes into account the change of the plasma wave amplitude and describes saturation of the Landau damping rate in terms of a single fluid equation, which simplifies the description of the inherently kinetic nature of Landau damping. A proposed fluid model, incorporating these simplifications, is verified numerically using a kinetic Vlasov code.

Determination of metal ions released by stainless steel arch bar into bio-fluids

Directory of Open Access Journals (Sweden)

Lori A. Joseph

2009-04-01

Full Text Available The amounts of cobalt, iron, manganese, nickel and chromium ions released from new and reused stainless steel arch bar used for maxillomandibular fixation was determined in Hank’s solutions of different hydrogen and chloride ions concentrations, whole blood serum and phosphate buffered saline (PBS in vitro, over a six-week immersion time at 37 oC, by atomic absorption spectrophotometry. The corrosion levels of the wires due to effects of media and incubation times in the bio-fluids were compared by Duncan’s two-way ANOVA (P less than 0.05. Pearson’s correlation was used in establishing relationship in the amounts of metal ions released by new and reused arch bars. The study indicated that the reused wires released more ions than new ones at all time points. The variation of pH and chloride ions of the bio-fluids had a significant effect on the amount of Ni, Mn and Cr ions released. Ageing prior use of arch bars significantly increased Ni ions released into the bio-fluids.

Bernstein modes in a non-neutral plasma column

Science.gov (United States)

Walsh, Daniel; Dubin, Daniel H. E.

2018-05-01

This paper presents theory and numerical calculations of electrostatic Bernstein modes in an inhomogeneous cylindrical plasma column. These modes rely on finite Larmor radius effects to propagate radially across the column until they are reflected when their frequency matches the upper hybrid frequency. This reflection sets up an internal normal mode on the column and also mode-couples to the electrostatic surface cyclotron wave (which allows the normal mode to be excited and observed using external electrodes). Numerical results predicting the mode spectra, using a novel linear Vlasov code on a cylindrical grid, are presented and compared to an analytical Wentzel Kramers Brillouin (WKB) theory. A previous version of the theory [D. H. E. Dubin, Phys. Plasmas 20(4), 042120 (2013)] expanded the plasma response in powers of 1/B, approximating the local upper hybrid frequency, and consequently, its frequency predictions are spuriously shifted with respect to the numerical results presented here. A new version of the WKB theory avoids this approximation using the exact cold fluid plasma response and does a better job of reproducing the numerical frequency spectrum. The effect of multiple ion species on the mode spectrum is also considered, to make contact with experiments that observe cyclotron modes in a multi-species pure ion plasma [M. Affolter et al., Phys. Plasmas 22(5), 055701 (2015)].

Laser Radiation Pressure Acceleration of Monoenergetic Protons in an Ultra-Thin Foil

Science.gov (United States)

Eliasson, Bengt; Liu, Chuan S.; Shao, Xi; Sagdeev, Roald Z.; Shukla, Padma K.

2009-11-01

We present theoretical and numerical studies of the acceleration of monoenergetic protons in a double layer formed by the laser irradiation of an ultra-thin film. The stability of the foil is investigated by direct Vlasov-Maxwell simulations for different sets of laser-plasma parameters. It is found that the foil is stable, due to the trapping of both electrons and ions in the thin laser-plasma interaction region, where the electrons are trapped in a potential well composed of the ponderomo-tive potential of the laser light and the electrostatic potential due to the ions, and the ions are trapped in a potential well composed of the inertial potential in an accelerated frame and the electrostatic potential due to the electrons. The result is a stable double layer, where the trapped ions are accelerated to monoenergetic energies up to 100 MeV and beyond, which makes them suitable for medical applications cancer treatment. The underlying physics of trapped and untapped ions in a double layer is also investigated theoretically and numerically.

Lie-transformed action principle for classical plasma dynamics

International Nuclear Information System (INIS)

Kaufman, A.N.

1984-06-01

The Lie transform for a single particle in a wave is embedded in a Lagrangian action principle for self-consistent plasma dynamics. Variation of the action then yields the Vlasov equation for the oscillation-center distribution, the ray equations and amplitude transport for the wave, and the Poisson equation for the quasistatic field

Implications of Navier-Stokes turbulence theory for plasma turbulence

International Nuclear Information System (INIS)

Montgomery, David

1977-01-01

A brief discussion of Navier-Stokes turbulence theory is given with particular reference to the two dimensional case. The MHD turbulence is introduced with possible applications of techniques developed in Navier-Stokes theory. Turbulence in Vlasov plasma is also discussed from the point of view of the ''direct interaction approximation'' (DIA). (A.K.)

Excitation of waves at 2 omega_pe and back propagating waves at omega_pe: a parametric study

Czech Academy of Sciences Publication Activity Database

Trávníček, Pavel; Hellinger, Petr; Schiver, D.; Taylor, M. G. G. T.

2003-01-01

Roč. 10, - (2003), s. 345-349 ISSN 1023-5809 R&D Projects: GA AV ČR IAB3042106 Grant - others:ESA PRODEX(NL) 14529/00/NL/SFe Institutional research plan: CEZ:AV0Z3042911 Keywords : plasma * foreshock * Vlasov simulations Subject RIV: DG - Athmosphere Sciences, Meteorology Impact factor: 0.682, year: 2003

Centroid and Envelope Eynamics of Charged Particle Beams in an Oscillating Wobbler and External Focusing Lattice for Heavy Ion Fusion Applications

International Nuclear Information System (INIS)

Davidson, Ronald C.; Logan, B. Grant

2011-01-01

Recent heavy ion fusion target studies show that it is possible to achieve ignition with direct drive and energy gain larger than 100 at 1MJ. To realize these advanced, high-gain schemes based on direct drive, it is necessary to develop a reliable beam smoothing technique to mitigate instabilities and facilitate uniform deposition on the target. The dynamics of the beam centroid can be explored as a possible beam smoothing technique to achieve a uniform illumination over a suitably chosen region of the target. The basic idea of this technique is to induce an oscillatory motion of the centroid for each transverse slice of the beam in such a way that the centroids of different slices strike different locations on the target. The centroid dynamics is controlled by a set of biased electrical plates called 'wobblers'. Using a model based on moments of the Vlasov-Maxwell equations, we show that the wobbler deflection force acts only on the centroid motion, and that the envelope dynamics are independent of the wobbler fields. If the conducting wall is far away from the beam, then the envelope dynamics and centroid dynamics are completely decoupled. This is a preferred situation for the beam wobbling technique, because the wobbler system can be designed to generate the desired centroid motion on the target without considering its effects on the envelope and emittance. A conceptual design of the wobbler system for a heavy ion fusion driver is briefly summarized.

Complex fluids with mobile charge-regulating macro-ions

Science.gov (United States)

Markovich, Tomer; Andelman, David; Podgornik, Rudi

2017-10-01

We generalize the concept of charge regulation of ionic solutions, and apply it to complex fluids with mobile macro-ions having internal non-electrostatic degrees of freedom. The suggested framework provides a convenient tool for investigating systems where mobile macro-ions can self-regulate their charge (e.g., proteins). We show that even within a simplified charge-regulation model, the charge dissociation equilibrium results in different and notable properties. Consequences of the charge regulation include a positional dependence of the effective charge of the macro-ions, a non-monotonic dependence of the effective Debye screening length on the concentration of the monovalent salt, a modification of the electric double-layer structure, and buffering by the macro-ions of the background electrolyte.

Behaviour of laser-produced plasma in a uniform magnetic field

International Nuclear Information System (INIS)

Okada, Shigefumi; Sato, Kohnosuke; Sekiguchi, Tadashi.

1979-11-01

A column of a laser-produced plasma is successfully made in a uniform magnetic field. The radius of the column increases and then decreases (bouncing motion). On the surface of this plasma column, where the steep density gradient exists with the scale length shorter than the ion Larmor radius, an azimuthal modulation appears in the plasma luminosity. This is indicative of the flute-like instability with the azimuthal wave number; k sub(perpendicular) -- 4 x 10 3 B sup(0.8) (in the MKSA system of units). The dispersion equation based on the linearized Vlasov equation with the local approximation is derived and the occurrence of the lower-hybrid-drift instability is predicted. A fairly good agreement between the theory and experiments is seen. (author)

Electromagnetic nonlinear gyrokinetics with polarization drift

International Nuclear Information System (INIS)

Duthoit, F.-X.; Hahm, T. S.; Wang, Lu

2014-01-01

A set of new nonlinear electromagnetic gyrokinetic Vlasov equation with polarization drift and gyrokinetic Maxwell equations is systematically derived by using the Lie-transform perturbation method in toroidal geometry. For the first time, we recover the drift-kinetic expression for parallel acceleration [R. M. Kulsrud, in Basic Plasma Physics, edited by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1983)] from the nonlinear gyrokinetic equations, thereby bridging a gap between the two formulations. This formalism should be useful in addressing nonlinear ion Compton scattering of intermediate-mode-number toroidal Alfvén eigenmodes for which the polarization current nonlinearity [T. S. Hahm and L. Chen, Phys. Rev. Lett. 74, 266 (1995)] and the usual finite Larmor radius effects should compete

Fluid aspects of electron streaming instability in electron-ion plasmas

International Nuclear Information System (INIS)

Jao, C.-S.; Hau, L.-N.

2014-01-01

Electrons streaming in a background electron and ion plasma may lead to the formation of electrostatic solitary wave (ESW) and hole structure which have been observed in various space plasma environments. Past studies on the formation of ESW are mostly based on the particle simulations due to the necessity of incorporating particle's trapping effects. In this study, the fluid aspects and thermodynamics of streaming instabilities in electron-ion plasmas including bi-streaming and bump-on-tail instabilities are addressed based on the comparison between fluid theory and the results from particle-in-cell simulations. The energy closure adopted in the fluid model is the polytropic law of d(pρ −γ )/dt=0 with γ being a free parameter. Two unstable modes are identified for the bump-on-tail instability and the growth rates as well as the dispersion relation of the streaming instabilities derived from the linear theory are found to be in good agreement with the particle simulations for both bi-streaming and bump-on-tail instabilities. At the nonlinear saturation, 70% of the electrons are trapped inside the potential well for the drift velocity being 20 times of the thermal velocity and the pρ −γ value is significantly increased. Effects of ion to electron mass ratio on the linear fluid theory and nonlinear simulations are also examined

Ion mobility spectrometry after supercritical fluid chromatography

International Nuclear Information System (INIS)

Morrissey, M.A.

1988-01-01

In this work, a Fourier transform ion mobility spectrometer (FT-IMS) was constructed and evaluated as a detector for supercritical fluid chromatography (SFC). The FT-IMS provides both quantitative and qualitative data of a wide range of compounds, selective and nonselective modes of chromatographic detection, and it is compatible with a wide range of SFC mobile phases. Drift spectra are presented for a number of samples, including polymers, lipids, herbicides, antibiotics, and pharmaceuticals. The unique properties of supercritical fluids made it possible to introduce these compounds into the spectrometer. While the drift spectra presented are generally simple, showing only a quasi-molecular ion, a few are surprising complex. Examples of selective and non-selective detection demonstrate the usefulness of the detector. Examples are presented for fish oil concentrate, bacon grease extract, soil extract, and polymer mixtures. In the case of Triton X-100, a non-ionic surfactant, the FT-IMS was able to selectively detect individual oligomers in the polymer mixture. In the case of a polydimethylsilicone mixture the detector isolated a contaminant in the mixture

The quantum HMF model: I. Fermions

International Nuclear Information System (INIS)

Chavanis, Pierre-Henri

2011-01-01

We study the thermodynamics of quantum particles with long-range interactions at T = 0. Specifically, we generalize the Hamiltonian mean-field (HMF) model to the case of fermions. We consider the Thomas–Fermi approximation that becomes exact in a proper thermodynamic limit N→+∞ with a coupling constant k ∼ N. The equilibrium configurations, described by the mean-field Fermi (or waterbag) distribution, are equivalent to polytropes of index n = 1/2. We show that the homogeneous phase, which is unstable in the classical regime, becomes stable in the quantum regime. The homogeneous phase is stabilized by the Pauli exclusion principle. This takes place through a first-order phase transition where the control parameter is the normalized Planck constant. The homogeneous phase is unstable for ℎ c ≡2/√(π), metastable for ℎ c t ≡1.16 and stable for ℎ>ℎ t . The inhomogeneous phase is stable for ℎ t , metastable for ℎ t * ≡1.18 and disappears for ℎ>ℎ * (for ℎ c * , there exists an unstable inhomogeneous phase with magnetization 0 * ≡ 0.37). We point out analogies between the fermionic HMF model and the concept of fermion stars in astrophysics. Finally, as a by-product of our analysis, we obtain new results concerning the Vlasov dynamical stability of the waterbag distribution which is the ground state of the Lynden-Bell distribution in the theory of violent relaxation of the classical HMF model. We show that spatially homogeneous waterbag distributions are Vlasov-stable iff ε ≥ ε c = 1/3 and spatially inhomogeneous waterbag distributions are Vlasov-stable iff ε ≤ ε * = 0.379 and b ≥ b * = 0.37, where ε and b are the normalized energy and magnetization. The magnetization curve displays a first-order phase transition at ε t = 0.352 and the domain of metastability ranges from ε c to ε *

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

Finite-Length Diocotron Modes in a Non-neutral Plasma Column

Science.gov (United States)

Walsh, Daniel; Dubin, Daniel

2017-10-01

Diocotron modes are 2D distortions of a non-neutral plasma column that propagate azimuthally via E × B drifts. While the infinite-length theory of diocotron modes is well-understood for arbitrary azimuthal mode number l, the finite-length mode frequency is less developed (with some exceptions), and is naturally of relevance to experiments. In this poster, we present an approach to address finite length effects, such as temperature dependence of the mode frequency. We use a bounce-averaged solution to the Vlasov Equation, in which the Vlasov Equation is solved using action-angle variables of the unperturbed Hamiltonian. We write the distribution function as a Fourier series in the bounce-angle variable ψ, keeping only the bounce-averaged term. We demonstrate a numerical solution to this equation for a realistic plasma with a finite Debye Length, compare to the existing l = 1 theory, and discuss possible extensions of the existing theory to l ≠ 1 . Supported by NSF/DOE Partnership Grants PHY1414570 and DESC0002451.

Quasilinear theory and simulation of Buneman instability

International Nuclear Information System (INIS)

Pavan, J.; Yoon, P. H.; Umeda, T.

2011-01-01

In a recently developed nonlinear theory of Buneman instability, a simplifying assumption of self-similarity was imposed for the electron distribution function, based upon which, a set of moment kinetic equations was derived and solved together with nonlinear wave kinetic equation [P. H. Yoon and T. Umeda, Phys. Plasmas 17, 112317 (2010)]. It was found that the theoretical result compared reasonably against one-dimensional electrostatic Vlasov simulation. In spite of this success, however, the simulated distribution deviated appreciably from the assumed self-similar form during the late stages of nonlinear evolution. In order to rectify this shortcoming, in this paper, the distribution function is computed on the basis of rigorous velocity space diffusion equation. A novel theoretical scheme is developed so that both the quasilinear particle diffusion equation and the adiabatic dispersion relation can be solved for an arbitrary particle distribution function. Comparison with Vlasov simulation over relatively early quasilinear phase of the instability shows a reasonable agreement, despite the fact that quasilinear theory lacks coherent nonlinear effects as well as mode-mode coupling effects.

Microbunching instability in a chicane: Two-dimensional mean field treatment

Directory of Open Access Journals (Sweden)

Gabriele Bassi

2009-08-01

Full Text Available We study the microbunching instability in a bunch compressor by a parallel code with some improved numerical algorithms. The two-dimensional charge/current distribution is represented by a Fourier series, with coefficients determined through Monte Carlo sampling over an ensemble of tracked points. This gives a globally smooth distribution with low noise. The field equations are solved accurately in the lab frame using retarded potentials and a novel choice of integration variables that eliminates singularities. We apply the scheme with parameters for the first bunch compressor system of FERMI@Elettra, with emphasis on the amplification of a perturbation at a particular wavelength and the associated longitudinal bunch spectrum. Gain curves are in rough agreement with those of the linearized Vlasov system at intermediate wavelengths, but show some deviation at the smallest wavelengths treated and show the breakdown of a coasting beam assumption at long wavelengths. The linearized Vlasov system is discussed in some detail. A new 2D integral equation is derived which reduces to a well-known 1D integral equation in the coasting beam case.

Threshold Studies of the Microwave Instability in Electron Storage Rings

International Nuclear Information System (INIS)

Bane, Karl

2010-01-01

We use a Vlasov-Fokker-Planck program and a linearized Vlasov solver to study the microwave instability threshold of impedance models: (1) a Q = 1 resonator and (2) shielded coherent synchrotron radiation (CSR), and find the results of the two programs agree well. For shielded CSR we show that only two dimensionless parameters, the shielding parameter Π and the strength parameter S csr , are needed to describe the system. We further show that there is a strong instability associated with CSR, and that the threshold, to good approximation, is given by (S csr )th = 0.5 + 0.12Π. In particular, this means that shielding has little effect in stabilizing the beam for Π ∼ -3/2 . We, in addition, find another instability in the vicinity of Π = 0.7 with a lower threshold, (S csr ) th ∼ 0.2. We find that the threshold to this instability depends strongly on damping time, (S csr ) th ∼ τ p -1/2 , and that the tune spread at threshold is small - both hallmarks of a weak instability.

Further development of the fast beam dynamics simulation tool V-code

Energy Technology Data Exchange (ETDEWEB)

Franke, Sylvain; Ackermann, Wolfgang; Weiland, Thomas [Institut fuer Theorie Elektromagnetischer Felder, TU Darmstadt (Germany)

2010-07-01

The Vlasov equation describes the evolution of a particle density under the effects of electromagnetic fields. It is derived from the fact that the volume occupied by a given number of particles in the six-dimensional phase space remains constant when only long-range interaction as for example Coulomb forces are relevant and other particle collisions can be neglected. Because this is the case for typical charged particle beams in accelerators, the Vlasov equation can be used to describe their evolution within the whole beam line. This equation is a partial differential equation in 6D and thus it is very expensive to solve it via classical numerical methods. A more efficient approach consists in representing the particle distribution function by a discrete set of characteristic moments. For each moment a time evolution equation can be stated. These ordinary differential equations can then be evaluated efficiently by means of time integration methods if all considered forces and a proper initial condition are known. The beam dynamics simulation tool V-Code implemented at TEMF utilizes this approach.

Introduction to fluid model for RHIC heavy ion collisions

International Nuclear Information System (INIS)

Muraya, Shin

2007-01-01

An introductory review of the fluid model which has been looked upon as the promising phenomenological model for the heavy ion scattering experiments at RHIC is presented here. Subjects are especially focused on the fundamental assumptions of the model and the decision process of the phenomenological parameters considering newcomers to hadron physics. Introduction of thermodynamical quantities, 1+1 dimension model, time-space evolution of fluid, correspondence of fluid to particles, initial condition, boundary condition and comparison of the equation of state of fluid model and that of hadron model are described. Limitation of fluid picture and the validity of the model are discussed finally. It is summarized that the present fluid model does not predict much about results in advance but gives interpretation after the event, nevertheless it reproduces much of the experimental results in natural form. It is expected that the parameter of the fluid model is to be used as the intermediate theory to relate experimental results with theory. (S. Funahashi)

Plasma physics and instabilities

International Nuclear Information System (INIS)

Lashmore-Davies, C.N.

1981-01-01

These lectures procide an introduction to the theory of plasmas and their instabilities. Starting from the Bogoliubov, Born, Green, Kirkwood, and Yvon (BBGKY) hierarchy of kinetic equations, the additional concept of self-consistent fields leads to the fundamental Vlasov equation and hence to the warm two-fluid model and the one-fluid MHD, or cold, model. The properties of small-amplitude waves in magnetized (and unmagnetized) plasmas, and the instabilities to which they give rise, are described in some detail, and a complete chapter is devoted to Landau damping. The linear theory of plasma instabilities is illustrated by the current-driven electrostatic kind, with descriptions of the Penrose criterion and the energy principle of ideal MHD. There is a brief account of the application of feedback control. The non-linear theory is represented by three examples: quasi-linear velocity-space instabilities, three-wave instabilities, and the stability of an arbitrarily largeamplitude wave in a plasma. (orig.)

Faraday rotation, stochastic magnetic fields and CMB maps

CERN Document Server

Giovannini, Massimo

2008-01-01

The high- and low-frequency descriptions of the pre-decoupling plasma are deduced from the Vlasov-Landau treatment generalized to curved space-times and in the presence of the relativistic fluctuations of the geometry. It is demonstrated that the interplay between one-fluid and two-fluid treatments is mandatory for a complete and reliable calculation of the polarization observables. The Einstein-Boltzmann hierarchy is generalized to handle the dispersive propagation of the electromagnetic disturbances in the pre-decoupling plasma. Given the improved physical and numerical framework, the polarization observables are computed within the magnetized $\\Lambda$CDM paradigm (m$\\Lambda$CDM). In particular, the Faraday-induced B-mode is consistently estimated by taking into account the effects of the magnetic fields on the initial conditions of the Boltzmann hierarchy, on the dynamical equations and on the dispersion relations. The complete calculations of the angular power spectra constitutes the first step for the d...

A diagrammatic approach to the theory of clumps in turbulent plasmas

International Nuclear Information System (INIS)

Balescu, R.; Misguich, J.H.

1983-05-01

It is shown that much insight is gained by the use of a diagrammatic method in the analysis and classification of both the one-particle fluctuations and the two-particle correlations in a turbulence Vlasov plasma. The various types of renormalization are discussed. The kinetic equation for the average background distribution function is discussed in some detail

Microwave stability at transition

International Nuclear Information System (INIS)

Holt, J.A.; Colestock, P.L.

1995-05-01

The question of microwave stability at transition is revisited using a Vlasov approach retaining higher order terms in the particle dynamics near the transition energy. A dispersion relation is derived which can be solved numerically for the complex frequency in terms of the longitudinal impedance and other beam parameters. Stability near transition is examined and compared with simulation results

Dynamics of Pierce instability of hot electron beams

International Nuclear Information System (INIS)

Ignatov, A.M.; Novikov, V.N.

1986-01-01

On the base of a new method of numerical solution of the Vlasov equation evolution of complete function of electron distribution at the injection of hot electron beams into plasma bounded with electrodes is investigated. It is shown that despite the development of electrostatic instabilities in the system the currents can run substantially exceeding the Pierce critical current

Kinetic theory in maximal-acceleration invariant phase space

International Nuclear Information System (INIS)

Brandt, H.E.

1989-01-01

A vanishing directional derivative of a scalar field along particle trajectories in maximal acceleration invariant phase space is identical in form to the ordinary covariant Vlasov equation in curved spacetime in the presence of both gravitational and nongravitational forces. A natural foundation is thereby provided for a covariant kinetic theory of particles in maximal-acceleration invariant phase space. (orig.)

Dynamical aspects of violent collisions in Ar + Ag reactions at E/A = 27 MeV

International Nuclear Information System (INIS)

Rivet, M.F.; Borderie, B.; Jouan, D.; Remaud, B.

1988-01-01

Intermediate-mass fragment studies were found to give an overview of the mechanisms involved in violent collisions between Ar and Ag at E/A = 27 MeV. A comparison is made with semi-classical calculations (Landau-Vlasov) which reproduce experimental observations well and sustain the persistence of dissipative processes at high incident relative velocity (∼ 0.2c)

Regularity and chaos in Vlasov evolution of nuclear matter

Energy Technology Data Exchange (ETDEWEB)

Jacquot, B.; Guarnera, A.; Chomaz, Ph.; Colonna, M.

1995-12-31

A careful analysis of the mean-field dynamics inside the spinodal instability region is performed. It is shown that, conversely to some recently published results the mean-field evolution appears mostly regular over a long time scale, while some disorder is observed only very late, when fragments are already formed This onset of chaos can be related to the fragment interaction which induces some coalescence effects. Moreover it is shown that the time scale over which the chaos start to develop are very sensitive to the range of the considered force. All the presented results support the various analyses of spinodal instabilities obtained using stochastic mean field approaches. (author). 16 refs. Submitted to Physical Review, C (US).

Nonlinear Alfvén Waves in a Vlasov Plasma

DEFF Research Database (Denmark)

Bell, T.F.

1965-01-01

Stationary solutions to the nonlinear Vlasov—Boltzmann equations are considered which represent one-dimensional electromagnetic waves in a hot magnetoplasma. These solutions appear in arbitrary reference frames as circularly polarized, sinusoidal waves of unlimited amplitude, i.e., as nonlinear...... Alfvén waves. Solutions are found implicitly by deriving a set of integral dispersion relations which link the wave characteristics with the particle distribution functions. A physical discussion is given of the way in which the Alfvén waves can trap particles, and it is shown that the presence...

Ionic magnetic fluids in polar solvents with tuned counter-ions

Energy Technology Data Exchange (ETDEWEB)

Lopes Filomeno, C. [Sorbonne Universités, UPMC Univ Paris 06, CNRS, Lab. PHENIX, Paris (France); Grupo de Fluidos Complexos Inst. de Quimica, Univ. de Brasília, Brasília (DF) (Brazil); Kouyaté, M. [Sorbonne Universités, UPMC Univ Paris 06, CNRS, Lab. PHENIX, Paris (France); Cousin, F. [Lab. Léon Brillouin – CE-Saclay, Gif-sur-Yvette (France); Demouchy, G. [Sorbonne Universités, UPMC Univ Paris 06, CNRS, Lab. PHENIX, Paris (France); Dpt de physique, Univ. de Cergy Pontoise, Cergy-Pontoise (France); Dubois, E.; Michot, L.; Mériguet, G. [Sorbonne Universités, UPMC Univ Paris 06, CNRS, Lab. PHENIX, Paris (France); Perzynski, R., E-mail: regine.perzynski@upmc.fr [Sorbonne Universités, UPMC Univ Paris 06, CNRS, Lab. PHENIX, Paris (France); Peyre, V.; Sirieix-Plénet, J. [Sorbonne Universités, UPMC Univ Paris 06, CNRS, Lab. PHENIX, Paris (France); Tourinho, F.A. [Grupo de Fluidos Complexos Inst. de Quimica, Univ. de Brasília, Brasília (DF) (Brazil)

2017-06-01

The aim of the present study is to propose a new reproducible method for preparing colloidal dispersions of electrostatically charged nanoparticles (NPs) in polar solvents with different kinds of counter-ions. Maghemite NPs are here dispersed in solvents of different dielectric constant, namely water, dimethylsulfoxide (DMSO) and an ionic liquid, ethylammonium nitrate (EAN). If the existence of a NP superficial charge happens to be necessary for the colloidal stability of the dispersions in these three solvents, the standard DLVO theory cannot be used any more to describe the colloidal stability in EAN. The structure of the dispersions and the strength of the interparticle repulsion are investigated by small angle X-ray scattering measurements, in association with Ludwig–Soret coefficient determinations. Specificities, associated to the nature of the counter-ions are identified in this work on the colloidal stability, on the interparticle repulsion and on the Ludwig–Soret coefficient. - Highlights: • A controlled synthesis of ionic magnetic fluids in three polar solvents is proposed. • Colloidal repulsion in the magnetic fluids depends on the counter-ion nature. • Soret coefficient of citrate-coated maghemite nanoparticles is probed in water-pH7. • Thermophilicity of nanoparticles depends on the nature of their counter-ions. • Nanoparticles dressed with same counter-ions have solvent-dependent thermoproperties.

Performance evaluation of citric ion-stabilized magnetic fluid heat pipe

Energy Technology Data Exchange (ETDEWEB)

Jeyadevan, B. [Graduate School of Environmental Studies, Department of Geoscience and Technology, Tohoku University, Aramaki, Aoba 01, Aoba-ku, Sendai 980-7589 (Japan)]. E-mail: jeya@mail.kankyo.tohoku.ac.jp; Koganezawa, H. [Graduate School of Environmental Studies, Department of Geoscience and Technology, Tohoku University, Aramaki, Aoba 01, Aoba-ku, Sendai 980-7589 (Japan); Nakatsuka, K. [Graduate School of Environmental Studies, Department of Geoscience and Technology, Tohoku University, Aramaki, Aoba 01, Aoba-ku, Sendai 980-7589 (Japan)

2005-03-15

The performance of heat pipe (HP) using citric ion-stabilized magnetic fluid (CMF) as working fluid (WF) was evaluated. The heat transferred was influenced by the application of magnetic field and was enhanced by a maximum of 30% compared to the field-free case. Furthermore, under the optimum magnetic field configuration, the heat transferred by CMF HP was 10% higher than that with water as WF.

Apar-T: code, validation, and physical interpretation of particle-in-cell results

Science.gov (United States)

Melzani, Mickaël; Winisdoerffer, Christophe; Walder, Rolf; Folini, Doris; Favre, Jean M.; Krastanov, Stefan; Messmer, Peter

2013-10-01

simulations. The other is that the level of electric field fluctuations scales as 1/ΛPIC ∝ p. We provide a corresponding exact expression, taking into account the finite superparticle size. We confirm both expectations with simulations. Fourth, we compare the Vlasov-Maxwell theory, often used for code benchmarking, to the PIC model. The former describes a phase-space fluid with Λ = + ∞ and no correlations, while the PIC plasma features a small Λ and a high level of correlations when compared to a real plasma. These differences have to be kept in mind when interpreting and validating PIC results against the Vlasov-Maxwell theory and when modeling real physical plasmas.

Feasibility of ion-pair/supercritical fluid extraction of an ionic compound--pseudoephedrine hydrochloride.

Science.gov (United States)

Eckard, P R; Taylor, L T

1997-02-01

The supercritical fluid extraction (SFE) of an ionic compound, pseudoephedrine hydrochloride, from a spiked-sand surface was successfully demonstrated. The effect of carbon dioxide density (CO2), supercritical fluid composition (pure vs. methanol modified), and the addition of a commonly used reversed-phase liquid chromatographic ion-pairing reagent, 1-heptanesulfonic acid, sodium salt, on extraction efficiency was examined. The extraction recoveries of pseudoephedrine hydrochloride with the addition of the ion-pairing reagent from a spiked-sand surface were shown to be statistically greater than the extraction recoveries without the ion-pairing reagent with both pure and methanol-modified carbon dioxide.

Dynamical effects in heavy ion collisions: neck emission in the Pb + Au system at 29 A.MeV

International Nuclear Information System (INIS)

Aboufirassi, M; Bizard, G.; Bougault, R.; Brou, R.; Buta, A.; Colin, J.; Cussol, D.; Durand, D.; Genoux-Lubain, A.; Horn, D.; Kerambrun, A.; Laville, J.L.; Le Brun, C.; Lecolley, J.F.; Lefebvres, F.; Lopez, O.; Louvel, M.; Meslin, C.; Metivier, V.; Nakagawa, T.; Peter, J.; Popescu, R.; Regimbart, R.; Steckmeyer, J.C.; Tamain, B.; Vient, E.; Wieloch, A.; Yuasa-Nakagawa, K.

1998-01-01

In the study of the Pb + Au system with the assembly NAUTILUS a special class of events were made evident. Three body complete events have allowed observing a dynamical behavior in the fragment emission. A plot of the correlation between the emission angle and the charges Z 1 and Z 2 of the two fragments associated to the event shows a contribution of an intermediate mass third fragment reflecting a dynamical emission subsequent to the interaction phase between the two partners of the deep inelastic scattering (a phenomenon featuring the neck emission). Such a process has been observed in the Kr + Au at 60 MeV/nucleon and Xe + Cu at 50 MeV/nucleon. The on-going analysis of the Xe + Sn at 50 MeV/nucleon reveals the existence of a similar mechanism. A complete kinematical analysis of this class of events has permitted making evident the impact parameter window, here implied; it is situated for the associated collisions to an reduced impact parameter around 0.8 b max , corresponding to an excitation energy for the bi-nucleus system of the order of 2 MeV/nucleon. This phenomenon may allow to constrain more strongly the models describing the dynamics of the heavy ion collisions, particularly the kinetic models of Landau-Vlasov type. Then, the different mean field potential prescriptions my be tested by comparison with the experimental data

Modelling of plasma generation and expansion in a vacuum arc: application to the vacuum arc remelting process

International Nuclear Information System (INIS)

Chapelle, P.; Bellot, J.P.; Duval, H.; Jardy, A.; Ablitzer, D.

2002-01-01

As part of a complete theoretical description of the behaviour of the electric arc in the vacuum arc remelting process, a model has been developed for the column of plasma generated by a single cluster of cathode spots. The model combines a kinetic approach, taking into account the formation of the plasma in the cathodic region, and a hydrodynamic approach, describing the expansion of the plasma in the vacuum between the electrodes. The kinetic model is based on a system of Boltzmann-Vlasov-Poisson equations and uses a particle-type simulation procedure, combining the PIC (particle in cell) and FPM (finite point set method) methods. In the two-dimensional hydrodynamic model, the plasma is assimilated to a mixture of two continuous fluids (the electrons and the ions), each described by a system of coupled transport equations. Finally, a simplified method has been defined for calculating the electric current density and the energy flux density transmitted by the plasma to the anode. The results of the numerical simulation presented are consistent with a certain number of experimental data available in the literature. In particular, the model predicts a percentage of the electric power of the cluster transmitted to the anode (25%) in good agreement with the value indicated in the literature. (author)

An assessment of ion temperature measurements in the boundary of the Alcator C-Mod tokamak and implications for ion fluid heat flux limiters

International Nuclear Information System (INIS)

Brunner, D; LaBombard, B; Churchill, R M; Hughes, J; Lipschultz, B; Ochoukov, R; Theiler, C; Walk, J; Rognlien, T D; Umansky, M V; Whyte, D

2013-01-01

The ion temperature is not frequently measured in the boundary of magnetic fusion devices. Comparisons among different ion temperature techniques and simulations are even rarer. Here we present a comparison of ion temperature measurements in the boundary of the Alcator C-Mod tokamak from three different diagnostics: charge exchange recombination spectroscopy (CXRS), an ion sensitive probe (ISP), and a retarding field analyzer (RFA). Comparison between CXRS and the ISP along with close examination of the ISP measurements reveals that the ISP is space charge limited. It is thus unable to measure ion temperature in the high density (>10 19 m −3 ) boundary plasma of C-Mod with its present geometry. Comparison of ion temperatures measured by CXRS and the RFA shows fair agreement. Ion and electron parallel heat flow is analyzed with a simple 1D fluid code. The code takes divertor measurements as input and results are compared to the measured ratios of upstream ion to electron temperature, as inferred respectively by CXRS and a Langmuir probe. The analysis reveals the limits of the fluid model at high Knudsen number. The upstream temperature ratio is under predicted by a factor of 2. Heat flux limiters (kinetic corrections) to the fluid model are necessary to match experimental data. The values required are found to be close to those reported in kinetic simulations. The 1D code is benchmarked against the 2D plasma fluid code UEDGE with good agreement. (paper)

An assessment of ion temperature measurements in the boundary of the Alcator C-Mod tokamak and implications for ion fluid heat flux limiters

Science.gov (United States)

Brunner, D.; LaBombard, B.; Churchill, R. M.; Hughes, J.; Lipschultz, B.; Ochoukov, R.; Rognlien, T. D.; Theiler, C.; Walk, J.; Umansky, M. V.; Whyte, D.

2013-09-01

The ion temperature is not frequently measured in the boundary of magnetic fusion devices. Comparisons among different ion temperature techniques and simulations are even rarer. Here we present a comparison of ion temperature measurements in the boundary of the Alcator C-Mod tokamak from three different diagnostics: charge exchange recombination spectroscopy (CXRS), an ion sensitive probe (ISP), and a retarding field analyzer (RFA). Comparison between CXRS and the ISP along with close examination of the ISP measurements reveals that the ISP is space charge limited. It is thus unable to measure ion temperature in the high density (>1019 m-3) boundary plasma of C-Mod with its present geometry. Comparison of ion temperatures measured by CXRS and the RFA shows fair agreement. Ion and electron parallel heat flow is analyzed with a simple 1D fluid code. The code takes divertor measurements as input and results are compared to the measured ratios of upstream ion to electron temperature, as inferred respectively by CXRS and a Langmuir probe. The analysis reveals the limits of the fluid model at high Knudsen number. The upstream temperature ratio is under predicted by a factor of 2. Heat flux limiters (kinetic corrections) to the fluid model are necessary to match experimental data. The values required are found to be close to those reported in kinetic simulations. The 1D code is benchmarked against the 2D plasma fluid code UEDGE with good agreement.

Electromagnetic radiation by parametric decay of upper hybrid waves in ionospheric modification experiments

International Nuclear Information System (INIS)

Leyser, T.B.

1994-01-01

A nonlinear dispersion relation for the parametric decay of an electrostatic upper hybrid wave into an ordinary mode electromagnetic wave, propagating parallel to the ambient magnetic field, and an electrostatic low frequency wave, being either a lower hybrid wave or a high harmonic ion Bernstein wave, is derived. The coherent and resonant wave interaction is considered to take place in a weakly magnetized and collisionless Vlasov plasma. The instability growth rate is computed for parameter values typical of ionospheric modification experiments, in which a powerful high frequency electromagnetic pump wave is injected into the ionospheric F-region from ground-based transmitters. The electromagnetic radiation which is excited by the decaying upper hybrid wave is found to be consistent with the prominent and commonly observed downshifted maximum (DM) emission in the spectrum of stimulated electromagnetic emission

Numerical simulation of electrostatic waves in plasmas

International Nuclear Information System (INIS)

Erz, U.

1981-08-01

In this paper the propagation of electrostatic waves in plasmas and the non-linear interactions, which occur in the case of large wave amplitudes, are studied using a new numerical method for plasma simulation. This mathematical description is based on the Vlasov-model. Changes in the distribution-function are taken into account and thus plasma kinetic effects can be treated. (orig./HT) [de

Cido fruit juice entangled in quality scare

Index Scriptorium Estoniae

2005-01-01

Leedu Veterinaar- ja Toidulabor avastas Lätis toodetud Cido greibimahlakontsentraadist 210 mg/kg mürkainet, mis on üle nelja korra lubatud määrast rohkem mürkainet. Cido turundusdirektori Dmitrijs Tairovsi sõnul leiti Lätis ja Saksamaal tehtud testide põhjal ainet tunduv alt vähem. Ettevõtte tegevdirektor Vadims Vlasovs kahtlustab Leedu konkurente

Dynamics of particle production by strong electric fields in non-Abelian plasmas

International Nuclear Information System (INIS)

Dawson, John F.; Mihaila, Bogdan; Cooper, Fred

2010-01-01

We develop methods for computing the dynamics of fermion pair production by strong color electric fields including backreaction using the semiclassical Boltzmann-Vlasov (B-V) equation. We implement the Schwinger pair production by inserting a source term in the B-V equation which includes Pauli-Blocking effects. We present numerical results for a model with SU(2) symmetries in (1+1) Cartesian dimensions.

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)

Two Methods For Simulating the Strong-Strong Beam-Beam Interaction in Hadron Colliders

International Nuclear Information System (INIS)

Warnock, Robert L.

2002-01-01

We present and compare the method of weighted macro particle tracking and the Perron-Frobenius operator technique for simulating the time evolution of two beams coupled via the collective beam-beam interaction in 2-D and 4-D (transverse) phase space. The coherent dipole modes, with and without lattice nonlinearities and external excitation, are studied by means of the Vlasov-Poisson system

Hamiltonian reductions in plasma physics about intrinsic gyrokinetic

International Nuclear Information System (INIS)

Guillebon de Resnes, L. de

2013-01-01

Gyrokinetic is a key model for plasma micro-turbulence, commonly used for fusion plasmas or small-scale astrophysical turbulence, for instance. The model still suffers from several issues, which could imply to reconsider the equations. This thesis dissertation clarifies three of them. First, one of the coordinates caused questions, both from a physical and from a mathematical point of view; a suitable constrained coordinate is introduced, which removes the issues from the theory and explains the intrinsic structures underlying the questions. Second, the perturbative coordinate transformation for gyrokinetic was computed only at lowest orders; explicit induction relations are obtained to go arbitrary order in the expansion. Third, the introduction of the coupling between the plasma and the electromagnetic field was not completely satisfactory; using the Hamiltonian structure of the dynamics, it is implemented in a more appropriate way, with strong consequences on the gyrokinetic equations, especially about their Hamiltonian structure. In order to address these three main points, several other results are obtained, for instance about the origin of the guiding-center adiabatic invariant, about a very efficient minimal guiding center transformation, or about an intermediate Hamiltonian model between Vlasov-Maxwell and gyrokinetic, where the characteristics include both the slow guiding-center dynamics and the fast gyro-angle dynamics. In addition, various reduction methods are used, introduced or developed, e.g. a Lie-transform of the equations of motion, a lifting method to transfer particle reductions to the corresponding Hamiltonian field dynamics, or a truncation method related both to Dirac's theory of constraints and to a projection onto a Lie-subalgebra. Besides gyrokinetic, this is useful to clarify other Hamiltonian reductions in plasma physics, for instance for incompressible or electrostatic dynamics, for magnetohydrodynamics, or for fluid closures including

On the formation of auroral arcs and acceleration of auroral electrons

International Nuclear Information System (INIS)

Swift, D.W.

1975-01-01

It is suggested that the highly structured auroral arc is caused by a current-driven laminar electrostatic shock oblique to the geomagnetic field. Electrons are accelerated by the potential jump associated with the shock. The shock is assumed to be confined to a plane. Self-consistent solutions to the Poisson-Vlasov systems are calculated for the electrostatic potential. A diabatic theory is used to calculate the ion number density in terms of the electrostatic potential and its derivatives. The electrons are assumed to be highly magnetized so they can only move parallel to the magnetic field. Solutions are exhibited for two plasma models: (1) streaming electrons and a two-temperature distribution of ions and (2) streaming electrons and ions and thermal electrons and ions. In the latter model, solutions can be obtained for an arbitrary potential jump across the shock. The shock is identified with the linear electrostatic ion cyclotron wave, and stability of these waves is examined to determine conditions for the formation of oblique shocks. Finally, the theory is discussed in the context of the magnetosphere, and possible model shocks are exhibited and discussed in terms of auroral arc formation

Fluid simulations of toroidal ion temperature gradient turbulence

International Nuclear Information System (INIS)

Sandberg, I.; Isliker, H.; Pavlenko, V.P.; Hizanidis, K.; Vlahos, L.

2006-01-01

The evolution of the toroidal ion temperature gradient mode instability is numerically studied by using the equations based on the standard reactive fluid model. The long-term dynamics of the instability are investigated using random-phase, small-amplitude fluctuations for initial conditions. The main events during the evolution of the instability that lead to the formation of large-scale coherent structures are described and the role of the dominant nonlinearities is clarified. The polarization drift nonlinearity leads to the inverse energy cascade while the convective ion heat nonlinearity is responsible for the saturation of the instability. Finally, the sensitivity of the saturated state to the initial plasma conditions is examined

Modified Poisson eigenfunctions for electrostatic Bernstein--Greene--Kruskal equilibria

International Nuclear Information System (INIS)

Ling, K.; Abraham-Shrauner, B.

1981-01-01

The stability of an electrostatic Bernstein--Greene--Kruskal equilibrium by Lewis and Symon's general linear stability analysis for spatially inhomogeneous Vlasov equilibria, which employs eigenfunctions and eigenvalues of the equilibrium Liouville operator and the modified Poisson operator, is considered. Analytic expressions for the Liouville eigenfuctions and eigenvalues have already been given; approximate analytic expressions for the dominant eigenfunction and eigenvalue of the modified Poisson operator are given. In the kinetic limit three methods are given: (i) the perturbation method, (ii) the Rayleigh--Ritz method, and (iii) a method based on a Hill's equation. In the fluid limit the Rayleigh--Ritz method is used. The dominant eigenfunction and eigenvalue are then substituted in the dispersion relation and the growth rate calculated. The growth rate agrees very well with previous results found by numerical simulation and by modified Poisson eigenfunctions calculated numerically

Towards a realistic plasma simulation code

International Nuclear Information System (INIS)

Anderson, D.V.

1991-06-01

Several new developments in the technology of simulating plasmas, both in particle and fluid models, now allow a stage of synthesis in which many of these advances can be combined into one simulation model. Accuracy and efficiency are the criteria to be satisfied in this quest. We want to build on the following research: 1. the development of the δf method of Barnes. 2. The moving node Galerkin model of Glasser, Miller and Carlson. 3. Particle moving schemes on unstructured grids by Ambrosiano and Bradon. 4. Particle simulations using sorted particles Anderson and Shumaker. Rather than being competing developments,these presumably can be combined into one computational model. We begin by summarizing the physics model for the plasma. The Vlasov equation can be solved as an initial value problem by integrating the plasma distribution function forward in time. 5 refs

Modes of storage ring coherent instabilities

Energy Technology Data Exchange (ETDEWEB)

Wang, J.M.

1986-12-01

Longitudinal impedance in a beam and various modes of longitudinal coherent instabilities are discussed. The coasting beam coherent instability, microwave instability, and single-bunch longitudinal coherent instabilities are considered. The Vlasov equation is formulated, and a method of solving it is developed. The synchrotron modes are treated, which take the possible bunch shape distortion fully into consideration. A method of treating the synchrotron mode coupling in the case of a small bunch is discussed which takes advantage of the fact that only a few of the synchrotron modes can contribute in such a case. The effect of many bunches on the coherent motion of the beam and the longitudinal symmetric coupled bunch modes are discussed. The transverse impedance is then introduced, and the transverse coasting beam instability is discussed. Various bunched beam instabilities are discussed, including both single bunch instabilities and coupled bunch instabilities. The Vlasov equation for transverse as well as longitudinal motion of particles is introduced as well as a method of solving it within a linear approximation. Head-tail modes and short bunch instabilities and strong coupling instabilities in the long bunch case are covered. (LEW)

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

A general method for propagation of the phase space distribution, with application to the saw-tooth instability

International Nuclear Information System (INIS)

Warnock, R.L.

2000-01-01

The authors propose and illustrate a general numerical method to follow the probability distribution in phase space as a function of time. It applies to any multiparticle system governed by Liouville, Vlasov or Vlasov-Fokker-Planck dynamics. The technique, based on discretization of the local Perron-Frobenius operator, is simple in concept, easy to implement, and numerically stable in examples studied to date. The authors illustrate by treating longitudinal dynamics in electron storage rings with realistic wake field. Applied to the SLC damping rings, the method gives the observed current threshold for bunch lengthening, and several aspects of observed behavior above threshold, including the presence of a bursting or sawtooth mode. In contrast to previous particle-in-cell simulations, the authors have very low numerical noise and the ability to follow the motion over several damping times. The method has also been applied to the coherent beam-beam interaction. It appears likely that this approach will be of interest for some of the central problems of this workshop, for instance matching of space-charge dominated beams to a focusing channel, and coherent synchrotron radiation with self-consistent charge/current density

Modes of storage ring coherent instabilities

International Nuclear Information System (INIS)

Wang, J.M.

1986-12-01

Longitudinal impedance in a beam and various modes of longitudinal coherent instabilities are discussed. The coasting beam coherent instability, microwave instability, and single-bunch longitudinal coherent instabilities are considered. The Vlasov equation is formulated, and a method of solving it is developed. The synchrotron modes are treated, which take the possible bunch shape distortion fully into consideration. A method of treating the synchrotron mode coupling in the case of a small bunch is discussed which takes advantage of the fact that only a few of the synchrotron modes can contribute in such a case. The effect of many bunches on the coherent motion of the beam and the longitudinal symmetric coupled bunch modes are discussed. The transverse impedance is then introduced, and the transverse coasting beam instability is discussed. Various bunched beam instabilities are discussed, including both single bunch instabilities and coupled bunch instabilities. The Vlasov equation for transverse as well as longitudinal motion of particles is introduced as well as a method of solving it within a linear approximation. Head-tail modes and short bunch instabilities and strong coupling instabilities in the long bunch case are covered

Aspects of electron acoustic wave physics in laser backscatter from plasmas

International Nuclear Information System (INIS)

Sircombe, N J; Arber, T D; Dendy, R O

2006-01-01

Recent experimental results from the Trident laser confirm the importance of kinetic effects in determining laser reflectivities at high intensities. Examples observed include scattering from low frequency electron acoustic waves (EAWs) and the first few stages of a cascade towards turbulence through the Langmuir decay instability. Interpretive and predictive computational capability in this area is assisted by the development of Vlasov codes, which offer high velocity space resolution in high energy regions of particle phase space and do not require analytical pre-processing of the fundamental equations. A direct Vlasov solver, capable of resolving these kinetic processes, is used here to address fundamental aspects of the existence and stability of the electron acoustic wave, together with its collective scattering properties. These simulations are extended to realistic laser and plasma parameters characteristic of single hot-spot experiments. Results are in qualitative agreement with experiments displaying both stimulated Raman and stimulated electron acoustic scattering. The amplitude of simulated EAWs is greater than that observed experimentally and is accompanied by a higher phase velocity. These minor differences can be attributed to the limitations of a one-dimensional collisionless model

On neutral plasma oscillations

International Nuclear Information System (INIS)

Shadwick, B.A.; Morrison, P.J.

1993-06-01

We examine the conditions for the existence of spectrally stable neutral modes in a Vlasov-Poisson plasma and show that for stable equilibria of systems that have unbounded spatial domain, the only possible neutral modes are those with phase velocities that correspond to stationary inflection points of the equilibrium distribution function. It is seen that these neutral modes can possess positive or negative free energy

Geometric Integration Of The Valsov-Maxwell System With A Variational Particle-in-cell Scheme

International Nuclear Information System (INIS)

Squire, J.; Qin, H.; Tang, W.M.

2012-01-01

A fully variational, unstructured, electromagnetic particle-in-cell integrator is developed for integration of the Vlasov-Maxwell equations. Using the formalism of Discrete Exterior Calculus [1], the field solver, interpolation scheme and particle advance algorithm are derived through minimization of a single discrete field theory action. As a consequence of ensuring that the action is invariant under discrete electromagnetic gauge transformations, the integrator exactly conserves Gauss's law.

Numerical method for the dispersion relation of a hot and inhomogeneous plasma with an electron beam

International Nuclear Information System (INIS)

Devia, A.; Orrego, C.E.; Buitrago, G.

1990-01-01

A numerical method that is based in kinetic theory (Vlasov-Poison equations) was developed in order to calculate the dispersion relation for the interaction between a hot cylindrical and electron beam in any temperature and density. The plasma-beam system is located in a strong magnetic field. Many examples showing the effect of the temperatures and densities on the dispersion relation are given. (Author)

On neutral plasma oscillations

International Nuclear Information System (INIS)

Shadwick, B.A.; Texas Univ., Austin; Morrison, P.J.; Texas Univ., Austin

1994-01-01

We examine the conditions for the existence of spectrally stable neutral modes in a Vlasov-Poisson plasma and show that for stable equilibria of systems that have unbounded spatial domain, the only possible neutral modes are those with phase velocities that correspond to stationary inflection points of the equilibrium distribution function. It is seen that these neutral modes can posses positive or negative free energy. (orig.)

Electrostatic turbulence in the Z pinch corona

International Nuclear Information System (INIS)

Terry, R.E.

1994-01-01

The microstability of electrostatic waves in the periphery of a Z pinch is formulated and resolved for a new class of Vlasov meta-equilibria admitting self-similar solutions in the electron gyrokinetic limit. These equilibria are subject to strong radial motions, and a mild deviation from charge neutrality arises to maintain ion acceleration close to that of the magnetized electrons. A unique class of profiles in density, axial current, temperature, and drift speed defines these equilibria. They are characterized by (i) the interior pinch current, (ii) the interior number density, (iii) the parallel and perpendicular temperatures, (iv) the exterior axial electric field value at the initial time, and (v) the radial ion acceleration relative to that of the electrons. Unstable ion sound waves arise in this medium by coupling radial and axial free energy to azimuthal longitudinal oscillations. The waves grow only for a limited range of radial or axial Exb/B drift speeds and electron temperatures. The growth rate, which can be as large as 0.115ω pi , is found to scale proportional to plasma frequency over the density range from 10 12 to 10 18 ions cm -3

Yield degradation in inertial-confinement-fusion implosions due to shock-driven kinetic fuel-species stratification and viscous heating

Science.gov (United States)

Taitano, W. T.; Simakov, A. N.; Chacón, L.; Keenan, B.

2018-05-01

Anomalous thermonuclear yield degradation (i.e., that not describable by single-fluid radiation hydrodynamics) in Inertial Confinement Fusion (ICF) implosions is ubiquitously observed in both Omega and National Ignition experiments. Multiple experimental and theoretical studies have been carried out to investigate the origin of such a degradation. Relative concentration changes of fuel-ion species, as well as kinetically enhanced viscous heating, have been among possible explanations proposed for certain classes of ICF experiments. In this study, we investigate the role of such kinetic plasma effects in detail. To this end, we use the iFP code to perform multi-species ion Vlasov-Fokker-Planck simulations of ICF capsule implosions with the fuel comprising various hydrodynamically equivalent mixtures of deuterium (D) and helium-3 (3He), as in the original Rygg experiments [J. R. Rygg et al., Phys. Plasmas 13, 052702 (2006)]. We employ the same computational setup as in O. Larroche [Phys. Plasmas 19, 122706 (2012)], which was the first to simulate the experiments kinetically. However, unlike the Larroche study, and in partial agreement with experimental data, we find a systematic yield degradation in multi-species simulations versus averaged-ion simulations when the D-fuel fraction is decreased. This yield degradation originates in the fuel-ion species stratification induced by plasma shocks, which imprints the imploding system and results in the relocation of the D ions from the core of the capsule to its periphery, thereby reducing the yield relative to a non-separable averaged-ion case. By comparing yields from the averaged-ion kinetic simulations and from the hydrodynamic scaling, we also observe yield variations associated with ion kinetic effects other than fuel-ion stratification, such as ion viscous heating, which is typically neglected in hydrodynamic implosions' simulations. Since our kinetic simulations are driven by hydrodynamic boundary conditions at the

Numerical Simulation of the Time Evolution of Small-Scale Irregularities in the F-Layer Ionospheric Plasma

Directory of Open Access Journals (Sweden)

O. V. Mingalev

2011-01-01

Full Text Available Dynamics of magnetic field-aligned small-scale irregularities in the electron concentration, existing in the F-layer ionospheric plasma, is investigated with the help of a mathematical model. The plasma is assumed to be a rarefied compound consisting of electrons and positive ions and being in a strong, external magnetic field. In the applied model, kinetic processes in the plasma are simulated by using the Vlasov-Poisson system of equations. The system of equations is numerically solved applying a macroparticle method. The time evolution of a plasma irregularity, having initial cross-section dimension commensurable with a Debye length, is simulated during the period sufficient for the irregularity to decay completely. The results of simulation indicate that the small-scale irregularity, created initially in the F-region ionosphere, decays accomplishing periodic damped vibrations, with the process being collisionless.

Landau damping of dust acoustic waves in the presence of hybrid nonthermal nonextensive electrons

Science.gov (United States)

El-Taibany, W. F.; Zedan, N. A.; Taha, R. M.

2018-06-01

Based on the kinetic theory, Landau damping of dust acoustic waves (DAWs) propagating in a dusty plasma composed of hybrid nonthermal nonextensive distributed electrons, Maxwellian distributed ions and negatively charged dust grains is investigated using Vlasov-Poisson's equations. The characteristics of the DAWs Landau damping are discussed. It is found that the wave frequency increases by decreasing (increasing) the value of nonextensive (nonthermal) parameter, q (α ). It is recognized that α plays a significant role in observing damping or growing DAW oscillations. For small values of α , damping modes have been observed until reaching a certain value of α at which ω i vanishes, then a growing mode appears in the case of superextensive electrons. However, only damping DAW modes are observed in case of subextensive electrons. The present study is useful in the space situations where such distribution exists.

Plasma oscillations and sound waves in collision-dominated two-component plasmas

International Nuclear Information System (INIS)

Hansen, J.P.; Sjoegren, L.

1982-01-01

Charge, mass, and electron density fluctuation spectra of strongly correlated, fully ionized two-component plasmas within the framework of the Mori--Zwanzig memory function formalism are analyzed. All dynamical correlation functions are expressed in terms of the memory functions of the ion and electron velocity autocorrelation functions by a generalized effective field approximation which preserves the exact initial values (i.e., static correlations). The theory reduces correctly to the mean field (or collisionless Vlasov) results in the weak coupling limit, and yields charge density fluctuation spectra in good agreement with available computer simulation data, as well as reasonable estimates of the transport coefficients. The collisional damping and frequency shift of the plasma oscillation mode are sizeable, even in the long wavelength limit. The theory also predicts the propagation of well-defined sound waves in dense plasmas in thermal equilibrium

A new treatment of localized modes in inhomogeneous Vlasov plasma

International Nuclear Information System (INIS)

Watanabe, Tsuguhiro; Sanuki, Heiji; Watanabe, Masaaki.

1978-04-01

A new eigenmode analysis is established in plasma with arbitrary density profile. Finite Larmor effect is taken into account even if k sub(x)rho>1. Eigenfrequencies are determined through a compact ''quantization condition''. (author)

Vlasov simulations of Kinetic Alfven Waves at proton kinetic scales

NARCIS (Netherlands)

C.L. Vasconez; F. Valentini (Francesco); E. Camporeale (Enrico); P. Veltri

2014-01-01

htmlabstractKinetic Alfv ́en waves represent an important subject in space plasma physics, since they are thought to play a crucial role in the development of the turbulent energy cascade in the solar wind plasma at short wavelengths (of the order of the proton inertial length d p and beyond). A

Ion cyclotron emission in tokamak plasmas; Emission cyclotronique ionique dans les plasmas de tokamak

Energy Technology Data Exchange (ETDEWEB)

Fraboulet, D.

1996-09-17

Detection of {alpha}(3.5 MeV) fusion products will be of major importance for the achievement of self sustained discharges in fusion thermonuclear reactors. Due to their cyclotronic gyration in the confining magnetic field of a tokamak, {alpha} particles are suspected to radiate in the radio-frequency band [RF: 10-500 MHz]. Our aim is to determine whether detection of RF emission radiated from a reactor plasma can provide information concerning those fusion products. We observed experimentally that the RF emission radiated from fast ions situated in the core of the discharge is detectable with a probe located at the plasma edge. For that purpose, fast temporal acquisition of spectral power was achieved in a narrow frequency band. We also propose two complementary models for this emission. In the first one, we describe locally the energy transfer between the photon population and the plasma and we compute the radiation equilibrium taking place in the tokamak. {alpha} particles are not the unique species involved in the equilibrium and it is necessary to take into account all other species present in the plasma (Deuterium, Tritium, electrons,...). Our second model consists in the numerical resolution of the Maxwell-Vlasov with the use of a variational formulation, in which all polarizations are considered and the 4 first cyclotronic harmonics are included in a 1-D slab geometry. The development of this second model leads to the proposal for an experimental set up aiming to the feasibility demonstration of a routine diagnostic providing the central {alpha} density in a reactor. (author). 166 refs.

Non linear interaction between a Langmuir wave and a ballistic perturbation

International Nuclear Information System (INIS)

Gervais, F.; Olivain, J.; Quemeneur, A.; Trocheris, M.

1979-05-01

The theoretical solutions of the Landau-Vlasov initial value problem giving mode-mode coupling usually neglect the free-streaming contribution. We solve theoretically this problem including the ballistic terms. We find that a new mode appears resulting from the nonlinear interaction between the Landau component and the ballistic perturbation. The amplitude of this mode is calculated as a function of distance and compared with experimental results in a plasma column

Single-mode saturation of the bump-on-tail instability

International Nuclear Information System (INIS)

Simon, A.; Rosenbluth, M.N.

1976-01-01

A slightly unstable plasma with only one or a few linear modes unstable is considered. Nonlinear saturation at small amplitudes has been treated by time-asymptotic analysis which is a generalization of the methods of Bogolyubov and co-workers. In this paper the method is applied to instability in a collisionless plasma governed by the vlasov equation. The bump-on-tail instability is considered for a one-dimensional plasma

An energy principle for two-dimensional collisionless relativistic plasmas

International Nuclear Information System (INIS)

Otto, A.; Schindler, K.

1984-01-01

Using relativistic Vlasov theory an energy principle for two-dimensional plasmas is derived, which provides a sufficient and necessary criterion for the stability of relativistic plasma equilibria. This energy principle includes charge separating effects since the exact Poisson equation was taken into consideration. Applying the variational principle to the case of the relativistic plane plasma sheet, the same marginal wave length is found as in the non-relativistic case. (author)

Electron heat flux instabilities in the solar wind

International Nuclear Information System (INIS)

Gary, S.P.; Feldman, W.C.; Forslund, D.W.; Montgomery, M.D.

1975-01-01

There are at least three plasma instabilities associated with the electron heat flux in the solar wind. This letter reports the study of the unstable fast magnetosonic, Alfven and whistler modes via a computer code which solves the full electromagnetic, linear, Vlasov dispersion relation. Linear theory demonstrates that both the magnetosonic and Alfven instabilities are candidates for turbulent limitation of the heat flux in the solar wind at 1 A.U

Minimum scaling laws in tokamaks

International Nuclear Information System (INIS)

Zhang, Y.Z.; Mahajan, S.M.

1986-10-01

Scaling laws governing anomalous electron transport in tokamaks with ohmic and/or auxiliary heating are derived using renormalized Vlasov-Ampere equations for low frequency electromagnetic microturbulence. It is also shown that for pure auxiliary heating (or when auxiliary heating power far exceeds the ohmic power), the energy confinement time scales as tau/sub E/ ∼ P/sub inj//sup -1/3/, where P/sub inj/ is the injected power

Analogies between classical statistical mechanics and quantum mechanics

International Nuclear Information System (INIS)

Uehara, M.

1986-01-01

Some analogies between nonequilibrium classical statistical mechanics and quantum mechanics, at the level of the Liouville equation and at the kinetic level, are commented on. A theorem, related to the Vlasov equation applied to a plasma, is proved. The theorem presents an analogy with Ehrenfest's theorem of quantum mechanics. An analogy between the plasma kinetic theory and Bohm's quantum theory with 'hidden variables' is also shown. (Author) [pt

Time characteristics for the spinodal decomposition in nuclear matter

Energy Technology Data Exchange (ETDEWEB)

Idier, D.; Farine, M.; Benhassine, B.; Remaud, B.; Sebille, F.

1992-12-31

Dynamics of the fluctuation growth are studied. Time characteristics are key quantities to determine the conditions under which spinodal decomposition could be observed. Dynamical instabilities arising from fluctuations in spinodal zone for nuclear matter are studied using Skyrme type interactions within a pseudo-particle model. Typical times for cluster formation are extracted. The numerical treatment is based on the Vlasov phase space transport equation. (K.A.) 11 refs.; 7 figs.

Time characteristics for the spinodal decomposition in nuclear matter

International Nuclear Information System (INIS)

Idier, D.; Farine, M.; Benhassine, B.; Remaud, B.; Sebille, F.

1992-01-01

Dynamics of the fluctuation growth are studied. Time characteristics are key quantities to determine the conditions under which spinodal decomposition could be observed. Dynamical instabilities arising from fluctuations in spinodal zone for nuclear matter are studied using Skyrme type interactions within a pseudo-particle model. Typical times for cluster formation are extracted. The numerical treatment is based on the Vlasov phase space transport equation. (K.A.) 11 refs.; 7 figs

Equilibrium and stability of off-axis periodically focused particle beams

International Nuclear Information System (INIS)

Moraes, J.S.; Pakter, R.; Rizzato, F.B.

2004-01-01

A general equation for the centroid motion of free, continuous, intense beams propagating off axis in solenoidal periodic focusing fields is derived. The centroid equation is found to be independent of the specific beam distribution and may exhibit unstable solutions. A new Vlasov equilibrium for off-axis beam propagation is also obtained. The properties of the equilibrium and the relevance of centroid motion to beam confinement are discussed

Super-Alfvénic Propagation and Damping of Reconnection Onset Signatures

Science.gov (United States)

Sharma Pyakurel, P.; Shay, M. A.; Haggerty, C. C.; Parashar, T. N.; Drake, J. F.; Cassak, P. A.; Gary, S. Peter

2018-01-01

The quadrupolar out-of-plane Hall magnetic field generated during collisionless reconnection propagates away from the x line as a kinetic Alfvén wave (KAW). While it has been shown that this KAW carries substantial Poynting flux and propagates super-Alfvenically, how this KAW damps as it propagates away from the x line is not well understood. In this study, this damping is examined using kinetic particle-in-cell simulations of antiparallel symmetric magnetic reconnection in a one-dimensional current sheet equilibrium. In the reconnection simulations, the KAW wave vector has a typical magnitude comparable to an inverse fluid Larmor radius (effectively an inverse ion Larmor radius) and a direction of 85-89° relative to the local magnetic field. We find that the damping of the reconnection KAW is consistent with linear Landau damping results from a numerical Vlasov dispersion solver. This knowledge allows us to generalize our damping predictions to regions in the magnetotail and solar corona where the magnetic geometry can be approximated as a current sheet. For the magnetotail, the KAW from reconnection will not damp away before propagating the approximately 20 Earth radii associated with global magnetotail distances. For the solar corona, on the other hand, these KAWs will completely damp before reaching the distances comparable to the flare loop length.

Colliding beam fusion reactor space propulsion system

International Nuclear Information System (INIS)

Wessel, Frank J.; Binderbauer, Michl W.; Rostoker, Norman; Rahman, Hafiz Ur; O'Toole, Joseph

2000-01-01

We describe a space propulsion system based on the Colliding Beam Fusion Reactor (CBFR). The CBFR is a high-beta, field-reversed, magnetic configuration with ion energies in the range of hundreds of keV. Repetitively-pulsed ion beams sustain the plasma distribution and provide current drive. The confinement physics is based on the Vlasov-Maxwell equation, including a Fokker Planck collision operator and all sources and sinks for energy and particle flow. The mean azimuthal velocities and temperatures of the fuel ion species are equal and the plasma current is unneutralized by the electrons. The resulting distribution functions are thermal in a moving frame of reference. The ion gyro-orbit radius is comparable to the dimensions of the confinement system, hence classical transport of the particles and energy is expected and the device is scaleable. We have analyzed the design over a range of 10 6 -10 9 Watts of output power (0.15-150 Newtons thrust) with a specific impulse of, I sp ∼10 6 sec. A 50 MW propulsion system might involve the following parameters: 4-meters diameterx10-meters length, magnetic field ∼7 Tesla, ion beam current ∼10 A, and fuels of either D-He 3 ,P-B 11 ,P-Li 6 ,D-Li 6 , etc

Comparing the Richtmyer-Meshkov instability of thermal and ion-species interfaces in two-fluid plasmas

Science.gov (United States)

Wheatley, Vincent; Bond, Daryl; Li, Yuan; Samtaney, Ravi; Pullin, Dale

2017-11-01

The Richtmyer-Meshkov instability (RMI) of a shock accelerated perturbed density interface is important in both inertial confinement fusion and astrophysics, where the materials involved are typically in the plasma state. Initial density interfaces can be due to either temperature or ion-species discontinuities. If the Atwood number of the interfaces and specific heat ratios of the fluids are matched, these two cases behave similarly when modeled using the equations of either hydrodynamics or magnetohydrodynamics. In the two-fluid ion-electron plasma model, however, there is a significant difference between them: In the thermal interface case, there is a discontinuity in electron density that is also subject to the RMI, while for the ion-species interface case there is not. It will be shown via ideal two-fluid plasma simulations that this causes substantial differences in the dynamics of the flow between the two cases. This work was partially supported by the KAUST Office of Sponsored Research under Award URF/1/2162-01.

Fourier–Hermite spectral representation for the Vlasov–Poisson system in the weakly collisional limit

KAUST Repository

Parker, Joseph T.

2015-02-03

Copyright © Cambridge University Press 2015. We study Landau damping in the 1+1D Vlasov-Poisson system using a Fourier-Hermite spectral representation. We describe the propagation of free energy in Fourier-Hermite phase space using forwards and backwards propagating Hermite modes recently developed for gyrokinetic theory. We derive a free energy equation that relates the change in the electric field to the net Hermite flux out of the zeroth Hermite mode. In linear Landau damping, decay in the electric field corresponds to forward propagating Hermite modes; in nonlinear damping, the initial decay is followed by a growth phase characterized by the generation of backwards propagating Hermite modes by the nonlinear term. The free energy content of the backwards propagating modes increases exponentially until balancing that of the forward propagating modes. Thereafter there is no systematic net Hermite flux, so the electric field cannot decay and the nonlinearity effectively suppresses Landau damping. These simulations are performed using the fully-spectral 5D gyrokinetics code SpectroGK, modified to solve the 1+1D Vlasov-Poisson system. This captures Landau damping via Hou-Li filtering in velocity space. Therefore the code is applicable even in regimes where phase mixing and filamentation are dominant.

DYNAMIC RESPONSE OF THICK PLATES ON TWO PARAMETER ELASTIC FOUNDATION UNDER TIME VARIABLE LOADING

OpenAIRE

Ozgan, Korhan; Daloglu, Ayse T.

2014-01-01

In this paper, behavior of foundation plates with transverse shear deformation under time variable loading is presented using modified Vlasov foundation model. Finite element formulation of thick plates on elastic foundation is derived by using an 8-noded finite element based on Mindlin plate theory. Selective reduced integration technique is used to avoid shear locking problem which arises when smaller plate thickness is considered for the evaluation of the stiffness matrices. After comparis...

Stability of longitudinal oscillations of a bunch propagating through an evacuated chamber with reactive impedance

International Nuclear Information System (INIS)

Besnier, G.

1979-01-01

The longitudinal space-charge force is assumed to vary like the derivative of the longitudinal beam density. Solutions of the linearized Vlasov equation are then given as an expansion of normal modes for the longitudinal phase-space density of a bunched beam. For a given bunch intensity, the method allows calculation of the required synchrotron frequency spread inside a parabolic bunch, in order to stabilize the beam against coherent oscillations by Landau-damping. (Auth.)

On the frequency scalings of RF guns

International Nuclear Information System (INIS)

Lin, L.C.; Chen, S.C.; Wurtele, J.S.

1995-01-01

A frequency scaling law for RF guns is derived from the normalized Vlasov-Maxwell equations. It shows that higher frequency RF guns can generate higher brightness beams under the assumption that the accelerating gradient and all beam and structure parameters are scaled with the RF frequency. Numerical simulation results using MAGIC confirm the scaling law. A discussion of the range of applicability of the law is presented. copyright 1995 American Institute of Physics

Nernst Effect in Magnetized Plasmas

OpenAIRE

Joglekar, Archis S.; Thomas, Alexander G. R.; Ridgers, Christopher P.; Kingham, Robert J.

2015-01-01

We present nanosecond timescale Vlasov-Fokker-Planck-Maxwell modeling of magnetized plasma transport and dynamics in a hohlraum with an applied external magnetic field, under conditions similar to recent experiments. Self-consistent modeling of the kinetic electron momentum equation allows for a complete treatment of the heat flow equation and Ohm's Law, including Nernst advection of magnetic fields. In addition to showing the prevalence of non-local behavior, we demonstrate that effects such...

Kinetic modeling of Nernst effect in magnetized hohlraums

OpenAIRE

Joglekar, A. S.; Ridgers, Christopher Paul; Kingham, R J; Thomas, A. G. R.

2016-01-01

We present nanosecond time-scale Vlasov-Fokker-Planck-Maxwell modeling of magnetized plasma transport and dynamics in a hohlraum with an applied external magnetic field, under conditions similar to recent experiments. Self-consistent modeling of the kinetic electron momentum equation allows for a complete treatment of the heat flow equation and Ohm's law, including Nernst advection of magnetic fields. In addition to showing the prevalence of nonlocal behavior, we demonstrate that effects such...

Nonlinear theory of surface-wave--particle interactions in a cylindrical plasma

International Nuclear Information System (INIS)

Dengra, A.; Palop, J.I.F.

1994-01-01

This work is an application of the specular reflection hypothesis to the study of the nonlinear surface-wave--particle interactions in a cylindrical plasma. The model is based on nonlinear resolution of the Vlasov equation by the method of characteristics. The expression obtained for the rate of increase of kinetic energy per electron has permitted us to investigate the temporal behavior of nonlinear collisionless damping for different situations as a function of the critical parameters

Oscillations in quasineutral plasmas

International Nuclear Information System (INIS)

Grenier, E.

1996-01-01

The purpose of this article is to describe the limit, as the vacuum electric permittivity goes to zero, of a plasma physics system, deduced from the Vlasov-Poisson system for special initial data (distribution functions which are analytic in the space variable, with compact support in velocity), a limit also called open-quotes quasineutral regimeclose quotes of the plasma, and the related oscillations of the electric field, with high frequency in time. 20 refs

Skin effect of microwaves and transverse pseudowaves in plasmas

International Nuclear Information System (INIS)

Minami, Kazuo

1977-09-01

Using linearized Vlasov-Maxwell equations, the skin effect of microwaves and transverse pseudowaves excited by an idealized grid antenna in plasmas are analyzed. It is shown that the latter is predominant over the former, in such a plasma that ω sub(p) v sub(t)/ωc >= 1, where ω sub(p) and ω are the plasma and microwave angular frequencies, v sub(t) and c are the electron thermal and light velocities, respectively. (auth.)

Coherent oscillations of a ring of relativistic particles

International Nuclear Information System (INIS)

Hofmann, I.

1976-07-01

The effect of ring curvature on the coherent perturbations of a ring of relativistic particles is studied within the framework of the linearized Vlasov equation. Finite curvature is shown to have a minor effect on the dynamics of the 'negative mass' mode; the 'transverse' mode in radial direction, however, is found to be coupled with a simultaneous longitudinal density modulation which modifies the dispersion relation. In the limit of small mode frequency (ω/Ω [de

Ergodic model for the expansion of spherical nanoplasmas.

Science.gov (United States)

Peano, F; Coppa, G; Peinetti, F; Mulas, R; Silva, L O

2007-06-01

Recently, the collisionless expansion of spherical nanoplasmas has been analyzed with a new ergodic model, clarifying the transition from hydrodynamiclike to Coulomb-explosion regimes, and providing accurate laws for the relevant features of the phenomenon. A complete derivation of the model is presented here. The important issue of the self-consistent initial conditions is addressed by analyzing the initial charging transient due to the electron expansion, in the approximation of immobile ions. A comparison among different kinetic models for the expansion is presented, showing that the ergodic model provides a simplified description, which retains the essential information on the electron distribution, in particular, the energy spectrum. Results are presented for a wide range of initial conditions (determined from a single dimensionless parameter), in excellent agreement with calculations from the exact Vlasov-Poisson theory, thus providing a complete and detailed characterization of all the stages of the expansion.

Space charge physics for particle accelerators

CERN Document Server

Hofmann, Ingo

2017-01-01

Understanding and controlling the physics of space charge effects in linear and circular proton and ion accelerators are essential to their operation, and to future high-intensity facilities. This book presents the status quo of this field from a theoretical perspective, compares analytical approaches with multi-particle computer simulations and – where available – with experiments. It discusses fundamental concepts of phase space motion, matched beams and modes of perturbation, along with mathematical models of analysis – from envelope to Vlasov-Poisson equations. The main emphasis is on providing a systematic description of incoherent and coherent resonance phenomena; parametric instabilities and sum modes; mismatch and halo; error driven resonances; and emittance exchange due to anisotropy, as well as the role of Landau damping. Their distinctive features are elaborated in the context of numerous sample simulations, and their potential impacts on beam quality degradation and beam loss are discussed....

Magnetic reconnection in plasma under inertial confinement fusion conditions driven by heat flux effects in Ohm's law.

Science.gov (United States)

Joglekar, A S; Thomas, A G R; Fox, W; Bhattacharjee, A

2014-03-14

In the interaction of high-power laser beams with solid density plasma there are a number of mechanisms that generate strong magnetic fields. Such fields subsequently inhibit or redirect electron flows, but can themselves be advected by heat fluxes, resulting in complex interplay between thermal transport and magnetic fields. We show that for heating by multiple laser spots reconnection of magnetic field lines can occur, mediated by these heat fluxes, using a fully implicit 2D Vlasov-Fokker-Planck code. Under such conditions, the reconnection rate is dictated by heat flows rather than Alfvènic flows. We find that this mechanism is only relevant in a high β plasma. However, the Hall parameter ωcτei can be large so that thermal transport is strongly modified by these magnetic fields, which can impact longer time scale temperature homogeneity and ion dynamics in the system.

Wake-field generation by the ponderomotive memory effect

International Nuclear Information System (INIS)

Wolf, U.; Schamel, H.

1997-01-01

An analytical and numerical investigation of the plasma response to an imposed high frequency wave packet with a slow explicit time-dependent envelope is presented. An underlying picture of ponderomotive effects is developed, which shows that the explicit time dependence forces us to treat the problem kinetically, and furthermore, that a wake field is generated by the ponderomotive memory effect. The latter supplements the well-known ponderomotive force and fake heating effect. Several perturbation schemes are compared showing that the influence of resonant particles, treated by the method of characteristics, has to be taken into account for Langmuir wave packets with kλ d ≥0.2, where k is the wave number and λ d the Debye length. A self-consistent Vlasov simulation shows the disappearance of the density depression in the case of immobile ions, whereas the wake-field pattern survives self-consistency. copyright 1997 The American Physical Society

Comparative evaluation of metal ions release from titanium and Ti-6Al-7Nb into bio-fluids

Directory of Open Access Journals (Sweden)

Lori A Joseph

2009-01-01

Full Text Available Background: The study was designed to investigate the effects of pH, chloride ions and nature of some bio-fluids on the amount of metal ions released from titanium and TiAl 6 Nb 7 plates following incubation in actual and simulated bio-fluids over time. Methods: The amounts of released metal ions from commercially pure titanium (CpTi and TiAl 6 Nb 7 of surgical grade on immersion in 20 mL Hank′s solution of pH 4.0 or 7.0, Hank′s solution of high chloride ions concentration, Whole Blood Serum (WBS and Phosphate Buffered Saline (PBS at 37° C were determined over an incubation time of 20 weeks using atomic absorption spectrophotometry. The levels of released metal ions were compared by two-way ANOVA and Duncan′s post-hoc tests. The amounts of titanium ions released by the samples were analyzed by Pearson′s correlation. Results: TiAl 6 Nb 7 plate showed no release of Ti ions into the test solutions until after 12 weeks of incubation, while Ti ions were released from the CpTi plate from the 1 day immersion time. The re-lease of measurable amount of Al ions from TiAl 6 Nb 7 was after 12 weeks of incubation. The rate of release of Ti and Al ions from the samples increased initially with incubation time and then stabilized due to adsorption-desorption equilibrium. Conclusion: The results showed that variations in pH and chloride ions of the test media has a sig-nificant effect on the amounts of Ti ions released, while increase in chloride ions concentration sig-nificantly elevates the release of Al ions into the bio-fluids.

Electron inertia effects for an electron fluid model by the applied-B ion diode

Energy Technology Data Exchange (ETDEWEB)

Gordeev, A V; Levchenko, S V [Kurchatov Institute, Moscow (Russian Federation). Nuclear Fusion Institute

1997-12-31

Numerical calculations within the framework of the one-dimensional vortex-like electron fluid model in applied-B ion diodes, taking account the electron inertia effects, are presented. The existence of the additional relation between the magnetic field and the electric potential offers an opportunity to reduce the ion diode problem to the system of the algebraic equations for the constants introduced. The ion current density in an ion diode is determined only by the magnetic flux cut out by the virtual cathode. As an illustration, the ion diode impedance for the KALIF device was calculated. (author). 2 figs., 6 refs.

Effects of ion and electron screening on thermonuclear reaction rates

International Nuclear Information System (INIS)

Brady, L.R. Jr.

1977-01-01

The effects of screening by ions and electrons on thermonuclear reaction rates in stellar plasmas are considered. The enhancement of the reaction rate ranges from negligible to extremely large (on the order of 10 26 or greater). In order to calculate these effects, the potential about a given reacting nucleus is determined. First, Boltzmann-Vlasov and Poisson-Boltzmann equations are solved to yield a Yukawa potential. A suitable approximation to this potential is integrated in the action integral to give the barrier penetration. The screened reaction rate is then found by the saddle-point method. In developing a general formalism to calculate the screened reaction rate and the screening factor, effects due to the finite size of the nucleus are considered and found to be negligible. An expression for the screening factor for resonant reaction rates is also derived. A different and relatively simple approach, based on work of Stewart and Pyatt (1966), is used to find the barrier penetration from the action integral in two approximations: a modified Coulomb potential and a constant-shift potential. Screening factors are calculated for carbon burning at T 6 = 100 and T 6 = 400 for a wide range of densities and also for several examples in late stellar evolution. These screening factors are, for the most part, greater than those given by most others by a few percent at low density to 4 or more orders of magnitude at T 6 = 100 and rho = 10 10 g/cm 3 . Near the edge of the crystalline lattice region, however, they are significantly lower than those of some others. The increase in reaction rates for carbon burning indicates that carbon ignition may occur at lower densities than previously thought and may affect the density at which a supernova shock may occur

Mathematical modeling and numerical study of a spray in a rarefied gas. Application to the simulation of dust particle transport in ITER in case of vacuum loss accident

International Nuclear Information System (INIS)

Charles, F.

2009-11-01

The thesis deals with kinetic models describing a rarefied spray. These models rely on coupling two Partial Differential Equations which describe the spatio-temporal evolution of the distribution of molecules and dust particles. The model presented in the first part is described by two Boltzmann-type equations where collisions between molecules and particles are modeled by two collision operators. We suggest two models of this collision operators. In the first one, collisions between dust particles and molecules are supposed to be elastic. In the second one, we assume those collisions are inelastic and given by a diffuse reflexion mechanism on the surface of dust specks. This leads to establish non classical collision operators. We prove that in the case of elastic collisions, the spatially homogeneous system has weak solutions which preserve mass and energy, and which satisfy an entropy inequality. We then describe the numerical simulation of the inelastic model, which is based on a Direct Simulation Method. This brings to light that the numerical simulation of the system becomes too expensive because the typical size of a dust particle is too large. We therefore introduce in the second part of this work a model constituted of a coupling (by a drag force term) between a Boltzmann equation and a Vlasov equation. To this end, we perform a scaling of the Boltzmann/Boltzmann system and an asymptotic expansion of one of the dimensionless collision operators with respect to the ratio of mass between a molecule of gas and a particle. A rigorous proof of the passage to the limit is given in the spatially homogeneous setting, for the elastic model of collision operators. It includes a new variant of Povzner's inequality in which the vanishing mass ratio is taken into account. Moreover, we numerically compare the Boltzmann/Boltzmann and Vlasov/Boltzmann systems with the inelastic collision operators. The simulation of the Vlasov equation is performed with a Particle

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

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

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

A MODEL FOR THE ELECTRICALLY CHARGED CURRENT SHEET OF A PULSAR

Energy Technology Data Exchange (ETDEWEB)

DeVore, C. R.; Antiochos, S. K.; Black, C. E. [Heliophysics Science Division, NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771 (United States); Harding, A. K.; Kalapotharakos, C.; Kazanas, D.; Timokhin, A. N., E-mail: c.richard.devore@nasa.gov [Astrophysics Science Division, NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771 (United States)

2015-03-10

Global-scale solutions for the magnetosphere of a pulsar consist of a region of low-lying, closed magnetic field near the star, bounded by opposite-polarity regions of open magnetic field along which the pulsar wind flows into space. Separating these open-field regions is a magnetic discontinuity—an electric current sheet—consisting of generally nonneutral plasma. We have developed a self-consistent model for the internal equilibrium structure of the sheet by generalizing the charge-neutral Vlasov/Maxwell equilibria of Harris and Hoh to allow for net electric charge. The resulting equations for the electromagnetic field are solved analytically and numerically. Our results show that the internal thermal pressure needed to establish equilibrium force balance, and the associated effective current-sheet thickness and magnetization, can differ by orders of magnitude from the Harris/Hoh charge-neutral limit. The new model provides a starting point for kinetic or fluid investigations of instabilities that can cause magnetic reconnection and flaring in pulsar magnetospheres.

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.

Nonlinear simulation of magnetic reconnection with a drift kinetic electron model

International Nuclear Information System (INIS)

Zwingmann, W.; Ottaviani, M.

2004-01-01

The process of reconnection allows for a change of magnetic topology inside a plasma. It is an important process for eruptive phenomena in astrophysical plasma, and the sawtooth relaxation in laboratory plasma close to thermonuclear conditions. The sawtooth relaxation is associated with the collisionless electron tearing instability, caused by the electron inertia. A thorough treatment therefore requires a kinetic model for the electron dynamics. In this contribution, we report on the numerical simulation of the electron tearing instability by solving the Vlasov equation directly. The results confirm results of an early paper on the same subject, and extends them to smaller values of the collision skin depth d e = 0.25. Our results suggest a faster than exponential growth in the early nonlinear phase of the instability. We observe as well an asymmetry of the resulting fields. It seems, however, that the field structure becomes closer to the fluid case for small values of d e

A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions

Science.gov (United States)

Chacón, L.; Chen, G.

2016-07-01

We extend a recently proposed fully implicit PIC algorithm for the Vlasov-Darwin model in multiple dimensions (Chen and Chacón (2015) [1]) to curvilinear geometry. As in the Cartesian case, the approach is based on a potential formulation (ϕ, A), and overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. Conservation theorems for local charge and global energy are derived in curvilinear representation, and then enforced discretely by a careful choice of the discretization of field and particle equations. Additionally, the algorithm conserves canonical-momentum in any ignorable direction, and preserves the Coulomb gauge ∇ ṡ A = 0 exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with numerical experiments in mapped meshes in 1D-3V and 2D-3V.

Counterstreaming magnetized plasmas. II. Perpendicular wave propagation

International Nuclear Information System (INIS)

Tautz, R.C.; Schlickeiser, R.

2006-01-01

The properties of longitudinal and transverse oscillations in magnetized symmetric counterstreaming Maxwellian plasmas with equal thermal velocities for waves propagating perpendicular to the stream direction are investigated on the basis of Maxwell equations and the nonrelativistic Vlasov equation. With the constraint of vanishing particle flux in the stream direction, three distinct dispersion relations are known, which are the ordinary-wave mode, the Bernstein wave mode, and the extraordinary electromagnetic wave mode, where the latter two are only approximations. In this article, all three dispersion relations are evaluated for a counterstreaming Maxwellian distribution function in terms of the hypergeometric function 2 F 2 . The growth rates for the ordinary-wave mode are compared to earlier results by Bornatici and Lee [Phys. Fluids 13, 3007 (1970)], who derived approximate results, whereas in this article the exact dispersion relation is solved numerically. The original results are therefore improved and show differences of up to 21% to the results obtained in this article

Effects of bunch density gradient in high-gain free-electron lasers

International Nuclear Information System (INIS)

Huang, Z.; Kim, K.-J.

1999-01-01

The authors investigate effects of the bunch density gradient in self-amplified spontaneous emission (SASE), including the role of coherent spontaneous emission (CSE) in the evolution of the free-electron laser (FEL) process. In the exponential gain regime, the authors solve the coupled Maxwell-Vlasov equations and extend the linear theory to a bunched beam with energy spread. A time-dependent, nonlinear simulation algorithm is used to study the CSE effect and the nonlinear evolution of the radiation pulse

Self-modulated dynamics of a relativistic charged particle beam in plasma wake field excitation

Energy Technology Data Exchange (ETDEWEB)

Akhter, T.; Fedele, R. [Dipartimento di Fisica ‘Ettore Pancini’, Università di Napoli Federico II and INFN Sezione di Napoli, Napoli (Italy); Nicola, S. De [CNR-SPIN and INFN Sezione di Napoli, Napoli (Italy); Tanjia, F. [Dipartimento di Fisica ‘Ettore Pancini’, Università di Napoli Federico II and INFN Sezione di Napoli, Napoli (Italy); Jovanović, D. [Institute of Physics, University of Belgrade, Belgrade (Serbia); Mannan, A. [Department of Physics, Jahangirnagar University, Savar, Dhaka (Bangladesh)

2016-09-01

The self-modulated dynamics of a relativistic charged particle beam is provided within the context of the theory of plasma wake field excitation. The self-consistent description of the beam dynamics is provided by coupling the Vlasov equation with a Poisson-type equation relating the plasma wake potential to the beam density. An analysis of the beam envelope self-modulation is then carried out and the criteria for the occurrence of the instability are discussed thereby.

Torsional actuation with extension-torsion composite coupling and a magnetostrictive actuator

Science.gov (United States)

Bothwell, Christopher M.; Chandra, Ramesh; Chopra, Inderjit

1995-04-01

An analytical-experimental study of using magnetostrictive actuators in conjunction with an extension-torsion coupled composite tube to actuate a rotor blade trailing-edge flap to actively control helicopter vibration is presented. Thin walled beam analysis based on Vlasov theory was used to predict the induced twist and extension in a composite tube with magnetostrictive actuation. The study achieved good correlation between theory and experiment. The Kevlar-epoxy systems showed good correlation between measured and predicted twist values.

Inextendibility of expanding cosmological models with symmetry

Energy Technology Data Exchange (ETDEWEB)

Dafermos, Mihalis [University of Cambridge, Department of Pure Mathematics and Mathematical Statistics, Wilberforce Road, Cambridge CB3 0WB (United Kingdom); Rendall, Alan D [Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Muehlenberg 1, D-14476 Golm (Germany)

2005-12-07

A new criterion for inextendibility of expanding cosmological models with symmetry is presented. It is applied to derive a number of new results and to simplify the proofs of existing ones. In particular, it shows that the solutions of the Einstein-Vlasov system with T{sup 2} symmetry, including the vacuum solutions, are inextendible in the future. The technique introduced adds a qualitatively new element to the available tool-kit for studying strong cosmic censorship. (letter to the editor)

Robust Markowitz mean-variance portfolio selection under ambiguous covariance matrix *

OpenAIRE

Ismail, Amine; Pham, Huyên

2016-01-01

This paper studies a robust continuous-time Markowitz portfolio selection pro\\-blem where the model uncertainty carries on the covariance matrix of multiple risky assets. This problem is formulated into a min-max mean-variance problem over a set of non-dominated probability measures that is solved by a McKean-Vlasov dynamic programming approach, which allows us to characterize the solution in terms of a Bellman-Isaacs equation in the Wasserstein space of probability measures. We provide expli...

Mathematical model of renal elimination of fluid and small ions during hyper- and hypovolemic conditions.

Science.gov (United States)

Gyenge, Christina C; Bowen, Bruce D; Reed, Rolf K; Bert, Joel L

2003-02-01

This study is concerned with the formulation of a 'kidney module' linked to the plasma compartment of a larger mathematical model previously developed. Combined, these models can be used to predict, amongst other things, fluid and small ion excretion rates by the kidney; information that should prove useful in evaluating values and trends related to whole-body fluid balance for different clinical conditions to establish fluid administration protocols and for educational purposes. The renal module assumes first-order, negative-feedback responses of the kidney to changes in plasma volume and/or plasma sodium content from their normal physiological set points. Direct hormonal influences are not explicitly formulated in this empiric model. The model also considers that the renal excretion rates of small ions other than sodium are proportional to the excretion rate of sodium. As part of the model development two aspects are emphasized (1): the estimation of parameters related to the renal elimination of fluid and small ions, and (2) model validation via comparisons between the model predictions and selected experimental data. For validation, model predictions of the renal dynamics are compared with new experimental data for two cases: plasma overload resulting from external fluid infusion (e.g. infusions of iso-osmolar solutions and/or hypertonic/hyperoncotic saline solutions), and untreated hypo volemic conditions that result from the external loss of blood. The present study demonstrates that the empiric kidney module presented above can provide good short-term predictions with respect to all renal outputs considered here. Physiological implications of the model are also presented. Copyright Acta Anaesthesiologica Scandinavica 47 (2003)

Gyrokinetic particle-in-cell global simulations of ion-temperature-gradient and collisionless-trapped-electron-mode turbulence in tokamaks

International Nuclear Information System (INIS)

Jolliet, S.

2009-02-01

The goal of thermonuclear fusion research is to provide power plants, that will be able to produce one gigawatt of electricity. Among the different ways to achieve fusion, the tokamak, based on magnetic confinement, is the most promising one. A gas is heated up to hundreds of millions of degrees and becomes a plasma, which is maintained - or confined - in a toroidal vessel by helical magnetic field lines. Then, deuterium and tritium are injected and fuse to create an α particle and an energetic neutron. In order to have a favorable power balance, the power produced by fusion reactions must exceed the power needed to heat the plasma and the power losses. This can be cast in a very simple expression which stipulates that the product of the density, the temperature and the energy confinement time must exceed some given value. Unfortunately, present-days tokamaks are not able to reach this condition, mostly due to plasma turbulence. The latter phenomenon enhances the heat losses and degrades the energy confinement time, which cannot be predicted by analytical theories such as the so-called neoclassical theory in which the heat losses are caused by Coulomb collisions. Therefore, numerical simulations are being developed to model plasma turbulence, mainly caused by the Ion and Electron Temperature-Gradient and the Trapped-Electron-Mode (TEM) instabilities. The plasma is described by a distribution function which evolves according to the Vlasov equation. The electromagnetic fields created by the particles are self-consistently obtained through Maxwell’s equations. The resulting Vlasov-Maxwell system is greatly simplified by using the gyrokinetic theory, which consists, through an appropriate ordering, of eliminating the fast gyromotion (compared to the typical frequency of instabilities). Nevertheless, it is still extremely difficult to solve this system numerically due to the large range of time and spatial scales to be resolved. In this thesis, the Vlasov

Generation of initial kinetic distributions for simulation of long-pulse charged particle beams with high space-charge intensity

Directory of Open Access Journals (Sweden)

Steven M. Lund

2009-11-01

Full Text Available Self-consistent Vlasov-Poisson simulations of beams with high space-charge intensity often require specification of initial phase-space distributions that reflect properties of a beam that is well adapted to the transport channel—both in terms of low-order rms (envelope properties as well as the higher-order phase-space structure. Here, we first review broad classes of kinetic distributions commonly in use as initial Vlasov distributions in simulations of unbunched or weakly bunched beams with intense space-charge fields including the following: the Kapchinskij-Vladimirskij (KV equilibrium, continuous-focusing equilibria with specific detailed examples, and various nonequilibrium distributions, such as the semi-Gaussian distribution and distributions formed from specified functions of linear-field Courant-Snyder invariants. Important practical details necessary to specify these distributions in terms of standard accelerator inputs are presented in a unified format. Building on this presentation, a new class of approximate initial kinetic distributions are constructed using transformations that preserve linear focusing, single-particle Courant-Snyder invariants to map initial continuous-focusing equilibrium distributions to a form more appropriate for noncontinuous focusing channels. Self-consistent particle-in-cell simulations are employed to show that the approximate initial distributions generated in this manner are better adapted to the focusing channels for beams with high space-charge intensity. This improved capability enables simulations that more precisely probe intrinsic stability properties and machine performance.

Nonlinear Brillouin amplification of finite-duration seeds in the strong coupling regime

International Nuclear Information System (INIS)

Lehmann, G.; Spatschek, K. H.

2013-01-01

Parametric plasma processes received renewed interest in the context of generating ultra-intense and ultra-short laser pulses up to the exawatt-zetawatt regime. Both Raman as well as Brillouin amplifications of seed pulses were proposed. Here, we investigate Brillouin processes in the one-dimensional (1D) backscattering geometry with the help of numerical simulations. For optimal seed amplification, Brillouin scattering is considered in the so called strong coupling (sc) regime. Special emphasis lies on the dependence of the amplification process on the finite duration of the initial seed pulses. First, the standard plane-wave instability predictions are generalized to pulse models, and the changes of initial seed pulse forms due to parametric instabilities are investigated. Three-wave-interaction results are compared to predictions by a new (kinetic) Vlasov code. The calculations are then extended to the nonlinear region with pump depletion. Generation of different seed layers is interpreted by self-similar solutions of the three-wave interaction model. Similar to Raman amplification, shadowing of the rear layers by the leading layers of the seed occurs. The shadowing is more pronounced for initially broad seed pulses. The effect is quantified for Brillouin amplification. Kinetic Vlasov simulations agree with the three-wave interaction predictions and thereby affirm the universal validity of self-similar layer formation during Brillouin seed amplification in the strong coupling regime

Analysis of different responses of ion and electron in six-field two-fluid ELM simulations

Science.gov (United States)

Ma, Chenhao; Xu, Xueqiao

2013-10-01

We report simulation results of a Landau-Fluid (GLF) extension of the BOUT++ six-field two-fluid Braginskii model which contributes to increasing the physics understanding of ELMs. Landau-Fluid closure can fill the gap for parallel dynamics between hot, collisionless pedestal region and cold, collisional SOL region in H-mode plasmas. Our goal is extending the classical parallel heat flux with Landau-Fluid closures and making comparisons with other closure models. Our simulations show that for weakly collisional pedestal plasmas, the calculated growth rate with Landau-Fluid closure introduces more effective damping on the peeling-ballooning modes than that with the classical thermal diffusivity. Further nonlinear simulation shows that ELM size with Landau-Fluid Closure is smaller than that with classical thermal diffusivity. We find an ELM crash has two phases: fast initial crash of ion temperature perturbation on the Alfven time scale and slow turbulence spreading. Turbulence transport phase is a slow encroachment of electron temperature perturbation due to the ELM event into pedestal region which is due to a positive phase shift around π / 2 between electron temperature and potential on pedestal region while ion temperature is in-phase with potential. This work was performed under the auspices of the U.S. DoE by LLNL under Contract DE-AC52-07NA27344 and also supported by the China Scholarship Committee under contract N0.2011601099.

Dynamical instabilities in hot expanding nuclear systems: a microscopic approach to the understanding of multifragmentation

International Nuclear Information System (INIS)

Suraud, E.

1989-01-01

We present a microscopic study of the quasi-fusion/explosion transition in the framework of Landau-Vlasov simulations and for intermediate energy heavy-ion collisions (beam energy from 10 to 100 MeV/A). After a short presentation of the results of schematic calculations, which furnish a guideline for microscopic investigations, we discuss the relevance of our approach for studying multifragmentation. Once the limitations of this kind of dynamical simulations exhibited, we perform a detailed analysis in terms of the equation of state of the system. In agreement with schematic models we find that the composite nuclear system formed in the collision actually explodes when it stays long enough in the mechanically unstable region (spinodal region). Quantitative estimates of the explosion threshold are given for central symmetric reactions (Ca + Ca and Ar + Ti). The link of the results with transport properties and the equation of state of nuclear matter are briefly discussed

Nonlinear delta f Simulations of Collective Effects in Intense Charged Particle Beams

CERN Document Server

Hong Qi

2003-01-01

A nonlinear delta(f) particle simulation method based on the Vlasov-Maxwell equations has been recently developed to study collective processes in high-intensity beams, where space-charge and magnetic self-field effects play a critical role in determining the nonlinear beam dynamics. Implemented in the Beam Equilibrium, Stability and Transport (BEST) code [H. Qin, R.C. Davidson, and W.W. Lee, Physical Review -- Special Topics on Accelerator and Beams 3 (2000) 084401; 3 (2000) 109901.], the nonlinear delta(f) method provides a low-noise and self-consistent tool for simulating collective interactions and nonlinear dynamics of high-intensity beams in modern and next-generation accelerators and storage rings, such as the Spallation Neutron Source and heavy ion fusion drivers. A wide range of linear eigenmodes of high-intensity charged-particle beams can be systematically studied using the BEST code. Simulation results for the electron-proton two-stream instability in the Proton Storage Ring experiment [R. Macek, ...

An algorithm for the calculation of three-dimensional ICRF fields in tokamak geometry

International Nuclear Information System (INIS)

Smithe, D.N.; Kammash, T.

1987-01-01

A computational scheme is developed which permits tractable calculation of three-dimensional full-wave solutions to the Vlasov-Maxwell equations under typical ion cyclotron range of frequencies (ICRF) experimental conditions. The method is unique in that power deposition to the plasma is determined via the anti-Hermitian part of a truncated warm plasma dielectric operator, rather than as the result of an assumed phenomenological collision frequency. The resulting computer code allows arbitrary variation of density, temperature, magnetic field and minority concentration in the poloidal plane by performing a convolution of poloidal modes to produce a coupled system of differential equations in the radial variable. By assuming no inhomogeneity along the toroidal axis, an inverse transform over k parallel is performed, yielding the global three-dimensional fast wave field solutions. The application of the code to TFTR-like plasmas shows a mild resonance structure in antenna loading related to the changing number of wavelengths between the antenna and the resonance layer. (author)

Slowly moving test charge in two-electron component non-Maxwellian plasma

International Nuclear Information System (INIS)

Ali, S.; Eliasson, B.

2015-01-01

Potential distributions around a slowly moving test charge are calculated by taking into account the electron-acoustic waves in an unmagnetized plasma. Considering a neutralizing background of static positive ions, the supra-thermal hot and cold electrons are described by the Vlasov equations to account for the Kappa (power-law in velocity space) and Maxwell equilibrium distributions. Fourier analysis further leads to the derivation of electrostatic potential showing the impact of supra-thermal hot electrons. The test charge moves slowly in comparison with the hot and cold electron thermal speeds and is therefore shielded by the electrons. This gives rise to a short-range Debye-Hückel potential decaying exponentially with distance and to a far field potential decaying as inverse third power of the distance from the test charge. The results are relevant for both laboratory and space plasmas, where supra-thermal hot electrons with power-law distributions have been observed

A Proton-Cyclotron Wave Storm Generated by Unstable Proton Distribution Functions in the Solar Wind

Science.gov (United States)

Wicks, R. T.; Alexander, R. L.; Stevens, M.; Wilson, L. B., III; Moya, P. S.; Vinas, A.; Jian, L. K.; Roberts, D. A.; O’Modhrain, S.; Gilbert, J. A.;

Distortions of the distribution function of collisionless particles by high-frequency gravitational waves

International Nuclear Information System (INIS)

Vainer, B.V.; Nasel'skii, P.D.

1983-01-01

Equations for the correlation functions of fluctuations in the spectra of relativistic collisionless particles are obtained from the combined system of Einstein's equations and the Vlasov equation. It is shown that the interaction of high-frequency gravitational waves with collisionless particles leads to diffusion of their spectrum in the momentum space. The distortions in the spectrum of the microwave background radiation in a cosmological model with high-frequency gravitational waves are discussed. Bounds are obtained on the spectral characteristics of background gravitational waves

The nuclear flow and the mass number dependence of the balance point

International Nuclear Information System (INIS)

Sebille, F.; de la Mota, V.; Remaud, B.; Schuck, P.

1990-01-01

The nuclear flow is studied theoretically with the Landau Vlasov equation in the E/A = 50 to 150 MeV energy domain using the finite range Gogny force. For comparison also other equations of states based on velocity independent mean fields are used. In this paper the mass number dependence of the balance point is investigated. A sensitivity of the flow on the equation of state as a function of mass and energies around and above the balance point can tentatively be advanced

Equilibrium distribution function in collisionless systems

International Nuclear Information System (INIS)

Pergamenshchik, V.M.

1988-01-01

Collisionless systems of a large number of N particles interacting by Coulomb forces are widely spread in cosmic and laboratory plasma. A statistical theory of equilibrium state of collisionless Coulomb systems which evolution obeys Vlasov equation is proposed. The developed formalism permits a sequential consideration of such distributed in one-particle six-dimensional phase space of a system and to obtain a simple result: equilibrium distribution function has the form of Fermi-Dirac distribution and doesn't depend on initial state factors

Velocity-space diffusion due to resonant wave-wave scattering of electromagnetic and electrostatic waves in a plasma

International Nuclear Information System (INIS)

Sugaya, Reija

1991-01-01

The velocity-space diffusion equation describing distortion of the velocity distribution function due to resonant wave-wave scattering of electromagnetic and electrostatic waves in an unmagnetized plasma is derived from the Vlasov-Maxwell equations by perturbation theory. The conservation laws for total energy and momentum densities of waves and particles are verified, and the time evolutions of the energy and momentum densities of particles are given in terms of the nonlinear wave-wave coupling coefficient in the kinetic wave equation. (author)

Plasma Wave Turbulence and Particle Heating Caused by Electron Beams, Radiation, and Pinches.

Science.gov (United States)

1983-01-01

34Vlasov turbulence, this means that Poisson’s equation for F(k;t )m dr exp(- k-r)(g (r,t)-’(0,t)) the field fluctuations must be taken into account ...effect can work in principle for a narrow band cm -. , and therefore an electron plasma frequency off, = 35 width spectrum. In Sec. IV, we discuss some...sufficiently intense to saturate the beam-unstable modes. Such levels appear to produce either fundmental or harmonic emission." 1 Both have been

Numerical simulation of whistler-triggered VLF emissions observed in Antartica

Energy Technology Data Exchange (ETDEWEB)

Nunn, D. [Southhampton Univ., Southhampton (United Kingdom); Smith, A.J. [British Antarctic Survey, Cambridge (United Kingdom)

1996-03-01

The authors have extracted from VLF databases from British Antarctica Survey data taken at Halley and Faraday stations, examples of whistler-triggered emissions (WTE). The WTE are relatively narrow band emissions triggered by natural background whistlers undergoing nonlinear wave particle interactions generally in the equatorial regions. They occur with either rising or falling frequency relative to the triggering waves. Using a Vlasov type code the authors are able to simulate the types of emissions which are observed. 24 refs., 8 figs., 3 tabs.

On the formation and evolution of clumps of galaxies in an expanding universe

Science.gov (United States)

Norman, C. A.; Silk, J.

1978-01-01

Results are derived for the development of phase-space clumps of mass points in a background spectrum of gravitational-potential fluctuations. The Vlasov equation and the pair correlation equation (in the weak coupling limit) are solved exactly in an Einstein-de Sitter cosmology, and the plasma-clumping theory is used to identify terms that yield important collective effects. Various astrophysical implications are discussed, including the formation of large-scale inhomogeneity and the enhanced generation of correlations in the distribution of galaxies.

Classical limit for semirelativistic Hartree systems

KAUST Repository

Aki, Gonca L.

2008-01-01

We consider the three-dimensional semirelativistic Hartree model for fast quantum mechanical particles moving in a self-consistent field. Under appropriate assumptions on the initial density matrix as a (fully) mixed quantum state we prove by using Wigner transformation techniques that its classical limit yields the well known relativistic Vlasov-Poisson system. The result holds for the case of attractive and repulsive mean-field interactions, with an additional size constraint in the attractive case. © 2008 American Institute of Physics.

Relativistic classical limit of quantum theory

International Nuclear Information System (INIS)

Shin, G.R.; Rafelski, J.

1993-01-01

We study the classical limit of the equal-time relativistic quantum transport theory. We discuss in qualitative terms the need to fold first the Wigner function with a coarse-graining function. Only then does the singularity at ℎ→0 seem to be manageable. In the limit ℎ→0, we obtain the relativistic Vlasov equations for the particle and the antiparticle sector of the Fock space. Similarly, we address the evolution equations of the spin and the magnetic-moment density

Tail reconnection in the global magnetospheric context: Vlasiator first results

Science.gov (United States)

Palmroth, Minna; Hoilijoki, Sanni; Juusola, Liisa; Pulkkinen, Tuija I.; Hietala, Heli; Pfau-Kempf, Yann; Ganse, Urs; von Alfthan, Sebastian; Vainio, Rami; Hesse, Michael

2017-11-01

The key dynamics of the magnetotail have been researched for decades and have been associated with either three-dimensional (3-D) plasma instabilities and/or magnetic reconnection. We apply a global hybrid-Vlasov code, Vlasiator, to simulate reconnection self-consistently in the ion kinetic scales in the noon-midnight meridional plane, including both dayside and nightside reconnection regions within the same simulation box. Our simulation represents a numerical experiment, which turns off the 3-D instabilities but models ion-scale reconnection physically accurately in 2-D. We demonstrate that many known tail dynamics are present in the simulation without a full description of 3-D instabilities or without the detailed description of the electrons. While multiple reconnection sites can coexist in the plasma sheet, one reconnection point can start a global reconfiguration process, in which magnetic field lines become detached and a plasmoid is released. As the simulation run features temporally steady solar wind input, this global reconfiguration is not associated with sudden changes in the solar wind. Further, we show that lobe density variations originating from dayside reconnection may play an important role in stabilising tail reconnection.

Adsorption of fluids in slitlike pores containing a small amount of mobile ions.

Science.gov (United States)

Borówko, M; Bucior, K; Sokołowski, S; Staszewski, T

2005-11-01

We apply density functional theory to investigate changes in the phase behavior of a fluid caused by the presence of mobile ions inside the pore. The approach has been based on the fundamental measure density functional theory and on the theory of nonuniform electrolytes developed recently by O. Pizio, A. Patrykiejew, S. Sokołowski [J. Chem. Phys. 121 (2005) 11,957]. We have evaluated capillary condensation phase diagrams for pores of different widths and for different concentrations of confined ions. The calculations have demonstrated that the presence of ions leads to lowering the critical temperature and to an increase of the value of the chemical potential at the capillary condensation point.

A hybrid gyrokinetic ion and isothermal electron fluid code for astrophysical plasma

Science.gov (United States)

Kawazura, Y.; Barnes, M.

2018-05-01

This paper describes a new code for simulating astrophysical plasmas that solves a hybrid model composed of gyrokinetic ions (GKI) and an isothermal electron fluid (ITEF) Schekochihin et al. (2009) [9]. This model captures ion kinetic effects that are important near the ion gyro-radius scale while electron kinetic effects are ordered out by an electron-ion mass ratio expansion. The code is developed by incorporating the ITEF approximation into AstroGK, an Eulerian δf gyrokinetics code specialized to a slab geometry Numata et al. (2010) [41]. The new code treats the linear terms in the ITEF equations implicitly while the nonlinear terms are treated explicitly. We show linear and nonlinear benchmark tests to prove the validity and applicability of the simulation code. Since the fast electron timescale is eliminated by the mass ratio expansion, the Courant-Friedrichs-Lewy condition is much less restrictive than in full gyrokinetic codes; the present hybrid code runs ∼ 2√{mi /me } ∼ 100 times faster than AstroGK with a single ion species and kinetic electrons where mi /me is the ion-electron mass ratio. The improvement of the computational time makes it feasible to execute ion scale gyrokinetic simulations with a high velocity space resolution and to run multiple simulations to determine the dependence of turbulent dynamics on parameters such as electron-ion temperature ratio and plasma beta.