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
Relativistic simulation of the Vlasov equation for plasma expansion into vacuum
Directory of Open Access Journals (Sweden)
H Abbasi
2012-12-01
Full Text Available In this study, relativistic Vlasov simulation of plasma for expansion of collisionless plasma for into vacuum is presented. The model is based on 1+1 dimensional phase space and electrostatic approximation. For this purpose, the electron dynamics is studied by the relativistic Vlasov equation. Regardless of the ions temperature, fluid equations are used for their dynamics. The initial electrons distribution function is the relativistic Maxwellian. The results show that due to the electrons relativistic temperature, the process of the plasma expansion takes place faster, the resulting electric field is stronger and the ions are accelerated to higher velocities, in comparison to the non-relativistic case.
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
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)
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.
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)
International Nuclear Information System (INIS)
Gross, F.
1986-01-01
Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs
Action principles for the Vlasov equation
International Nuclear Information System (INIS)
Ye, H.; Morrison, P.J.
1992-01-01
Five action principles for the Vlasov--Poisson and Vlasov--Maxwell equations, which differ by the variables incorporated to describe the distribution of particles in phase space, are presented. Three action principles previously known for the Vlasov--Maxwell equations are altered so as to produce the Vlasov--Poisson equation upon variation with respect to only the particle variables, and one action principle previously known for the Vlasov--Poisson equation is altered to produce the Vlasov--Maxwell equations upon variations with respect to particle and field variables independently. Also, a new action principle for both systems, which is called the leaf action, is presented. This new action has the desirable features of using only a single generating function as the dynamical variable for describing the particle distribution, and manifestly preserving invariants of the system known as Casimir invariants. The relationships between the various actions are described, and it is shown that the leaf action is a link between actions written in terms of Lagrangian and Eulerian variables
Kinetic Boltzmann, Vlasov and Related Equations
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
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.
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.
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)
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)
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
Variational principle for nonlinear gyrokinetic Vlasov--Maxwell equations
International Nuclear Information System (INIS)
Brizard, Alain J.
2000-01-01
A new variational principle for the nonlinear gyrokinetic Vlasov--Maxwell equations is presented. This Eulerian variational principle uses constrained variations for the gyrocenter Vlasov distribution in eight-dimensional extended phase space and turns out to be simpler than the Lagrangian variational principle recently presented by H. Sugama [Phys. Plasmas 7, 466 (2000)]. A local energy conservation law is then derived explicitly by the Noether method. In future work, this new variational principle will be used to derive self-consistent, nonlinear, low-frequency Vlasov--Maxwell bounce-gyrokinetic equations, in which the fast gyromotion and bounce-motion time scales have been eliminated
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...
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.
Hamiltonian formalism of two-dimensional Vlasov kinetic equation.
Pavlov, Maxim V
2014-12-08
In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.
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
Guthrey, Pierson Tyler
) argument requires. The maximum stable time-step scales inversely with the highest degree in the DG polynomial approximation space and becomes progressively smaller with each added spatial dimension. In this work, we overcome this difficulty by introducing a novel time-stepping strategy: the regionally-implicit discontinuous Galerkin (RIDG) method. The RIDG is method is based on an extension of the Lax-Wendroff DG (LxW-DG) method, which previously had been shown to be equivalent (for linear constant coefficient problems) to a predictor-corrector approach, where the prediction is computed by a space-time DG method (STDG). The corrector is an explicit method that uses the space-time reconstructed solution from the predictor step. In this work, we modify the predictor to include not just local information, but also neighboring information. With this modification, we show that the stability is greatly enhanced; we show that we can remove the polynomial degree dependence of the maximum time-step and show vastly improved time-steps in multiple spatial dimensions. Upon the development of the general RIDG method, we apply it to the non-relativistic 1D1V Vlasov-Poisson equations and the relativistic 1D2V Vlasov-Maxwell equations. For each we validate the high-order method on several test cases. In the final test case, we demonstrate the ability of the method to simulate the acceleration of electrons to relativistic speeds in a simplified test case.
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
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
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 Integration of the Vlasov Equation of Two Colliding Beams
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...
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)
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 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
Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations
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.
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.
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)
The relativistic electron wave equation
International Nuclear Information System (INIS)
Dirac, P.A.M.
1977-08-01
The paper was presented at the European Conference on Particle Physics held in Budapest between the 4th and 9th July of 1977. A short review is given on the birth of the relativistic electron wave equation. After Schroedinger has shown the equivalence of his wave mechanics and the matrix mechanics of Heisenberg, a general transformation theory was developed by the author. This theory required a relativistic wave equation linear in delta/delta t. As the Klein--Gordon equation available at this time did not satisfy this condition the development of a new equation became necessary. The equation which was found gave the value of the electron spin and magnetic moment automatically. (D.P.)
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.''
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.
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
Stability analysis of cylindrical Vlasov equilibria
International Nuclear Information System (INIS)
Short, R.W.
1979-01-01
A general method of stability analysis is described which may be applied to a large class of such problems, namely those which are described dynamically by the Vlasov equation, and geometrically by cylindrical symmetry. The method is presented for the simple case of the Vlasov-Poisson (electrostatic) equations, and the results are applied to a calculation of the lower-hybrid-drift instability in a plasma with a rigid rotor distribution function. The method is extended to the full Vlasov-Maxwell (electromagnetic) equations. These results are applied to a calculation of the instability of the extraordinary electromagnetic mode in a relativistic E-layer interacting with a background plasma
Stability analysis of cylindrical Vlasov equilibria
International Nuclear Information System (INIS)
Short, R.W.
1979-01-01
A general method of stability analysis is described which may be applied to a large class of such problems, namely those which are described dynamically by the Vlasov equation, and geometrically by clindrical symmetry. The method is presented for the simple case of the Vlasov-Poisson (electrostatic) equations, and the results are applied to a calculation of the lower-hybrid-drift instability in a plasma with a rigid rotor distribution function. The method is extended to the full Vlasov-Maxwell (electromagnetic) equations. These results are applied to a calculation of the instability of the extraordinary electromagnetic mode in a relativistic E-layer interacting with a background plasma
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 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)
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.
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.)
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
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.
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
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
Solving the Vlasov equation in two spatial dimensions with the Schrödinger method
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.
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.)
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)
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
The ionisation equation in a relativistic gas
International Nuclear Information System (INIS)
Kichenassamy, S.; Krikorian, R.A.
1983-01-01
By deriving the relativistic form of the ionisation equation for a perfect gas it is shown that the usual Saha equation is valid to 3% for temperatures below one hundred million Kelvin. Beyond 10 9 K, the regular Saha equation is seriously incorrect and a relativistic distribution function for electrons must be taken into account. Approximate forms are derived when only the electrons are relativistic (appropriate up to 10 12 K) and also for the ultrarelativistic case (temperatures greater than 10 15 K). (author)
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
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)
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
Global existence proof for relativistic Boltzmann equation
International Nuclear Information System (INIS)
Dudynski, M.; Ekiel-Jezewska, M.L.
1992-01-01
The existence and causality of solutions to the relativistic Boltzmann equation in L 1 and in L loc 1 are proved. The solutions are shown to satisfy physically natural a priori bounds, time-independent in L 1 . The results rely upon new techniques developed for the nonrelativistic Boltzmann equation by DiPerna and Lions
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.
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.)
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.)
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.
Liouville equation of relativistic charged fermion
International Nuclear Information System (INIS)
Wang Renchuan; Zhu Dongpei; Huang Zhuoran; Ko Che-ming
1991-01-01
As a form of density martrix, the Wigner function is the distribution in quantum phase space. It is a 2 X 2 matrix function when one uses it to describe the non-relativistic fermion. While describing the relativistic fermion, it is usually represented by 4 x 4 matrix function. In this paper authors obtain a Wigner function for the relativistic fermion in the form of 2 x 2 matrix, and the Liouville equation satisfied by the Wigner function. this equivalent to the Dirac equation of changed fermion in QED. The equation is also equivalent to the Dirac equation in the Walecka model applied to the intermediate energy nuclear collision while the nucleon is coupled to the vector meson only (or taking mean field approximation for the scalar meson). Authors prove that the 2 x 2 Wigner function completely describes the quantum system just the same as the relativistic fermion wave function. All the information about the observables can be obtained with above Wigner function
Relativistic supersymmetric quantum mechanics based on Klein-Gordon equation
International Nuclear Information System (INIS)
Znojil, Miloslav
2004-01-01
Witten's the non-relativistic formalism of supersymmetric quantum mechanics was based on a factorization and partnership between Schroedinger equations. We show how it accommodates a transition to the partnership between relativistic Klein-Gordon equations
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 ⊙
Relativistic equations of state at finite temperature
International Nuclear Information System (INIS)
Santos, A.M.S.; Menezes, D.P.
2004-01-01
In this work we study the effects of temperature on the equations of state obtained within a relativistic model with and without β equilibrium, over a wide range of densities. We integrate the TOV equations. We also compare the results of the equation of state, effective mass and strangeness fraction from the TM1, NL3 and GL sets of parameters, as well as investigating the importance of antiparticles in the treatment. The have checked that TM1 and NL3 are not appropriate for the description of neutron and protoneutron stars. (author)
Multilevel and Multi-index Monte Carlo methods for the McKean–Vlasov equation
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.
Relativistic many-body theory of atomic transitions: the relativistic equation-of-motion approach
International Nuclear Information System (INIS)
Huang, K.N.
1981-01-01
An equation-of-motion approach is used to develop the relativistic many-body theory of atomic transitions. The relativistic equations of motion for transition matrices are formulated using techniques of quantum field theory. To reduce the equation of motion to a tractable form which is appropriate for numerical calculations, a graphical method is employed to resolve the complication arising from the antisymmetrization and angular momentum coupling. The relativistic equation-of-motion method allows an ab initio treatment of correlation and relativistic effects in both closed- and open-shell many-body systems. A special case of the present formulation reduces to the relativistic random-phase approximation
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)
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)
Relativistic wave equations and compton scattering
International Nuclear Information System (INIS)
Sutanto, S.H.; Robson, B.A.
1998-01-01
Full text: Recently an eight-component relativistic wave equation for spin-1/2 particles was proposed.This equation was obtained from a four-component spin-1/2 wave equation (the KG1/2 equation), which contains second-order derivatives in both space and time, by a procedure involving a linearisation of the time derivative analogous to that introduced by Feshbach and Villars for the Klein-Gordon equation. This new eight-component equation gives the same bound-state energy eigenvalue spectra for hydrogenic atoms as the Dirac equation but has been shown to predict different radiative transition probabilities for the fine structure of both the Balmer and Lyman a-lines. Since it has been shown that the new theory does not always give the same results as the Dirac theory, it is important to consider the validity of the new equation in the case of other physical problems. One of the early crucial tests of the Dirac theory was its application to the scattering of a photon by a free electron: the so-called Compton scattering problem. In this paper we apply the new theory to the calculation of Compton scattering to order e 2 . It will be shown that in spite of the considerable difference in the structure of the new theory and that of Dirac the cross section is given by the Klein-Nishina formula
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
Balance equations for a relativistic plasma. Pt. 1
International Nuclear Information System (INIS)
Hebenstreit, H.
1983-01-01
Relativistic power moments of the four-momentum are decomposed according to a macroscopic four-velocity. The thus obtained quantities are identified as relativistic generalization of the nonrelativistic orthogonal moments, e.g. diffusion flow, heat flow, pressure, etc. From the relativistic Boltzmann equation we then derive balance equations for these quantities. Explicit expressions for the relativistic mass conservation, energy balance, pressure balance, heat flow balance are presented. The weak relativistic limit is discussed. The derivation of higher order balance equations is sketched. (orig.)
The Einstein-Vlasov System/Kinetic Theory.
Andréasson, Håkan
2011-01-01
The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to a good comprehension of kinetic theory in general relativity.
Nonlinear dynamics in the relativistic field equation
International Nuclear Information System (INIS)
Tanaka, Yosuke; Mizuno, Yuji; Kado, Tatsuhiko; Zhao, Hua-An
2007-01-01
We have investigated relativistic equations and chaotic behaviors of the gravitational field with the use of general relativity and nonlinear dynamics. The space component of the Friedmann equation shows chaotic behaviors in case of the inflation (h=G-bar /G>0) and open (ζ=-1) universe. In other cases (h= 0 andx-bar 0 ) and the parameters (a, b, c and d); (2) the self-similarity of solutions in the x-x-bar plane and the x-ρ plane. We carried out the numerical calculations with the use of the microsoft EXCEL. The self-similarity and the hierarchy structure of the universe have been also discussed on the basis of E-infinity theory
Relativistic covariant wave equations and acausality in external fields
International Nuclear Information System (INIS)
Pijlgroms, R.B.J.
1980-01-01
The author considers linear, finite dimensional, first order relativistic wave equations: (βsup(μ)ideltasub(μ)-β)PSI(x) = 0 with βsup(μ) and β constant matrices. Firstly , the question of the relativistic covariance conditions on these equations is considered. Then the theory of these equations with β non-singular is summarized. Theories with βsup(μ), β square matrices and β singular are also discussed. Non-square systems of covariant relativistic wave equations for arbitrary spin > 1 are then considered. Finally, the interaction with external fields and the acausality problem are discussed. (G.T.H.)
Relativistic three-particle dynamical equations: I. Theoretical development
International Nuclear Information System (INIS)
Adhikari, S.K.; Tomio, L.; Frederico, T.
1993-11-01
Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, three dimensional scattering integral equations satisfying constrains of relativistic unitarity and covariance are rederived. These equations were first derived by Weinberg and by Blankenbecler and Sugar. These two-particle equations are shown to be related by a transformation of variables. Hence it is shown to perform and relate dynamical calculation using these two equations. Similarly, starting from the Bethe-Salpeter-Faddeev equation for the three-particle system and integrating over the time component of momentum, several three dimensional three-particle scattering equations satisfying constraints of relativistic unitary and covariance are derived. Two of these three-particle equations are related by a transformation of variables as in the two-particle case. The three-particle equations obtained are very practical and suitable for performing relativistic scattering calculations. (author)
Relativistic many-body theory of atomic transitions. The relativistic equation-of-motion approach
International Nuclear Information System (INIS)
Huang, K.
1982-01-01
An equation-of-motion approach is used to develop the relativistic many-body theory of atomic transitions. The relativistic equations of motion for transition matrices are formulated with the use of techniques of quantum-field theory. To reduce the equations of motion to a tractable form which is appropriate for numerical calculations, a graphical method to resolve the complication arising from the antisymmetrization and angular-momentum coupling is employed. The relativistic equation-of-motion method allows an ab initio treatment of correlation and relativistic effects in both closed- and open-shell many-body systems. A special case of the present formulation reduces to the relativistic random-phase approximation
Equations of motion in relativistic gravity
Lämmerzahl, Claus; Schutz, Bernard
2015-01-01
The present volume aims to be a comprehensive survey on the derivation of the equations of motion, both in General Relativity as well as in alternative gravity theories. The topics covered range from the description of test bodies, to self-gravitating (heavy) bodies, to current and future observations. Emphasis is put on the coverage of various approximation methods (e.g., multipolar, post-Newtonian, self-force methods) which are extensively used in the context of the relativistic problem of motion. Applications discussed in this volume range from the motion of binary systems -- and the gravitational waves emitted by such systems -- to observations of the galactic center. In particular the impact of choices at a fundamental theoretical level on the interpretation of experiments is highlighted. This book provides a broad and up-do-date status report, which will not only be of value for the experts working in this field, but also may serve as a guideline for students with background in General Relativity who ...
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
The Poisson equation at second order in relativistic cosmology
International Nuclear Information System (INIS)
Hidalgo, J.C.; Christopherson, Adam J.; Malik, Karim A.
2013-01-01
We calculate the relativistic constraint equation which relates the curvature perturbation to the matter density contrast at second order in cosmological perturbation theory. This relativistic ''second order Poisson equation'' is presented in a gauge where the hydrodynamical inhomogeneities coincide with their Newtonian counterparts exactly for a perfect fluid with constant equation of state. We use this constraint to introduce primordial non-Gaussianity in the density contrast in the framework of General Relativity. We then derive expressions that can be used as the initial conditions of N-body codes for structure formation which probe the observable signature of primordial non-Gaussianity in the statistics of the evolved matter density field
Relativistic Spinning Particle without Grassmann Variables and the Dirac Equation
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A. A. Deriglazov
2011-01-01
Full Text Available We present the relativistic particle model without Grassmann variables which, being canonically quantized, leads to the Dirac equation. Classical dynamics of the model is in correspondence with the dynamics of mean values of the corresponding operators in the Dirac theory. Classical equations for the spin tensor are the same as those of the Barut-Zanghi model of spinning particle.
Relativistic hydrodynamics with QHD-I equation of state
International Nuclear Information System (INIS)
Menezes, D.P.
1993-04-01
We derive the equation of state of the QHD-I lagrangian in a classical approach. The obtained equation of state is then used as input in a relativistic hydrodynamical numerical routine. Rapidity and transverse momentum distributions are calculated and compared with experimental data on heavy ion collisions obtained at BNL-AGS and CERN-SPS. (orig.). 7 figs
Relativistic Tsiolkovsky equation -- a case study in special relativity
Redd, Jeremy; Panin, Alexander
2011-10-01
A possibility of using antimatter in future space propulsion systems is seriously discussed in scientific literature. Annihilation of matter and antimatter is not only the energy source of ultimate density 9x10^16 J/kg (provided that antimatter fuel is available on board or can be collected along the journey) but also potentially allows to reach ultimate exhaust speed -- speed of light c. Using relativistic rocket equation we discuss the feasibility of achieving relativistic velocities with annihilation powered photon engine, as well as the advantages and disadvantages of interstellar travel with relativistic and ultrarelativistic velocities.
Reduced Vlasov-Maxwell simulations
International Nuclear Information System (INIS)
Helluy, P.; Navoret, L.; Pham, N.; Crestetto, A.
2014-01-01
The Maxwell-Vlasov system is a fundamental model in physics. It can be applied to plasma simulations, charged particles beam, astrophysics, etc. The unknowns are the electromagnetic field, solution to the Maxwell equations and the distribution function, solution to the Vlasov equation. In this paper we review two different numerical methods for Vlasov-Maxwell simulations. The first method is based on a coupling between a Discontinuous Galerkin (DG) Maxwell solver and a Particle-In-Cell (PIC) Vlasov solver. The second method only uses a DG approach for the Vlasov and Maxwell equations. The Vlasov equation is first reduced to a space-only hyperbolic system thanks to the finite-element method. The two numerical methods are implemented using OpenCL in order to achieve high performance on recent Graphic Processing Units (GPU). We obtained interesting speedups, but we also observe that the PIC method is the most expensive part of the computation. Therefore we propose another fully Eulerian approach. Thanks to a decomposition of the distribution function on velocity basis functions, we obtain a reduced Vlasov model, which appears to be a hyperbolic system of conservation laws written only in the (x,t) space. We can thus adapt very easily our DG solver to the reduced model
Electromagnetic interactions in relativistic infinite component wave equations
International Nuclear Information System (INIS)
Gerry, C.C.
1979-01-01
The electromagnetic interactions of a composite system described by relativistic infinite-component wave equations are considered. The noncompact group SO(4,2) is taken as the dynamical group of the systems, and its unitary irreducible representations, which are infinite dimensional, are used to find the energy spectra and to specify the states of the systems. First the interaction mechanism is examined in the nonrelativistic SO(4,2) formulation of the hydrogen atom as a heuristic guide. A way of making a minimal relativistic generalization of the minimal ineractions in the nonrelativistic equation for the hydrogen atom is proposed. In order to calculate the effects of the relativistic minimal interactions, a covariant perturbation theory suitable for infinite-component wave equations, which is an algebraic and relativistic version of the Rayleigh-Schroedinger perturbation theory, is developed. The electric and magnetic polarizabilities for the ground state of the hydrogen atom are calculated. The results have the correct nonrelativistic limits. Next, the relativistic cross section of photon absorption by the atom is evaluated. A relativistic expression for the cross section of light scattering corresponding to the seagull diagram is derived. The Born amplitude is combusted and the role of spacelike solutions is discussed. Finally, internal electromagnetic interactions that give rise to the fine structure splittings, the Lamb shifts and the hyperfine splittings are considered. The spin effects are introduced by extending the dynamical group
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)
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.
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)
International Nuclear Information System (INIS)
Chen Baoqiu; Ma Zhongyu
1992-01-01
Relativistic microscopic optical potential of nucleon-nucleus is derived from the relativistic Brueckner-Bethe-Goldstone (RBBG) equation. The complex effective mass of a nucleon is determined by a fit to 200 MeV p- 40 Ca scattering data. The relativistic microscopic optical potentials with this effective mass are obtained from RBBG for p- 16O , 40 Ca, 90 Zr and 208 Pb scattering in energy range from 160 to 800 MeV. The microscopic optical potential is used to study the proton- 40 Ca scattering problem at 200 MeV. The results, such as differential cross section, analyzing power and spin rotation function are compared with those calculated from phenomenological relativistic optical potential
The Einstein-Vlasov System/Kinetic Theory
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Håkan Andréasson
2002-12-01
Full Text Available The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on nonrelativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. The Vlasov equation describes matter phenomenologically, and it should be stressed that most of the theorems presented in this article are not presently known for other such matter models (i.e., fluid models. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to good comprehension of kinetic theory in general relativity.
General relativistic Boltzmann equation, II: Manifestly covariant treatment
Debbasch, F.; van Leeuwen, W.A.
2009-01-01
In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p(2) = m(2)c(2). Due to this restriction, the resulting Boltzmann
Relativistic phenomenological equations and transformation laws of relative coefficients
Directory of Open Access Journals (Sweden)
Patrizia Rogolino
2017-06-01
Full Text Available The aim of this paper is to derive the phenomenological equations in the context of special relativistic non-equilibrium thermodynamics with internal variables. In particular, after introducing some results developed in our previous paper, by means of classical non-equilibrium thermodynamic procedure and under suitable assumptions on the entropy density production, the phenomenological equations and transformation laws of phenomenological coefficients are derived. Finally, some symmetries of aforementioned coefficients are obtained.
International Nuclear Information System (INIS)
Fochesato, Ch.; Bouche, D.
2007-01-01
The numerical solution of Maxwell equations is a challenging task. Moreover, the range of applications is very wide: microwave devices, diffraction, to cite a few. As a result, a number of methods have been proposed since the sixties. However, among all these methods, none has proved to be free of drawbacks. The finite difference scheme proposed by Yee in 1966, is well suited for Maxwell equations. However, it only works on cubical mesh. As a result, the boundaries of complex objects are not properly handled by the scheme. When classical nodal finite elements are used, spurious modes appear, which spoil the results of simulations. Edge elements overcome this problem, at the price of rather complex implementation, and computationally intensive simulations. Finite volume methods, either generalizing Yee scheme to a wider class of meshes, or applying to Maxwell equations methods initially used in the field of hyperbolic systems of conservation laws, are also used. Lastly, 'Discontinuous Galerkin' methods, generalizing to arbitrary order of accuracy finite volume methods, have recently been applied to Maxwell equations. In this report, we more specifically focus on the coupling of a Maxwell solver to a PIC (Particle-in-cell) method. We analyze advantages and drawbacks of the most widely used methods: accuracy, robustness, sensitivity to numerical artefacts, efficiency, user judgment. (authors)
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.
Newtonian hydrodynamic equations with relativistic pressure and velocity
Energy Technology Data Exchange (ETDEWEB)
Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 702-701 (Korea, Republic of); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejeon 305-348 (Korea, Republic of); Fabris, Júlio; Piattella, Oliver F.; Zimdahl, Winfried, E-mail: jchan@knu.ac.kr, E-mail: hr@kasi.re.kr, E-mail: fabris@pq.cnpq.br, E-mail: oliver.piattella@pq.cnpq.br, E-mail: winfried.zimdahl@pq.cnpq.br [Departamento de Fisica, Universidade Federal do Espirito Santo, Vitória (Brazil)
2016-07-01
We present a new approximation to include fully general relativistic pressure and velocity in Newtonian hydrodynamics. The energy conservation, momentum conservation and two Poisson's equations are consistently derived from Einstein's gravity in the zero-shear gauge assuming weak gravity and action-at-a-distance limit. The equations show proper special relativity limit in the absence of gravity. Our approximation is complementary to the post-Newtonian approximation and the equations are valid in fully nonlinear situations.
Relativistic Photoionization Computations with the Time Dependent Dirac Equation
2016-10-12
Naval Research Laboratory Washington, DC 20375-5320 NRL/MR/6795--16-9698 Relativistic Photoionization Computations with the Time Dependent Dirac... Photoionization Computations with the Time Dependent Dirac Equation Daniel F. Gordon and Bahman Hafizi Naval Research Laboratory 4555 Overlook Avenue, SW...Unclassified Unlimited Unclassified Unlimited 22 Daniel Gordon (202) 767-5036 Tunneling Photoionization Ionization of inner shell electrons by laser
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.
Non-relativistic and relativistic quantum kinetic equations in nuclear physics
International Nuclear Information System (INIS)
Botermans, W.M.M.
1989-01-01
In this thesis an attempt is made to draw up a quantummechanical tranport equation for the explicit calculation oof collision processes between two (heavy) ions, by making proper approaches of the exact equations (non-rel.: N-particles Schroedinger equation; rel.: Euler-Lagrange field equations.). An important starting point in the drag-up of the theory is the behaviour of nuclear matter in equilibrium which is determined by individual as well as collective effects. The central point in this theory is the effective interaction between two nucleons both surrounded by other nucleons. In the derivation of the tranport equations use is made of the green's function formalism as developed by Schwinger and Keldys. For the Green's function kinematic equations are drawn up and are solved by choosing a proper factorization of three- and four-particle Green's functions in terms of one- and two-particle Green's functions. The necessary boundary condition is obtained by explicitly making use of Boltzmann's assumption that colliding particles are statistically uncorrelated. Finally a transport equation is obtained in which the mean field as well as the nucleon-nucleon collisions are given by the same (medium dependent) interaction. This interaction is the non-equilibrium extension of the interaction as given in the Brueckner theory of nuclear matter. Together, kinetic equation and interaction, form a self-consistent set of equations for the case of a non-relativistic as well as for the case of a relativistic starting point. (H.W.) 148 refs.; 6 figs.; 411 schemes
Noureen, S.; Abbas, G.; Sarfraz, M.
2018-01-01
The study of relativistic degenerate plasmas is important in many astrophysical and laboratory environments. Using linearized relativistic Vlasov-Maxwell equations, a generalized expression for the plasma conductivity tensor is derived. Employing Fermi-Dirac distribution at zero temperature, the dispersion relation of the extraordinary mode in a relativistic degenerate electron plasma is investigated. The propagation characteristics are examined in different relativistic density ranges. The shifting of cutoff points due to relativistic effects is observed analytically and graphically. Non-relativistic and ultra-relativistic limiting cases are also presented.
N-body bound state relativistic wave equations
International Nuclear Information System (INIS)
Sazdjian, H.
1988-06-01
The manifestly covariant formalism with constraints is used for the construction of relativistic wave equations to describe the dynamics of N interacting spin 0 and/or spin 1/2 particles. The total and relative time evolutions of the system are completely determined by means of kinematic type wave equations. The internal dynamics of the system is 3 N-1 dimensional, besides the contribution of the spin degrees of freedom. It is governed by a single dynamical wave equation, that determines the eigenvalue of the total mass squared of the system. The interaction is introduced in a closed form by means of two-body potentials. The system satisfies an approximate form of separability
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.
Relativistic equation of the orbit of a particle in a arbitrary central force field
International Nuclear Information System (INIS)
Aaron, Francisc D.
2005-01-01
The equation of the orbit of a relativistic particle moving in an arbitrary central force field is derived. Straightforward generalizations of well-known first and second order differential equations are given. It is pointed out that the relativistic equation of the orbit has the same form as in the non-relativistic case, the only changes consisting in the appearance of additional terms proportional to 1/c 2 in both potential and total energies. (author)
Energy Technology Data Exchange (ETDEWEB)
Gavrilov, S.P. [Universidade Federal de Sergipe (UFS), Aracaju, SE (Brazil); Gitman, D.M. [Sao Paulo Univ. (USP), SP (Brazil). Inst. de Fisica
2000-07-01
Full text follows: There is a common opinion that the construction of a consistent relativistic quantum mechanics on the base of a relativistic wave equation meets well-known difficulties related to the existence of infinite number of negative energy levels, to the existence of negative vector norms, and so on, which may be only solved in a second-quantized theory, see, for example, two basic papers devoted to the problem L.Foldy, S.Wouthuysen, Phys. Rep.78 (1950) 29; H.Feshbach, F.Villars, Rev. Mod. Phys. 30 (1958) 24, whose arguments are repeated in all handbooks in relativistic quantum theory. Even Dirac trying to solve the problem had turned last years to infinite-component relativistic wave equations, see P.A.M. Dirac, Proc. R. Soc. London, A328 (1972) 1. We believe that a consistent relativistic quantum mechanics may be constructed on the base of an extended (charge symmetric) equation, which unite both a relativistic wave equation for a particle and for an antiparticle. We present explicitly the corresponding construction, see for details hep-th/0003112. We support such a construction by two demonstrations: first, in course of a careful canonical quantization of the corresponding classical action of a relativistic particle we arrive just to such a consistent quantum mechanics; second, we demonstrate that a reduction of the QFT of a corresponding field (scalar, spinor, etc.) to one-particle sector, if such a reduction may be done, present namely this quantum mechanics. (author)
A new perspective on relativistic transformation for Maxwell's equations of electrodynamics
International Nuclear Information System (INIS)
Huang, Y.-S.
2009-01-01
A new scheme for relativistic transformation of the electromagnetic fields is formulated through relativistic transformation in the wavevector space, instead of the space-time space. Maxwell's equations of electrodynamics are shown to be form-invariant among inertial frames in accordance with this new scheme of relativistic transformation. This new perspective on relativistic transformation not only fulfills the principle of relativity, but is also compatible with quantum theory.
Relativistic wave equations without the Velo-Zwanziger pathology
International Nuclear Information System (INIS)
Khalil, M.A.K.
1976-06-01
For particles described by relativistic wave equations of the form: (-iGAMMA x delta + m) psi(x) = 0 interacting with an external field B(x) it is known that the ''noncausal'' propagation characteristics are not present when (1) GAMMA 0 is diagonalizable and (2) B(x) = -eGAMMA/sub mu/A/sup mu/(x) (Amar--Dozzio). The ''noncausality''difficulties arise for the Rarita--Schwinger spin 3 / 2 equation, with nondiagonalizable GAMMA 0 , in minimal coupling (i.e., B(x) = -eGAMMA x A(x)) and the PDK spin 1 equation, with diagonalizable GAMMA 0 , in a quadrupole coupling (Velo--Zwanziger) where either (1) or (2) of the Amar--Dozzio (sufficient) conditions are violated. Some sufficient conditions are derived and explored where the Velo--Zwanziger ''noncausality'' pathology can be avoided, even though one, or the other, or both of the conditions (1) and (2) are violated. Examples with both reducible and irreducible wave equations are included
Relativistic dissipative hydrodynamics and the nuclear equation of state
International Nuclear Information System (INIS)
Olson, T.S.; Hiscock, W.A.
1989-01-01
The theory of dissipative, relativistic fluids due to Israel and Stewart is used to constrain the form of the nuclear equation of state. In the Israel-Stewart theory, there are conditions on the equation of state and other thermodynamic properties (the ''second-order'' coefficients) of a fluid which, if satisfied, guarantee that equilibria are stable and that fluid perturbations propagate causally and obey hyperbolic equations. The second-order coefficients in the Israel-Stewart theory, which are relaxation times for the dissipative degrees of freedom and coupling constants between different forms of dissipation, are derived for a free, degenerate Fermi gas. It is shown rigorously that the free, degenerate Fermi gas is stable (and hence causal) at all temperatures in this theory. These values for the second-order coefficients are then used in the stability conditions to constrain various proposed expressions for the nuclear ground-state energy. The stability conditions are found to provide significantly more stringent constraints on the proposed equations of state than the usual simple restriction that the adiabatic sound speed be less than the speed of light
General-relativistic celestial mechanics. II. Translational equations of motion
International Nuclear Information System (INIS)
Damour, T.; Soffel, M.; Xu, C.
1992-01-01
The translational laws of motion for gravitationally interacting systems of N arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies are obtained at the first post-Newtonian approximation of general relativity. The derivation uses our recently introduced multi-reference-system method and obtains the translational laws of motion by writing that, in the local center-of-mass frame of each body, relativistic inertial effects combine with post-Newtonian self- and externally generated gravitational forces to produce a global equilibrium (relativistic generalization of d'Alembert's principle). Within the first post-Newtonian approximation [i.e., neglecting terms of order (v/c) 4 in the equations of motion], our work is the first to obtain complete and explicit results, in the form of infinite series, for the laws of motion of arbitrarily composed and shaped bodies. We first obtain the laws of motion of each body as an infinite series exhibiting the coupling of all the (Blanchet-Damour) post-Newtonian multipole moments of this body to the post-Newtonian tidal moments (recently defined by us) felt by this body. We then give the explicit expression of these tidal moments in terms of post-Newtonian multipole moments of the other bodies
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.
Chiral symmetry breaking and confinement - solutions of relativistic wave equations
International Nuclear Information System (INIS)
Murugesan, P.
1983-01-01
In this thesis, an attempt is made to explore the question whether confinement automatically leads to chiral symmetry breaking. While it should be accepted that chiral symmetry breaking manifests in nature in the absence of scalar partners of pseudoscalar mesons, it does not necessarily follow that confinement should lead to chiral symmetry breaking. If chiral conserving forces give rise to observed spectrum of hadrons, then the conjuncture that confinement is responsible for chiral symmetry breaking is not valid. The method employed to answer the question whether confinement leads to chiral symmetry breaking or not is to solve relativistic wave equations by introducing chiral conserving as well as chiral breaking confining potentials and compare the results with experimental observations. It is concluded that even though chiral symmetry is broken in nature, confinement of quarks need not be the cause of it
Intertwining solutions for magnetic relativistic Hartree type equations
Cingolani, Silvia; Secchi, Simone
2018-05-01
We consider the magnetic pseudo-relativistic Schrödinger equation where , m > 0, is an external continuous scalar potential, is a continuous vector potential and is a convolution kernel, is a constant, , . We assume that A and V are symmetric with respect to a closed subgroup G of the group of orthogonal linear transformations of . If for any , the cardinality of the G-orbit of x is infinite, then we prove the existence of infinitely many intertwining solutions assuming that is either linear in x or uniformly bounded. The results are proved by means of a new local realization of the square root of the magnetic laplacian to a local elliptic operator with Neumann boundary condition on a half-space. Moreover we derive an existence result of a ground state intertwining solution for bounded vector potentials, if G admits a finite orbit.
Relativistic quantum vorticity of the quadratic form of the Dirac equation
International Nuclear Information System (INIS)
Asenjo, Felipe A; Mahajan, Swadesh M
2015-01-01
We explore the fluid version of the quadratic form of the Dirac equation, sometimes called the Feynman–Gell-Mann equation. The dynamics of the quantum spinor field is represented by equations of motion for the fluid density, the velocity field, and the spin field. In analogy with classical relativistic and non-relativistic quantum theories, the fully relativistic fluid formulation of this equation allows a vortex dynamics. The vortical form is described by a total tensor field that is the weighted combination of the inertial, electromagnetic and quantum forces. The dynamics contrives the quadratic form of the Dirac equation as a total vorticity free system. (paper)
Hot QCD equations of state and relativistic heavy ion collisions
Chandra, Vinod; Kumar, Ravindra; Ravishankar, V.
2007-11-01
We study two recently proposed equations of state obtained from high-temperature QCD and show how they can be adapted to use them for making predictions for relativistic heavy ion collisions. The method involves extracting equilibrium distribution functions for quarks and gluons from the equation of state (EOS), which in turn will allow a determination of the transport and other bulk properties of the quark gluon-plasma. Simultaneously, the method also yields a quasiparticle description of interacting quarks and gluons. The first EOS is perturbative in the QCD coupling constant and has contributions of O(g5). The second EOS is an improvement over the first, with contributions up to O[g6ln(1/g)]; it incorporates the nonperturbative hard thermal contributions. The interaction effects are shown to be captured entirely by the effective chemical potentials for the gluons and the quarks, in both cases. The chemical potential is seen to be highly sensitive to the EOS. As an application, we determine the screening lengths, which are, indeed, the most important diagnostics for QGP. The screening lengths are seen to behave drastically differently depending on the EOS considered and therefore yield a way to distinguish the two equations of state in heavy ion collisions.
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)
Arzeliès, Henri
1972-01-01
Relativistic Point Dynamics focuses on the principles of relativistic dynamics. The book first discusses fundamental equations. The impulse postulate and its consequences and the kinetic energy theorem are then explained. The text also touches on the transformation of main quantities and relativistic decomposition of force, and then discusses fields of force derivable from scalar potentials; fields of force derivable from a scalar potential and a vector potential; and equations of motion. Other concerns include equations for fields; transfer of the equations obtained by variational methods int
The incompressible non-relativistic Navier-Stokes equation from gravity
International Nuclear Information System (INIS)
Bhattacharyya, Sayantani; Minwalla, Shiraz; Wadia, Spenta R.
2009-01-01
We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a forcing function identical to the action of a background electromagnetic field on the effectively charged fluid. We demonstrate that special conformal symmetries of the parent relativistic theory descend to 'accelerated boost' symmetries of the Navier-Stokes equations, uncovering a conformal symmetry structure of these equations. Applying our scaling limit to holographically induced fluid dynamics, we find gravity dual descriptions of an arbitrary solution of the forced non-relativistic incompressible Navier-Stokes equations. In the holographic context we also find a simple forced steady state shear solution to the Navier-Stokes equations, and demonstrate that this solution turns unstable at high enough Reynolds numbers, indicating a possible eventual transition to turbulence.
Relativistic two-fermion equations with form factors and anomalous magnetic moment interactions
International Nuclear Information System (INIS)
Ahmed, S.
1977-04-01
Relativistic equations for two-fermion systems are derived from quantum field theory taking into account the form factors of the particles. When the q 2 dependence of the form factors is disregarded, in the static approximation, the two-fermion equations with Coulomb and anomalous magnetic moment interactions are obtained. Separating the angular variables, a sixteen-component relativistic radial equation are finally given
Quasi-linear equation for magnetoplasma oscillations in the weakly relativistic approximation
International Nuclear Information System (INIS)
Rizzato, F.B.
1985-01-01
Some limitations which are present in the dynamical equations for collisionless plasmas are discussed. Some elementary corrections to the linear theories are obtained in a heuristic form, which directly lead to the so-called quasi-linear theories in its non-relativistic and relativistic forms. The effect of the relativistic variation of the gyrofrequency on the diffusion coefficient is examined in a typically perturbative approximation. (author)
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.
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
Relativistic n-body wave equations in scalar quantum field theory
International Nuclear Information System (INIS)
Emami-Razavi, Mohsen
2006-01-01
The variational method in a reformulated Hamiltonian formalism of Quantum Field Theory (QFT) is used to derive relativistic n-body wave equations for scalar particles (bosons) interacting via a massive or massless mediating scalar field (the scalar Yukawa model). Simple Fock-space variational trial states are used to derive relativistic n-body wave equations. The equations are shown to have the Schroedinger non-relativistic limits, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Some examples of approximate ground state solutions of the n-body relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields
Time-dependent field equations for paraxial relativistic electron beams: Beam Research Program
International Nuclear Information System (INIS)
Sharp, W.M.; Yu, S.S.; Lee, E.P.
1987-01-01
A simplified set of field equations for a paraxial relativistic electron beam is presented. These equations for the beam electrostatic potential phi and pinch potential Phi identical to A/sub z/ - phi retain previously neglected time-dependent terms and for axisymmetric beams reduce exactly to Maxwell's equations
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Donker, H.C.; Katsnelson, M.I.; De Raedt, H.; Michielsen, K.
2016-01-01
The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein–Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space–time data collected by probing the particle is obtained from the most robust experiment and that on average, the classical relativistic equation of motion of a particle holds. - Highlights: • Logical inference applied to relativistic, massive, charged, and spinless particle experiments leads to the Klein–Gordon equation. • The relativistic Hamilton–Jacobi is scrutinized by employing a field description for the four-velocity. • Logical inference allows analysis of experiments with uncertainty in detection events and experimental conditions.
Relativistic three-particle dynamical equations: II. Application to the trinucleon system
International Nuclear Information System (INIS)
Adhikari, S.K.; Tomio, L.
1993-11-01
The contribution of relativistic dynamics on the neutron-deuteron scattering length and triton binding energy is calculated employing five sets tri nucleon potential models and four types of three-dimensional relativistic three-body equations suggested in the preceding paper. The relativistic correction to binding energy may vary a lot and even change sign depending on the relativistic formulation employed. The deviations of these observables from those obtained in nonrelativistic models follow the general universal trend of deviations introduced by off- and on-shell variations of two- and three-nucleon potentials in a nonrelativistic model calculation. Consequently, it will be difficult to separate unambiguously the effect of off-and on-shell variations of two and three-nucleon potentials on low-energy three-nucleon observables from the effect of relativistic dynamics. (author)
The investigation of relativistic microscopic optical potential based on RBBG equation
International Nuclear Information System (INIS)
Chen Baoqiu; Ma Zhongyu
1992-01-01
The relativistic microscopic optical potential is derived from the RBBG equation. The nucleon complex effective mass is determined phenomenologically by a fit to 200 MeV proton-nucleus scattering data. Then the relativistic microscopic optical potentials of proton scattered from different targets: 16 O, 40 Ca, 90 Zr and 208 Pb in the energies range from 160 to 800 MeV have been got. The relativistic microscopic optical potentials have been used to study proton- 40 Ca scattering at 200 MeV. Theoretical predictions for cross section and spin observables are compared with experimental data and phenomenological Dirac optical potential
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)
International Nuclear Information System (INIS)
Serva, M.
1986-01-01
In this paper we give probabilistic solutions to the equations describing non-relativistic quantum electrodynamical systems. These solutions involve, besides the usual diffusion processes, also birth and death processes corresponding to the 'photons number' variables. We state some inequalities and in particular we establish bounds to the ground state energy of systems composed by a non relativistic particle interacting with a field. The result is general and it is applied as an example to the polaron problem. (orig.)
Linear relativistic gyrokinetic equation in general magnetically confined plasmas
International Nuclear Information System (INIS)
Tsai, S.T.; Van Dam, J.W.; Chen, L.
1983-08-01
The gyrokinetic formalism for linear electromagnetic waves of arbitrary frequency in general magnetic-field configurations is extended to include full relativistic effects. The derivation employs the small adiabaticity parameter rho/L 0 where rho is the Larmor radius and L 0 the equilibrium scale length. The effects of the plasma and magnetic field inhomogeneities and finite Larmor-radii effects are also contained
Explosions in Landau Vlasov dynamics
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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
Relativistic particle in a box: Klein-Gordon versus Dirac equations
Alberto, Pedro; Das, Saurya; Vagenas, Elias C.
2018-03-01
The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantised energy spectra. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one- and three-dimensional box using the Klein-Gordon equation in the Feshbach-Villars formalism. We compare the solutions and the energy spectra obtained with the corresponding ones from the Dirac equation for a spin one-half relativistic particle. We note the similarities and differences, in particular the spin effects in the relativistic energy spectrum. As expected, the non-relativistic limit is the same for both kinds of particles, since, for a particle in a box, the spin contribution to the energy is a relativistic effect.
A discussion of the relativistic equal-time equation
International Nuclear Information System (INIS)
Chengrui, Q.; Danhua, Q.
1981-03-01
Ruan Tu-nan et al have proposed an equal-time equation for composite particles which is derived from Bethe-Salpeter (B-S) equation. Its advantage is that the kernel of this equation is a completely definite single rearrangement of the B-S irreducible kernel without any artificial assumptions. In this paper we shall give a further discussion of the properties of this equation. We discuss the behaviour of this equation as the mass of one of the two particles approaches the limit M 2 → infinite in the ladder approximation of single photon exchange. We show that up to order O(α 4 ) this equation is consistent with the Dirac equation. If the crossed two photon exchange diagrams are taken into account the difference between them is of order O(α 6 ). (author)
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}=(
A relativistic extended Fermi-Thomas-like equation for a self-gravitating system of fermions
International Nuclear Information System (INIS)
Merloni, A.; Ruffini, R.; Torroni, V.
1998-01-01
The authors extend previous results of a Fermi-Thomas model, describing self-gravitating fermions in their ground state, to a relativistic gravitational theory in Minkowski space. In such a theory the source term of the gravitational potential depends both on the pressure and the density of the fluid. It is shown that, in correspondence of this relativistic treatment, still a Fermi-Thomas-like equation can be derived for the self-gravitating system, though the non-linearities are much more complex. No Fermi-Thomas-like equation can be obtained in the General Relativistic treatment. The canonical results for neutron stars and white dwarfs are recovered and also some erroneous statements in the scientific literature are corrected
Irreversible energy flow in forced Vlasov dynamics
Plunk, Gabriel G.
2014-10-01
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag. The recent paper of Plunk [G.G. Plunk, Phys. Plasmas 20, 032304 (2013)] considered the forced linear Vlasov equation as a model for the quasi-steady state of a single stable plasma wavenumber interacting with a bath of turbulent fluctuations. This approach gives some insight into possible energy flows without solving for nonlinear dynamics. The central result of the present work is that the forced linear Vlasov equation exhibits asymptotically zero (irreversible) dissipation to all orders under a detuning of the forcing frequency and the characteristic frequency associated with particle streaming. We first prove this by direct calculation, tracking energy flow in terms of certain exact conservation laws of the linear (collisionless) Vlasov equation. Then we analyze the steady-state solutions in detail using a weakly collisional Hermite-moment formulation, and compare with numerical solution. This leads to a detailed description of the Hermite energy spectrum, and a proof of no dissipation at all orders, complementing the collisionless Vlasov result.
Irreversible energy flow in forced Vlasov dynamics
Plunk, Gabriel G.; Parker, Joseph T.
2014-01-01
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag. The recent paper of Plunk [G.G. Plunk, Phys. Plasmas 20, 032304 (2013)] considered the forced linear Vlasov equation as a model for the quasi-steady state of a single stable plasma wavenumber interacting with a bath of turbulent fluctuations. This approach gives some insight into possible energy flows without solving for nonlinear dynamics. The central result of the present work is that the forced linear Vlasov equation exhibits asymptotically zero (irreversible) dissipation to all orders under a detuning of the forcing frequency and the characteristic frequency associated with particle streaming. We first prove this by direct calculation, tracking energy flow in terms of certain exact conservation laws of the linear (collisionless) Vlasov equation. Then we analyze the steady-state solutions in detail using a weakly collisional Hermite-moment formulation, and compare with numerical solution. This leads to a detailed description of the Hermite energy spectrum, and a proof of no dissipation at all orders, complementing the collisionless Vlasov result.
The connection of two-particle relativistic quantum mechanics with the Bethe-Salpeter equation
International Nuclear Information System (INIS)
Sazdjian, H.
1986-02-01
We show the formal equivalence between the wave equations of two-particle relativistic quantum mechanics, based on the manifestly covariant hamiltonian formalism with constraints, and the Bethe-Salpeter equation. This is achieved by algebraically transforming the latter so as to separate it into two independent equations which match the equations of hamiltonian relativistic quantum mechanics. The first equation determines the relative time evolution of the system, while the second one yields a three-dimensional eigenvalue equation. A connection is thus established between the Bethe-Salpeter wave function and its kernel on the one hand and the quantum mechanical wave function and interaction potential on the other. For the sector of solutions of the Bethe-Salpeter equation having non-relativistic limits, this relationship can be evaluated in perturbation theory. We also device a generalized form of the instantaneous approximation which simplifies the various expressions involved in the above relations. It also permits the evaluation of the normalization condition of the quantum mechanical wave function as a three-dimensional integral
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
Lorentz-like covariant equations of non-relativistic fluids
International Nuclear Information System (INIS)
Montigny, M de; Khanna, F C; Santana, A E
2003-01-01
We use a geometrical formalism of Galilean invariance to build various hydrodynamics models. It consists in embedding the Newtonian spacetime into a non-Euclidean 4 + 1 space and provides thereby a procedure that unifies models otherwise apparently unrelated. After expressing the Navier-Stokes equation within this framework, we show that slight modifications of its Lagrangian allow us to recover the Chaplygin equation of state as well as models of superfluids for liquid helium (with both its irrotational and rotational components). Other fluid equations are also expressed in a covariant form
Poincare group and relativistic wave equations in 2+1 dimensions
Energy Technology Data Exchange (ETDEWEB)
Gitman, Dmitri M. [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo, SP (Brazil); Shelepin, A.L. [Moscow Institute of Radio Engenering, Electronics and Automation, Moscow (Russian Federation)
1997-09-07
Using the generalized regular representation, an explicit construction of the unitary irreducible representations of the (2+1)-Poincare group is presented. A detailed description of the angular momentum and spin in 2+1 dimensions is given. On this base the relativistic wave equations for all spins (including fractional) are constructed. (author)
Three-parameter relativistic dynamics. 1. Equation of motion, energy conservation
International Nuclear Information System (INIS)
Rogachevskii, A.G.
1995-01-01
A formally geometric analog of the relativistic dynamics of a point charged particle is constructed. Time as a function of the spatial coordinates is taken as the trajectory equation, i.e., the trajectory is a hypersurface in Minkowski space. The dynamics is presented. The law of open-quotes energyclose quotes conservation is examined
Relativistic Equations for Spin Particles: What can We Learn from Noncommutativity?
International Nuclear Information System (INIS)
Dvoeglazov, V. V.
2009-01-01
We derive relativistic equations for charged and neutral spin particles. The approach for higher-spin particles is based on generalizations of the Bargmann-Wigner formalism. Next, we study, what new physical information can give the introduction of non-commutativity. Additional non-commutative parameters can provide a suitable basis for explanation of the origin of mass.
Relativistic wave equations for particles in electromagnetic fields
International Nuclear Information System (INIS)
Good, R.H. Jr.
1989-01-01
A new type of generalization of the Dirac equation of higher spin particles and antiparticles is given, in case only the terms proportional to the external fields need to be retained. copyright 1989 Academic Press, Inc
Relativistic transport equation for a discontinuity wave of multiplicity one
Energy Technology Data Exchange (ETDEWEB)
Giambo, S; Palumbo, A [Istituto di Matematica, Universita degli Studi, Messina (Italy)
1980-04-14
In the framework of the theory of the singular hypersurfaces, the transport equation for the amplitude of a discontinuity wave, corresponding to a simple characteristic of a quasi-linear hyperbolic system, is established in the context of special relativity.
Relativistic equations for axisymmetric gravitational collapse with escaping neutrinos
International Nuclear Information System (INIS)
Patel, M.D.
1979-01-01
Einstein's field equations for the dynamics of a self-gravitating axially symmetric source of a perfect fluid, presented by Chandrasekhar and Friedman (1964), are modified to allow emission of neutrinos. The boundary conditions at the outer surface of the radiating axisymmetric source are obtained by matching to an exterior solution of an axisymmetric rotating, radiating core. (auth.)
Relativistic two-body equation for one Dirac and one Duffin-Kemmer particle
International Nuclear Information System (INIS)
Krolikowski, W.
1983-01-01
A new relativistic two-body wave equation is proposed for one spin-1/2 and one spin-0 or spin-1 particle which, if isolated from each other, are described by the Dirac and the Duffin-Kemmer equation, respectively. For a static mutual interaction this equation splits into two equations: a two-body wave equation for one Dirac and one Klein-Gordon particle (which was introduced by the author previously) and a new two-body wave equation for one Dirac and one Proca particle. The proposed equation may be applied in particular to the quark-diquark system. In Appendix, however, an alternative approach is sketched, where the diquark is described as the point limit of a very close Breit system rather than a Duffin-Kemmer particle. (Author)
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.
International Nuclear Information System (INIS)
Sugaya, R.; Ue, A.; Maehara, T.; Sugawa, M.
1996-01-01
Acceleration and heating of a relativistic electron beam by cascading nonlinear Landau damping involving three or four intense electromagnetic waves in a plasma are studied theoretically based on kinetic wave equations and transport equations derived from relativistic Vlasov endash Maxwell equations. Three or four electromagnetic waves excite successively two or three nonresonant beat-wave-driven relativistic electron plasma waves with a phase velocity near the speed of light [v p =c(1-γ -2 p ) 1/2 , γ p =ω/ω pe ]. Three beat waves interact nonlinearly with the electron beam and accelerate it to a highly relativistic energy γ p m e c 2 more effectively than by the usual nonlinear Landau damping of two electromagnetic waves. It is proved that the electron beam can be accelerated to more highly relativistic energy in the plasma whose electron density decreases temporally with an appropriate rate because of the temporal increase of γ p . copyright 1996 American Institute of Physics
Energy Technology Data Exchange (ETDEWEB)
Fochesato, Ch. [CEA Bruyeres-le-Chatel, Dept. de Conception et Simulation des Armes, Service Simulation des Amorces, Lab. Logiciels de Simulation, 91 (France); Bouche, D. [CEA Bruyeres-le-Chatel, Dept. de Physique Theorique et Appliquee, Lab. de Recherche Conventionne, Centre de Mathematiques et Leurs Applications, 91 (France)
2007-07-01
The numerical solution of Maxwell equations is a challenging task. Moreover, the range of applications is very wide: microwave devices, diffraction, to cite a few. As a result, a number of methods have been proposed since the sixties. However, among all these methods, none has proved to be free of drawbacks. The finite difference scheme proposed by Yee in 1966, is well suited for Maxwell equations. However, it only works on cubical mesh. As a result, the boundaries of complex objects are not properly handled by the scheme. When classical nodal finite elements are used, spurious modes appear, which spoil the results of simulations. Edge elements overcome this problem, at the price of rather complex implementation, and computationally intensive simulations. Finite volume methods, either generalizing Yee scheme to a wider class of meshes, or applying to Maxwell equations methods initially used in the field of hyperbolic systems of conservation laws, are also used. Lastly, 'Discontinuous Galerkin' methods, generalizing to arbitrary order of accuracy finite volume methods, have recently been applied to Maxwell equations. In this report, we more specifically focus on the coupling of a Maxwell solver to a PIC (Particle-in-cell) method. We analyze advantages and drawbacks of the most widely used methods: accuracy, robustness, sensitivity to numerical artefacts, efficiency, user judgment. (authors)
Analytic properties of the relativistic Thomas-Fermi equation and the total energy of atomic ions
International Nuclear Information System (INIS)
March, N.H.; Senatore, G.
1985-06-01
The analytic properties of solutions of the relativistic Thomas-Fermi equation which tend to zero at infinity are first examined, the neutral atom solution being a member of this class. A new length is shown to enter the theory, proportional to the square root of the fine structure constant. This information is used to develop a perturbation expansion around the neutral atom solution, corresponding to positive atomic ions with finite but large radii. The limiting law relating ionic radius to the degree of ionization is thereby displayed in functional form, and solved explicitly to lowest order in the fine structure constant. To embrace this knowledge of heavy positive ions, as well as results from the one-electron Dirac equation, a proposal is then advanced as to the analytic form of the relativistic total energy E(Z,N) of an atomic ion with nuclear charge Ze and total number of electrons N. The fact that, for N>1, the nucleus is known only to bind Z+n electrons, where n is 1 or 2, indicates non-analyticity in the complex Z plane, represented by a circle of radius Z approx.= N. Such non-analyticity is also a property of the non-relativistic energy derived from the many-electron Schroedinger equation. The relativistic theory, however, must also embody a second type of non-analyticity associated with the known property for N=1 that the Dirac equation predicts electron-positron pair production when the electronic binding energy becomes equal to twice the electron rest mass energy. This corresponds to a second circle of non-analyticity in E(Z,N), and hence to a Taylor-Laurent expansion of this quantity in the atomic number Z. The relation of this expansion to the Layzer-Bahcall series is finally discussed. (author)
International Nuclear Information System (INIS)
Brenner, S.E.; Gandyl', E.M.; Podkopaev, A.P.
1995-01-01
The dynamics of high-current relativistic electron beam moving trough the cylindrical drift space has been modelled by the large particles, the shape of which allows to solve the Poisson equations exactly, and in such a way to avoid the linearization being usually used in those problems. The expressions for the components of own electric field of electron beam passing through the cylindrical drift space have been obtained. (author). 11 refs., 1 fig
Numerical solution of special ultra-relativistic Euler equations using central upwind scheme
Ghaffar, Tayabia; Yousaf, Muhammad; Qamar, Shamsul
2018-06-01
This article is concerned with the numerical approximation of one and two-dimensional special ultra-relativistic Euler equations. The governing equations are coupled first-order nonlinear hyperbolic partial differential equations. These equations describe perfect fluid flow in terms of the particle density, the four-velocity and the pressure. A high-resolution shock-capturing central upwind scheme is employed to solve the model equations. To avoid excessive numerical diffusion, the considered scheme avails the specific information of local propagation speeds. By using Runge-Kutta time stepping method and MUSCL-type initial reconstruction, we have obtained 2nd order accuracy of the proposed scheme. After discussing the model equations and the numerical technique, several 1D and 2D test problems are investigated. For all the numerical test cases, our proposed scheme demonstrates very good agreement with the results obtained by well-established algorithms, even in the case of highly relativistic 2D test problems. For validation and comparison, the staggered central scheme and the kinetic flux-vector splitting (KFVS) method are also implemented to the same model. The robustness and efficiency of central upwind scheme is demonstrated by the numerical results.
General relativistic continuum mechanics and the post-Newtonian equations of motion
International Nuclear Information System (INIS)
Morrill, T.H.
1991-01-01
Aspects are examined of general relativistic continuum mechanics. Perfectly elastic materials are dealt with but not exclusively. The derivation of their equations of motion is emphasized, in the post-Newtonian approximation. A reformulation is presented based on the tetrad formalism, of Carter and Quintana's theory of general relativistic elastic continua. A field Lagrangian is derived describing perfect material media; show that the usual covariant conservations law for perfectly elastic media is fully equivalent to the Euler-Lagrange equations describing these same media; and further show that the equations of motion for such materials follow directly from Einstein's field equations. In addition, a version of this principle shows that the local mass density in curved space-time partially depends on the amount and distribution of mass energy in the entire universe and is related to the mass density that would occur if space-time were flat. The total Lagrangian was also expanded in an EIH (Einstein, Infeld, Hoffmann) series to obtain a total post-Newtonian Lagrangian. The results agree with those found by solving Einstein's equations for the metric coefficients and by deriving the post-Newtonian equations of motion from the covariant conservation law
Vlasov dynamics of periodically driven systems
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.
Application of Central Upwind Scheme for Solving Special Relativistic Hydrodynamic Equations
Yousaf, Muhammad; Ghaffar, Tayabia; Qamar, Shamsul
2015-01-01
The accurate modeling of various features in high energy astrophysical scenarios requires the solution of the Einstein equations together with those of special relativistic hydrodynamics (SRHD). Such models are more complicated than the non-relativistic ones due to the nonlinear relations between the conserved and state variables. A high-resolution shock-capturing central upwind scheme is implemented to solve the given set of equations. The proposed technique uses the precise information of local propagation speeds to avoid the excessive numerical diffusion. The second order accuracy of the scheme is obtained with the use of MUSCL-type initial reconstruction and Runge-Kutta time stepping method. After a discussion of the equations solved and of the techniques employed, a series of one and two-dimensional test problems are carried out. To validate the method and assess its accuracy, the staggered central and the kinetic flux-vector splitting schemes are also applied to the same model. The scheme is robust and efficient. Its results are comparable to those obtained from the sophisticated algorithms, even in the case of highly relativistic two-dimensional test problems. PMID:26070067
International Nuclear Information System (INIS)
Tanimura, Shogo
1992-01-01
R. P. Feynman showed F. J. Dyson a proof of the Lorentz force law and the homogeneous Maxwell equations, which he obtained starting from Newton's law of motion and the commutation relations between position and velocity for a single nonrelativistic particle. The author formulate both a special relativistic and a general relativistic version of Feynman's derivation. Especially in the general relativistic version they prove that the only possible fields that can consistently act on a quantum mechanical particle are scalar, gauge, and gravitational fields. They also extend Feynman's scheme to the case of non-Abelian gauge theory in the special relativistic context. 8 refs
Some solutions of the equations of motion of the relativistic string with massive ends
International Nuclear Information System (INIS)
Barbashov, B.M.
1977-01-01
The classical theory is discussed for the relativistic string with point masses at its ends. The dynamical equations are solved for the class of motions of this system when the time evolution parameter tau is the proper time of both massive string ends. In this case the solution of the boundary equations is given by the almost periodic functions. Constraints on the normal modes resulting from the orthonormal gauge conditions differ essentially from the Virasoro ones. Incidentally one obtains an exact solution for the half-infinite string with mass at one end. It is also proved that the exact solution for the string with massive ends cannot be a periodic function. (Auth.)
Study of the O-mode in a relativistic degenerate electron plasma
Azra, Kalsoom; Ali, Muddasir; Hussain, Azhar
2017-03-01
Using the linearized relativistic Vlasov-Maxwell equations, a generalized expression for the plasma conductivity tensor is derived. The dispersion relation for the O-mode in a relativistic degenerate electron plasma is investigated by employing the Fermi-Dirac distribution function. The propagation characteristics of the O-mode (cut offs, resonances, propagation regimes, harmonic structure) are examined by using specific values of the density and the magnetic field that correspond to different relativistic dense environments. Further, it is observed that due to the relativistic effects the cut off and the resonance points are shifted to low frequency values, as a result the propagation regime is reduced. The dispersion relations for the non-relativistic and the ultra-relativistic limits are also presented.
The two-fermion relativistic wave equations of Constraint Theory in the Pauli-Schroedinger form
International Nuclear Information System (INIS)
Mourad, J.; Sazdjian, H.
1994-01-01
The two-fermion relativistic wave equations of Constraint Theory are reduced, after expressing the components of the 4x4 matrix wave function in terms of one of the 2x2 components, to a single equation of the Pauli-Schroedinger type, valid for all sectors of quantum numbers. The potentials that are present belong to the general classes of scalar, pseudoscalar and vector interactions and are calculable in perturbation theory from Feynman diagrams. In the limit when one of the masses becomes infinite, the equation reduces to the two-component form of the one-particle Dirac equation with external static potentials. The Hamiltonian, to order 1/c 2 , reproduces most of the known theoretical results obtained by other methods. The gauge invariance of the wave equation is checked, to that order, in the case of QED. The role of the c.m. energy dependence of the relativistic interquark confining potential is emphasized and the structure of the Hamiltonian, to order 1/c 2 , corresponding to confining scalar potentials, is displayed. (authors). 32 refs., 2 figs
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
Study of the equations of a particle in Non- Relativistic Quantum Mechanics
International Nuclear Information System (INIS)
Miltao, Milton Souza Ribeiro; Silva, Vanessa Santos Teles da
2011-01-01
Full text: The study of group theory is relevant to the treatment of physical problems, in which concepts of invariance and symmetry are important. In the field of Non-Relativistic Quantum Mechanics, we can do algebraic considerations taking into account the principles of symmetry, considering the framework of the study of Galileo transformations, which have characteristics of group. Therefore, we discuss the Stern-Gerlach experiment that had the historical importance of demonstrating that the electron has an intrinsic angular momentum. Through discussion of this experiment, we found that the spin appears in Non-Relativistic Quantum Mechanics as a feature of the algebraic structure underlying any physical theory represented by a group. From these studies, we have algebraic considerations for physical systems in non-relativistic domain, which are described by the Schroedinger and Pauli equations, describing the dynamics of particles of spin zero and 1/2 respectively, taking into account the structure of the transformations Galileo. Due to the operatorial, we represent Galileo's transformations by matrices by choosing an appropriate basis of space-time. Using these arrays, we saw group characteristics associated with these transformations, which we call the Galileo Group. We note the invariance of the Schroedinger and Pauli equations after these changes, as well as the physical state associated with it, which is represented by a radius vector in Hilbert space. (author)
Anomalous dynamics triggered by a non-convex equation of state in relativistic flows
Ibáñez, J. M.; Marquina, A.; Serna, S.; Aloy, M. A.
2018-05-01
The non-monotonicity of the local speed of sound in dense matter at baryon number densities much higher than the nuclear saturation density (n0 ≈ 0.16 fm-3) suggests the possible existence of a non-convex thermodynamics which will lead to a non-convex dynamics. Here, we explore the rich and complex dynamics that an equation of state (EoS) with non-convex regions in the pressure-density plane may develop as a result of genuinely relativistic effects, without a classical counterpart. To this end, we have introduced a phenomenological EoS, the parameters of which can be restricted owing to causality and thermodynamic stability constraints. This EoS can be regarded as a toy model with which we may mimic realistic (and far more complex) EoSs of practical use in the realm of relativistic hydrodynamics.
Solution of the relativistic 2-D Fokker-Planck equation for LH current drive
International Nuclear Information System (INIS)
Hizanidis, K.; Hewett, D.W.; Bers, A.
1984-03-01
We solve numerically the steady-state two-dimensional relativistic Fokker-Planck equation with strong rf diffusion using spectra relevant to recent experiments in ALCATOR-C. The results (current generated, power dissipated, and the distribution of energetic electrons) are sensitive to the location of the spectrum in momentum space. Relativistic effects play an important role, especially for wide spectra. The dependence on the ionic charge number Z/sub i/ is also investigated. Particular attention is paid to the perpendicular temperature inside the resonant region and beyond, as well as to the angular energetic particle-temperature distribution, T/sub μ/, a function of the pitch angle parameter μ. The dependence of the perpendicular temperature on the location of the spectrum is also investigated analytically with a model based on the method of moments and the results compared with those found numerically
Cosmology in one dimension: Vlasov dynamics.
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 energy of perturbations for Vlasov plasmas
International Nuclear Information System (INIS)
Morrison, P.J.
1994-02-01
The energy content of electrostatic perturbations about homogeneous equilibria is discussed. The calculation leading to the well-known dielectric (or as it is sometimes called the wave) energy is revisited and interpreted in light of Vlasov theory. It is argued that this quantity is deficient because resonant particles are not correctly handled. A linear integral transform is presented that solves the linear Vlasov-Poisson equation. This solution together with the Kruskal-Oberman energy [Phys. Fluids 1, 275 (1958)] is used to obtain an energy expression in terms of the electric field [Phys. Fluids B 4, 3038 (1992)]. It is described how the integral transform amounts to a change to normal coordinates in an infinite dimensional Hamiltonian system
On analytic solutions of (1+3)D relativistic ideal hydrodynamic equations
International Nuclear Information System (INIS)
Lin Shu; Liao Jinfeng
2010-01-01
In this paper, we find various analytic (1+3)D solutions to relativistic ideal hydrodynamic equations based on embedding of known low-dimensional scaling solutions. We first study a class of flows with 2D Hubble embedding, for which a single ordinary differential equation for the remaining velocity field can be derived. Using this equation, all solutions with transverse 2D Hubble embedding and power law ansatz for the remaining longitudinal velocity field will be found. Going beyond the power law ansatz, we further find a few solutions with transverse 2D Hubble embedding and nontrivial longitudinal velocity field. Finally we investigate general scaling flows with each component of the velocity fields scaling independently, for which we also find all possible solutions.
Aguayo-Ortiz, A; Mendoza, S; Olvera, D
2018-01-01
In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and "Rankine-Hugoniot" jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges.
Supergroup extensions: from central charges to quantization through relativistic wave equations
International Nuclear Information System (INIS)
Aldaya, V.; Azcarraga, J.A. de.
1982-07-01
We give in this paper the finite group law of a family of supergroups including the U(1)-extended N=2 super-Poincare group. From this family of supergroups, and by means of a canonical procedure, we are able to derive the Klein-Gordon and Dirac equations for the fields contained in the superfield. In the process, the physical content of the central charge as the mass parameter and the role of covariant derivatives are shown to come out canonically from the group structure, and the U(1)-extended supersymmetry is seen as necessary for the geometric quantization of the relativistic elementary systems. (author)
Hartree Fock-type equations in relativistic quantum electrodynamics with non-linear gauge fixing
International Nuclear Information System (INIS)
Dietz, K.; Hess, B.A.
1990-08-01
Relativistic mean-field equations are obtained by minimizing the effective energy obtained from the gauge-invariant energy density by eliminating electro-magnetic degrees of freedom in certain characteristic non-linear gauges. It is shown that by an appropriate choice of gauge many-body correlations, e.g. screening, three-body 'forces' etc. can be included already at the mean-field level. The many-body perturbation theory built on the latter is then expected to show improved 'convergence'. (orig.)
PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY
Energy Technology Data Exchange (ETDEWEB)
Tsai, Shang-Hsi; Yang, Jaw-Yen, E-mail: shanghsi@gmail.com [Institute of Applied Mechanics, National Taiwan University, Taipei 10764, Taiwan (China)
2015-07-20
A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.
Self-consistent relativistic Boltzmann-Uehling-Uhlenbeck equation for the Δ distribution function
International Nuclear Information System (INIS)
Mao, G.; Li, Z.; Zhuo, Y.
1996-01-01
We derive the self-consistent relativistic Boltzmann-Uehling-Uhlenbeck (RBUU) equation for the delta distribution function within the framework which we have done for nucleon close-quote s. In our approach, the Δ isobars are treated in essentially the same way as nucleons. Both mean field and collision terms of Δ close-quote s RBUU equation are derived from the same effective Lagrangian and presented analytically. We calculate the in-medium NΔ elastic and inelastic scattering cross sections up to twice nuclear matter density and the results show that the in-medium cross sections deviate substantially from Cugnon close-quote s parametrization that is commonly used in the transport model. copyright 1996 The American Physical Society
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Barashenkov, I.V.; Getmanov, B.S.; Kovtun, V.E.
1992-01-01
The scheme for unified description of integrable relativistic massive systems provides an inverse scattering formalism that covers universally all (1+1)- dimensional systems of this kind. In this work we construct the N-soliton solution (over an arbitrary background) for some generic system which is associated with the sl(2,C) case of the scheme and whose reductions include the complex sine-Gordon equation, the massive Thirring model and other equations, both in the Euclidean and Minkowski spaces. Thus the N-soliton solutions for all these systems emerge in a unified form differing only in the type of constraints imposed on their parameters. In an earlier paper the case of the zero background was considered while here we concentrate on the case of the non-vanishing constant background i.e., on the N-kink solutions. (author). 18 refs
Numerical solution of ordinary differential equations. For classical, relativistic and nano systems
International Nuclear Information System (INIS)
Greenspan, D.
2006-01-01
An up-to-date survey on numerical solutions with theory, intuition and applications. Ordinary differential equations (ODE) play a significant role in mathematics, physics and engineering sciences, and thus are part of relevant college and university courses. Many problems, however, both traditional and modern, do not possess exact solutions, and must be treated numerically. Usually this is done with software packages, but for this to be efficient requires a sound understanding of the mathematics involved. This work meets the need for an affordable textbook that helps in understanding numerical solutions of ODE. Carefully structured by an experienced textbook author, it provides a survey of ODE for various applications, both classical and modern, including such special applications as relativistic and nano systems. The examples are carefully explained and compiled into an algorithm, each of which is presented generically, independent of a specific programming language, while each chapter is rounded off with exercises. The text meets the demands of MA200 courses and of the newly created Numerical Solution of Differential Equations courses, making it ideal for both students and lecturers in physics, mathematics, mechanical engineering, electrical engineering, as well as for physicists, mathematicians, engineers, and electrical engineers. From the Contents - Euler's Method - Runge-Kutta Methods - The Method of Taylor Expansions - Large Second Order Systems with Application to Nano Systems - Completely Conservative, Covariant Numerical Methodology - Instability - Numerical Solution of Tridiagonal Linear Algebraic Systems and Related Nonlinear Systems - Approximate Solution of Boundary Value Problems - Special Relativistic Motion - Special Topics - Appendix: Basic Matrix Operations - Bibliography. (orig.) (orig.)
International Nuclear Information System (INIS)
Woesler, Richard
2007-01-01
The computations of the present text with non-relativistic quantum teleportation equations and special relativity are totally speculative, physically correct computations can be done using quantum field theory, which remain to be done in future. Proposals for what might be called statistical time loop experiments with, e.g., photon polarization states are described when assuming the simplified non-relativistic quantum teleportation equations and special relativity. However, a closed time loop would usually not occur due to phase incompatibilities of the quantum states. Histories with such phase incompatibilities are called inconsistent ones in the present text, and it is assumed that only consistent histories would occur. This is called an exclusion principle for inconsistent histories, and it would yield that probabilities for certain measurement results change. Extended multiple parallel experiments are proposed to use this statistically for transmission of classical information over distances, and regarding time. Experiments might be testable in near future. However, first a deeper analysis, including quantum field theory, remains to be done in future
International Nuclear Information System (INIS)
Kunihiro, Teiji; Minami, Yuki; Tsumura, Kyosuke
2009-01-01
The dynamical density fluctuations around the QCD critical point (CP) are analyzed using relativistic dissipative fluid dynamics, and we show that the sound mode around the QCD CP is strongly attenuated whereas the thermal fluctuation stands out there. We speculate that if possible suppression or disappearance of a Mach cone, which seems to be created by the partonic jets at RHIC, is observed as the incident energy of the heavy-ion collisions is decreased, it can be a signal of the existence of the QCD CP. We have presented the Israel-Stewart type fluid dynamic equations that are derived rigorously on the basis of the (dynamical) renormalization group method in the second part of the talk, which we omit here because of a lack of space.
Kunihiro, Teiji; Minami, Yuki; Tsumura, Kyosuke
2009-11-01
The dynamical density fluctuations around the QCD critical point (CP) are analyzed using relativistic dissipative fluid dynamics, and we show that the sound mode around the QCD CP is strongly attenuated whereas the thermal fluctuation stands out there. We speculate that if possible suppression or disappearance of a Mach cone, which seems to be created by the partonic jets at RHIC, is observed as the incident energy of the heavy-ion collisions is decreased, it can be a signal of the existence of the QCD CP. We have presented the Israel-Stewart type fluid dynamic equations that are derived rigorously on the basis of the (dynamical) renormalization group method in the second part of the talk, which we omit here because of a lack of space.
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
Electromagnetic wave propagation in relativistic magnetized plasmas
International Nuclear Information System (INIS)
Weiss, I.
1985-01-01
An improved mathematical technique and a new code for deriving the conductivity tensor for collisionless plasmas have been developed. The method is applicable to a very general case, including both hot (relativistic) and cold magnetized plasmas, with only isotropic equilibrium distributions being considered here. The usual derivation starts from the relativistic Vlasov equation and leads to an integration over an infinite sum of Bessel functions which has to be done numerically. In the new solution the integration is carried out over a product of two Bessel functions only. This reduces the computing time very significantly. An added advantage over existing codes is our capability to perform the computations for waves propagating obliquely to the magnetic field. Both improvements greatly facilitate investigations of properties of the plasma under conditions hitherto unexplored
Well-posedness for Semi-relativistic Hartree Equations of Critical Type
International Nuclear Information System (INIS)
Lenzmann, Enno
2007-01-01
We prove local and global well-posedness for semi-relativistic, nonlinear Schroedinger equations with initial data in H s (R 3 ). Here F(u) is a critical Hartree nonlinearity that corresponds to Coulomb or Yukawa type self-interactions. For focusing F(u), which arise in the quantum theory of boson stars, we derive global-in-time existence for small initial data, where the smallness condition is expressed in terms of the L 2 -norm of solitary wave ground states. Our proof of well-posedness does not rely on Strichartz type estimates. As a major benefit from this, our method enables us to consider external potentials of a quite general class
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
Hamiltonian dynamics of spatially-homogeneous Vlasov-Einstein systems
International Nuclear Information System (INIS)
Okabe, Takahide; Morrison, P. J.; Friedrichsen, J. E. III; Shepley, L. C.
2011-01-01
We introduce a new matter action principle, with a wide range of applicability, for the Vlasov equation in terms of a conjugate pair of functions. Here we apply this action principle to the study of matter in Bianchi cosmological models in general relativity. The Bianchi models are spatially-homogeneous solutions to the Einstein field equations, classified by the three-dimensional Lie algebra that describes the symmetry group of the model. The Einstein equations for these models reduce to a set of coupled ordinary differential equations. The class A Bianchi models admit a Hamiltonian formulation in which the components of the metric tensor and their time derivatives yield the canonical coordinates. The evolution of anisotropy in the vacuum Bianchi models is determined by a potential due to the curvature of the model, according to its symmetry. For illustrative purposes, we examine the evolution of anisotropy in models with Vlasov matter. The Vlasov content is further simplified by the assumption of cold, counter-streaming matter, a kind of matter that is far from thermal equilibrium and is not describable by an ordinary fluid model nor other more simplistic matter models. Qualitative differences and similarities are found in the dynamics of certain vacuum class A Bianchi models and Bianchi type I models with cold, counter-streaming Vlasov-matter potentials analogous to the curvature potentials of corresponding vacuum models.
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
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)
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
Moshinsky, M; Nikitin, A G; Smirnov, Yu F
1998-01-01
In 1945 Bhabha was probably the first to discuss the problem of a free relativistic particle with arbitrary spin in terms of a single linear equation in the four-momentum vector p subnu, but substituting the gamma supnu matrices of Dirac by other ones. He determined the latter by requiring that their appropriate Lorentz transformations lead to their formulation in terms of the generators of the O(5) group. His program was later extensively amplified by Krajcik, Nieto and others. We returned to this problem because we had an ab-initio procedure for deriving a Lorentz-invariant equation of arbitrary spin and furthermore could express the matrices appearing in them in terms of ordinary and what we called sign spins. Our procedure was similar to that of the ordinary and isotopic spin in nuclear physics that give rise to supermultiplets, hence the appearance of this word in the title. In the ordinary and sign spin formulation it is easy to transform our equation into one linear in both the p subnu and some of the ...
International Nuclear Information System (INIS)
Goncalves, Bruno; Dias Junior, Mario Marcio
2013-01-01
Full text: The discussion of experimental manifestations of torsion at low energies is mainly related to the torsion-spin interaction. In this respect the behavior of Dirac field and the spinning particle in an external torsion field deserves and received very special attention. In this work, we consider the combined action of torsion and magnetic field on the massive spinor field. In this case, the Dirac equation is not straightforward solved. We suppose that the spinor has two components. The equations have mixed terms between the two components. The electromagnetic field is introduced in the action by the usual gauge transformation. The torsion field is described by the field S μ . The main purpose of the work is to get an explicit form to the equation of motion that shows the possible interactions between the external fields and the spinor in a Hamiltonian that is independent to each component. We consider that S 0 is constant and is the unique non-vanishing term of S μ . This simplification is taken just to simplify the algebra, as our main point is not to describe the torsion field itself. In order to get physical analysis of the problem, we consider the non-relativistic approximation. The final result is a Hamiltonian that describes a half spin field in the presence of electromagnetic and torsion external fields. (author)
International Nuclear Information System (INIS)
Parra, Felix I.; Catto, Peter J.
2009-01-01
A recent publication [F. I. Parra and P. J. Catto, Plasma Phys. Controlled Fusion 50, 065014 (2008)] warned against the use of the lower order gyrokinetic Poisson equation at long wavelengths because the long wavelength, radial electric field must remain undetermined to the order the equation is obtained. Another reference [W. W. Lee and R. A. Kolesnikov, Phys. Plasmas 16, 044506 (2009)] criticizes these results by arguing that the higher order terms neglected in the most common gyrokinetic Poisson equation are formally smaller than the terms that are retained. This argument is flawed and ignores that the lower order terms, although formally larger, must cancel without determining the long wavelength, radial electric field. The reason for this cancellation is discussed. In addition, the origin of a nonlinear term present in the gyrokinetic Poisson equation [F. I. Parra and P. J. Catto, Plasma Phys. Controlled Fusion 50, 065014 (2008)] is explained.
Low-lying qq(qq)-bar states in a relativistic model based on the Bethe-Salpeter equation
International Nuclear Information System (INIS)
Ram, B.; Kriss, V.
1985-01-01
Low-lying qq(qq)-bar states are analysed in a previously given relativistic model based on the Bethe-Salpeter equation. It is not got M-diquonia, P-mesonia, or meson molecules, but it is got T-diquonia
Tetrahedron equations and the relativistic S-matrix of straight-strings in 2+1-dimensions
International Nuclear Information System (INIS)
Zamolodchikov, A.B.
1981-01-01
The quantum S-matrix theory of straight-strings (infinite one-dimensioanl objects like straight domain walls) in 2 + 1-dimensions is considered. The S-matrix is supposed to be purely elastic and factorized. The tetrahedron equations (which are the factorization conditions) are investigated for the special two-colour model. The relativistic three-string S-matrix, which apparently satisfies this tetrahedron equation, is proposed. (orig.)
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.
Second relativistic mean field and virial equation of state for astrophysical simulations
International Nuclear Information System (INIS)
Shen, G.; Horowitz, C. J.; O'Connor, E.
2011-01-01
We generate a second equation of state (EOS) of nuclear matter for a wide range of temperatures, densities, and proton fractions for use in supernovae, neutron star mergers, and black hole formation simulations. We employ full relativistic mean field (RMF) calculations for matter at intermediate density and high density, and the virial expansion of a nonideal gas for matter at low density. For this EOS we use the RMF effective interaction FSUGold, whereas our earlier EOS was based on the RMF effective interaction NL3. The FSUGold interaction has a lower pressure at high densities compared to the NL3 interaction. We calculate the resulting EOS at over 100 000 grid points in the temperature range T=0 to 80 MeV, the density range n B =10 -8 to 1.6 fm -3 , and the proton fraction range Y p =0 to 0.56. We then interpolate these data points using a suitable scheme to generate a thermodynamically consistent equation of state table on a finer grid. We discuss differences between this EOS, our NL3-based EOS, and previous EOSs by Lattimer-Swesty and H. Shen et al. for the thermodynamic properties, composition, and neutron star structure. The original FSUGold interaction produces an EOS, which we call FSU1.7, that has a maximum neutron star mass of 1.7 solar masses. A modification in the high-density EOS is introduced to increase the maximum neutron star mass to 2.1 solar masses and results in a slightly different EOS that we call FSU2.1. The EOS tables for FSU1.7 and FSU2.1 are available for download.
Ferwerda, H.A.; Hoenders, B.J.; Slump, C.H.
The fully relativistic quantum mechanical treatment of paraxial electron-optical image formation initiated in the previous paper (this issue) is worked out and leads to a rigorous foundation of the linear transfer theory. Moreover, the status of the relativistic scaling laws for mass and wavelength,
International Nuclear Information System (INIS)
Monnai, Akihiko; Hirano, Tetsufumi
2010-01-01
We derive the second order hydrodynamic equations for the relativistic system of multi-components with multiple conserved currents by generalizing the Israel-Stewart theory and Grad's moment method. We find that, in addition to the conventional moment equations, extra moment equations associated with conserved currents should be introduced to consistently match the number of equations with that of unknowns and to satisfy the Onsager reciprocal relations. Consistent expansion of the entropy current leads to constitutive equations which involve the terms not appearing in the original Israel-Stewart theory even in the single component limit. We also find several terms which exhibit thermal diffusion such as Soret and Dufour effects. We finally compare our results with those of other existing formalisms.
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.
Neutron star properties and the relativistic nuclear equation of state of many-baryon matter
International Nuclear Information System (INIS)
Weber, F.; Weigel, M.K.
1989-01-01
A relativistic model of baryons interacting via the exchange of σ-, ω-, π- and ρ-mesons (scalar-vector-isovector (SVI) theory) is used to describe the properties of both dense and superdense matter. For the theoretical frame, we used the temperature-dependent Green's function formalism. The equation of state (EOS) is calculated for nuclear as well as neutron matter in the Hartree (H) and Hartree-Fock (HF) approximation. The existence of phase transitions has been investigated. The isotherms of pressure as a function of density show for nuclear matter a critical temperature of about T c HF =16.6 MeV. (As in the usual scalar-vector (SV) theory, the phase transition is absent for neutron matter. A phase transition of both many-baryon systems in the high-pressure and high-density region, which has been found within the SV many-baryon theory, appears in the SVI theory too. The calculated maximum stable masses of neutron stars depend on 1. the underlying parameter set and/or 2. on the chosen approximation (i.e., H, HF; SV-, SVI theory, respectively). Hartree calculations lead to a mass stability limit of M max H ≤2.87 M sun (M max H ≤2.44 M sun when hyperons are taken into account). For the HF calculations we obtained M max HF ≤3.00 M sun (M max HF ≤2.85 M sun ). The corresponding maximum radii are (same notation as above) R H ≤13.2 km (R H ≤11.8 km), R HF ≤14.0 km (R HF ≤13.94 km).) The influence of the approximations, parameter sets and hyperons on the neutron star's moment of inertia is exhibited. (orig.)
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
International Nuclear Information System (INIS)
Barakat, T
2012-01-01
Based on the simple similarity transformation, we were able to transform the Dirac equation whose potential contains vector V (r) = -A/r + B 1 r and scalar S(r) = B 2 r types into a form nearly identical to the Schrödinger equation. The transformed equation is so simple that one can solve it by means of the asymptotic iteration method. Moreover, within the same framework we were able to obtain the relativistic energy eigenvalues for the Dirac equation with vector Coulomb plus scalar linear, and with pure scalar linear potentials; V (r) = -A/r, S(r) = B 2 r, and V (r) = 0, S(r) = B 2 r, respectively.
Yang-Mills-Vlasov system in the temporal gauge
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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
International Nuclear Information System (INIS)
de Jong, F.; Malfliet, R.
1991-01-01
Starting from a relativistic Lagrangian we derive a ''conserving'' approximation for the description of nuclear matter. We show this to be a nontrivial extension over the relativistic Dirac-Brueckner scheme. The saturation point of the equation of state calculated agrees very well with the empirical saturation point. The conserving character of the approach is tested by means of the Hugenholtz--van Hove theorem. We find the theorem fulfilled very well around saturation. A new value for compression modulus is derived, K=310 MeV. Also we calculate the occupation probabilities at normal nuclear matter densities by means of the spectral function. The average depletion κ of the Fermi sea is found to be κ∼0.11
International Nuclear Information System (INIS)
Schoenhofen, M.; Cubero, M.; Gering, M.; Sambataro, M.; Feldmeier, H.; Noerenberg, W.
1989-06-01
Within the framework of relativistic field theory for nucleons, deltas, scalar and vector mesons, a systematic study of the nuclear equation of state and its relation to pion yields in heavy-ion collisions is presented. Not the compressibility but the effective nucleon mass at normal nuclear density turns out to be the most sensitive parameter. Effects from vaccum fluctuations are well modelled within the mean-field no-sea approximation by self-interaction terms for the scalar meson field. Incomplete thermalization in the fireball may be the reason for the low pion yields observed in heavy-ion collisions. (orig.)
Komathiraj, K.; Sharma, Ranjan
2018-05-01
In this paper, we present a formalism to generate a family of interior solutions to the Einstein-Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere matched to the exterior Reissner-Nordström space-time. By reducing the Einstein-Maxwell system to a recurrence relation with variable rational coefficients, we show that it is possible to obtain closed-form solutions for a specific range of model parameters. A large class of solutions obtained previously are shown to be contained in our general class of solutions. We also analyse the physical viability of our new class of solutions.
Comment on 'analytic solution of the relativistic Coulomb problem for a spinless Salpeter equation'
International Nuclear Information System (INIS)
Lucha, W.; Schoeberl, F.F.
1994-01-01
We demonstrate that the analytic solution for the set of energy eigenvalues of the semi-relativistic Coulomb problem reported by B. and L. Durand is in clear conflict with an upper bound on the ground-state energy level derived by some straightforward variational procedure. (authors)
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Schlei, B.R.
1998-01-01
Experimental spectra of the CERN/SPS experiments NA44 and NA49 are fitted while using four different equations of state of nuclear matter within a relativistic hydrodynamic framework. For the freeze-out temperatures, T f = 139 MeV and T f = 116 MeV, respectively, the corresponding freeze-out hypersurfaces and Bose-Einstein correlation functions for identical pion pairs are discussed. It is concluded, that the Bose-Einstein interferometry measures the relation between the temperature and the energy density in the equation of state of nuclear matter at the late hadronic stage of the fireball expansion. It is necessary, to use the detailed detector acceptances in the calculations for the Bose-Einstein correlations
Energy Technology Data Exchange (ETDEWEB)
Ohsuga, Ken; Takahashi, Hiroyuki R. [National Astronomical Observatory of Japan, Osawa, Mitaka, Tokyo 181-8588 (Japan)
2016-02-20
We develop a numerical scheme for solving the equations of fully special relativistic, radiation magnetohydrodynamics (MHDs), in which the frequency-integrated, time-dependent radiation transfer equation is solved to calculate the specific intensity. The radiation energy density, the radiation flux, and the radiation stress tensor are obtained by the angular quadrature of the intensity. In the present method, conservation of total mass, momentum, and energy of the radiation magnetofluids is guaranteed. We treat not only the isotropic scattering but also the Thomson scattering. The numerical method of MHDs is the same as that of our previous work. The advection terms are explicitly solved, and the source terms, which describe the gas–radiation interaction, are implicitly integrated. Our code is suitable for massive parallel computing. We present that our code shows reasonable results in some numerical tests for propagating radiation and radiation hydrodynamics. Particularly, the correct solution is given even in the optically very thin or moderately thin regimes, and the special relativistic effects are nicely reproduced.
Energy Technology Data Exchange (ETDEWEB)
Wu, Kailiang [School of Mathematical Sciences, Peking University, Beijing 100871 (China); Tang, Huazhong, E-mail: wukl@pku.edu.cn, E-mail: hztang@math.pku.edu.cn [HEDPS, CAPT and LMAM, School of Mathematical Sciences, Peking University, Beijing 100871 (China)
2017-01-01
The ideal gas equation of state (EOS) with a constant adiabatic index is a poor approximation for most relativistic astrophysical flows, although it is commonly used in relativistic hydrodynamics (RHD). This paper develops high-order accurate, physical-constraints-preserving (PCP), central, discontinuous Galerkin (DG) methods for the one- and two-dimensional special RHD equations with a general EOS. It is built on our theoretical analysis of the admissible states for RHD and the PCP limiting procedure that enforce the admissibility of central DG solutions. The convexity, scaling invariance, orthogonal invariance, and Lax–Friedrichs splitting property of the admissible state set are first proved with the aid of its equivalent form. Then, the high-order central DG methods with the PCP limiting procedure and strong stability-preserving time discretization are proved, to preserve the positivity of the density, pressure, specific internal energy, and the bound of the fluid velocity, maintain high-order accuracy, and be L {sup 1}-stable. The accuracy, robustness, and effectiveness of the proposed methods are demonstrated by several 1D and 2D numerical examples involving large Lorentz factor, strong discontinuities, or low density/pressure, etc.
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
On completeness and orthogonality of solutions of relativistic wave equations on zero plane
International Nuclear Information System (INIS)
Gitman, D.M.; Shakhmatov, V.M.; Shvartsman, Sh.M.
1975-01-01
The work considers the possible redeterminations of the scalar product for the relativistic wave fields, such as the Klein-Gordon and Dirac ones. It has been shown that a whole class of new exact solutions, for which the usual scalar product on the plane x 0 =const. could not be previously determinated, allows a correct scalar product on the zero plane x 0 -x 3 =const. The relations of orthogonality and completeness with respect to the above scalar product have been proved. Possible applications of the obtained results are discussed
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.
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.
International Nuclear Information System (INIS)
Matsyuk, R.Ya.
1985-01-01
The problem on the existence of the invariant third-order Euler-Poisson equations in the pseudo-Euclidean space is investigated. The locally variational problem is determined by the Lagrangian density over the space of the second-order jets. The one - parameter family of the invariant third-order Euler-Poisson equations is groved to be the only one in the three-dimensional pseudo-Euclidean space. No invariant third-order Euler-Poisson equations exist in the four-dimensional pseudo-Euclidean space. It is shown that the Mathisson equation and the equation of geodesic circles in particular cases may be considered in the context of the Ostrogradiskij mechanics and the Kavaguchi geometry
Gholibeigian, Hassan; Amirshahkarami, Abdolazim; Gholibeigian, Kazem
2017-01-01
In special relativity theory, time dilates in velocity of near light speed. Also based on ``Substantial motion'' theory of Sadra, relative time (time flux); R = f (mv , σ , τ) , for each atom is momentum of its involved fundamental particles, which is different from the other atoms. In this way, for modification of the relativistic classical equation of string theory and getting more precise results, we should use effect of dilation and contraction of time in equation. So we propose to add two derivatives of the time's flux to the equation as follows: n.tp∂/R ∂ τ +∂2Xμ/(σ , τ) ∂τ2 = n .tp (∂/R ∂ σ ) +c2∂2Xμ/(σ , τ) ∂σ2 In which, Xμ is space-time coordinates of the string, σ & τ are coordinates on the string world sheet, respectively space and time along the string, string's mass m , velocity of string's motion v , factor n depends on geometry of each hidden extra dimension which relates to its own flux time, and tp is Planck's time. AmirKabir University of Technology, Tehran, Iran.
International Nuclear Information System (INIS)
Jiang Weizhou; Li Baozn; Chen Liewen
2007-01-01
Using in-medium hadron properties according to the Brown-Rho scaling due to the chiral symmetry restoration at high densities and considering naturalness of the coupling constants, we have newly constructed several relativistic mean-field Lagrangians with chiral limits. The model parameters are adjusted such that the symmetric part of the resulting equation of state at supra-normal densities is consistent with that required by the collective flow data from high energy heavy-ion reactions, while the resulting density dependence of the symmetry energy at sub-saturation densities agrees with that extracted from the recent isospin diffusion data from intermediate energy heavy-ion reactions. The resulting equations of state have the special feature of being soft at intermediate densities but stiff at high densities naturally. With these constrained equations of state, it is found that the radius of a 1.4M o canonical neutron star is in the range of 11.9 km≤R≤13.1 km, and the maximum neutron star mass is around 2.0M o close to the recent observations
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.
Relativistic two-and three-particle scattering equations using instant and light-front dynamics
International Nuclear Information System (INIS)
Adhikari, S.K.; Tomio, L.; Frederico, T.
1992-01-01
Starting from the Bethe-Salpeter equation for two particles in the ladder approximation and integrating over the time component of momentum we derive three dimensional scattering integral equations satisfying constraints of unitarity and relativity, both employing the light-front and instant-form variables. The equations we arrive at are those first derived by Weinberg and by Blankenbecler and Sugar, and are shown to be related by a transformation of variables. Hence we show how to perform and relate identical dynamical calculation using these two equations. We extends this procedure to the case of three particles interacting via two-particle separable potentials. Using light-front and instant form variables we suggest a couple of three dimensional three-particle scattering equations satisfying constraints of two and three-particle unitarity and relativity. The three-particle light-front equation is shown to be approximately related by a transformation of variables to one of the instant-form three-particle equations. (author)
Prompt form of relativistic equations of motion in a model of singular lagrangian formalism
International Nuclear Information System (INIS)
Gajda, R.P.; Duviryak, A.A.; Klyuchkovskij, Yu.B.
1983-01-01
The purpose of the paper is to develope the way of transition from equations of motion in singular lagrangian formalism to three-dimensional equations of Newton type in the prompt form of dynamics in the framework of c -2 parameter expansion (s. c. quasireltativistic approaches), as well as to find corresponding integrals of motion. The first quasirelativistifc approach for Dominici, Gomis, Longhi model was obtained and investigated
Solution of the Fokker-Planck equation for axially-channeled relativistic electrons
International Nuclear Information System (INIS)
Muralev, V.A.; Telegin, V.I.
1981-01-01
A method of the two dimensional kinetic equation of the Fokker-Planck type for axially-channeled electrons is proposed. This equation has been obtained recently by Beloshitsky and Kumakhov to describe the diffusion of channeling negative particles over the transverse energy and angular momentum. The results of computation of the dechanneling function of 1 GeV electrons in tungsten are presented. (author)
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 (ℎ/2π)-expansion for Regge-trajectories. 2. Relativistic equations
International Nuclear Information System (INIS)
Stepanov, S.S.; Tutik, R.S.
1992-01-01
The (h/2π)-expansion method, proposed earlier for deriving Regge trajectories for bound states of central potentials in the Schroedinger equation framework, is extended to the Klein-Gordon and Dirac equations with potentials having vector and scalar components. The simple recursion formulae, with the same form both for the parent and daughter Regge trajectories, are obtained. They provide, in principle, the calculation of the (h/2π)-expansion terms up to an arbitrary order. As an illustration, a superposition of the vector and scalar Coulomb potentials, and the funnel-shaped potential are treated with the technique developed. 20 refs.; 3 figs.; 1 table. (author)
On the relativistic transport equation for a discontinuity wave of multiplicity one
International Nuclear Information System (INIS)
Giambo, Sebastiano; Palumbo, Annunziata
1980-01-01
In the framework of the theory of the singular hypersurfaces, the transport equation for the amplitude of a discontinuity wave, corresponding to a simple characteristic of a quasi-linear hyperbolic system, is established in the context of special relativity [fr
Classical relativistic equations for particles with spin moving in external fields
Dam, H. van; Ruijgrok, Th.W.
1980-01-01
We derive equations of motion for a point particle with spin in an external electromagnetic and in an external scalar field. The derivation is based on the ten conservation laws of linear and angular momentum and on a general expression for the current by which the particle interacts with the
Analytic solution of the relativistic Coulomb problem for a spinless Salpeter equation
International Nuclear Information System (INIS)
Durand, B.; Durand, L.
1983-01-01
We construct an analytic solution to the spinless S-wave Salpeter equation for two quarks interacting via a Coulomb potential, [2(-del 2 +m 2 )/sup 1/2/-M-α/r] psi(r) = 0, by transforming the momentum-space form of the equation into a mapping or boundary-value problem for analytic functions. The principal part of the three-dimensional wave function is identical to the solution of a one-dimensional Salpeter equation found by one of us and discussed here. The remainder of the wave function can be constructed by the iterative solution of an inhomogeneous singular integral equation. We show that the exact bound-state eigenvalues for the Coulomb problem are M/sub n/ = 2m/(1+α 2 /4n 2 )/sup 1/2/, n = 1,2,..., and that the wave function for the static interaction diverges for r→0 as C(mr)/sup -nu/, where #betta# = (α/π)(1+α/π+...) is known exactly
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.
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
Continuum Vlasov Simulation in Four Phase-space Dimensions
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).
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
3D Relativistic Hydrodynamic Computations Using Lattice-QCD-Inspired Equations of State
International Nuclear Information System (INIS)
Hama, Yogiro; Andrade, Rone P.G.; Grassi, Frederique; Socolowski, Otavio; Kodama, Takeshi; Tavares, Bernardo; Padula, Sandra S.
2006-01-01
In this communication, we report results of three-dimensional hydrodynamic computations, by using equations of state with a critical end point as suggested by the lattice QCD. Some of the results are an increase of the multiplicity in the mid-rapidity region and a larger elliptic-flow parameter v 2 . We discuss also the effcts of the initial-condition fluctuations and the continuous emission
3D Relativistic Hydrodynamic Computations Using Lattice-QCD-Inspired Equations of State
Energy Technology Data Exchange (ETDEWEB)
Hama, Yogiro [Instituto de Fisica, Universidade de Sao Paulo (Brazil); Andrade, Rone P.G. [Instituto de Fisica, Universidade de Sao Paulo (Brazil); Grassi, Frederique [Instituto de Fisica, Universidade de Sao Paulo (Brazil); Socolowski, Otavio [Instituto Tecnologico da Aeronautica (Brazil); Kodama, Takeshi [Instituto de Fisica, Universidade Federal do Rio de Janeiro (Brazil); Tavares, Bernardo [Instituto de Fisica, Universidade Federal do Rio de Janeiro (Brazil); Padula, Sandra S. [Instituto de Fisica Teorica, Universidade Estadual Paulista (Brazil)
2006-08-07
In this communication, we report results of three-dimensional hydrodynamic computations, by using equations of state with a critical end point as suggested by the lattice QCD. Some of the results are an increase of the multiplicity in the mid-rapidity region and a larger elliptic-flow parameter v{sub 2}. We discuss also the effcts of the initial-condition fluctuations and the continuous emission.
International Nuclear Information System (INIS)
Zhang Yongde.
1987-03-01
In this paper, the neutron Dirac-equation is presented. After decoupling it into two equations of the simple spinors, the rigorous solution of this equation is obtained in the case of slab-like uniform magnetic fields at perpendicular incidence. At non-relativistic approximation and first order approximation of weak field (NRWFA), our results have included all results that have been obtained in references for this case up to now. The corresponding transformations of the neutron's spin vectors are given. The single particle spectrum and its approximate expression are obtained. The characteristics of quantum statistics with the approximate expression of energy spectrum are studied. (author). 15 refs
Integral representations of solutions of the wave equation based on relativistic wavelets
International Nuclear Information System (INIS)
Perel, Maria; Gorodnitskiy, Evgeny
2012-01-01
A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine Poincaré group, i.e. with the help of translations, dilations in space and time and Lorentz transformations. The representation can be interpreted in terms of the initial-boundary value problem for the wave equation in a half-plane. It gives the solution as an integral representation of two types of solutions: propagating localized solutions running away from the boundary under different angles and packet-like surface waves running along the boundary and exponentially decreasing away from the boundary. Properties of elementary solutions are discussed. A numerical investigation of coefficients of the decomposition is carried out. An example of the decomposition of the field created by sources moving along a line with different speeds is considered, and the dependence of coefficients on speeds of sources is discussed. (paper)
Energy Technology Data Exchange (ETDEWEB)
Decker, J.; Peysson, Y
2004-12-01
A new original code for solving the 3-D relativistic and bounce-averaged electron drift kinetic equation is presented. It designed for the current drive problem in tokamak with an arbitrary magnetic equilibrium. This tool allows self-consistent calculations of the bootstrap current in presence of other external current sources. RF current drive for arbitrary type of waves may be used. Several moments of the electron distribution function are determined, like the exact and effective fractions of trapped electrons, the plasma current, absorbed RF power, runaway and magnetic ripple loss rates and non-thermal Bremsstrahlung. Advanced numerical techniques have been used to make it the first fully implicit (reverse time) 3-D solver, particularly well designed for implementation in a chain of code for realistic current drive calculations in high {beta}{sub p} plasmas. All the details of the physics background and the numerical scheme are presented, as well a some examples to illustrate main code capabilities. Several important numerical points are addressed concerning code stability and potential numerical and physical limitations. (authors)
International Nuclear Information System (INIS)
Barbashov, B.M.; Chervyakov, A.M.
1991-01-01
The classical histories of the relativistic string with massive ends in space-time are examined in terms of geometric invariants of both the string world surface and world lines of the point masses at the string ends. In this formulation the string variables are completely defined by means of the constant curvatures and torsions of the endpoint trajectories which are subjected to a system of differential equations with a delayed arguments that incorporates retardation effects of the interaction of two point masses through the string. The well-known example of the rotating straight-line string with massive ends corresponds to a particular solution of this system for the constant torsions. A new exact solution for the periodic torsions of the world trajectories of the massive string ends is found. In this case the string coordinates are represented in terms of normal elliptic integrals and describe a more intricate motion including its transverse vibrations than rotation of a stretched string in a given plane. 17 refs
International Nuclear Information System (INIS)
Decker, J.; Peysson, Y.
2004-12-01
A new original code for solving the 3-D relativistic and bounce-averaged electron drift kinetic equation is presented. It designed for the current drive problem in tokamak with an arbitrary magnetic equilibrium. This tool allows self-consistent calculations of the bootstrap current in presence of other external current sources. RF current drive for arbitrary type of waves may be used. Several moments of the electron distribution function are determined, like the exact and effective fractions of trapped electrons, the plasma current, absorbed RF power, runaway and magnetic ripple loss rates and non-thermal Bremsstrahlung. Advanced numerical techniques have been used to make it the first fully implicit (reverse time) 3-D solver, particularly well designed for implementation in a chain of code for realistic current drive calculations in high β p plasmas. All the details of the physics background and the numerical scheme are presented, as well a some examples to illustrate main code capabilities. Several important numerical points are addressed concerning code stability and potential numerical and physical limitations. (authors)
Stability analysis of a Vlasov-Wave system describing particles interacting with their environment
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.
Non-geometrical optics investigation of mode conversion in weakly relativistic inhomogeneous plasmas
International Nuclear Information System (INIS)
Imre, K.
1985-06-01
Electron cyclotron resonance heating of plasmas by waves incident to the fundamental and second harmonic layer is investigated. When the wave propagation is nearly perpendicular to the equilibrium field in a weakly inhomogeneous plasma the standard geometrical optics breaks down and the relativistic corrections become significant at the resonance layer. Unlike the previous studies of this problem, the governing equations are derived from the linearized relativistic Vlasov equation coupled with Maxwell's equations, rather than using the uniform field dispersion relation to construct equations by replacing the refractive index by some spatial differential operations. We employ a boundary layer analysis at the resonance region and match the inner and outer solutions in the usual manner. We obtain not only the full wave solution of the problem, but also the set of physical parameters and their ranges in which the analysis is valid. Although we obtain analytic results for the asymptotic solutions, our analysis usually requires a numerical procedure when the relativistic and/or nonzero parallel refractive index are included
Vlasov fluid model with electron pressure
International Nuclear Information System (INIS)
Gerwin, R.
1975-11-01
The Vlasov-ion, fluid-electron model of Freidberg for studying the linear stability of hot-ion pinch configurations is here extended to include electron pressure. Within the framework of an adiabatic electron-gas picture, it is shown that this model is still amenable to the numerical methods described by Lewis and Freidberg
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
International Nuclear Information System (INIS)
Bugaev, K.A.; Gorenshtejn, M.I.; Zhdanov, V.I.
1987-01-01
Theoretical basis for general stability criterion of relativistic shocks in baryonic matter is proposed. Different formulations of shock mechanical stability are considered and applied to the analysis of rarefaction shock hadronization transition. 13 refs.; 2 figs
Dissipative relativistic hydrodynamics
International Nuclear Information System (INIS)
Imshennik, V.S.; Morozov, Yu.I.
1989-01-01
Using the comoving reference frame in the general non-inertial case, the relativistic hydrodynamics equations are derived with an account for dissipative effects in the matter. From the entropy production equation, the exact from for the dissipative tensor components is obtained. As a result, the closed system of equations of dissipative relativistic hydrodynamics is obtained in the comoving reference frame as a relativistic generalization of the known Navier-Stokes equations for Lagrange coordinates. Equations of relativistic hydrodynamics with account for dissipative effects in the matter are derived using the assocoated reference system in general non-inertial case. True form of the dissipative tensor components is obtained from entropy production equation. Closed system of equations for dissipative relativistic hydrodynamics is obtained as a result in the assocoated reference system (ARS) - relativistic generalization of well-known Navier-Stokes equations for Lagrange coordinates. Equation system, obtained in this paper for ARS, may be effectively used in numerical models of explosive processes with 10 51 erg energy releases which are characteristic for flashes of supernovae, if white dwarf type compact target suggested as presupernova
Progress on a Vlasov Treatment of Coherent Synchrotron Radiation from Arbitrary Planar Orbits
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...
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.
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
International Nuclear Information System (INIS)
Barbashov, B.M.
1996-01-01
Boundary equations for the relativistic string with masses at ends are formulated in terms of geometrical invariants of world trajectories of masses at the string ends. In the three-dimensional Minkowski space E 2 1 , there are two invariants of that sort, the curvature K and torsion κ. Curvatures of trajectories of the string ends with masses are always constant, K i =γ/m i (i=1,2), whereas torsions κ i obey a system of differential equations with deviating arguments. For these equations with periodic κ i (τ+nl)=κ(τ), constants of motion are obtained (part 1) and exact solutions are presented (part 2) for periods l and 2l where l is the string length in the plane of parameters τ and σ(σ 1 =0, σ 2 =l). 7 refs
International Nuclear Information System (INIS)
Shkarofsky, I.P.
1997-01-01
The relativistic Fokker-Planck collision term in Braams and Karney [Phys. Fluids B 1, 1355 (1989)] is expanded using Cartesian tensors (equivalent to associated Legendre spherical harmonics) retaining all non-linear terms and an arbitrary zeroth order distribution background. Expressions are given for collision terms between all harmonics and the background distribution in terms of the j and y functions in Braams and Karney. The results reduce to Braams and Karney for the first order harmonic term with a Maxwellian background and to those given by Shkarofsky [Can. J. Phys. 41, 1753 (1963)] in the non-relativistic limit. Expressions for the energy and momentum transfer associated with relativistic Coulomb collisions are given. The fast two dimensional Fokker-Planck solver in Shoucri and Shkarofsky [Comput. Phys. Commun. 82, 287 (1994)] has been extended to include the second order harmonic term. copyright 1997 American Institute of Physics
Energy Technology Data Exchange (ETDEWEB)
Bobylev, Yu. V. [L.N. Tolstoy Tula State Pedagogical University (Russian Federation); Kuzelev, M. V. [Moscow State University (Russian Federation); Rukhadze, A. A. [Russian Academy of Sciences, Prokhorov Institute of General Physics (Russian Federation)
2008-02-15
A general mathematical model is proposed that is based on the Vlasov kinetic equation with a self-consistent field and describes the nonlinear dynamics of the electromagnetic instabilities of a relativistic electron beam in a spatially bounded plasma. Two limiting cases are analyzed, namely, high-frequency (HF) and low-frequency (LF) instabilities of a relativistic electron beam, of which the LF instability is a qualitatively new phenomenon in comparison with the known Cherenkov resonance effects. For instabilities in the regime of the collective Cherenkov effect, the equations containing cubic nonlinearities and describing the nonlinear saturation of the instabilities of a relativistic beam in a plasma are derived by using the methods of expansion in small perturbations of the trajectories and momenta of the beam electrons. Analytic expressions for the amplitudes of the interacting beam and plasma waves are obtained. The analytical results are shown to agree well with the exact solutions obtained numerically from the basic general mathematical model of the instabilities in question. The general mathematical model is also used to discuss the effects associated with variation in the constant component of the electron current in a beam-plasma system.
Strongly enhanced flow effect from Landau-Vlasov versus Vlasov-Uehling-Uhlenbeck approach
International Nuclear Information System (INIS)
Gregoire, C.; Remaud, B.; Sebille, F.; Schuck, P.
1988-01-01
The simulation of the collision integral in the Landau-Vlasov approach for heavy ion collisions is examined. It turns out that quantities like the nucleon mean free path can be compared with parallel ensemble models. Convergency of results with time step and sampling is clearly established. Quadratic quantities, like the internal pressure, are found to be strongly underestimated in parallel ensemble models
Vereshchagin, Gregory V.; Aksenov, Alexey G.
2017-02-01
Preface; Acknowledgements; Acronyms and definitions; Introduction; Part I. Theoretical Foundations: 1. Basic concepts; 2. Kinetic equation; 3. Averaging; 4. Conservation laws and equilibrium; 5. Relativistic BBGKY hierarchy; 6. Basic parameters in gases and plasmas; Part II. Numerical Methods: 7. The basics of computational physics; 8. Direct integration of Boltzmann equations; 9. Multidimensional hydrodynamics; Part III. Applications: 10. Wave dispersion in relativistic plasma; 11. Thermalization in relativistic plasma; 12. Kinetics of particles in strong fields; 13. Compton scattering in astrophysics and cosmology; 14. Self-gravitating systems; 15. Neutrinos, gravitational collapse and supernovae; Appendices; Bibliography; Index.
Sarfraz, M.; Farooq, H.; Abbas, G.; Noureen, S.; Iqbal, Z.; Rasheed, A.
2018-03-01
Thermal momentum space anisotropy is ubiquitous in many astrophysical and laboratory plasma environments. Using Vlasov-Maxwell's model equations, a generalized polarization tensor for a collisionless ultra-relativistic unmagnetized electron plasma is derived. In particular, the tensor is obtained by considering anisotropy in the momentum space. The integral of moments of Fermi-Dirac distribution function in terms of Polylog functions is used for describing the border line plasma systems (T/e TF e ≈1 ) comprising arbitrary electron degeneracy, where Te and TF e, are thermal and Fermi temperatures, respectively. Furthermore, the effects of variation in thermal momentum space anisotropy on the electron equilibrium number density and the spectrum of electromagnetic waves are analyzed.
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
Relativistic magnetohydrodynamics
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Hernandez, Juan; Kovtun, Pavel [Department of Physics and Astronomy, University of Victoria,Victoria, BC, V8P 5C2 (Canada)
2017-05-02
We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfvén waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfvén-like waves with a quadratic dispersion relation. We relate the transport coefficients in the “conventional” magnetohydrodynamics (formulated using Maxwell’s equations in matter) to those in the “dual” version of magnetohydrodynamics (formulated using the conserved magnetic flux).
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
International Nuclear Information System (INIS)
Peysson, Y.
1997-09-01
A full implicit numerical procedure based on the use of a nine-point difference operator is presented to solve the two dimensional (2 D ) relativistic Fokker-Planck equation for the current drive problem and synergetic effects between the lower hybrid and the electron cyclotron waves in tokamaks. As compared to the standard approach based on the use of a five-point difference operator [M. Shoucri, I. Shkarofsky, Comput. Phys. Comm. 82 (1994) 287], the convergence rate towards the steady state solution may be significantly enhanced with no loss of accuracy on the distribution function. Moreover, it is shown that the numerical stability may be strongly improved without a large degradation of the CPU time consumption as in the five-point scheme, making this approach very attractive for a fast solution of the 2-D Fokker-Planck equation on a fine grid in conjunction with other numerical codes for realistic plasma simulations. This new algorithm, based on an approximate matrix factorization technique, may be applied to all numerical problems with large sets of equations which involve nine-point difference operators. (author)
Energy Technology Data Exchange (ETDEWEB)
Peysson, Y. [Association Euratom-CEA, CEA Grenoble, 38 (France). Dept. de Recherches sur la Fusion Controlee; Choucri, M. [Centre Canadien de Fusion Magnetique, Varennes, PQ (Canada)
1997-09-01
A full implicit numerical procedure based on the use of a nine-point difference operator is presented to solve the two dimensional (2{sub D}) relativistic Fokker-Planck equation for the current drive problem and synergetic effects between the lower hybrid and the electron cyclotron waves in tokamaks. As compared to the standard approach based on the use of a five-point difference operator [M. Shoucri, I. Shkarofsky, Comput. Phys. Comm. 82 (1994) 287], the convergence rate towards the steady state solution may be significantly enhanced with no loss of accuracy on the distribution function. Moreover, it is shown that the numerical stability may be strongly improved without a large degradation of the CPU time consumption as in the five-point scheme, making this approach very attractive for a fast solution of the 2-D Fokker-Planck equation on a fine grid in conjunction with other numerical codes for realistic plasma simulations. This new algorithm, based on an approximate matrix factorization technique, may be applied to all numerical problems with large sets of equations which involve nine-point difference operators. (author) 21 refs.
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
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
Relativistic viscoelastic fluid mechanics
International Nuclear Information System (INIS)
Fukuma, Masafumi; Sakatani, Yuho
2011-01-01
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.
Relativistic viscoelastic fluid mechanics.
Fukuma, Masafumi; Sakatani, Yuho
2011-08-01
A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.
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.
International Nuclear Information System (INIS)
Delker, L.; Dugan, G.; Wu, C.S.; Lu, D.C.; Caffrey, A.J.; Cheng, Y.T.; Lee, Y.K.
1979-01-01
A newly designed, large-aperture and high-resolution bent-crystal spectrometer has been used to observe high-intensity sources of pionic x rays. The pionic x-ray source was a target of natural titanium which was placed adjacent to a copper pion-production target in the external beam of the Nevis synchrocyclotron. The energy difference between the 5g → 4f and 5f → 4d transitions in pionic titanium was measured to be 87.6 +- 1.8 eV. Comparison with the prediction of the Klein-Gordon equation is made
Relativistic non-Hamiltonian mechanics
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2010-01-01
Relativistic particle subjected to a general four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u μ u μ + c 2 = 0, where c is the speed of light in vacuum. In the general case, four-forces are non-potential, and the relativistic particle is a non-Hamiltonian system in four-dimensional pseudo-Euclidean space-time. We consider non-Hamiltonian and dissipative systems in relativistic mechanics. Covariant forms of the principle of stationary action and the Hamilton's principle for relativistic mechanics of non-Hamiltonian systems are discussed. The equivalence of these principles is considered for relativistic particles subjected to potential and non-potential forces. We note that the equations of motion which follow from the Hamilton's principle are not equivalent to the equations which follow from the variational principle of stationary action. The Hamilton's principle and the principle of stationary action are not compatible in the case of systems with nonholonomic constraint and the potential forces. The principle of stationary action for relativistic particle subjected to non-potential forces can be used if the Helmholtz conditions are satisfied. The Hamilton's principle and the principle of stationary action are equivalent only for a special class of relativistic non-Hamiltonian systems.
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
Energy Technology Data Exchange (ETDEWEB)
Zhang, Dong-Rui; Jiang, Wei-Zhou; Wei, Si-Na; Yang, Rong-Yao [Southeast University, Department of Physics, Nanjing (China); Xiang, Qian-Fei [Chinese Academy of Sciences, Institute of High Energy Physics, Beijing (China)
2016-05-15
It has been a puzzle whether quarks may exist in the interior of massive neutron stars, since the hadron-quark phase transition softens the equation of state (EOS) and reduce the neutron star (NS) maximum mass very significantly. In this work, we consider the light U-boson that increases the NS maximum mass appreciably through its weak coupling to fermions. The inclusion of the U-boson may thus allow the existence of the quark degrees of freedom in the interior of large mass neutron stars. Unlike the consequence of the U-boson in hadronic matter, the stiffening role of the U-boson in the hybrid EOS is not sensitive to the choice of the hadron phase models. In addition, we have also investigated the effect of the effective QCD correction on the hybrid EOS. This correction may reduce the coupling strength of the U-boson that is needed to satisfy NS maximum mass constraint. While the inclusion of the U-boson also increases the NS radius significantly, we find that appropriate in-medium effects of the U-boson may reduce the NS radii significantly, satisfying both the NS radius and mass constraints well. (orig.)
Demianski, Marek
2013-01-01
Relativistic Astrophysics brings together important astronomical discoveries and the significant achievements, as well as the difficulties in the field of relativistic astrophysics. This book is divided into 10 chapters that tackle some aspects of the field, including the gravitational field, stellar equilibrium, black holes, and cosmology. The opening chapters introduce the theories to delineate gravitational field and the elements of relativistic thermodynamics and hydrodynamics. The succeeding chapters deal with the gravitational fields in matter; stellar equilibrium and general relativity
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.
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)
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
Hanauske, Matthias; Steinheimer, Jan; Bovard, Luke; Mukherjee, Ayon; Schramm, Stefan; Takami, Kentaro; Papenfort, Jens; Wechselberger, Natascha; Rezzolla, Luciano; Stöcker, Horst
2017-07-01
The underlying open questions in the fields of general relativistic astrophysics and elementary particle and nuclear physics are strongly connected and their results are interdependent. Although the physical systems are quite different, the 4D-simulation of a merger of a binary system of two neutron stars and the properties of the hot and dense matter created in high energy heavy ion collisions, strongly depend on the equation of state of fundamental elementary matter. Neutron star mergers represent optimal astrophysical laboratories to investigate the QCD phase structure using a spectrogram of the post-merger phase of the emitted gravitational waves. These studies can be supplemented by observations from heavy ion collisions to possibly reach a conclusive picture on the QCD phase structure at high density and temperature. As gravitational waves (GWs) emitted from merging neutron star binaries are on the verge of their first detection, it is important to understand the main characteristics of the underlying merging system in order to predict the expected GW signal. Based on numerical-relativity simulations of merging neutron star binaries, the emitted GW and the interior structure of the generated hypermassive neutron stars (HMNS) have been analyzed in detail. This article will focus on the internal and rotational HMNS properties and their connection with the emitted GW signal. Especially, the appearance of the hadon-quark phase transition in the interior region of the HMNS and its conjunction with the spectral properties of the emitted GW will be addressed and confronted with the simulation results of high energy heavy ion collisions.
Relativistic theories of materials
Bressan, Aldo
1978-01-01
The theory of relativity was created in 1905 to solve a problem concerning electromagnetic fields. That solution was reached by means of profound changes in fundamental concepts and ideas that considerably affected the whole of physics. Moreover, when Einstein took gravitation into account, he was forced to develop radical changes also in our space-time concepts (1916). Relativistic works on heat, thermodynamics, and elasticity appeared as early as 1911. However, general theories having a thermodynamic basis, including heat conduction and constitutive equations, did not appear in general relativity until about 1955 for fluids and appeared only after 1960 for elastic or more general finitely deformed materials. These theories dealt with materials with memory, and in this connection some relativistic versions of the principle of material indifference were considered. Even more recently, relativistic theories incorporating finite deformations for polarizable and magnetizable materials and those in which couple s...
Partial Differential Equations in General Relativity
International Nuclear Information System (INIS)
Choquet-Bruhat, Yvonne
2008-01-01
General relativity is a physical theory basic in the modeling of the universe at the large and small scales. Its mathematical formulation, the Einstein partial differential equations, are geometrically simple, but intricate for the analyst, involving both hyperbolic and elliptic PDE, with local and global problems. Many problems remain open though remarkable progress has been made recently towards their solutions. Alan Rendall's book states, in a down-to-earth form, fundamental results used to solve different types of equations. In each case he gives applications to special models as well as to general properties of Einsteinian spacetimes. A chapter on ODE contains, in particular, a detailed discussion of Bianchi spacetimes. A chapter entitled 'Elliptic systems' treats the Einstein constraints. A chapter entitled 'Hyperbolic systems' is followed by a chapter on the Cauchy problem and a chapter 'Global results' which contains recently proved theorems. A chapter is dedicated to the Einstein-Vlasov system, of which the author is a specialist. On the whole, the book surveys, in a concise though precise way, many essential results of recent interest in mathematical general relativity, and it is very clearly written. Each chapter is followed by an up to date bibliography. In conclusion, this book will be a valuable asset to relativists who wish to learn clearly-stated mathematical results and to mathematicians who want to penetrate into the subtleties of general relativity, as a mathematical and physical theory. (book review)
Partial Differential Equations in General Relativity
Energy Technology Data Exchange (ETDEWEB)
Choquet-Bruhat, Yvonne
2008-09-07
General relativity is a physical theory basic in the modeling of the universe at the large and small scales. Its mathematical formulation, the Einstein partial differential equations, are geometrically simple, but intricate for the analyst, involving both hyperbolic and elliptic PDE, with local and global problems. Many problems remain open though remarkable progress has been made recently towards their solutions. Alan Rendall's book states, in a down-to-earth form, fundamental results used to solve different types of equations. In each case he gives applications to special models as well as to general properties of Einsteinian spacetimes. A chapter on ODE contains, in particular, a detailed discussion of Bianchi spacetimes. A chapter entitled 'Elliptic systems' treats the Einstein constraints. A chapter entitled 'Hyperbolic systems' is followed by a chapter on the Cauchy problem and a chapter 'Global results' which contains recently proved theorems. A chapter is dedicated to the Einstein-Vlasov system, of which the author is a specialist. On the whole, the book surveys, in a concise though precise way, many essential results of recent interest in mathematical general relativity, and it is very clearly written. Each chapter is followed by an up to date bibliography. In conclusion, this book will be a valuable asset to relativists who wish to learn clearly-stated mathematical results and to mathematicians who want to penetrate into the subtleties of general relativity, as a mathematical and physical theory. (book review)
Relativistic Quantum Mechanics
International Nuclear Information System (INIS)
Antoine, J-P
2004-01-01
The aim of relativistic quantum mechanics is to describe the finer details of the structure of atoms and molecules, where relativistic effects become nonnegligible. It is a sort of intermediate realm, between the familiar nonrelativistic quantum mechanics and fully relativistic quantum field theory, and thus it lacks the simplicity and elegance of both. Yet it is a necessary tool, mostly for quantum chemists. Pilkuhn's book offers to this audience an up-to-date survey of these methods, which is quite welcome since most previous textbooks are at least ten years old. The point of view of the author is to start immediately in the relativistic domain, following the lead of Maxwell's equations rather than classical mechanics, and thus to treat the nonrelativistic version as an approximation. Thus Chapter 1 takes off from Maxwell's equations (in the noncovariant Coulomb gauge) and gradually derives the basic aspects of Quantum Mechanics in a rather pedestrian way (states and observables, Hilbert space, operators, quantum measurement, scattering,. Chapter 2 starts with the Lorentz transformations, then continues with the Pauli spin equation and the Dirac equation and some of their applications (notably the hydrogen atom). Chapter 3 is entitled 'Quantum fields and particles', but falls short of treating quantum field theory properly: only creation/annihilation operators are considered, for a particle in a box. The emphasis is on two-electron states (the Pauli principle, the Foldy--Wouthuysen elimination of small components of Dirac spinors, Breit projection operators. Chapter 4 is devoted to scattering theory and the description of relativistic bound states. Chapter 5, finally, covers hyperfine interactions and radiative corrections. As we said above, relativistic quantum mechanics is by nature limited in scope and rather inelegant and Pilkuhn's book is no exception. The notation is often heavy (mostly noncovariant) and the mathematical level rather low. The central topic
The Wigner function in the relativistic quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Kowalski, K., E-mail: kowalski@uni.lodz.pl; Rembieliński, J.
2016-12-15
A detailed study is presented of the relativistic Wigner function for a quantum spinless particle evolving in time according to the Salpeter equation. - Highlights: • We study the Wigner function for a quantum spinless relativistic particle. • We discuss the relativistic Wigner function introduced by Zavialov and Malokostov. • We introduce relativistic Wigner function based on the standard definition. • We find analytic expressions for relativistic Wigner functions.
SPECIAL RELATIVISTIC HYDRODYNAMICS WITH GRAVITATION
Energy Technology Data Exchange (ETDEWEB)
Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu (Korea, Republic of); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejon (Korea, Republic of)
2016-12-20
Special relativistic hydrodynamics with weak gravity has hitherto been unknown in the literature. Whether such an asymmetric combination is possible has been unclear. Here, the hydrodynamic equations with Poisson-type gravity, considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit, are consistently derived from Einstein’s theory of general relativity. An analysis is made in the maximal slicing, where the Poisson’s equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the general hypersurface condition. Our formulation includes the anisotropic stress.
Some problems in relativistic thermodynamics
International Nuclear Information System (INIS)
Veitsman, E. V.
2007-01-01
The relativistic equations of state for ideal and real gases, as well as for various interface regions, have been derived. These dependences help to eliminate some controversies in the relativistic thermodynamics based on the special theory of relativity. It is shown, in particular, that the temperature of system whose velocity tends to the velocity of light in vacuum varies in accordance with the Ott law T = T 0 /√1 - v 2 /c 2 . Relativistic dependences for heat and mass transfer, for Ohm's law, and for a viscous flow of a liquid have also been derived
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
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.
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
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
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
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
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
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.
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.
On the convexity of relativistic hydrodynamics
International Nuclear Information System (INIS)
Ibáñez, José M; Martí, José M; Cordero-Carrión, Isabel; Miralles, Juan A
2013-01-01
The relativistic hydrodynamic system of equations for a perfect fluid obeying a causal equation of state is hyperbolic (Anile 1989 Relativistic Fluids and Magneto-Fluids (Cambridge: Cambridge University Press)). In this report, we derive the conditions for this system to be convex in terms of the fundamental derivative of the equation of state (Menikoff and Plohr1989 Rev. Mod. Phys. 61 75). The classical limit is recovered. Communicated by L Rezzolla (note)
Relativistic nuclear collisions: theory
International Nuclear Information System (INIS)
Gyulassy, M.
1980-07-01
Some of the recent theoretical developments in relativistic (0.5 to 2.0-GeV/nucleon) nuclear collisions are reviewed. The statistical model, hydrodynamic model, classical equation of motion calculations, billiard ball dynamics, and intranuclear cascade models are discussed in detail. Inclusive proton and pion spectra are analyzed for a variety of reactions. Particular attention is focused on how the complex interplay of the basic reaction mechanism hinders attempts to deduce the nuclear matter equation of state from data. 102 references, 19 figures
Recent development of relativistic molecular theory
International Nuclear Information System (INIS)
Takahito, Nakajima; Kimihiko, Hirao
2005-01-01
Today it is common knowledge that relativistic effects are important in the heavy-element chemistry. The continuing development of the relativistic molecular theory is opening up rows of the periodic table that are impossible to treat with the non-relativistic approach. The most straightforward way to treat relativistic effects on heavy-element systems is to use the four-component Dirac-Hartree-Fock approach and its electron-correlation methods based on the Dirac-Coulomb(-Breit) Hamiltonian. The Dirac-Hartree-Fock (DHF) or Dirac-Kohn-Sham (DKS) equation with the four-component spinors composed of the large- and small-components demands severe computational efforts to solve, and its applications to molecules including heavy elements have been limited to small- to medium-size systems. Recently, we have developed a very efficient algorithm for the four-component DHF and DKS approaches. As an alternative approach, several quasi-relativistic approximations have also been proposed instead of explicitly solving the four-component relativistic equation. We have developed the relativistic elimination of small components (RESC) and higher-order Douglas-Kroll (DK) Hamiltonians within the framework of the two-component quasi-relativistic approach. The developing four-component relativistic and approximate quasi-relativistic methods have been implemented into a program suite named REL4D. In this article, we will introduce the efficient relativistic molecular theories to treat heavy-atomic molecular systems accurately via the four-component relativistic and the two-component quasi-relativistic approaches. We will also show several chemical applications including heavy-element systems with our relativistic molecular approaches. (author)
Relativistic neoclassical transport coefficients with momentum correction
International Nuclear Information System (INIS)
Marushchenko, I.; Azarenkov, N.A.
2016-01-01
The parallel momentum correction technique is generalized for relativistic approach. It is required for proper calculation of the parallel neoclassical flows and, in particular, for the bootstrap current at fusion temperatures. It is shown that the obtained system of linear algebraic equations for parallel fluxes can be solved directly without calculation of the distribution function if the relativistic mono-energetic transport coefficients are already known. The first relativistic correction terms for Braginskii matrix coefficients are calculated.
Relativistic few body calculations
International Nuclear Information System (INIS)
Gross, F.
1988-01-01
A modern treatment of the nuclear few-body problem must take into account both the quark structure of baryons and mesons, which should be important at short range, and the relativistic exchange of mesons, which describes the long range, peripheral interactions. A way to model both of these aspects is described. The long range, peripheral interactions are calculated using the spectator model, a general approach in which the spectators to nucleon interactions are put on their mass-shell. Recent numerical results for a relativistic OBE model of the NN interaction, obtained by solving a relativistic equation with one-particle on mass-shell, will be presented and discussed. Two meson exchange models, one with only four mesons (π,σ,/rho/,ω) but with a 25% admixture of γ 5 coupling for the pion, and a second with six mesons (π,σ,/rho/,ω,δ,/eta/) but pure γ 5 γ/sup μ/ pion coupling, are shown to give very good quantitative fits to the NN scattering phase shifts below 400 MeV, and also a good description of the /rvec p/ 40 Ca elastic scattering observables. Applications of this model to electromagnetic interactions of the two body system, with emphasis on the determination of relativistic current operators consistent with the dynamics and the exact treatment of current conservation in the presence of phenomenological form factors, will be described. 18 refs., 8 figs
Luciano, Rezzolla
2013-01-01
Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field. The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solut...
An introduction to relativistic hydrodynamics
Energy Technology Data Exchange (ETDEWEB)
Font, Jose A [Departamento de AstronomIa y AstrofIsica, Universidad de Valencia, Dr. Moliner 50, 46100 Burjassot (Valencia) (Spain)
2007-11-15
We review formulations of the equations of (inviscid) general relativistic hydrodynamics and (ideal) magnetohydrodynamics, along with methods for their numerical solution. Both systems can be cast as first-order, hyperbolic systems of conservation laws, following the explicit choice of an Eulerian observer and suitable fluid and magnetic field variables. During the last fifteen years, the so-called (upwind) high-resolution shock-capturing schemes based on Riemann solvers have been successfully extended from classical to relativistic fluid dynamics, both special and general. Nowadays, general relativistic hydrodynamical simulations in relativistic astrophysics are routinely performed, particularly within the test-fluid approximation but also for dynamical spacetimes. While such advances also hold true in the case of the MHD equations, the astrophysical applications investigated so far are still limited, yet the field is bound to witness major developments in the near future. The article also presents a brief overview of numerical techniques, providing state-of-the-art examples of their applicability to general relativistic fluids and magneto-fluids in characteristic scenarios of relativistic astrophysics.
A Primer to Relativistic MOND Theory
Bekenstein, J.D..; Sanders, R.H.
2005-01-01
Abstract: We first review the nonrelativistic lagrangian theory as a framework for the MOND equation. Obstructions to a relativistic version of it are discussed leading up to TeVeS, a relativistic tensor-vector-scalar field theory which displays both MOND and Newtonian limits. The whys for its
Price, R H
1993-01-01
Work reported in the workshop on relativistic astrophysics spanned a wide varicy of topics. Two speciﬁc areas seemed of particular interest. Much attention was focussed on gravitational wave sources, especially on the waveforms they produce, and progress was reported in theoretical and observational aspects of accretion disks.
Sahoo, Raghunath
2016-01-01
This lecture note covers Relativistic Kinematics, which is very useful for the beginners in the field of high-energy physics. A very practical approach has been taken, which answers "why and how" of the kinematics useful for students working in the related areas.
International Nuclear Information System (INIS)
Font, J. A.
2015-01-01
The relativistic astrophysics is the field of astrophysics employing the theory of relativity Einstein as physical-mathematical model is to study the universe. This discipline analyzes astronomical contexts in which the laws of classical mechanics of Newton's law of gravitation are not valid. (Author)
Relativistic gravitational instabilities
International Nuclear Information System (INIS)
Schutz, B.F.
1987-01-01
The purpose of these lectures is to review and explain what is known about the stability of relativistic stars and black holes, with particular emphases on two instabilities which are due entirely to relativistic effects. The first of these is the post-Newtonian pulsational instability discovered independently by Chandrasekhar (1964) and Fowler (1964). This effectively ruled out the then-popular supermassive star model for quasars, and it sets a limit to the central density of white dwarfs. The second instability was also discovered by Chandrasekhar (1970): the gravitational wave induced instability. This sets an upper bound on the rotation rate of neutron stars, which is near that of the millisecond pulsar PSR 1937+214, and which is beginning to constrain the equation of state of neutron matter. 111 references, 5 figures
Relativistic effects in the Thomas--Fermi atom
International Nuclear Information System (INIS)
Waber, J.T.; Canfield, J.M.
1975-01-01
Two methods of applying relativistic corrections to the Thomas--Fermi atom are considered, and numerical calculations are discussed. Radial charge distributions calculated from a relativistic Thomas--Fermi equation agree in gross form with those from more complicated self-consistent calculations. Energy eigenvalues for mercury, as determined from the relativistic Thomas--Fermi solution, are compared with other calculated and experimental values
Nonlinear bound on unstable field energy in relativistic electron beams and plasmas
International Nuclear Information System (INIS)
Davidson, R.C.; Yoon, P.H.
1989-01-01
This paper makes use of Fowler's method [J. Math Phys. 4, 559 (1963)] to determine the nonlinear thermodynamic bound on field energy in unstable plasmas or electron beams in which the electrons are relativistic. Treating the electrons as the only active plasma component, the nonlinear Vlasov--Maxwell equations and the associated global conservation constraints are used to calculate the lowest upper bound on the field energy [ΔE-script/sub F/]/sub max/ that can evolve for the general initial electron distribution function f/sub b//sub / 0 equivalentf/sub b/(x,p,0). The results are applied to three choices of the initial distribution function f/sub b//sub / 0 . Two of the distribution functions have an inverted population in momentum p/sub perpendicular/ perpendicular to the magnetic field B 0 e/sub z/, and the third distribution function reduces to a bi-Maxwellian in the nonrelativistic limit. The lowest upper bound on the efficiency of radiation generation, eta/sub max/ = [ΔE-script/sub F/]/sub max//[V -1 ∫ d 3 x∫ d 3 p(γ-1)mc 2 f/sub b//sub / 0 ], is calculated numerically over a wide range of system parameters for varying degrees of initial anisotropy
A theory of two-stream instability in two hollow relativistic electron beams
International Nuclear Information System (INIS)
Uhm, H.S.
1993-01-01
Stability properties of two-stream instability of two hollow electron beams are investigated. The equilibrium configuration consists of two intense relativistic hollow electron beams propagating through a grounded conducting cylinder. Analysis of the longitudinal two-stream instability is carried out within the framework of the linearized Vlasov--Maxwell equations for the equilibrium distribution function, in which beam electrons have a Lorentzian distribution in the axial momentum. Dispersion relation of the longitudinal two-stream instability is derived. Stability criteria from this dispersion relation indicate that the normalized velocity difference Δβ between the beams should be within a certain range of value to be unstable. Growth rate of the instability is a substantial fraction of the real frequency, thereby indicating that the longitudinal two-stream instability is an effective means of beam current modulation. Transverse instability of hollow electron beams is also investigated. Dispersion relation of the coupled transverse oscillation of the beams is derived and numerical investigation of this dispersion relation is carried out. Growth rate of the kink instability is a substantial fraction of the diocotron frequency, which may pose a serious threat to the two-stream klystron
Relativistic Celestial Mechanics of the Solar System
Kopeikin, Sergei; Efroimsky, Michael; Kaplan, George
2011-09-01
commission are to: * clarify the geometrical and dynamical concepts of fundamental astronomy within a relativistic framework, * provide adequate mathematical and physical formulations to be used in fundamental astronomy, * deepen the understanding of relativity among astronomers and students of astronomy, and * promote research needed to accomplish these tasks. The present book is intended to make a theoretical contribution to the efforts undertaken by this commission. The first three chapters of the book review the foundations of celestial mechanics as well as those of special and general relativity. Subsequent chapters discuss the theoretical and experimental principles of applied relativity in the solar system. The book is written for graduate students and researchers working in the area of gravitational physics and its applications inmodern astronomy. Chapters 1 to 3 were written by Michael Efroimsky and Sergei Kopeikin, Chapters 4 to 8 by Sergei Kopeikin, and Chapter 9 by George Kaplan. Sergei Kopeikin also edited the overall text. It hardly needs to be said that Newtonian celestial mechanics is a very broad area. In Chapter 1, we have concentrated on derivation of the basic equations, on explanation of the perturbed two-body problem in terms of osculating and nonosculating elements, and on discussion of the gauge freedom in the six-dimensional configuration space of the orbital parameters. The gauge freedom of the configuration space has many similarities to the gauge freedom of solutions of the Einstein field equations in general theory of relativity. It makes an important element of the Newtonian theory of gravity, which is often ignored in the books on classic celestial mechanics. Special relativity is discussed in Chapter 2. While our treatment is in many aspects similar to the other books on special relativity, we have carefully emphasised the explanation of the Lorentz and Poincaré transformations, and the appropriate transformation properties of geometric
Fourth sound in relativistic superfluidity theory
International Nuclear Information System (INIS)
Vil'chinskij, S.I.; Fomin, P.I.
1995-01-01
The Lorentz-covariant equations describing propagation of the fourth sound in the relativistic theory of superfluidity are derived. The expressions for the velocity of the fourth sound are obtained. The character of oscillation in sound is determined
International Nuclear Information System (INIS)
Allen, M.A.; Azuma, O.; Callin, R.S.
1989-03-01
Experimental work is underway by a SLAC-LLNL-LBL collaboration to investigate the feasibility of using relativistic klystrons as a power source for future high gradient accelerators. Two different relativistic klystron configurations have been built and tested to date: a high grain multicavity klystron at 11.4 GHz and a low gain two cavity subharmonic buncher driven at 5.7 GHz. In both configurations power is extracted at 11.4 GHz. In order to understand the basic physics issues involved in extracting RF from a high power beam, we have used both a single resonant cavity and a multi-cell traveling wave structure for energy extraction. We have learned how to overcome our previously reported problem of high power RF pulse shortening, and have achieved peak RF power levels of 170 MW with the RF pulse of the same duration as the beam current pulse. 6 refs., 3 figs., 3 tabs
Fundamental laws of relativistic classical dynamics revisited
International Nuclear Information System (INIS)
Blaquiere, Augustin
1977-01-01
By stating that a linear differential form, whose coefficients are the components of the momentum and the energy of a particle, has an antiderivative, the basic equations of the dynamics of points are obtained, in the relativistic case. From the point of view of optimization theory, a connection between our condition and the Bellman-Isaacs equation of dynamic programming is discussed, with a view to extending the theory to relativistic wave mechanics [fr
Dechanneling function for relativistic axially channeled electrons
International Nuclear Information System (INIS)
Muralev, V.A.; Telegin, V.I.
1981-01-01
Behaviour of the x(t) dechanneling function depending on the depth is theoretically studied. Theoretical consideration of x(t) for axial channeled relativistic electrons in anisotropic medium results in two-dimensional kinetic equation with mixed derivatives of the parabolic type. The kinetic equation in the approximation of the continuous Lindchard model for relativistic axial channeled electrons is numerically solved. The depth dependence of the x(t) dechanneling function is obtained [ru
Hakim, Rémi
1994-01-01
Il existe à l'heure actuelle un certain nombre de théories relativistes de la gravitation compatibles avec l'expérience et l'observation. Toutefois, la relativité générale d'Einstein fut historiquement la première à fournir des résultats théoriques corrects en accord précis avec les faits.
International Nuclear Information System (INIS)
Marks, R.
1985-09-01
Theoretical analysis is presented of a relativisic klystron; i.e. a high-relativistic bunched electron beam which is sent through a succession of tuned cavities and has its energy replenished by periodic induction accelerator units. Parameters are given for a full-size device and for an experimental device using the FEL at the ETA; namely the ELF Facility. 6 refs., 2 figs
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.
Future relativistic heavy ion experiments
International Nuclear Information System (INIS)
Pugh, H.G.
1980-12-01
Equations of state for nuclear matter and ongoing experimental studies are discussed. Relativistic heavy ion physics is the only opportunity to study in the laboratory the properties of extended multiquark systems under conditions such that quarks might run together into new arrangements previously unobserved. Several lines of further study are mentioned
A relativistic radiation transfer benchmark
International Nuclear Information System (INIS)
Munier, A.
1988-01-01
We use the integral form of the radiation transfer equation in an one dimensional slab to determine the time-dependent propagation of the radiation energy, flux and pressure in a collisionless homogeneous medium. First order v/c relativistic terms are included and the solution is given in the fluid frame and the laboratory frame
Coordinates in relativistic Hamiltonian mechanics
International Nuclear Information System (INIS)
Sokolov, S.N.
1984-01-01
The physical (covariant and measurable) coordinates of free particles and covariant coordinates of the center of inertia are found for three main forms of relativistic dynamics. In the point form of dynamics, the covariant coordinates of two directly interacting particles are found, and the equations of motion are brought to the explicitly covariant form. These equations are generalized to the case of interaction with an external electromagnetic field
Relativistic mechanics with reduced fields
International Nuclear Information System (INIS)
Sokolov, S.N.
1996-01-01
A new relativistic classical mechanics of interacting particles using a concept of a reduced field (RF) os proposed. RF is a mediator of interactions, the state of which is described by a finite number of two-argument functions. Ten of these functions correspond to the generators of the Poincare group. Equations of motion contain the retardation of interactions required by the causality principle and have form of a finite system of ordinary hereditary differential equations [ru
New derivation of relativistic dissipative fluid dynamics
International Nuclear Information System (INIS)
Jaiswal, Amaresh; Bhalerao, Rajeev S.; Pal, Subrata
2012-01-01
Relativistic dissipative hydrodynamics has been quite successful in explaining the spectra and azimuthal anisotropy of particles produced in heavy-ion collisions at the RHIC and recently at the LHC. The first-order dissipative fluid dynamics or the relativistic Navier-Stokes (NS) theory involves parabolic differential equations and suffers from a causality and instability. The second-order or Israel-Stewart (IS) theory with its hyperbolic equations restores causality but may not guarantee stability. The correct formulation of relativistic viscous fluid dynamics is far from settled and is under intense investigation
The de Sitter relativistic top theory
International Nuclear Information System (INIS)
Armenta, J.; Nieto, J.A.
2005-01-01
We discuss the relativistic top theory from the point of view of the de Sitter (or anti-de Sitter) group. Our treatment rests on the Hanson-Regge spherical relativistic top Lagrangian formulation. We propose an alternative method for studying spinning objects via Kaluza-Klein theory. In particular, we derive the relativistic top equations of motion starting with the geodesic equation for a point particle in 4+N dimensions. We compare our approach with Fukuyama's formulation of spinning objects, which is also based on Kaluza-Klein theory. We also report a generalization of our approach to a 4+N+D dimensional theory
Corinaldesi, Ernesto
1963-01-01
Geared toward advanced undergraduate and graduate students of physics, this text provides readers with a background in relativistic wave mechanics and prepares them for the study of field theory. The treatment originated as a series of lectures from a course on advanced quantum mechanics that has been further amplified by student contributions.An introductory section related to particles and wave functions precedes the three-part treatment. An examination of particles of spin zero follows, addressing wave equation, Lagrangian formalism, physical quantities as mean values, translation and rotat
Relativistic quarkonium dynamics
International Nuclear Information System (INIS)
Sazdjian, H.
1985-06-01
We present, in the framework of relativistic quantum mechanics of two interacting particles, a general model for quarkonium systems satisfying the following four requirements: confinement, spontaneous breakdown of chiral symmetry, soft explicit chiral symmetry breaking, short distance interactions of the vector type. The model is characterized by two arbitrary scalar functions entering in the large and short distance interaction potentials, respectively. Using relationships with corresponding quantities of the Bethe-Salpeter equation, we also present the normalization condition of the wave functions, as well as the expressions of the meson decay coupling constants. The quark masses appear in this model as free parameters
International Nuclear Information System (INIS)
Araujo, Wilson Roberto Barbosa de
1995-01-01
In this dissertation, we present a model for the nucleon, which is composed by three relativistic quarks interacting through a contract force. The nucleon wave-function was obtained from the Faddeev equation in the null-plane. The covariance of the model under kinematical null-plane boots is discussed. The electric proton form-factor, calculated from the Faddeev wave-function, was in agreement with the data for low-momentum transfers and described qualitatively the asymptotic region for momentum transfers around 2 GeV. (author)
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.
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
On the Magnetic Shield for a Vlasov-Poisson Plasma
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.
Radiatively driven relativistic spherical winds under relativistic radiative transfer
Fukue, J.
2018-05-01
We numerically investigate radiatively driven relativistic spherical winds from the central luminous object with mass M and luminosity L* under Newtonian gravity, special relativity, and relativistic radiative transfer. We solve both the relativistic radiative transfer equation and the relativistic hydrodynamical equations for spherically symmetric flows under the double-iteration processes, to obtain the intensity and velocity fields simultaneously. We found that the momentum-driven winds with scattering are quickly accelerated near the central object to reach the terminal speed. The results of numerical solutions are roughly fitted by a relation of \\dot{m}=0.7(Γ _*-1)\\tau _* β _* β _out^{-2.6}, where \\dot{m} is the mass-loss rate normalized by the critical one, Γ* the central luminosity normalized by the critical one, τ* the typical optical depth, β* the initial flow speed at the central core of radius R*, and βout the terminal speed normalized by the speed of light. This relation is close to the non-relativistic analytical solution, \\dot{m} = 2(Γ _*-1)\\tau _* β _* β _out^{-2}, which can be re-expressed as β _out^2/2 = (Γ _*-1)GM/c^2 R_*. That is, the present solution with small optical depth is similar to that of the radiatively driven free outflow. Furthermore, we found that the normalized luminosity (Eddington parameter) must be larger than unity for the relativistic spherical wind to blow off with intermediate or small optical depth, i.e. Γ _* ≳ \\sqrt{(1+β _out)^3/(1-β _out)}. We briefly investigate and discuss an isothermal wind.
Rotating relativistic neutron stars
Energy Technology Data Exchange (ETDEWEB)
Weber, F.; Glendenning, N.K.
1991-07-21
Models of rotating neutron stars are constructed in the framework of Einstein's theory of general relativity. For this purpose a refined version of Hartle's method is applied. The properties of these objects, e.g. gravitational mass, equatorial and polar radius, eccentricity, red- and blueshift, quadrupole moment, are investigated for Kepler frequencies of 4000 s{sup {minus}1} {le} {Omega}{sub K} {le} 9000 s{sup {minus}1}. Therefore a self-consistency problem inherent in the determination of {Omega}{sub K} must be solved. The investigation is based on neutron star matter equations of state derived from the relativistic Martin-Schwinger hierarch of coupled Green's functions. By means of introducing the Hartree, Hartree-Fock, and ladder ({Lambda}) approximations, models of the equation of state derived. A special feature of the latter approximation scheme is the inclusion of dynamical two-particle correlations. These have been calculated from the relativistic T-matrix applying both the HEA and Bonn meson-exchange potentials of the nucleon-nucleon force. The nuclear forces of the former two treatments are those of the standard scalar-vector-isovector model of quantum hadron dynamics, with parameters adjusted to the nuclear matter data. An important aspect of this work consists in testing the compatibility of different competing models of the nuclear equation of state with data on pulsar periods. By this the fundamental problem of nuclear physics concerning the behavior of the equation of state at supernuclear densities can be treated.
Zhang, Bing; Li, Kunyang
2018-02-01
The “Breakthrough Starshot” aims at sending near-speed-of-light cameras to nearby stellar systems in the future. Due to the relativistic effects, a transrelativistic camera naturally serves as a spectrograph, a lens, and a wide-field camera. We demonstrate this through a simulation of the optical-band image of the nearby galaxy M51 in the rest frame of the transrelativistic camera. We suggest that observing celestial objects using a transrelativistic camera may allow one to study the astronomical objects in a special way, and to perform unique tests on the principles of special relativity. We outline several examples that suggest transrelativistic cameras may make important contributions to astrophysics and suggest that the Breakthrough Starshot cameras may be launched in any direction to serve as a unique astronomical observatory.
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,.
Stability of Nonlinear Wave Patterns to the Bipolar Vlasov-Poisson-Boltzmann System
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.
Relativistic Boltzmann theory for a plasma
International Nuclear Information System (INIS)
Erkelens, H. van.
1984-01-01
This thesis gives a self-contained treatment of the relativistic Boltzmann theory for a plasma. Here plasma means any mixture containing electrically charged particles. The relativistic Boltzmann equation is linearized for the case of a plasma. The Chapman-Enskog method is elaborated further for transport phenomena. Linear laws for viscous phenomena are derived. Then the collision term in the Boltzmann theory is dealt with. Using the transport equation, a kinetic theory of wave phenomena is developed and the dissipation of hydromagnetic waves in a relativistic plasma is investigated. In the final chapter, it is demonstrated how the relativistic Boltzmann theory can be applied in cosmology. In doing so, expressions are derived for the electric conductivity of the cosmological plasma in the lepton era, the plasma era and the annihilation era. (Auth.)
Circular relativistic motion of two identical bodies
International Nuclear Information System (INIS)
Shavokhina, N.S.
1983-01-01
Circular relativistic motion of two bodies as a solution of the earlier obtained equations with a deflecting argument where the self-deflection of the argument is an unknown function of time is considered. In case of circular motion the argument deflection is independent from time and it is the root of the transcendental equation obtained in the paper
Lagrangian formulation of a consistent relativistic guiding center theory
International Nuclear Information System (INIS)
Wimmel, H.K.
1983-02-01
A new relativistic guiding center mechanics is presented that conserves energy (in time-independent fields) and satisfies a Liouville's theorem. The theory reduces to Littlejohn's theory in the non-relativistic limit and agrees to leading orders in epsilon identical rsub(g)/L with the relativistic theory by Morozov and Solov'ev (which generally lacks a Liouville's theorem). The new theory is developed from an appropriate Lagrangian and is supplemented by a collisionless relativistic kinetic equation for the guiding centers. Moment equations for guiding center density and energy density are also derived. (orig.)
Relativistic charged fluids: hydrodynamic and kinetic approaches
International Nuclear Information System (INIS)
Debbasch, F.; Bonnaud, G.
1991-10-01
This report gives a rigorous and consistent hydrodynamic and kinetic description of a charged fluid and the basis equations, in a relativistic context. This study should lead to a reliable model, as much analytical as numerical, of relativistic plasmas which will appear in the interaction of a strong laser field with a plasma. For simplicity, we limited our study to a perfect fluid or, in other words, we disregarded the energy dissipation processes inside the fluid [fr
Double Relativistic Electron Accelerating Mirror
Directory of Open Access Journals (Sweden)
Saltanat Sadykova
2013-02-01
Full Text Available In the present paper, the possibility of generation of thin dense relativistic electron layers is shown using the analytical and numerical modeling of laser pulse interaction with ultra-thin layers. It was shown that the maximum electron energy can be gained by optimal tuning between the target width, intensity and laser pulse duration. The optimal parameters were obtained from a self-consistent system of Maxwell equations and the equation of motion of electron layer. For thin relativistic electron layers, the gaining of maximum electron energies requires a second additional overdense plasma layer, thus cutting the laser radiation off the plasma screen at the instant of gaining the maximum energy (DREAM-schema.
Hypocoercivity for linear kinetic equations conserving mass
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
Hypocoercivity for linear kinetic equations conserving mass
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
A relativistic quarkonium potential model
International Nuclear Information System (INIS)
Klima, B.; Maor, U.
1984-04-01
We review a recently developed relativistic quark-antiquark bound state equation using the expansion in intermediate states. Using a QCD motivated potential we succeeded very well to fit both the heavy systems (banti b, canti c) and the light systems (santi s, uanti u and danti d). Here we emphasize our results on heavy-light sustems and on the possible (tanti t) family. (orig.)
Optical analogue of relativistic Dirac solitons in binary waveguide arrays
Energy Technology Data Exchange (ETDEWEB)
Tran, Truong X., E-mail: truong.tran@mpl.mpg.de [Department of Physics, Le Quy Don University, 236 Hoang Quoc Viet str., 10000 Hanoi (Viet Nam); Max Planck Institute for the Science of Light, Günther-Scharowsky str. 1, 91058 Erlangen (Germany); Longhi, Stefano [Department of Physics, Politecnico di Milano and Istituto di Fotonica e Nanotecnologie del Consiglio Nazionale delle Ricerche, Piazza L. da Vinci 32, I-20133 Milano (Italy); Biancalana, Fabio [Max Planck Institute for the Science of Light, Günther-Scharowsky str. 1, 91058 Erlangen (Germany); School of Engineering and Physical Sciences, Heriot-Watt University, EH14 4AS Edinburgh (United Kingdom)
2014-01-15
We study analytically and numerically an optical analogue of Dirac solitons in binary waveguide arrays in the presence of Kerr nonlinearity. Pseudo-relativistic soliton solutions of the coupled-mode equations describing dynamics in the array are analytically derived. We demonstrate that with the found soliton solutions, the coupled mode equations can be converted into the nonlinear relativistic 1D Dirac equation. This paves the way for using binary waveguide arrays as a classical simulator of quantum nonlinear effects arising from the Dirac equation, something that is thought to be impossible to achieve in conventional (i.e. linear) quantum field theory. -- Highlights: •An optical analogue of Dirac solitons in nonlinear binary waveguide arrays is suggested. •Analytical solutions to pseudo-relativistic solitons are presented. •A correspondence of optical coupled-mode equations with the nonlinear relativistic Dirac equation is established.
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.
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.
International Nuclear Information System (INIS)
Unterberger, A.
1987-01-01
We study the Klein-Gordon symbolic calculus of operators acting on solutions of the free Klein-Gordon equation. It contracts to the Weyl calculus as c→∞. Mathematically, it may also be considered as a pseudodifferential analysis on the unit ball of R n [fr
Relativistic thermodynamics of fluids
International Nuclear Information System (INIS)
Souriau, J.-M.
1977-05-01
The relativistic covariant definition of a statistical equilibrium, applied to a perfect gas, involves a 'temperature four-vector', whose direction is the mean velocity of the fluid, and whose length is the reciprocal temperature. The hypothesis of this 'temperature four-vector' being a relevant variable for the description of the dissipative motions of a simple fluid is discussed. The kinematics is defined by using a vector field and measuring the number of molecules. Such a dissipative fluid is subject to motions involving null entropy generation; the 'temperature four-vector' is then a Killing vector; the equations of motion can be completely integrated. Perfect fluids can be studied by this way and the classical results of Lichnerowicz are obtained. In weakly dissipative motions two viscosity coefficient appear together with the heat conductibility coefficient. Two other coefficients perharps measurable on real fluids. Phase transitions and shock waves are described with using the model [fr
Relativistic plasma dispersion functions
International Nuclear Information System (INIS)
Robinson, P.A.
1986-01-01
The known properties of plasma dispersion functions (PDF's) for waves in weakly relativistic, magnetized, thermal plasmas are reviewed and a large number of new results are presented. The PDF's required for the description of waves with small wave number perpendicular to the magnetic field (Dnestrovskii and Shkarofsky functions) are considered in detail; these functions also arise in certain quantum electrodynamical calculations involving strongly magnetized plasmas. Series, asymptotic series, recursion relations, integral forms, derivatives, differential equations, and approximations for these functions are discussed as are their analytic properties and connections with standard transcendental functions. In addition a more general class of PDF's relevant to waves of arbitrary perpendicular wave number is introduced and a range of properties of these functions are derived
RANKINE-HUGONIOT RELATIONS IN RELATIVISTIC COMBUSTION WAVES
International Nuclear Information System (INIS)
Gao Yang; Law, Chung K.
2012-01-01
As a foundational element describing relativistic reacting waves of relevance to astrophysical phenomena, the Rankine-Hugoniot relations classifying the various propagation modes of detonation and deflagration are analyzed in the relativistic regime, with the results properly degenerating to the non-relativistic and highly relativistic limits. The existence of negative-pressure downstream flows is noted for relativistic shocks, which could be of interest in the understanding of the nature of dark energy. Entropy analysis for relativistic shock waves is also performed for relativistic fluids with different equations of state (EoS), denoting the existence of rarefaction shocks in fluids with adiabatic index Γ < 1 in their EoS. The analysis further shows that weak detonations and strong deflagrations, which are rare phenomena in terrestrial environments, are expected to exist more commonly in astrophysical systems because of the various endothermic reactions present therein. Additional topics of relevance to astrophysical phenomena are also discussed.
Relativistic treatment of fermion-antifermion bound states
International Nuclear Information System (INIS)
Lucha, W.; Rupprecht, H.; Schoeberl, F.F.
1990-01-01
We discuss the relativistic treatment of fermion-antifermion bound states by an effective-Hamiltonian method which imitates their description in terms of nonrelativistic potential models: the effective interaction potential, to be used in a Schroedinger equation which incorporates relativistic kinematics, is derived from the underlying quantum field theory. This approach is equivalent to the instantaneous approximation to the Bethe-Salpeter equation called Salpeter equation but comes closer to physical intuition than the latter one. (Author) 14 refs
Extended Galilean symmetries of non-relativistic strings
Energy Technology Data Exchange (ETDEWEB)
Batlle, Carles [Departament de Matemàtiques and IOC, Universitat Politècnica de Catalunya, EPSEVG,Av. V. Balaguer 1, E-08808 Vilanova i la Geltrú (Spain); Gomis, Joaquim; Not, Daniel [Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos (ICCUB),Universitat de Barcelona,Martí i Franquès 1, E-08028 Barcelona (Spain)
2017-02-09
We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.
Energy Technology Data Exchange (ETDEWEB)
Aminmansoor, F.; Abbasi, H., E-mail: abbasi@aut.ac.ir [Faculty of Energy Engineering and Physics, Amirkabir University of Technology, P.O. Box 15875-4413, Tehran (Iran, Islamic Republic of)
2015-08-15
The present paper is devoted to simulation of nonlinear disintegration of a localized perturbation into ion-acoustic solitons train in a plasma with hot electrons and cold ions. A Gaussian initial perturbation is used to model the localized perturbation. For this purpose, first, we reduce fluid system of equations to a Korteweg de-Vries equation by the following well-known assumptions. (i) On the ion-acoustic evolution time-scale, the electron velocity distribution function (EVDF) is assumed to be stationary. (ii) The calculation is restricted to small amplitude cases. Next, in order to generalize the model to finite amplitudes cases, the evolution of EVDF is included. To this end, a hybrid code is designed to simulate the case, in which electrons dynamics is governed by Vlasov equation, while cold ions dynamics is, like before, studied by the fluid equations. A comparison between the two models shows that although the fluid model is capable of demonstrating the general features of the process, to have a better insight into the relevant physics resulting from the evolution of EVDF, the use of kinetic treatment is of great importance.
International Nuclear Information System (INIS)
Safronov, A.N.
2007-01-01
Full text: The pion-nucleon dynamics is one of the most fundamental problems in nuclear and particle physics. It is now widely believed that QCD is fundamental theory of strong interactions. On this basis all hadron-hadron interactions are completely determined by the underlying quark-gluon dynamics. However, due to the formidable mathematical problems raised by the non-perturbative character of QCD at low and intermediate energies, we are still far from a quantitative understanding hadron-hadron interactions from this point of view. Recently the relativistic approaches to constructing effective interaction operators between strongly interacting composite particles has been proposed on the basis of analytic S-matrix theory and methods for solving the inverse quantum scattering problem. The kernel of Marchenko equation in theory of inverse scattering problem can be expressed in terms of the discontinuity of the partial wave amplitude on dynamic cut in the complex s=k 2 plane, k being the relative momentum of colliding particles. The discontinuities of partial-wave amplitudes are determined by model-independent quantities (renormalized vertex constants and amplitudes of sub-processes involving on-mass-shell particles off physical region) and can be calculated by methods of relativistic quantum field theory within various dynamical approaches. In particular, effective field theory can be used to calculate the discontinuities across dynamical cuts closest to physical region. In present work a new manifestly Poincare-invariant approach to solving the inverse scattering problem is developed with allowance for inelasticity effects. The equations of the N/D method are used as dynamical equations in this approach. With the help of N/D-equations it was earlier shown that solution of a scattering problem in case of nonzero angular momentum does not exist for arbitrary discontinuity of partial-wave amplitude. The method is elaborated allowing to determine contributions of
Relativistic quantum mechanics and introduction to field theory
Energy Technology Data Exchange (ETDEWEB)
Yndurain, F.J. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica
1996-12-01
The following topics were dealt with: relativistic transformations, the Lorentz group, Klein-Gordon equation, spinless particles, spin 1/2 particles, Dirac particle in a potential, massive spin 1 particles, massless spin 1 particles, relativistic collisions, S matrix, cross sections, decay rates, partial wave analysis, electromagnetic field quantization, interaction of radiation with matter, interactions in quantum field theory and relativistic interactions with classical sources.
Relativistic quantum mechanics and introduction to field theory
International Nuclear Information System (INIS)
Yndurain, F.J.
1996-01-01
The following topics were dealt with: relativistic transformations, the Lorentz group, Klein-Gordon equation, spinless particles, spin 1/2 particles, Dirac particle in a potential, massive spin 1 particles, massless spin 1 particles, relativistic collisions, S matrix, cross sections, decay rates, partial wave analysis, electromagnetic field quantization, interaction of radiation with matter, interactions in quantum field theory and relativistic interactions with classical sources
The relativistic virial theorem
International Nuclear Information System (INIS)
Lucha, W.; Schoeberl, F.F.
1989-11-01
The relativistic generalization of the quantum-mechanical virial theorem is derived and used to clarify the connection between the nonrelativistic and (semi-)relativistic treatment of bound states. 12 refs. (Authors)
Slowly rotating general relativistic superfluid neutron stars with relativistic entrainment
International Nuclear Information System (INIS)
Comer, G.L.
2004-01-01
Neutron stars that are cold enough should have two or more superfluids or supercondutors in their inner crusts and cores. The implication of superfluidity or superconductivity for equilibrium and dynamical neutron star states is that each individual particle species that forms a condensate must have its own, independent number density current and equation of motion that determines that current. An important consequence of the quasiparticle nature of each condensate is the so-called entrainment effect; i.e., the momentum of a condensate is a linear combination of its own current and those of the other condensates. We present here the first fully relativistic modeling of slowly rotating superfluid neutron stars with entrainment that is accurate to the second-order in the rotation rates. The stars consist of superfluid neutrons, superconducting protons, and a highly degenerate, relativistic gas of electrons. We use a relativistic σ-ω mean field model for the equation of state of the matter and the entrainment. We determine the effect of a relative rotation between the neutrons and protons on a star's total mass, shape, and Kepler, mass-shedding limit
Relativistic gas in a Schwarzschild metric
International Nuclear Information System (INIS)
Kremer, Gilberto M
2013-01-01
A relativistic gas in a Schwarzschild metric is studied within the framework of a relativistic Boltzmann equation in the presence of gravitational fields, where Marle’s model for the collision operator of the Boltzmann equation is employed. The transport coefficients of the bulk and shear viscosities and thermal conductivity are determined from the Chapman–Enskog method. It is shown that the transport coefficients depend on the gravitational potential. Expressions for the transport coefficients in the presence of weak gravitational fields in the non-relativistic (low temperature) and ultra-relativistic (high temperature) limiting cases are given. Apart from the temperature gradient the heat flux has two relativistic terms. The first one, proposed by Eckart, is due to the inertia of energy and represents an isothermal heat flux when matter is accelerated. The other, suggested by Tolman, is proportional to the gravitational potential gradient and indicates that—in the absence of an acceleration field—a state of equilibrium of a relativistic gas in a gravitational field can be attained only if the temperature gradient is counterbalanced by a gravitational potential gradient. (paper)
International Nuclear Information System (INIS)
Kotel'nikov, G.A.
1994-01-01
An algorithm id proposed for research the symmetries of mathematical physics equation. The application of this algorithm to the Schroedinger equation permitted to establish, that in addition to the known symmetry the Schroedinger equation possesses also the relativistic symmetry
Time Operator in Relativistic Quantum Mechanics
Khorasani, Sina
2017-07-01
It is first shown that the Dirac’s equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 × 4 relativistic time operator for spin-1/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly small but non-zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli’s objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time operator, a bosonic field referred here to as energons may be created, whose number state representations in non-relativistic momentum space can be explicitly found.
Draws on a relativistic pinch with a longitudinal magnetic field
International Nuclear Information System (INIS)
Trubnikov, B.A.
1991-01-01
The problems of draws on a relativistic pinch with longitudinal magnetic field are discussed. The absence of collisions promoting the energy exchange between different degrees of particle freedom is assumed. The calculations are conducted using the ideal relativistic anisotropic magnetic hydrodynamics equations. The spectrum of particles accelerated in the draws, is determined
Particle Acceleration and Radiative Losses at Relativistic Shocks
Dempsey, P.; Duffy, P.
A semi-analytic approach to the relativistic transport equation with isotropic diffusion and consistent radiative losses is presented. It is based on the eigenvalue method first introduced in Kirk & Schneider [5]and Heavens & Drury [3]. We demonstrate the pitch-angle dependence of the cut-off in relativistic shocks.
On the relativistic extended Thomas-Fermi method
International Nuclear Information System (INIS)
Centelles, M.; Vinas, X.; Barranco, M.; Schuck, P.
1990-01-01
We have derived the semiclassical relativistic energy functional for a set of fermions moving in the mean field arising from scalar and vector fields, including up to ℎ 2 corrective terms. The method is applied to a relativistic harmonic oscillator model for which the semiclassical result can be compared with the exact solution of the Dirac equation. (orig.)
On the relativistic extended Thomas-Fermi method
International Nuclear Information System (INIS)
Centelles, M.; Vinas, X.; Barranco, M.; Schuck, P.
1990-01-01
We have derived the semiclassical relativistic energy functional for a set of fermions moving in the mean field arising from scalar and vector fields, including up to ℎ 2 corrective terms. The method is applied to a relativistic harmonic oscillator model for which the semiclassical result can be compared with the exact solution of the Dirac equation
Transient growth of a Vlasov plasma in a weakly inhomogeneous magnetic field
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
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.
Chaos and maps in relativistic rynamical systems
Directory of Open Access Journals (Sweden)
L. P. Horwitz
2000-01-01
Full Text Available The basic work of Zaslavskii et al showed that the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on the phase space; the resulting evolution contains a stochastic flow to unbounded energy. Subsequent studies have formulated the problem in terms of a relativistic charged particle in interaction with the electromagnetic field. We review the structure of the covariant Lorentz force used to study this problem. We show that the Lorentz force equation can be derived as well from the manifestly covariant mechanics of Stueckelberg in the presence of a standard Maxwell field, establishing a connection between these equations and mass shell constraints. We argue that these relativistic generalizations of the problem are intrinsically inaccurate due to an inconsistency in the structure of the relativistic Lorentz force, and show that a reformulation of the relativistic problem, permitting variations (classically in both the particle mass and the effective “mass” of the interacting electromagnetic field, provides a consistent system of classical equations for describing such processes.
Relativistic quantum mechanics of bosons
International Nuclear Information System (INIS)
Ghose, P.; Home, D.; Sinha Roy, M.N.
1993-01-01
We show that it is possible to use the Klein-Gordon, Proca and Maxwell formulations to construct multi-component relativistic configuration space wavefunctions of spin-0 and spin-1 bosons in an external field. These wavefunctions satisfy the first-order Kemmer-Duffin equation. The crucial ingredient is the use of the future-causal normal n μ (n μ n μ =1, n 0 >0) to the space-like hypersurfaces foliating space-time, inherent in the concept of a relativistic wavefunction, to construct a conserved future-causal probability current four-vector from the second-rank energy-momentum tensor, following Holland's prescription. The existence of a Hermitian position operator, localized solutions, compatibility with the second quantized theories and the question of interpretation are discussed. (orig.)
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
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.)
Relativistic transport theory for cosmic-rays
International Nuclear Information System (INIS)
Webb, G.M.
1985-01-01
Various aspects of the transport of cosmic-rays in a relativistically moving magnetized plasma supporting a spectrum of hydromagnetic waves that scatter the cosmic-rays are presented. A local Lorentz frame moving with the waves or turbulence scattering the cosmic-rays is used to specify the individual particle momentum. The comoving frame is in general a noninertial frame in which the observer's volume element is expanding and shearing, geometric energy change terms appear in the cosmic-ray transport equation which consist of the relativistic generalization of the adiabatic deceleration term and a further term involving the acceleration vector of the scatterers. A relativistic version of the pitch angle evolution equation, including the effects of adiabatic focussing, pitch angle scattering, and energy changes is presented
Relativistic modeling capabilities in PERSEUS extended MHD simulation code for HED plasmas
Energy Technology Data Exchange (ETDEWEB)
Hamlin, Nathaniel D., E-mail: nh322@cornell.edu [438 Rhodes Hall, Cornell University, Ithaca, NY, 14853 (United States); Seyler, Charles E., E-mail: ces7@cornell.edu [Cornell University, Ithaca, NY, 14853 (United States)
2014-12-15
We discuss the incorporation of relativistic modeling capabilities into the PERSEUS extended MHD simulation code for high-energy-density (HED) plasmas, and present the latest hybrid X-pinch simulation results. The use of fully relativistic equations enables the model to remain self-consistent in simulations of such relativistic phenomena as X-pinches and laser-plasma interactions. By suitable formulation of the relativistic generalized Ohm’s law as an evolution equation, we have reduced the recovery of primitive variables, a major technical challenge in relativistic codes, to a straightforward algebraic computation. Our code recovers expected results in the non-relativistic limit, and reveals new physics in the modeling of electron beam acceleration following an X-pinch. Through the use of a relaxation scheme, relativistic PERSEUS is able to handle nine orders of magnitude in density variation, making it the first fluid code, to our knowledge, that can simulate relativistic HED plasmas.
Causal dissipation for the relativistic dynamics of ideal gases.
Freistühler, Heinrich; Temple, Blake
2017-05-01
We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.
A relativistic theory for continuous measurement of quantum fields
International Nuclear Information System (INIS)
Diosi, L.
1990-04-01
A formal theory for the continuous measurement of relativistic quantum fields is proposed. The corresponding scattering equations were derived. The proposed formalism reduces to known equations in the Markovian case. Two recent models for spontaneous quantum state reduction have been recovered in the framework of this theory. A possible example of the relativistic continuous measurement has been outlined in standard Quantum Electrodynamics. The continuous measurement theory possesses an alternative formulation in terms of interacting quantum and stochastic fields. (author) 23 refs
Anomalous magnetohydrodynamics in the extreme relativistic domain
Giovannini, Massimo
2016-01-01
The evolution equations of anomalous magnetohydrodynamics are derived in the extreme relativistic regime and contrasted with the treatment of hydromagnetic nonlinearities pioneered by Lichnerowicz in the absence of anomalous currents. In particular we explore the situation where the conventional vector currents are complemented by the axial-vector currents arising either from the pseudo Nambu-Goldstone bosons of a spontaneously broken symmetry or because of finite fermionic density effects. After expanding the generally covariant equations in inverse powers of the conductivity, the relativistic analog of the magnetic diffusivity equation is derived in the presence of vortical and magnetic currents. While the anomalous contributions are generally suppressed by the diffusivity, they are shown to disappear in the perfectly conducting limit. When the flow is irrotational, boost-invariant and with vanishing four-acceleration the corresponding evolution equations are explicitly integrated so that the various physic...
Dirac's aether in relativistic quantum mechanics
International Nuclear Information System (INIS)
Petroni, N.C.; Bari Univ.; Vigier, J.P.
1984-01-01
The paper concerns Dirac's aether model, based on a stochastic covariant distribution of subquantum motions. Stochastic derivation of the relativistic quantum equations; deterministic nonlocal interpretation of the Aspect-Rapisarda experiments on the EPR paradox; and photon interference with itself; are all discussed. (U.K.)
Summary of the Relativistic Heavy Ion Sessions
International Nuclear Information System (INIS)
Harris, J.W.
1988-07-01
This paper briefly discusses the topics covered in the relativistic heavy ion in sessions. The prime motivation for these investigations is the possibility of forming quark matter, therefore the formation of a quark-gluon plasma. Topics on suppression of J//psi/ production, th equation of state of nuclear matter, transverse energy distributions and two pion interferometry techniques are discussed. 38 refs
Shock waves in relativistic nuclear matter, I
International Nuclear Information System (INIS)
Gleeson, A.M.; Raha, S.
1979-02-01
The relativistic Rankine-Hugoniot relations are developed for a 3-dimensional plane shock and a 3-dimensional oblique shock. Using these discontinuity relations together with various equations of state for nuclear matter, the temperatures and the compressibilities attainable by shock compression for a wide range of laboratory kinetic energy of the projectile are calculated. 12 references
Relativistic magnetohydrodynamics as a Hamiltonian system
International Nuclear Information System (INIS)
Holm, D.D.; Kupershmidt, A.
1985-01-01
The equations of ideal relativistic magnetohydrodynamics in the laboratory frame form a noncanonical Hamiltonian system with the same Poisson bracket as for the nonrelativistic system, but with dynamical variables and Hamiltonian obtained via a regular deformation of their nonrelativistic counterparts [fr
Instabilities in a Relativistic Viscous Fluid
Corona-Galindo, M. G.; Klapp, J.; Vazquez, A.
1990-11-01
RESUMEN. Las ecuaciones hidrodinamicas de un fluido imperfecto relativista son resueltas, y los modos hidrodinamicos son analizados con el prop6sito de estabiecer correlaciones con las estructuras cosmol6gicas. ABSTRACT The hydrodynamical equations of a relativistic imperfect fluid are solved, and the hydrodynamical modes are analysed with the aim to establish correlations with cosmological structures. Ke, words: COSMOLOGY - HYDRODYNAMICS - RELATIVITY
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
Multilevel and Multi-index Monte Carlo methods for the McKean–Vlasov equation
Haji Ali, Abdul Lateef; Tempone, Raul
2017-01-01
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
Fundamentals of the relativistic theory of gravitation
International Nuclear Information System (INIS)
Logunov, A.A.; Mestvirishvili, M.A.
1986-01-01
An extended exposition of the relativistic theory of gravitation (RTG) proposed by Logunov, Vlasov, and Mestvirishvili is presented. The RTG was constructed uniquely on the basis of the relativity principle and the geometrization principle by regarding the gravitational field as a physical field in the spirit of Faraday and Maxwell possessing energy, momentum, and spins 2 and 0. In the theory, conservation laws for the energy, momentum, and angular momentum for the matter and gravitational field taken together are strictly satisfied. The theory explains all the existing gravitational experiments. When the evolution of the universe is analyzed, the theory leads to the conclusion that the universe is infinite and flat, and it is predicted to contain a large amount of hidden mass. This missing mass exceeds by almost 40 times the amount of matter currently observed in the universe. The RTG predicts that gravitational collapse, which for a comoving observer occurs after a finite proper time, does not lead to infinite compression of matter but is halted at a certain finite density of the collapsing body. Therefore, according to the RTG there cannot be any objects in nature in which the gravitational contraction of matter to infinite density occurs, i.e., there are no black holes
Numerical simulation of collision-free plasma using Vlasov hybrid simulation
International Nuclear Information System (INIS)
Nunn, D.
1990-01-01
A novel scheme for the numerical simulation of wave particle interactions in space plasmas has been developed. The method, termed VHS or Vlasov Hybrid Simulation, is applicable to hot collision free plasmas in which the unperturbed distribution functions is smooth and free of delta function singularities. The particle population is described as a continuous Vlasov fluid in phase space-granularity and collisional effects being ignored. In traditional PIC/CIC codes the charge/current due to each simulation particle is assigned to a fixed spatial grid. In the VHS method the simulation particles sample the Vlasov fluid and provide information about the value of distribution function (F(r,v) at random points in phase space. Values of F are interpolated from the simulation particles onto a fixed grid in velocity/position or phase space. With distribution function defined on a phase space grid the plasma charge/current field is quickly calculated. The simulation particles serve only to provide information, and thus the particle population may be dynamic. Particles no longer resonant with the wavefield may be discarded from the simulation, and new particles may be inserted into the Vlasov fluid where required
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
Stability analysis of sharp-boundary Vlasov-fluid screw-pinch equilibria
International Nuclear Information System (INIS)
Lewis, H.R.; Turner, L.
1975-01-01
The Vlasov-fluid model is being used to study the linear stability of sharp-boundary screw pinches numerically. The numerical method appears to work well, and some preliminary results are reported. The sharp-boundary calculation is useful for gaining insight and for comparing with known MHD results. (auth)
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
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
Relativistic Linear Restoring Force
Clark, D.; Franklin, J.; Mann, N.
2012-01-01
We consider two different forms for a relativistic version of a linear restoring force. The pair comes from taking Hooke's law to be the force appearing on the right-hand side of the relativistic expressions: d"p"/d"t" or d"p"/d["tau"]. Either formulation recovers Hooke's law in the non-relativistic limit. In addition to these two forces, we…
Lorentz Covariance of Langevin Equation
International Nuclear Information System (INIS)
Koide, T.; Denicol, G.S.; Kodama, T.
2008-01-01
Relativistic covariance of a Langevin type equation is discussed. The requirement of Lorentz invariance generates an entanglement between the force and noise terms so that the noise itself should not be a covariant quantity. (author)
Similarity flows in relativistic hydrodynamics
International Nuclear Information System (INIS)
Blaizot, J.P.; Ollitrault, J.Y.
1986-01-01
In ultra-relativistic heavy ion collisions, one expects in particular to observe a deconfinement transition leading to a formation of quark gluon plasma. In the framework of the hydrodynamic model, experimental signatures of such a plasma may be looked for as observable consequences of a first order transition on the evolution of the system. In most of the possible scenario, the phase transition is accompanied with discontinuities in the hydrodynamic flow, such as shock waves. The method presented in this paper has been developed to treat without too much numerical effort such discontinuous flow. It relies heavily on the use of similarity solutions of the hydrodynamic equations
International Nuclear Information System (INIS)
Mittelstaedt, P.
1983-01-01
on the basis of the well-known quantum logic and quantum probability a formal language of relativistic quantum physics is developed. This language incorporates quantum logical as well as relativistic restrictions. It is shown that relativity imposes serious restrictions on the validity regions of propositions in space-time. By an additional postulate this relativistic quantum logic can be made consistent. The results of this paper are derived exclusively within the formal quantum language; they are, however, in accordance with well-known facts of relativistic quantum physics in Hilbert space. (author)
Equations of multiparticle dynamics
International Nuclear Information System (INIS)
Chao, A.W.
1987-01-01
The description of the motion of charged-particle beams in an accelerator proceeds in steps of increasing complexity. The first step is to consider a single-particle picture in which the beam is represented as a collection on non-interacting test particles moving in a prescribed external electromagnetic field. Knowing the external field, it is then possible to calculate the beam motion to a high accuracy. The real beam consists of a large number of particles, typically 10 11 per beam bunch. It is sometimes inconvenient, or even impossible, to treat the real beam behavior using the single particle approach. One way to approach this problem is to supplement the single particle by another qualitatively different picture. The commonly used tools in accelerator physics for this purpose are the Vlasov and the Fokker-Planck equations. These equations assume smooth beam distributions and are therefore strictly valid in the limit of infinite number of micro-particles, each carrying an infinitesimal charge. The hope is that by studying the two extremes -- the single particle picture and the picture of smooth beam distributions -- we will be able to describe the behavior of our 10 11 -particle system. As mentioned, the most notable use of the smooth distribution picture is the study of collective beam instabilities. However, the purpose of this lecture is not to address this more advanced subject. Rather, it has the limited goal to familiarize the reader with the analytical tools, namely the Vlasov and the Fokker-Planck equations, as a preparation for dealing with the more advanced problems at later times. We will first derive these equations and then illustrate their applications by several examples which allow exact solutions
Lectures on relativistic quantum mechanics and path integration
International Nuclear Information System (INIS)
Gunn, J.M.F.
1989-02-01
The question posed is why bother with relativistic quantum mechanics? Three reasons are given: First that there are many experimental phenomena which cannot be explained in non-relativistic terms. Secondly it would be unsatisfactory if relativity and quantum mechanics could not be united. Thirdly, there are theoretical reasons why new effects can be expected at relativistic velocities. The objectives of the course are to set up relativistic analogues of the Schroedinger equation and to understand their consequences. In doing so there are some questions which are raised and discussed such as can a first order equation be used to describe spin 0 particles and a second order equation be used to describe spin 1/ 2 (author)
Relativistic kinetic theory with applications in astrophysics and cosmology
Vereshchagin, Gregory V
2017-01-01
Relativistic kinetic theory has widespread application in astrophysics and cosmology. The interest has grown in recent years as experimentalists are now able to make reliable measurements on physical systems where relativistic effects are no longer negligible. This ambitious monograph is divided into three parts. It presents the basic ideas and concepts of this theory, equations and methods, including derivation of kinetic equations from the relativistic BBGKY hierarchy and discussion of the relation between kinetic and hydrodynamic levels of description. The second part introduces elements of computational physics with special emphasis on numerical integration of Boltzmann equations and related approaches, as well as multi-component hydrodynamics. The third part presents an overview of applications ranging from covariant theory of plasma response, thermalization of relativistic plasma, comptonization in static and moving media to kinetics of self-gravitating systems, cosmological structure formation and neut...
General Relativistic Calculations for White Dwarf Stars
Mathew, Arun; Nandy, Malay K.
2014-01-01
The mass-radius relations for white dwarf stars are investigated by solving the Newtonian as well as Tolman-Oppenheimer-Volkoff (TOV) equations for hydrostatic equilibrium assuming the electron gas to be non-interacting. We find that the Newtonian limiting mass of $1.4562M_\\odot$ is modified to $1.4166M_\\odot$ in the general relativistic case for $^4_2$He (and $^{12}_{\\ 6}$C) white dwarf stars. Using the same general relativistic treatment, the critical mass for $^{56}_{26}$Fe white dwarf is ...
Cosmic anisotropy with reduced relativistic gas
Energy Technology Data Exchange (ETDEWEB)
Castardelli dos Reis, Simpliciano [Universidade Federal de Juiz de Fora, Departamento de Fisica, ICE, Juiz de Fora, MG (Brazil); Shapiro, Ilya L. [Universidade Federal de Juiz de Fora, Departamento de Fisica, ICE, Juiz de Fora, MG (Brazil); Tomsk State Pedagogical University, Tomsk (Russian Federation); Tomsk State University, Tomsk (Russian Federation)
2018-02-15
The dynamics of cosmological anisotropies is investigated for Bianchi type I universe filled by a relativistic matter represented by the reduced relativistic gas model (RRG), with equation of state interpolating between radiation and matter. Previously it was shown that the interpolation is observed in the background cosmological solutions for homogeneous and isotropic universe and also for the linear cosmological perturbations. We extend the application of RRG to the Bianchi type I anisotropic model and find that the solutions evolve to the isotropic universe with the pressureless matter contents. (orig.)
Non-relativistic spinning particle in a Newton-Cartan background
Barducci, Andrea; Casalbuoni, Roberto; Gomis, Joaquim
2018-01-01
We construct the action of a non-relativistic spinning particle moving in a general torsionless Newton-Cartan background. The particle does not follow the geodesic equations, instead the motion is governed by the non-relativistic analog of Papapetrou equation. The spinning particle is described in terms of Grassmann variables. In the flat case the action is invariant under the non-relativistic analog of space-time vector supersymmetry.
Relativistic quantum mechanics; Mecanique quantique relativiste
Energy Technology Data Exchange (ETDEWEB)
Ollitrault, J.Y. [CEA Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique]|[Universite Pierre et Marie Curie, 75 - Paris (France)
1998-12-01
These notes form an introduction to relativistic quantum mechanics. The mathematical formalism has been reduced to the minimum in order to enable the reader to calculate elementary physical processes. The second quantification and the field theory are the logical followings of this course. The reader is expected to know analytical mechanics (Lagrangian and Hamiltonian), non-relativistic quantum mechanics and some basis of restricted relativity. The purpose of the first 3 chapters is to define the quantum mechanics framework for already known notions about rotation transformations, wave propagation and restricted theory of relativity. The next 3 chapters are devoted to the application of relativistic quantum mechanics to a particle with 0,1/5 and 1 spin value. The last chapter deals with the processes involving several particles, these processes require field theory framework to be thoroughly described. (A.C.) 2 refs.
Towards relativistic quantum geometry
Energy Technology Data Exchange (ETDEWEB)
Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)
2015-12-17
We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.
Norbury, John W.
1992-01-01
Nuclear fission reactions induced by the electromagnetic field of relativistic nuclei are studied for energies relevant to present and future relativistic heavy ion accelerators. Cross sections are calculated for U-238 and Pu-239 fission induced by C-12, Si-28, Au-197, and U-238 projectiles. It is found that some of the cross sections can exceed 10 b.
Relativistic Shock Acceleration
International Nuclear Information System (INIS)
Duffy, P.; Downes, T.P.; Gallant, Y.A.; Kirk, J.G.
1999-01-01
In this paper we briefly review the basic theory of shock waves in relativistic hydrodynamics and magneto-hydrodynamics, emphasising some astrophysically interesting cases. We then present an overview of the theory of particle acceleration at such shocks describing the methods used to calculate the spectral indices of energetic particles. Recent results on acceleration at ultra-relativistic shocks are discussed. (author)
Transport theory for relativistic ionized gases
International Nuclear Information System (INIS)
Georgiou, A.
1985-01-01
The phenomenological non-equilibrium thermodynamics is adapted to the description of relativistic multicomponent plasmas. The general and special forms of matter energy-momentum tensor are given and the physical meaning of the different terms are discussed. A delicate problem of such theories, the contribution of ionized components of plasmas to the electromagnetic energy-momentum tensor is analyzed and illustrated by special examples. The relativistic form of Gibbs equation leads to the balance equation of entropy density. The theory is compared to the nonrelativistic one. The linear transport equations are derived by assuming the linear dependence of currents on deviations. The thermodynamical fluxes and forces are identified and the interference of cross phenomena is discussed. (D.Gy.)
Meson spectra using relativistic quark models
International Nuclear Information System (INIS)
Eggers, M.C.
1985-01-01
The complexity of QCD has led to the use of simpler, phenomenological models for hadrons, notably potential models. A short overview of the origin, rationale, merits and demerits of such models is given. Nonrelativistic models and scaling laws are discussed using the WKB technique for illustrative purposes. The failure of nonrelativistic models to describe the lighter mesons motivates the introduction of relativistic equations. Relativistic kinematics are incorporated into a Schroedinger formalism using equations derived by A. Barut, while two-body kinematics are brought into a one-body form via a substitution related to the Todorov equation. The potential used involves a semi-analytic solution to a harmonic oscillator modified by a spin-spin interaction term. The results seem to indicate that such a harmonic oscillator is unsuitable to describe diquark systems adequately
Relativistic formulations with Blankenbecler-Sugar reduction technique for the three-particle system
International Nuclear Information System (INIS)
Morioka, S.; Afnan, I.R.
1980-05-01
A critical comparison for two-types of three-dimensional covariant equations for the three-particle system obtained by the Blankenbecler-Sugar reduction technique with the Whitghtman-Garding momenta and the usual Jacobi variables is presented. The relations between the relativistic and non-relativistic equations in the low energy limit are discussed
Relativistic three-particle theory
International Nuclear Information System (INIS)
Hochauser, S.
1979-01-01
In keeping with recent developments in experimental nuclear physics, a formalism is developed to treat interactions between three relativistic nuclear particles. The concept of unitarity and a simple form of analyticity are used to construct coupled, integral, Faddeev-type equations and, with the help of analytic separable potentials, these are cast in simple, one-dimensional form. Energy-dependent potentials are introduced so as to take into account the sign-change of some phase shifts in the nucleon-nucleon interaction and parameters for these potentials are obtained. With regard to the success of such local potentials as the Yukawa potential, a recently developed method for expanding these in separable form is discussed. Finally, a new method for the numerical integration of the Faddeev equations along the real axis is introduced, thus avoiding the traditional need for contour rotations into the complex plane. (author)
Vlasov simulations of electron hole dynamics in inhomogeneous magnetic field
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
Spinning relativistic particles in external fields
International Nuclear Information System (INIS)
Pomeranskii, Andrei A; Sen'kov, Roman A; Khriplovich, Iosif B
2000-01-01
The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. The self-consistent equations of motion are built with the noncovariant description of spin and with the usual, 'naive' definition of the coordinate of a relativistic particle. A simple derivation of the gravitational interaction of first order in spin is presented for a relativistic particle. The approach developed allows one to consider effects of higher order in spin. Concrete calculations are performed for the second order. The gravimagnetic moment is discussed, a special spin effect in general relativity. We also consider the contributions of the spin interactions of first and second order to the gravitational radiation of compact binary stars. (from the current literature)
Nonlinear relativistic plasma resonance: Renormalization group approach
Energy Technology Data Exchange (ETDEWEB)
Metelskii, I. I., E-mail: metelski@lebedev.ru [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation); Kovalev, V. F., E-mail: vfkvvfkv@gmail.com [Dukhov All-Russian Research Institute of Automatics (Russian Federation); Bychenkov, V. Yu., E-mail: bychenk@lebedev.ru [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation)
2017-02-15
An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy of the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined.
Theory of relativistic radiation reflection from plasmas
Gonoskov, Arkady
2018-01-01
We consider the reflection of relativistically strong radiation from plasma and identify the physical origin of the electrons' tendency to form a thin sheet, which maintains its localisation throughout its motion. Thereby, we justify the principle of relativistic electronic spring (RES) proposed in [Gonoskov et al., Phys. Rev. E 84, 046403 (2011)]. Using the RES principle, we derive a closed set of differential equations that describe the reflection of radiation with arbitrary variation of polarization and intensity from plasma with an arbitrary density profile for an arbitrary angle of incidence. We confirm with ab initio PIC simulations that the developed theory accurately describes laser-plasma interactions in the regime where the reflection of relativistically strong radiation is accompanied by significant, repeated relocation of plasma electrons. In particular, the theory can be applied for the studies of plasma heating and coherent and incoherent emissions in the RES regime of high-intensity laser-plasma interaction.
Viscous photons in relativistic heavy ion collisions
International Nuclear Information System (INIS)
Dion, Maxime; Paquet, Jean-Francois; Young, Clint; Jeon, Sangyong; Gale, Charles; Schenke, Bjoern
2011-01-01
Theoretical studies of the production of real thermal photons in relativistic heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) are performed. The space-time evolution of the colliding system is modelled using music, a 3+1D relativistic hydrodynamic simulation, using both its ideal and viscous versions. The inclusive spectrum and its azimuthal angular anisotropy are studied separately, and the relative contributions of the different photon sources are highlighted. It is shown that the photon v 2 coefficient is especially sensitive to the details of the microscopic dynamics like the equation of state, the ratio of shear viscosity over entropy density, η/s, and to the morphology of the initial state.
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.
Relativistic bound state wave functions
International Nuclear Information System (INIS)
Micu, L.
2005-01-01
A particular method of writing the bound state wave functions in relativistic form is applied to the solutions of the Dirac equation with confining potentials in order to obtain a relativistic description of a quark antiquark bound system representing a given meson. Concerning the role of the effective constituent in the present approach we first observe that without this additional constituent we couldn't expand the bound state wave function in terms of products of free states. Indeed, we notice that if the wave function depends on the relative coordinates only, all the expansion coefficients would be infinite. Secondly we remark that the effective constituent enabled us to give a Lorentz covariant meaning to the potential energy of the bound system which is now seen as the 4th component of a 4-momentum. On the other side, by relating the effective constituent to the quantum fluctuations of the background field which generate the binding, we provided a justification for the existence of some spatial degrees of freedom accompanying the interaction potential. These ones, which are quite unusual in quantum mechanics, in our model are the natural consequence of the the independence of the quarks and can be seen as the effect of the imperfect cancellation of the vector momenta during the quantum fluctuations. Related with all these we remark that the adequate representation for the relativistic description of a bound system is the momentum representation, because of the transparent and easy way of writing the conservation laws and the transformation properties of the wave functions. The only condition to be fulfilled is to find a suitable way to take into account the potential energy of the bound system. A particular feature of the present approach is that the confining forces are due to a kind of glue where both quarks are embedded. This recalls other bound state models where the wave function is factorized in terms of constituent wave functions and the confinement is
New exact solutions of the Dirac equation. 11
International Nuclear Information System (INIS)
Bagrov, V.G.; Noskov, M.D.
1984-01-01
Investigations into determining new exact solutions of relativistic wave equations started in another paper were continued. Exact solutions of the Dirac, Klein-Gordon equations and classical relativistic equations of motion in four new types of external electromagnetic fields were found
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
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.
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
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.
Vlasov Fluid stability of a 2-D plasma with a linear magnetic field null
International Nuclear Information System (INIS)
Kim, J.S.
1984-01-01
Vlasov Fluid stability of a 2-dimensional plasma near an O type magnetic null is investigated. Specifically, an elongated Z-pinch is considered, and applied to Field Reversed Configurations at Los Alamos National Laboratory by making a cylindrical approximation of the compact torus. The orbits near an elliptical O type null are found to be very complicated; the orbits are large and some are stochastic. The kinetic corrections to magnetohydrodynamics (MHD) are investigated by evaluating the expectation values of the growth rates of a Vlasov Fluid dispersion functional by using a set of trial functions based on ideal MHD. The dispersion functional involves fluid parts and orbit dependent parts. The latter involves phase integral of two time correlations. The phase integral is replaced by the time integral both for the regular and for the stochastic orbits. Two trial functions are used; one has a large displacement near the null and the other away from the null
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.
The relativistic titls of Giza pyramids' entrance-passages
Aboulfotouh, H.
The tilts of Giza pyramids' entrance-passages have never been considered as if they were the result of relativistic mathematical equations, and never been thought to encode the Earth's obliquity parameters. This paper presents an attempt to retrieve the method of establishing the equations that the pyramids' designer used to quantify the entrance-passages' tilts of these architectonic masterpieces. It proves that the pyramids' designer was able to include the geographic, astronomical and time parameters in one relativistic equation, encoding the date of the design of the Giza pyramids in the tilt of the entrance passage of the great pyramid.
Towards an exact relativistic theory of Earth's geoid undulation
Kopeikin, Sergei M.; Mazurova, Elena M.; Karpik, Alexander P.
2015-08-01
The present paper extends the Newtonian concept of the geoid in classic geodesy towards the realm of general relativity by utilizing the covariant geometric methods of the perturbation theory of curved manifolds. It yields a covariant definition of the anomalous (disturbing) gravity potential and formulates differential equation for it in the form of a covariant Laplace equation. The paper also derives the Bruns equation for calculation of geoid's height with full account for relativistic effects beyond the Newtonian approximation. A brief discussion of the relativistic Bruns formula is provided.
Relativistic quantum chaos-An emergent interdisciplinary field.
Lai, Ying-Cheng; Xu, Hong-Ya; Huang, Liang; Grebogi, Celso
2018-05-01
Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics-all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.
Relativistic quantum chaos—An emergent interdisciplinary field
Lai, Ying-Cheng; Xu, Hong-Ya; Huang, Liang; Grebogi, Celso
2018-05-01
Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics—all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.
Nucleon self-energy in the relativistic Brueckner theory
Energy Technology Data Exchange (ETDEWEB)
Waindzoch, T; Fuchs, C; Faessler, A [Inst. fuer Theoretische Physik, Univ. Tuebingen (Germany)
1998-06-01
The self-energy of the nucleon in nuclear matter is calculated in the relativistic Brueckner theory. We solve the Thompson equation for the two nucleon scattering in the medium using different Bonn potentials. The self-energy has a rather strong momentum dependence while the equation of state compares well with previous calculations. (orig.)
Unification of Gravitation and Electromagnetism in a Relativistic ...
African Journals Online (AJOL)
A theory of gravitation is considered in a relativistic version of Finslerian geometry. It is found that both the geodesic equations and the Finslerian analogue of the Einstein\\'s field equations have terms that involve the electromagnetic field tensor, thereby pointing out to the geometrization of electrodynamics and hence to a ...
Nucleon self-energy in the relativistic Brueckner theory
International Nuclear Information System (INIS)
Waindzoch, T.; Fuchs, C.; Faessler, A.
1998-01-01
The self-energy of the nucleon in nuclear matter is calculated in the relativistic Brueckner theory. We solve the Thompson equation for the two nucleon scattering in the medium using different Bonn potentials. The self-energy has a rather strong momentum dependence while the equation of state compares well with previous calculations. (orig.)
Plasma relativistic microwave electronics
International Nuclear Information System (INIS)
Kuzelev, M.V.; Loza, O.T.; Rukhadze, A.A.; Strelkov, P.S.; Shkvarunets, A.G.
2001-01-01
One formulated the principles of plasma relativistic microwave electronics based on the induced Cherenkov radiation of electromagnetic waves at interaction of a relativistic electron beam with plasma. One developed the theory of plasma relativistic generators and accelerators of microwave radiation, designed and studied the prototypes of such devices. One studied theoretically the mechanisms of radiation, calculated the efficiencies and the frequency spectra of plasma relativistic microwave generators and accelerators. The theory findings are proved by the experiment: intensity of the designed sources of microwave radiation is equal to 500 μW, the frequency of microwave radiation is increased by 7 times (from 4 up to 28 GHz), the width of radiation frequency band may vary from several up to 100%. The designed sources of microwave radiation are no else compared in the electronics [ru
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...
Three-dimensional formulation of the relativistic two-body problem in terms of rapidities
International Nuclear Information System (INIS)
Amirkhanov, I.V.; Grusha, G.V.; Mir-Kasimov, R.M.
1976-01-01
The scheme, based on the three-dimensional relativistic equation of the quasi-potential type is developed. As a basic variable rapidity, canonically conjugated to the relativistic relative distance is adopted. The free Green function has a simple pole in the complex rapidity plane, ensuring the fulfillment of the elastic unitarity for real potentials. In the local potential case the corresponding partial wave equation in configurational r-representation is a differential second-order equation. The problem of boundary conditions, which is a non-trivial one in the relativistic r-space, is studied. The exact solutions of the equation in simple cases have been found
Ion-acoustic envelope modes in a degenerate relativistic electron-ion plasma
Energy Technology Data Exchange (ETDEWEB)
McKerr, M.; Kourakis, I. [Centre for Plasma Physics, School of Mathematics and Physics, Queen' s University Belfast, BT7 1NN Belfast, Northern Ireland (United Kingdom); Haas, F. [Instituto de Física, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves 9500, Porto Alegre, RS (Brazil)
2016-05-15
A self-consistent relativistic two-fluid model is proposed for one-dimensional electron-ion plasma dynamics. A multiple scales perturbation technique is employed, leading to an evolution equation for the wave envelope, in the form of a nonlinear Schrödinger type equation (NLSE). The inclusion of relativistic effects is shown to introduce density-dependent factors, not present in the non-relativistic case—in the conditions for modulational instability. The role of relativistic effects on the linear dispersion laws and on envelope soliton solutions of the NLSE is discussed.
Energy Technology Data Exchange (ETDEWEB)
Antippa, Adel F [Departement de Physique, Universite du Quebec a Trois-Rivieres, Trois-Rivieres, Quebec G9A 5H7 (Canada)
2009-05-15
We solve the problem of the relativistic rocket by making use of the relation between Lorentzian and Galilean velocities, as well as the laws of superposition of successive collinear Lorentz boosts in the limit of infinitesimal boosts. The solution is conceptually simple, and technically straightforward, and provides an example of a powerful method that can be applied to a wide range of special relativistic problems of linear acceleration.
Exact Relativistic `Antigravity' Propulsion
Felber, Franklin S.
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
International Nuclear Information System (INIS)
Strange, P.
2010-01-01
Quantum revivals are now a well-known phenomena within nonrelativistic quantum theory. In this Letter we display the effects of relativity on revivals and quantum carpets. It is generally believed that revivals do not occur within a relativistic regime. Here we show that while this is generally true, it is possible, in principle, to set up wave packets with specific mathematical properties that do exhibit exact revivals within a fully relativistic theory.
Kinematics of a relativistic particle with de Sitter momentum space
International Nuclear Information System (INIS)
Arzano, Michele; Kowalski-Glikman, Jerzy
2011-01-01
We discuss kinematical properties of a free relativistic particle with deformed phase space in which momentum space is given by (a submanifold of) de Sitter space. We provide a detailed derivation of the action, Hamiltonian structure and equations of motion for such a free particle. We study the action of deformed relativistic symmetries on the phase space and derive explicit formulae for the action of the deformed Poincare group. Finally we provide a discussion on parametrization of the particle worldlines stressing analogies and differences with ordinary relativistic kinematics.
Electromagnetic solitons in degenerate relativistic electron–positron plasma
International Nuclear Information System (INIS)
Berezhiani, V I; Shatashvili, N L; Tsintsadze, N L
2015-01-01
The existence of soliton-like electromagnetic (EM) distributions in a fully degenerate electron–positron plasma is studied applying relativistic hydrodynamic and Maxwell equations. For a circularly polarized wave it is found that the soliton solutions exist both in relativistic as well as nonrelativistic degenerate plasmas. Plasma density in the region of soliton pulse localization is reduced considerably. The possibility of plasma cavitation is also shown. (invited comment)
Calculation of relativistic model stars using Regge calculus
International Nuclear Information System (INIS)
Porter, J.
1987-01-01
A new approach to the Regge calculus, developed in a previous paper, is used in conjunction with the velocity potential version of relativistic fluid dynamics due to Schutz [1970, Phys. Rev., D, 2, 2762] to calculate relativistic model stars. The results are compared with those obtained when the Tolman-Oppenheimer-Volkov equations are solved by other numerical methods. The agreement is found to be excellent. (author)
Quantum theoretical physics is statistical and relativistic
International Nuclear Information System (INIS)
Harding, C.
1980-01-01
A new theoretical framework for the quantum mechanism is presented. It is based on a strict deterministic behavior of single systems. The conventional QM equation, however, is found to describe statistical results of many classical systems. It will be seen, moreover, that a rigorous synthesis of our theory requires relativistic kinematics. So, QM is not only a classical statistical theory, it is, of necessity, a relativistic theory. The equation of the theory does not just duplicate QM, it indicates an inherent nonlinearity in QM which is subject to experimental verification. It is shown, therefore, that conventional QM is a corollary of classical deterministic principles. It is suggested that this concept of nature conflicts with that prevalent in modern physics. (author)
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)
General relativistic chaos and nonlinear dynamics
International Nuclear Information System (INIS)
Barrow, J.D.
1982-01-01
How new ideas in dynamical systems theory find application in the description of general relativistic systems is described. The concept of dynamical entropy is explained and the associated invariant evaluated for the Mixmaster cosmological model. The description of cosmological models as measure preserving dynamical systems leads to a number of interconnections with new ideas in non-linear dynamics. This may provide a new avenue of approach to ascertaining the nature of the general solution to Einstein's equations. (author)
General relativistic chaos and nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Barrow, J D [California Univ., Berkeley (USA). Dept. of Physics
1982-06-01
How new ideas in dynamical systems theory find application in the description of general relativistic systems is described. The concept of dynamical entropy is explained and the associated invariant evaluated for the Mixmaster cosmological model. The description of cosmological models as measure preserving dynamical systems leads to a number of interconnections with new ideas in non-linear dynamics. This may provide a new avenue of approach to ascertaining the nature of the general solution to Einstein's equations.
Relativistic electron precipitation in the auroral zone
International Nuclear Information System (INIS)
Simons, D.J.
1975-01-01
The energy spectra and pitch angle distributions of electrons in the energy range 50 keV to 2 MeV have been determined by a solid state electron energy spectrometer during the Relativistic Electron Precipitation (REP) event of 31 May 1972. The experiment was carried aboard a Nike-Cajun sounding rocket as the University of Maryland component of a joint American-Norwegian (NASA-NDRE) ionospheric investigation. The difficulty of determining the expected electron flux prior to the experiment required an instrument with a large dynamic range. The design and theoretical modeling of this instrument is described in great detail. The electron pitch angle distributions are determined from a knowledge of the rocket aspect and the direction in space of the Earth's magnetic field. The electron fluxes during the REP event were highly variable demonstrating correlated energy, flux and pitch angle pulsations with time periods less than one second. Increases in flux were accompanied by marked filling of the loss cone at lower energies (near 50 keV). Drawing upon the quasilinear equations of plasma wave-electron interactions, a theoretical model for the production of relativistic electrons is proposed. A self consistent set of fully relativistic equations for the evolution of the electron distribution function due to the interaction of the electrons with parallel propagating whistler waves is derived in the Appendix. An examination of these equations leads to the conclusion that at comparatively low background electron densities, the anomalous Doppler resonance leads to the acceleration of near relativistic particles. The results of a computer solution of the five coupled integrodifferential quasilinear equations confirms this conclusion
Parton distribution in relativistic hadrons
International Nuclear Information System (INIS)
Kopeliovich, B.Z.; Lapidus, L.I.; Zamolodchikov, Al.B.
1979-01-01
The distribution in the slow-parton number in the relativistic hadron is considered as a function of its rapidity (y). Neglecting corrections due to the tarton chain recombination the equation is derived and its explicit solution is found. It describes this distribution depending on the initial distribution at y approximately 1. Comparison with the reggeon diagrams results in relations between the parton model and the regaeon field theory parameters. The interpretation of the cutting rules in the framework of the parton model is presented. The numerical estimation of the parton model parameters is performed. It is shown that the slow-parton density corresponding to accessible energies seems to be close to the saturated density. Therefore, the enhanced graphs contributions turn out to be of considerable importance
International Nuclear Information System (INIS)
Hwang, Jai-chan; Noh, Hyerim
2007-01-01
We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity perturbation equations of general relativistic zero-pressure, irrotational, single-component fluid in a spatially flat background coincide exactly with the ones known in Newton's theory without using the gravitational potential. We also have shown the effect of gravitational waves to the second order, and pure general relativistic correction terms appearing in the third-order perturbations. Here, we present results of second-order perturbations relaxing all the assumptions made in our previous works. We derive the general relativistic correction terms arising due to (i) pressure, (ii) multicomponent, (iii) background spatial curvature, and (iv) rotation. In the case of multicomponent zero-pressure, irrotational fluids under the flat background, we effectively do not have relativistic correction terms, thus the relativistic equations expressed in terms of density and velocity perturbations again coincide with the Newtonian ones. In the other three cases we generally have pure general relativistic correction terms. In the case of pressure, the relativistic corrections appear even in the level of background and linear perturbation equations. In the presence of background spatial curvature, or rotation, pure relativistic correction terms directly appear in the Newtonian equations of motion of density and velocity perturbations to the second order; to the linear order, without using the gravitational potential (or metric perturbations), we have relativistic/Newtonian correspondences for density and velocity perturbations of a single-component fluid including the rotation even in the presence of background spatial curvature. In the small-scale limit (far inside the horizon), to the second-order, relativistic equations of density and
Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems
International Nuclear Information System (INIS)
Marquette, Ian
2011-01-01
There exists a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude and the Schroedinger equation. We obtain the relativistic energy spectrum for the four relativistic quantum Smorodinsky-Winternitz systems from their quasi-Hamiltonian and the quadratic algebras studied by Daskaloyannis in the nonrelativistic context. We also apply the quadratic algebra approach directly to the initial Dirac equation for these four systems and show that the quadratic algebras obtained are the same than those obtained from the quasi-Hamiltonians. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras can be applied to the quantum relativistic case.
Selectivity of the nucleon-induced deuteron breakup and relativistic effects
Witała, H.; Golak, J.; Skibiński, R.
2006-01-01
Theoretical predictions for the nucleon induced deuteron breakup process based on solutions of the three-nucleon Faddeev equation including such relativistic features as the relativistic kinematics and boost effects are presented. Large changes of the breakup cross section in some complete configurations are found at higher energies. The predicted relativistic effects, which are mostly of dynamical origin, seem to be supported by existing data.
Influence of a relativistic kinematics on s-wave KN phase shifts in a quark model
International Nuclear Information System (INIS)
Lemaire, S.; Labarsouque, J.; Silvestre-Brac, B.
2001-01-01
The I = 1 and I = 0 kaon-nucleon s-wave phase shifts have been calculated in a quark potential model using the resonating group method (RGM) and a relativistic kinematics. The spinless Salpeter equation has been solved numerically using the Fourier grid Hamiltonian method. The results have been compared to the non-relativistic ones. For each isospin channel the phase shifts obtained are not so far from the non-relativistic results. (author)
Thermal relaxation time of a mixture of relativistic electrons and neutrinos
International Nuclear Information System (INIS)
Herrera, M.A.; Hacyan, S.
1987-01-01
The interaction between the components of a relativistic binary mixture is studied by means of a fully covariant formalism. Assuming both components to differ slightly in temperature, an application of the relativistic Boltzmann equation yields general expressions for the energy transfer rate and for the relaxation time of the system. The resulting relation is then applied to a mixture of relativistic electrons and neutrinos to obtain numerical values of its relaxation time. (author)
Relativistic and non-relativistic studies of nuclear matter
Banerjee, MK; Tjon, JA
2002-01-01
We point out that the differences between the results of the non-relativistic lowest order Brueckner theory (LOBT) and the relativistic Dirac-Brueckner analysis predominantly arise from two sources. Besides effects from a nucleon mass modification M* in nuclear medium we have in a relativistic
Relativistic mean field model for entrainment in general relativistic superfluid neutron stars
International Nuclear Information System (INIS)
Comer, G.L.; Joynt, R.
2003-01-01
General relativistic superfluid neutron stars have a significantly more intricate dynamics than their ordinary fluid counterparts. Superfluidity allows different superfluid (and superconducting) species of particles to have independent fluid flows, a consequence of which is that the fluid equations of motion contain as many fluid element velocities as superfluid species. Whenever the particles of one superfluid interact with those of another, the momentum of each superfluid will be a linear combination of both superfluid velocities. This leads to the so-called entrainment effect whereby the motion of one superfluid will induce a momentum in the other superfluid. We have constructed a fully relativistic model for entrainment between superfluid neutrons and superconducting protons using a relativistic σ-ω mean field model for the nucleons and their interactions. In this context there are two notions of 'relativistic': relativistic motion of the individual nucleons with respect to a local region of the star (i.e. a fluid element containing, say, an Avogadro's number of particles), and the motion of fluid elements with respect to the rest of the star. While it is the case that the fluid elements will typically maintain average speeds at a fraction of that of light, the supranuclear densities in the core of a neutron star can make the nucleons themselves have quite high average speeds within each fluid element. The formalism is applied to the problem of slowly rotating superfluid neutron star configurations, a distinguishing characteristic being that the neutrons can rotate at a rate different from that of the protons
Energy Technology Data Exchange (ETDEWEB)
Suparmi, A., E-mail: suparmiuns@gmail.com; Cari, C., E-mail: suparmiuns@gmail.com [Physics Department, Post Graduate Study, Sebelas Maret University (Indonesia); Angraini, L. M. [Physics Department, Mataram University (Indonesia)
2014-09-30
The bound state solutions of Dirac equation for Hulthen and trigonometric Rosen Morse non-central potential are obtained using finite Romanovski polynomials. The approximate relativistic energy spectrum and the radial wave functions which are given in terms of Romanovski polynomials are obtained from solution of radial Dirac equation. The angular wave functions and the orbital quantum number are found from angular Dirac equation solution. In non-relativistic limit, the relativistic energy spectrum reduces into non-relativistic energy.
Relativistic quantum mechanics
International Nuclear Information System (INIS)
Ollitrault, J.Y.
1998-12-01
These notes form an introduction to relativistic quantum mechanics. The mathematical formalism has been reduced to the minimum in order to enable the reader to calculate elementary physical processes. The second quantification and the field theory are the logical followings of this course. The reader is expected to know analytical mechanics (Lagrangian and Hamiltonian), non-relativistic quantum mechanics and some basis of restricted relativity. The purpose of the first 3 chapters is to define the quantum mechanics framework for already known notions about rotation transformations, wave propagation and restricted theory of relativity. The next 3 chapters are devoted to the application of relativistic quantum mechanics to a particle with 0,1/5 and 1 spin value. The last chapter deals with the processes involving several particles, these processes require field theory framework to be thoroughly described. (A.C.)
Relativistic solitons and pulsars
Energy Technology Data Exchange (ETDEWEB)
Karpman, V I [Inst. of Terrestrial Magnetism, Ionosphere, and Radio-Wave Propagation, Moscow; Norman, C A; ter Haar, D; Tsytovich, V N
1975-05-01
A production mechanism for stable electron bunches or sheets of localized electric fields is investigated which may account for pulsar radio emission. Possible soliton phenomena in a one-dimensional relativistic plasma are analyzed, and it is suggested that the motion of a relativistic soliton, or ''relaton'', along a curved magnetic-field line may produce radio emission with the correct polarization properties. A general MHD solution is obtained for relatons, the radiation produced by a relativistic particle colliding with a soliton is evaluated, and the emission by a soliton moving along a curved field line is estimated. It is noted that due to a number of severe physical restrictions, curvature radiation is not a very likely solution to the problem of pulsar radio emission. (IAA)
Relativistic quantum mechanics
Horwitz, Lawrence P
2015-01-01
This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semigroup evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. Th...
Handbook of relativistic quantum chemistry
International Nuclear Information System (INIS)
Liu, Wenjian
2017-01-01
This handbook focuses on the foundations of relativistic quantum mechanics and addresses a number of fundamental issues never covered before in a book. For instance: How can many-body theory be combined with quantum electrodynamics? How can quantum electrodynamics be interfaced with relativistic quantum chemistry? What is the most appropriate relativistic many-electron Hamiltonian? How can we achieve relativistic explicit correlation? How can we formulate relativistic properties? - just to name a few. Since relativistic quantum chemistry is an integral component of computational chemistry, this handbook also supplements the ''Handbook of Computational Chemistry''. Generally speaking, it aims to establish the 'big picture' of relativistic molecular quantum mechanics as the union of quantum electrodynamics and relativistic quantum chemistry. Accordingly, it provides an accessible introduction for readers new to the field, presents advanced methodologies for experts, and discusses possible future perspectives, helping readers understand when/how to apply/develop the methodologies.
Handbook of relativistic quantum chemistry
Energy Technology Data Exchange (ETDEWEB)
Liu, Wenjian (ed.) [Peking Univ., Beijing (China). Center for Computational Science and Engineering
2017-03-01
This handbook focuses on the foundations of relativistic quantum mechanics and addresses a number of fundamental issues never covered before in a book. For instance: How can many-body theory be combined with quantum electrodynamics? How can quantum electrodynamics be interfaced with relativistic quantum chemistry? What is the most appropriate relativistic many-electron Hamiltonian? How can we achieve relativistic explicit correlation? How can we formulate relativistic properties? - just to name a few. Since relativistic quantum chemistry is an integral component of computational chemistry, this handbook also supplements the ''Handbook of Computational Chemistry''. Generally speaking, it aims to establish the 'big picture' of relativistic molecular quantum mechanics as the union of quantum electrodynamics and relativistic quantum chemistry. Accordingly, it provides an accessible introduction for readers new to the field, presents advanced methodologies for experts, and discusses possible future perspectives, helping readers understand when/how to apply/develop the methodologies.
Biquaternions and relativistic kinematics
International Nuclear Information System (INIS)
Bogush, A.A.; Kurochkin, Yu.A.; Fedorov, F.I.
1979-01-01
The problems concerning the use of quaternion interpretation of the Lorentz group vector parametrization are considered for solving relativistic kinematics problems. A vector theory convenient for describing the characteristic features of the Lobachevsky space is suggested. The kinematics of elementary particle scattering is investigated on the basis of this theory. A synthesis of vector parametrization and of quaternion calculation has been shown to lead to natural formulation of the theory of vectors in the three-dimensional Lobachevsky space, realized on mass hyperboloids of relativistic particles
Relativistic heavy ion collisions
International Nuclear Information System (INIS)
Barz, H.W.; Kaempfer, B.; Schulz, H.
1984-12-01
An elementary introduction is given into the scenario of relativistic heavy ion collisions. It deals with relativistic kinematics and estimates of energy densities, extrapolations of the present knowledge of hadron-hadron and hadron-nuleus to nucleus-nucleus collisions, the properties of the quark-gluon plasma and the formation of the plasma and possible experimental signatures. Comments are made on a cosmic ray experiment which could be interpreted as a first indication of the quark-gluon phase of the matter. (author)
Calculating Relativistic Transition Matrix Elements for Hydrogenic Atoms Using Monte Carlo Methods
Alexander, Steven; Coldwell, R. L.
2015-03-01
The nonrelativistic transition matrix elements for hydrogen atoms can be computed exactly and these expressions are given in a number of classic textbooks. The relativistic counterparts of these equations can also be computed exactly but these expressions have been described in only a few places in the literature. In part, this is because the relativistic equations lack the elegant simplicity of the nonrelativistic equations. In this poster I will describe how variational Monte Carlo methods can be used to calculate the energy and properties of relativistic hydrogen atoms and how the wavefunctions for these systems can be used to calculate transition matrix elements.
The Dirac equation and its solutions
Energy Technology Data Exchange (ETDEWEB)
Bagrov, Vladislav G. [Tomsk State Univ., Tomsk (Russian Federation). Dept. of Quantum Field Theroy; Gitman, Dmitry [Sao Paulo Univ. (Brazil). Inst. de Fisica; P.N. Lebedev Physical Institute, Moscow (Russian Federation); Tomsk State Univ., Tomsk (Russian Federation). Faculty of Physics
2013-07-01
The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly. In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.
The Dirac equation and its solutions
Bagrov, Vladislav G
2014-01-01
Dirac equations are of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly.In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.
The Dirac equation and its solutions
International Nuclear Information System (INIS)
Bagrov, Vladislav G.; Gitman, Dmitry; P.N. Lebedev Physical Institute, Moscow; Tomsk State Univ., Tomsk
2013-01-01
The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly. In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.
Relativistic finite-temperature Thomas-Fermi model
Faussurier, Gérald
2017-11-01
We investigate the relativistic finite-temperature Thomas-Fermi model, which has been proposed recently in an astrophysical context. Assuming a constant distribution of protons inside the nucleus of finite size avoids severe divergence of the electron density with respect to a point-like nucleus. A formula for the nuclear radius is chosen to treat any element. The relativistic finite-temperature Thomas-Fermi model matches the two asymptotic regimes, i.e., the non-relativistic and the ultra-relativistic finite-temperature Thomas-Fermi models. The equation of state is considered in detail. For each version of the finite-temperature Thomas-Fermi model, the pressure, the kinetic energy, and the entropy are calculated. The internal energy and free energy are also considered. The thermodynamic consistency of the three models is considered by working from the free energy. The virial question is also studied in the three cases as well as the relationship with the density functional theory. The relativistic finite-temperature Thomas-Fermi model is far more involved than the non-relativistic and ultra-relativistic finite-temperature Thomas-Fermi models that are very close to each other from a mathematical point of view.
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)
Trapped Electron Instability of Electron Plasma Waves: Vlasov simulations and theory
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.
The cosmic-ray shock structure problem for relativistic shocks
Webb, G. M.
1985-01-01
The time asymptotic behaviour of a relativistic (parallel) shock wave significantly modified by the diffusive acceleration of cosmic-rays is investigated by means of relativistic hydrodynamical equations for both the cosmic-rays and thermal gas. The form of the shock structure equation and the dispersion relation for both long and short wavelength waves in the system are obtained. The dependence of the shock acceleration efficiency on the upstream fluid spped, long wavelength Mach number and the ratio N = P sub co/cP sub co+P sub go)(Psub co and P sub go are the upstream cosmic-ray and thermal gas pressures respectively) are studied.
Relativistic Bosons in Time-Harmonic Electric Fields
Buhucianu, Ovidiu; Dariescu, Marina-Aura; Dariescu, Ciprian
2012-02-01
In the present paper, we consider a bi-dimensional thin sample, placed in a strong harmonically oscillating electric field and a static magnetic induction, both directed along the normal to the sample's plane. The Klein-Gordon equation describing the relativistic bosons leads to a Mathieu's type equation for the temporal part of the wave functions. It follows that, for the electric field pulsation inside a computable range, depending on the external fields intensities, the amplitude functions are turning from oscillatory to exponentially growing modes. For ultra-relativistic particles, one can recover the periodic stationary amplitude behavior.
Relativistic nuclear fluid dynamics and VUU kinetic theory
International Nuclear Information System (INIS)
Molitoris, J.J.; Hahn, D.; Alonso, C.; Collazo, I.; D'Alessandris, P.; McAbee, T.; Wilson, J.; Zingman, J.
1987-01-01
Relativistic kinetic theory may be used to understand hot dense hadronic matter. We address the questions of collective flow and pion production in a 3 D relativistic fluid dynamic model and in the VUU microscopic theory. The GSI/LBL collective flow and pion data point to a stiff equation of state. The effect of the nuclear equation of state on the thermodynamic parameters is discussed. The properties of dense hot hadronic matter are studied in Au + Au collisions from 0.1 to 10 GeV/nucleon. 22 refs., 5 figs
The Post-Newtonian Approximation for Relativistic Compact Binaries
Directory of Open Access Journals (Sweden)
Futamase Toshifumi
2007-03-01
Full Text Available We discuss various aspects of the post-Newtonian approximation in general relativity. After presenting the foundation based on the Newtonian limit, we show a method to derive post-Newtonian equations of motion for relativistic compact binaries based on a surface integral approach and the strong field point particle limit. As an application we derive third post-Newtonian equations of motion for relativistic compact binaries which respect the Lorentz invariance in the post-Newtonian perturbative sense, admit a conserved energy, and are free from any ambiguity.
A note on relativistic Feynman-type integrals
International Nuclear Information System (INIS)
Namsrai, Kh.
1979-01-01
An attempt is made to generalize the definition of Feynman path integral to the relativistic case within the framework of the Kershaw stochastic model. The Smoluchowski type equations are used which allow one to obtain easily the Schrodinger, Klein-Gordon and Dirac equations. The interaction is introduced by using Weyl's gaude theory. In the model developed the Feynman process may formally by interpreted as a stochastic diffusion process in complex times with a real probability measure which occurs in the Euclidean space. Feynman path integrals themselves are not obtained in the model, nonetheless it represents an interest as one of possibilities of the relativistic generalization of Feynman type integrals
Fundamental problem in the relativistic approach to atomic structure theory
International Nuclear Information System (INIS)
Kagawa, Takashi
1987-01-01
It is known that the relativistic atomic structure theory contains a serious fundamental problem, so-called the Brown-Ravenhall (BR) problem or variational collapse. This problem arises from the fact that the energy spectrum of the relativistic Hamiltonian for many-electron systems is not bounded from below because the negative-energy solutions as well as the positive-energy ones are obtained from the relativistic equation. This report outlines two methods to avoid the BR problem in the relativistic calculation, that is, the projection operator method and the general variation method. The former method is described first. The use of a modified Hamiltonian containing a projection operator which projects the positive-energy solutions in the relativistic wave equation has been proposed to remove the BR difficulty. The problem in the use of the projection operator method is that the projection operator for the system cannot be determined uniquely. The final part of this report outlines the general variation method. This method can be applied to any system, such as relativistic ones whose Hamiltonian is not bounded from below. (Nogami, K.)
Relativistic particle in a box
Alberto, P.; Fiolhais, Carlos; Gil, Victor
1996-01-01
The problem of a relativistic spin 1/2 particle confined to a one-dimensional box is solved in a way that resembles closely the solution of the well known quantum-mechanical textbook problem of a non-relativistic particle in a box. The energy levels and probability density are computed and compared with the non-relativistic case
Relativistic transport theory for hadronic matter
International Nuclear Information System (INIS)
Shun-Jin Wang; Bao-An Li; Bauer, W.; Randrup, J.
1991-01-01
We derive coupled equations of motion for the density matrices for nucleons, Δ resonances, and π mesons, as well as for the pion--baryon interaction vertex function for the description of nuclear reactions at intermediate energies. We start from an effective hadronic Lagrangian density with minimal coupling between baryons and mesons. By truncating at the level of three-body correlations and using the G-matrix method to solve the equations of motion for the two-body correlation functions, a closed equation of motion for the one-body density matrices is obtained. A subsequent Wigner transformation then leads to a tractable set of relativistic transport equations for interacting nucleons, deltas, and pions. copyright 1991 Academic Press, Inc
Relativistic electrodynamics of dissipative elastic media
International Nuclear Information System (INIS)
Kranys, M.
1980-01-01
A phenomenological general relativistic electrodynamics is proposed for a dissipative elastic solid which is polarizable and magnetizable and whose governing equations form a hyperbolic system. Non-stationary transport equations are proposed for dissipative fluxes (and constitutive equations of electrodynamics) containing new cross-effect terms, as required for compatibility with an entropy principle expressed by a new balance equation (including a new Gibbs equation). The dynamic equations are deduced from the unified Minkowski-Abraham-Eckart energy-momentum tensor. The theory, formed by a set of 29 (reducible to 23) partial differential equations (in special relativity) governing the material behaviour of the system characterized by generalizing the constitutive equations of quasineutral media, together with Maxwell's equations, may be referred to as the electrodynamics of dissipative elastic media (or fluid). The proposed transport laws for polarization and magnetization generalize the well-known Debye law for relaxation and show the influence of shear and bulk viscosity on polarization and magentization. Besides the form of the entropy function, the free energy function in the non-stationary regime is also formulated. (auth)
Relativistic effects in elastic scattering of electrons in TEM
International Nuclear Information System (INIS)
Rother, Axel; Scheerschmidt, Kurt
2009-01-01
Transmission electron microscopy typically works with highly accelerated thus relativistic electrons. Consequently the scattering process is described within a relativistic formalism. In the following, we will examine three different relativistic formalisms for elastic electron scattering: Dirac, Klein-Gordon and approximated Klein-Gordon, the standard approach. This corresponds to a different consideration of spin effects and a different coupling to electromagnetic potentials. A detailed comparison is conducted by means of explicit numerical calculations. For this purpose two different formalisms have been applied to the approaches above: a numerical integration with predefined boundary conditions and the multislice algorithm, a standard procedure for such simulations. The results show a negligibly small difference between the different relativistic equations in the vicinity of electromagnetic potentials, prevailing in the electron microscope. The differences between the two numeric approaches are found to be small for small-angle scattering but eventually grow large for large-angle scattering, recorded for instance in high-angle annular dark field.
Pion production in relativistic collisions of nuclear drops
International Nuclear Information System (INIS)
Alonso, C.T.; Wilson, J.R.; McAbee, T.L.; Zingman, J.A.
1988-09-01
In a continuation of the long-standing effort of the nuclear physics community to model atomic nuclei as droplets of a specialized nuclear fluid, we have developed a hydrodynamic model for simulating the collisions of heavy nuclei at relativistic speeds. Our model couples ideal relativistic hydrodynamics with a new Monte Carlo treatment of dynamic pion production and tracking. The collective flow for low-energy (200 MeV/N) collisions predicted by this model compares favorably with results from earlier hydrodynamic calculations which used quite different numerical techniques. Our pion predictions at these lower energies appear to differ, however, from the experimental data on pion multiplicities. In this case of ultra-relativistic (200 GeV/N) collisions, our hydrodynamic model has produced baryonic matter distributions which are in reasonable agreement with recent experimental data. These results may shed some light on the sensitivity of relativistic collision data to the nuclear equation of state. 20 refs., 12 figs
Relativistic theory of electron-impact ionization
International Nuclear Information System (INIS)
Rosenberg, Leonard
2010-01-01
A relativistic version of an earlier, non-relativistic, formulation of the theory of ionization of an atomic system by electron impact is presented. With a time-independent resolvent operator taken as the basis for the dynamics, a wave equation is derived for a system with open channels consisting of two positive-energy electrons in an external field generated by the residual ion. Virtual intermediate states can be accounted for by the effective Hamiltonian that appears in the wave equation and which in principle may be constructed perturbatively. The asymptotic form of the wavefunction, modified by the effects of the long-range Coulomb interactions of the two electrons in the external field, is derived. These electrons are constrained, by projection operators which appear naturally in the theory, to propagate in positive-energy states only. The long-range Coulomb effects take the form of phase factors similar to those that are found in the non-relativistic version of the theory. With the boundary conditions established, an integral identity for the ionization amplitude is derived, and used to set up a distorted-wave Born expansion for the transition amplitude involving Coulomb-modified propagating waves.
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Relativistic impulse dynamics.
Swanson, Stanley M
2011-08-01
Classical electrodynamics has some annoying rough edges. The self-energy of charges is infinite without a cutoff. The calculation of relativistic trajectories is difficult because of retardation and an average radiation reaction term. By reconceptuallizing electrodynamics in terms of exchanges of impulses rather than describing it by forces and potentials, we eliminate these problems. A fully relativistic theory using photonlike null impulses is developed. Numerical calculations for a two-body, one-impulse-in-transit model are discussed. A simple relationship between center-of-mass scattering angle and angular momentum was found. It reproduces the Rutherford cross section at low velocities and agrees with the leading term of relativistic distinguishable-particle quantum cross sections (Møller, Mott) when the distance of closest approach is larger than the Compton wavelength of the particle. Magnetism emerges as a consequence of viewing retarded and advanced interactions from the vantage point of an instantaneous radius vector. Radiation reaction becomes the local conservation of energy-momentum between the radiating particle and the emitted impulse. A net action is defined that could be used in developing quantum dynamics without potentials. A reinterpretation of Newton's laws extends them to relativistic motion.
Non-relativistic supersymmetry
International Nuclear Information System (INIS)
Clark, T.E.; Love, S.T.
1984-01-01
The most general one- and two-body hamiltonian invariant under galilean supersymmetry is constructed in superspace. The corresponding Feynman rules are given for the superfield Green functions. As demonstrated by a simple example, it is straightforward to construct models in which the supersymmetry is spontaneously broken by the non-relativistic vacuum. (orig.)
International Nuclear Information System (INIS)
Contopoulos, G.
1983-01-01
In this paper, three main areas of relativistic stellar dynamics are reviewed: (a) The dynamics of clusters, or nuclei of galaxies, of very high density; (b) The dynamics of systems containing a massive black hole; and (c) The dynamics of particles (and photons) in an expanding Universe. The emphasis is on the use of orbit perturbations. (Auth.)
Directory of Open Access Journals (Sweden)
Bialynicki-Birula Iwo
2014-01-01
Full Text Available Original definition of the Wigner function can be extended in a natural manner to relativistic domain in the framework of quantum field theory. Three such generalizations are described. They cover the cases of the Dirac particles, the photon, and the full electromagnetic field.
Antippa, Adel F.
2009-01-01
We solve the problem of the relativistic rocket by making use of the relation between Lorentzian and Galilean velocities, as well as the laws of superposition of successive collinear Lorentz boosts in the limit of infinitesimal boosts. The solution is conceptually simple, and technically straightforward, and provides an example of a powerful…
Relativistic Polarizable Embedding
DEFF Research Database (Denmark)
Hedegård, Erik Donovan; Bast, Radovan; Kongsted, Jacob
2017-01-01
Most chemistry, including chemistry where relativistic effects are important, occurs in an environment, and in many cases, this environment has a significant effect on the chemistry. In nonrelativistic quantum chemistry, a lot of progress has been achieved with respect to including environments s...
Relativistic length agony continued
Directory of Open Access Journals (Sweden)
Redžić D.V.
2014-01-01
Full Text Available We made an attempt to remedy recent confusing treatments of some basic relativistic concepts and results. Following the argument presented in an earlier paper (Redžić 2008b, we discussed the misconceptions that are recurrent points in the literature devoted to teaching relativity such as: there is no change in the object in Special Relativity, illusory character of relativistic length contraction, stresses and strains induced by Lorentz contraction, and related issues. We gave several examples of the traps of everyday language that lurk in Special Relativity. To remove a possible conceptual and terminological muddle, we made a distinction between the relativistic length reduction and relativistic FitzGerald-Lorentz contraction, corresponding to a passive and an active aspect of length contraction, respectively; we pointed out that both aspects have fundamental dynamical contents. As an illustration of our considerations, we discussed briefly the Dewan-Beran-Bell spaceship paradox and the ‘pole in a barn’ paradox. [Projekat Ministarstva nauke Republike Srbije, br. 171028
Relativistic Coulomb excitation
International Nuclear Information System (INIS)
Winther, A.; Alder, K.
1979-01-01
Coulomb excitation of both target and projectile in relativistic heavy ion collisions is evaluated including the lowest order correction for the deviation from a straight line trajectory. Explicit results for differential and total cross sections are given in the form of tables and figures. (Auth.)
Fundamental Relativistic Rotator
International Nuclear Information System (INIS)
Staruszkiewicz, A.
2008-01-01
Professor Jan Weyssenhoff was Myron Mathisson's sponsor and collaborator. He introduced a class of objects known in Cracow as '' kreciolki Weyssenhoffa '', '' Weyssenhoff's rotating little beasts ''. The Author describes a particularly simple object from this class. The relativistic rotator described in the paper is such that its both Casimir invariants are parameters rather than constants of motion. (author)
International Nuclear Information System (INIS)
Roussel, Eleonore
2014-01-01
Relativistic electron bunches circulating in storage rings are used to produce intense radiation from far-infrared to X-rays. However, above a density threshold value, the interaction between the electron bunch and its own radiation can lead to a spatio-temporal instability called micro bunching instability. This instability is characterized by a strong emission of coherent THz radiation (typically 105 times stronger than the classical synchrotron radiation) which is a signature of the presence of microstructures (at mm scale) in the electron bunch. This instability is known to be a fundamental limitation of the operation of synchrotron light sources at high beam current. In this thesis, we have focused on this instability from a nonlinear dynamics point of view by combining experimental studies carried out at the Synchrotron Soleil and UVSOR storage rings with numerical studies mainly based on the Vlasov-Fokker-Planck equation. In a first step, due to the very indirect nature of the experimental observations, we have sought to deduce information on the microstructure wavenumber either by looking at the temporal evolution of the THz signal emitted during the instability or by studying the response of the electron bunch to a laser perturbation. In a second step, we have achieved direct, real time observations of the microstructures dynamics through two new, very different, detection techniques: a thin-film superconductor-based detector at UVSOR, and a spectrally-encoded electro-optic detection technique at Soleil. These new available experimental observations have allowed severe comparisons with the theoretical models. (author)
Relativistic mechanics of two interacting particles and bilocal theory
International Nuclear Information System (INIS)
Takabayasi, Takehiko
1975-01-01
New relativistic mechanics of two-particle system is set forth, where the two constituent particles are interacting by an arbitrary (central) action-at-a-distance. The fundamental equations are presented in a form covariant under general transformation of parameters parametrizing the world lines of constituent particles. The theory represents the proper relativistic generalization of the usual Newtonian mechanics in the sense that it tends in the non-relativistic (and weak interaction) limit to the usual mechanics of two particles moving under a corresponding non-relativistic potential. For the analysis of theory it is convenient to choose a certain particular gauge (i.e., parametrization) fixed by two gauge relations. This brings the theory to a canonical formalism accompanied by two weak equations, and in this gauge quantization can be performed. The result verifies that the relativistic quantum mechanics for two particles interacting by an action-at-a-distance is just represented by a bilocal wave equation and a subsidiary condition, with the clarification of its correspondence-theoretical foundation and internal dynamics. As an example the case of Hooke-type force is illustrated, where the internal motions are elliptic oscillations in the center-of-mass frame. Its quantum theory just reproduces the original form of bilocal theory giving bound states lying on a straightly rising trajectory and on its daughter trajectories. (auth.)
Strong-field relativistic processes in highly charged ions
Energy Technology Data Exchange (ETDEWEB)
Postavaru, Octavian
2010-12-08
In this thesis we investigate strong-field relativistic processes in highly charged ions. In the first part, we study resonance fluorescence of laser-driven highly charged ions in the relativistic regime by solving the time-dependent master equation in a multi-level model. Our ab initio approach based on the Dirac equation allows for investigating highly relativistic ions, and, consequently, provides a sensitive means to test correlated relativistic dynamics, bound-state quantum electrodynamic phenomena and nuclear effects by applying coherent light with x-ray frequencies. Atomic dipole or multipole moments may be determined to unprecedented accuracy by measuring the interference-narrowed fluorescence spectrum. Furthermore, we investigate the level structure of heavy hydrogenlike ions in laser beams. Interaction with the light field leads to dynamic shifts of the electronic energy levels, which is relevant for spectroscopic experiments. We apply a fully relativistic description of the electronic states by means of the Dirac equation. Our formalism goes beyond the dipole approximation and takes into account non-dipole effects of retardation and interaction with the magnetic field components of the laser beam. We predicted cross sections for the inter-shell trielectronic recombination (TR) and quadruelectronic recombination processes which have been experimentally confirmed in electron beam ion trap measurements, mainly for C-like ions, of Ar, Fe and Kr. For Kr{sup 30}+, inter-shell TR contributions of nearly 6% to the total resonant photorecombination rate were found. (orig.)
Relativistic ''potential model'' for N-particle systems
International Nuclear Information System (INIS)
Noyes, H.P.
1986-08-01
Neither quantum field theory nor S-Matrix theory have a well defined procedure for going over to an approximation that can be reliably used in non-relativistic models for nuclear physics. We meet the problem here by constructing a finite particle number relativistic scattering theory for (scalar) particles and mesons using integral equations of the Faddeev-Yakubovsky type. Restricted to N particles and one meson, we can go from the relativistic theory to a ''potential theory'' in the integral equation formulation by using boundary states which do not contain the meson asymptotically. The meson-particle input amplitudes contain a pole at the particle mass, and the particle-particle input amplitudes are null. This gives unique definition (numerically calculable) to the particle-particle off-shell amplitude, and hence to the covariant ''scattering potential'' (but not to the noninvariant concept of ''potential energy''). As we have commented before, if we take these scattering amplitudes as iput for relativistic Faddeev equations, the results are identical to those obtained from the same model starting from three particles and one meson. In this paper we explore how far we can extend this relativistic ''potential model'' to higher numbers of particles and mesons. 10 refs
Relativistic quantum chemistry on quantum computers
DEFF Research Database (Denmark)
Veis, L.; Visnak, J.; Fleig, T.
2012-01-01
The past few years have witnessed a remarkable interest in the application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, proof-of-principle experimental realizations have been reported. However, so far only...... the nonrelativistic regime (i.e., the Schrodinger equation) has been explored, while it is well known that relativistic effects can be very important in chemistry. We present a quantum algorithm for relativistic computations of molecular energies. We show how to efficiently solve the eigenproblem of the Dirac......-Coulomb Hamiltonian on a quantum computer and demonstrate the functionality of the proposed procedure by numerical simulations of computations of the spin-orbit splitting in the SbH molecule. Finally, we propose quantum circuits with three qubits and nine or ten controlled-NOT (CNOT) gates, which implement a proof...
Relativistic theory of tidal Love numbers
International Nuclear Information System (INIS)
Binnington, Taylor; Poisson, Eric
2009-01-01
In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.
Fundamental relativistic solution for the rail gun
International Nuclear Information System (INIS)
Liboff, R.L.; Schenter, G.K.
1986-01-01
A fully relativistic analysis is made of the dynamics of a rail gun based on three assumptions: (1) Ohm's law is valid in the rest frame of the plasma, (2) total electron momentum is transferred to the projectile, and (3) motion of the projectile is constrained to one direction. With these assumptions, a relativistic equation for the velocity of the projectile is obtained, whose solution monotonically increases to one of two values depending on field strengths. For B>E, the maximum velocity is cE/B, whereas for E>B it is c, where c is the speed of light, and E and B are applied electric and magnetic fields, respectively (in cgs)
Non-modal stability analysis and transient growth in a magnetized Vlasov plasma
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.
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.
Non-modal stability analysis and transient growth in a magnetized Vlasov plasma
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.
International Nuclear Information System (INIS)
Kahana, S.
1986-01-01
The role of the nuclear equation of state in determining the fate of the collapsing cores of massive stars is examined in light of both recent theoretical advances in this subject and recent experimental measurements with relativistic heavy ions. The difficulties existing in attempts to bring the softer nuclear matter apparently required by the theory of Type II supernovae into consonance with the heavy ion data are discussed. Relativistic mean field theory is introduced as a candidate for derivation of the equation of state, and a simple form for the saturation compressibility is obtained. 28 refs., 4 figs., 1 tab
Energy Technology Data Exchange (ETDEWEB)
Kahana, S.
1986-01-01
The role of the nuclear equation of state in determining the fate of the collapsing cores of massive stars is examined in light of both recent theoretical advances in this subject and recent experimental measurements with relativistic heavy ions. The difficulties existing in attempts to bring the softer nuclear matter apparently required by the theory of Type II supernovae into consonance with the heavy ion data are discussed. Relativistic mean field theory is introduced as a candidate for derivation of the equation of state, and a simple form for the saturation compressibility is obtained. 28 refs., 4 figs., 1 tab.
Fundamentals of equations of state
Eliezer, Shalom; Hora, Heinrich
2002-01-01
The equation of state was originally developed for ideal gases, and proved central to the development of early molecular and atomic physics. Increasingly sophisticated equations of state have been developed to take into account molecular interactions, quantization, relativistic effects, etc. Extreme conditions of matter are encountered both in nature and in the laboratory, for example in the centres of stars, in relativistic collisions of heavy nuclei, in inertial confinement fusion (where a temperature of 10 9 K and a pressure exceeding a billion atmospheres can be achieved). A sound knowledg
Electron-acoustic Instability Simulated By Modified Zakharov Equations
Jásenský, V.; Fiala, V.; Vána, O.; Trávnícek, P.; Hellinger, P.
We present non-linear equations describing processes in plasma when electron - acoustic waves are excited. These waves are present for instance in the vicinity of Earth's bow shock and in the polar ionosphere. Frequently they are excited by an elec- tron beam in a plasma with two electron populations, a cold and hot one. We derive modified Zakharov equations from kinetic theory for such a case together with numer- ical method for solving of this type of equations. Bispectral analysis is used to show which non-linear wave processes are of importance in course of the instability. Finally, we compare these results with similar simulations using Vlasov approach.
Equation with the many fathers
DEFF Research Database (Denmark)
Kragh, Helge
1984-01-01
In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein-Gordon equation. In 1926 several physicists, among them Klein, Fock, Schrödinger, and de Broglie, announced this equation as a candidate for a relativistic generalization of the us...... as electrodynamics. Although this ambitious attempt attracted some interest in 1926, its impact on the mainstream of development in quantum mechanics was virtually nil....... of the usual Schrödinger equation. In most of the early versions the Klein-Gordon equation was connected with the general theory of relativity. Klein and some other physicists attempted to express quantum mechanics within a five-dimensional unified theory, embracing general relativity as well...
Towards an exact relativistic theory of Earth's geoid undulation
International Nuclear Information System (INIS)
Kopeikin, Sergei M.; Mazurova, Elena M.; Karpik, Alexander P.
2015-01-01
The present paper extends the Newtonian concept of the geoid in classic geodesy towards the realm of general relativity by utilizing the covariant geometric methods of the perturbation theory of curved manifolds. It yields a covariant definition of the anomalous (disturbing) gravity potential and formulates differential equation for it in the form of a covariant Laplace equation. The paper also derives the Bruns equation for calculation of geoid's height with full account for relativistic effects beyond the Newtonian approximation. A brief discussion of the relativistic Bruns formula is provided. - Highlights: • We apply general relativity to define the exact concept of relativistic geoid. • We derive relativistic equation of geoid and the reference level surface. • We employ the manifold perturbation theory to discuss geoid's undulation
Towards an exact relativistic theory of Earth's geoid undulation
Energy Technology Data Exchange (ETDEWEB)
Kopeikin, Sergei M., E-mail: kopeikins@missouri.edu [Department of Physics & Astronomy, University of Missouri, Columbia, MO 65211 (United States); Siberian State Geodetic Academy, 10 Plakhotny St., Novosibirsk 630108 (Russian Federation); Mazurova, Elena M., E-mail: e_mazurova@mail.ru [Moscow State University of Geodesy and Cartography, 4 Gorokhovsky Alley, Moscow 105064 (Russian Federation); Siberian State Geodetic Academy, 10 Plakhotny St., Novosibirsk 630108 (Russian Federation); Karpik, Alexander P., E-mail: rector@ssga.ru [Siberian State Geodetic Academy, 10 Plakhotny St., Novosibirsk 630108 (Russian Federation)
2015-08-14
The present paper extends the Newtonian concept of the geoid in classic geodesy towards the realm of general relativity by utilizing the covariant geometric methods of the perturbation theory of curved manifolds. It yields a covariant definition of the anomalous (disturbing) gravity potential and formulates differential equation for it in the form of a covariant Laplace equation. The paper also derives the Bruns equation for calculation of geoid's height with full account for relativistic effects beyond the Newtonian approximation. A brief discussion of the relativistic Bruns formula is provided. - Highlights: • We apply general relativity to define the exact concept of relativistic geoid. • We derive relativistic equation of geoid and the reference level surface. • We employ the manifold perturbation theory to discuss geoid's undulation.
Solid neutron matter the energy density in the relativistic harmonic approximation
International Nuclear Information System (INIS)
Cattani, M.; Fernandes, N.C.
A relativistic expression for the energy density as a function of particle density for solid neutron matter is obtained using Dirac's equation with a truncated harmonic potential. Ultrabaric and superluminous effects are not found in our approach [pt
The relativistic gravity train
Seel, Max
2018-05-01
The gravity train that takes 42.2 min from any point A to any other point B that is connected by a straight-line tunnel through Earth has captured the imagination more than most other applications in calculus or introductory physics courses. Brachystochron and, most recently, nonlinear density solutions have been discussed. Here relativistic corrections are presented. It is discussed how the corrections affect the time to fall through Earth, the Sun, a white dwarf, a neutron star, and—the ultimate limit—the difference in time measured by a moving, a stationary and the fiducial observer at infinity if the density of the sphere approaches the density of a black hole. The relativistic gravity train can serve as a problem with approximate and exact analytic solutions and as numerical exercise in any introductory course on relativity.
Relativistic studies in actinides
International Nuclear Information System (INIS)
Weinberger, P.; Gonis, A.
1987-01-01
In this review the theoretical background is given for a relativistic description for actinide systems. A short introduction is given of the density functional theory which forms the basis for a fully relativistic single-particle theory. A section on the Dirac Hamiltonian is followed by a brief summary on group theoretical concepts. Single site scattering is presented such that formal extensions to the case of the presence of an internal (external) magnetic field and/or anisotropic scattering are evident. Multiple scattering is discussed such that it can readily be applied also to the problem of dislocations. In connection with the problem of selfconsistency particular attention is drawn to the use of complex energies. Finally the various theoretical aspects discussed are illustrated through the results of numerical calculations. 101 refs.; 37 figs.; 5 tabs
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
Relativistic quantum transport theory approach to multiparticle production
International Nuclear Information System (INIS)
Carruthers, P.; Zachariasen, F.
1976-01-01
The field-theoretic description of multiparticle production processes is cast in a form analogous to ordinary transport theory. Inclusive differential cross sections are shown to be given by integrals of covariant phase-space distributions. The single-particle distribution function F (p, R) is defined as the Fourier transform of a suitable correlation function in analogy with the nonrelativistic (Wigner) phase-space distribution function. Its transform F (p, q) is observed to be essentially the discontinuity of a multiparticle scattering amplitude. External-field problems are studied to exhibit the physical content of the formalism. When q = 0 one recovers the single-particle distribution exactly. The equation of motion for F (p, R) generates an infinite hierarchy of coupled equations for various distribution functions. In the Hartree approximation one obtains nonlinear integral equations analogous to the Vlasov equation in plasma physics. Such equations are convenient for exhibiting collective motions; in particular it appears that a collective mode exists in a phi 4 theory for a uniform infinite medium. It is speculated that such collective modes could provide a theoretical basis for clustering effects in multiparticle production
Relativistic three-body model of pion-deuton elasic scattering
International Nuclear Information System (INIS)
Giraud, Noel.
1978-01-01
The Aaron-Amado-Young equations for the relativistic three-body problem are derived following the Blauckenbecker - Sugar method. The angular momentum reduction is carried out using suitable relative momenta. The pion-deuteron elastic scattering is calculated using the equations in which relativistic kinematics are retained only for the pion. After a general study of the observables in the energy range 25 to 256 MeV, detailed calculations are performed at 142 MeV [fr
International Nuclear Information System (INIS)
Hines, D.F.; Frankel, N.E.
1979-01-01
The charged Bose has been previously studied as a many body problem of great intrinsic interest which can also serve as a model of some real physical systems, for example, superconductors, white dwarf stars and neutron stars. In this article the excitation spectrum of a relativistic spin-zero charged Bose gas is obtained in a dielectric response formulation. Relativity introduces a dip in the spectrum and consequences of this dip for the thermodynamic functions are discussed
Relativistic heavy ion reactions
Energy Technology Data Exchange (ETDEWEB)
Brink, D M
1989-08-01
The theory of quantum chromodynamics predicts that if nuclear matter is heated to a sufficiently high temperature then quarks might become deconfined and a quark-gluon plasma could be produced. One of the aims of relativistic heavy ion experiments is to search for this new state of matter. These lectures survey some of the new experimental results and give an introduction to the theories used to interpret them. 48 refs., 4 tabs., 11 figs.