Kinetic equations for plasmas subjected to a strong time-dependent external field. Part 1. General theory

1974 ◽  
Vol 11 (3) ◽  
pp. 357-375 ◽  
Author(s):  
R. Balescu ◽  
J. H. Misguich
Keyword(s):  
Distribution Function ◽  
Kinetic Equation ◽  
General Theory ◽  
External Field ◽  
Projection Operator ◽  
Nonlinear Response ◽  
Particle Distribution ◽  
Kinetic Equations ◽  
Time Dependent ◽  
Distribution Vector

It is shown that the concept of subdynamics introduced by Prigogine, George & Henin, and extended by Balescu & Wallenborn, can be generalized nontrivially to systems submitted to time-dependent external fields. The distribution vector of the system is split into two components by means of a time- dependent projection operator. Each of these obeys an independent equation of evolution. The description of the evolution of one of these components (the superkinetic component) can be reduced to a kinetic equation for a one-particle distribution function. It is shown that, when the external field vanishes for all times t ≤ t0, and if the system has reached a (field-free) equilibrium (or a ‘kinetic state’) at time t0, then for t ≥ t0 the kinetic equation derived here provides an exact and complete description of the evolution. A general expression for the nonlinear response of the system to the external field is derived.

Kinetic equations for plasmas subjected to a strong time-dependent external field: Part 3. Stochastic equations for plasma turbulence

1975 ◽  
Vol 13 (1) ◽  
pp. 33-51 ◽  
Author(s):  
R. Balescu ◽  
J. H. Misguich
Keyword(s):  
Distribution Function ◽  
Kinetic Equation ◽  
External Field ◽  
Vlasov Equation ◽  
General Equation ◽  
Kinetic Equations ◽  
Plasma Turbulence ◽  
Stochastic Equations ◽  
Time Dependent ◽  
Average Distribution

The kinetic equation obtained in parts 1 and 2 is treated stochastically: the external field is stochastic, with an average and a fluctuating part. The turbulence of the system is described by the induced fluctuations in the plasma, and a general equation is derived for the average distribution function. As a particular case, the stochastic Vlasov equation is treated explicitly, and compared with the descriptions of Dupree, Weinstock and Benford & Thomson.

Kinetic equations for plasmas subjected to a strong time-dependent extenal field. Part 2. The weak-interaction approximation

1974 ◽  
Vol 11 (3) ◽  
pp. 377-387 ◽  
Author(s):  
R. Balescu ◽  
J. H. Misguich
Keyword(s):  
Kinetic Equation ◽  
General Theory ◽  
Weak Interaction ◽  
Weak Coupling ◽  
Kinetic Equations ◽  
Time Dependent ◽  
External Fields ◽  
Interaction Approximation

The general theory developed in part 1 is illustrated for a plasma described by the weak-coupling (Landau) approximation. The kinetic equation, valid for arbitrarily strong external fields, is written out explicitly.

Kinetic equations for plasmas subjected to a strong time-dependent external field: Part 4. Dynamics of stochastic correlations

1975 ◽  
Vol 13 (1) ◽  
pp. 53-61 ◽  
Author(s):  
R. Balescu ◽  
J. H. Misguich
Keyword(s):  
Kinetic Equation ◽  
External Field ◽  
Initial Conditions ◽  
Kinetic Equations ◽  
Time Dependent ◽  
Close Analogy ◽  
Closed Equation ◽  
Average Function

In close analogy with part 1, the dynamics of stochastic correlations is used to reformulate the preceding treatment of turbulent equations. The result is an exact and closed equation for an average function, involving only asymptotic stochastic correlations, and no initial fluctuation. This stochastic kinetic equation is valid for all initial conditions, and the corresponding function is a significant particular projection on an independent subspace R(t).

scholarly journals Boltzmann Equation Theory of Charged Particle Transport in Neutral Gases: Perturbation Treatment

1999 ◽  
Vol 52 (6) ◽  
pp. 999 ◽  
Author(s):  
Slobodan B. Vrhovac ◽  
Zoran Lj. Petrovic
Keyword(s):  
Distribution Function ◽  
Perturbation Theory ◽  
Charged Particle ◽  
Boltzmann Equation ◽  
Particle Transport ◽  
Kinetic Equations ◽  
Initial Distribution ◽  
Formal Structure ◽  
Time Dependent ◽  
Charged Particle Transport

This paper examines the formal structure of the Boltzmann equation (BE) theory of charged particle transport in neutral gases. The initial value problem of the BE is studied by using perturbation theory generalised to non-Hermitian operators. The method developed by R�sibois was generalised in order to be applied for the derivation of the transport coecients of swarms of charged particles in gases. We reveal which intrinsic properties of the operators occurring in the kinetic equation are sucient for the generalised diffusion equation (GDE) and the density gradient expansion to be valid. Explicit expressions for transport coecients from the (asymmetric) eigenvalue problem are also deduced. We demonstrate the equivalence between these microscopic expressions and the hierarchy of kinetic equations. The establishment of the hydrodynamic regime is further analysed by using the time-dependent perturbation theory. We prove that for times t ? τ0 (τ0 is the relaxation time), the one-particle distribution function of swarm particles can be transformed into hydrodynamic form. Introducing time-dependent transport coecients ? *(p) (?q,t), which can be related to various Fourier components of the initial distribution function, we also show that for the long-time limit all ? *(p) (?q,t) become time and ?q independent in the same characteristic time and achieve their hydrodynamic values.

An action principle for the Vlasov equation and associated Lie perturbation equations. Part 2. The Vlasov–Maxwell system

1993 ◽  
Vol 49 (2) ◽  
pp. 255-270 ◽  
Author(s):  
Jonas Larsson
Keyword(s):  
Distribution Function ◽  
Vlasov Equation ◽  
Maxwell Equations ◽  
Particle Distribution ◽  
Action Principle ◽  
Time Dependent ◽  
Maxwell System ◽  
Dynamical Equations ◽  
Hamiltonian Structures ◽  
Small Parameters

An action principle for the Vlasov–Maxwell system in Eulerian field variables is presented. Thus the (extended) particle distribution function appears as one of the fields to be freely varied in the action. The Hamiltonian structures of the Vlasov–Maxwell equations and of the reduced systems associated with small-ampliltude perturbation calculations are easily obtained. Previous results for the linearized Vlasov–Maxwell system are generalized. We find the Hermitian structure also when the background is time-dependent, and furthermore we may now also include the case of non-Hamiltonian perturbations within the Hamiltonian-Hermitian context. The action principle for the Vlasov–Maxwell system appears to be suitable for the derivation of reduced dynamical equations by expanding the action in various small parameters.

Numerical Study of Nonequilibrium Diagram Theory

1972 ◽  
Vol 50 (4) ◽  
pp. 317-335 ◽  
Author(s):  
Gary R. Dowling ◽  
H. Ted Davis
Keyword(s):  
Distribution Function ◽  
Correlation Function ◽  
Kinetic Equation ◽  
Numerical Study ◽  
Pair Correlation ◽  
Transport Coefficients ◽  
Kinetic Equations ◽  
Collision Operator ◽  
Dense Fluid ◽  
Equilibrium Pair

In this paper we numerically analyze the first few diagrams in a Boltzmann-like collision operator that occurs in Severne's exact kinetic equation for the singlet distribution function. A similar analysis was used by Allen and Cole in deriving their singlet and doublet kinetic equations. Our analysis shows that the diagrams neglected by Allen and Cole in their kinetic equations are not negligible and these should be incorporated into dense fluid theories. The Allen–Cole kinetic transport coefficients and equilibrium pair correlation function are presented and calculated for dense argon. These results are not promising.

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