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

Abstract

In this work, we establish the plasma kinetic equations starting from the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy of equations. We demonstrate that relations existing between correlation functions may help to justify the truncation of the hierarchy. Then we obtain the kinetic equations of a stable or unstable plasma. They do not reduce to an equation for the one-body distribution function, but generally involve two coupled equations for the one-body distribution function and the spectral density of the fluctuating electric field. We study limiting cases where the Balescu-Lenard equation, the quasi-linear theory, the Pines-Schrieffer equations and the equations of weak turbulence in the random phase approximation are recovered. At last we generalise the H-theorem for the system of equations and we define conditions for irreversible behaviour. (authors) [French] Dans ce travail nous etablissons les equations cinetiques d'un plasma a partir des equations de la recurrence de Bogoliubov, Born, Green, Kirkwood et Yvon. Nous demontrons qu'entre les fonctions de correlation d'un plasma existent des relations qui permettent de justifier la troncature de la recurrence. Nous obtenons alors les equations cinetiques d'un plasma stable ou instable. En general elles ne se reduisent pas a une equation d'evolution pour la densite simple, mais se composent de deux  More>>
Authors:
Laval, G; Pellat, R [1] 
  1. Commissariat a l'Energie Atomique, Fontenay-aux-Roses (France). Centre d'Etudes Nucleaires
Publication Date:
Jul 01, 1968
Product Type:
Technical Report
Report Number:
CEA-R-3525
Resource Relation:
Other Information: 72 refs; PBD: 1968
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BBGKY EQUATION; CORRELATION FUNCTIONS; DISTRIBUTION FUNCTIONS; H THEOREM; IONIZED GASES; KINETIC EQUATIONS; PLASMA; SPECTRAL DENSITY; THERMALIZATION
OSTI ID:
20523310
Research Organizations:
CEA Fontenay-aux-Roses, 92 (France)
Country of Origin:
France
Language:
French
Other Identifying Numbers:
TRN: FR04R3525091365
Availability:
Available from INIS in electronic form
Submitting Site:
FRN
Size:
[138] pages
Announcement Date:
Dec 10, 2004

Citation Formats

Laval, G, and Pellat, R. Kinetic equations for an unstable plasma; Equations cinetiques d'un plasma instable. France: N. p., 1968. Web.
Laval, G, & Pellat, R. Kinetic equations for an unstable plasma; Equations cinetiques d'un plasma instable. France.
Laval, G, and Pellat, R. 1968. "Kinetic equations for an unstable plasma; Equations cinetiques d'un plasma instable." France.
@misc{etde_20523310,
title = {Kinetic equations for an unstable plasma; Equations cinetiques d'un plasma instable}
author = {Laval, G, and Pellat, R}
abstractNote = {In this work, we establish the plasma kinetic equations starting from the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy of equations. We demonstrate that relations existing between correlation functions may help to justify the truncation of the hierarchy. Then we obtain the kinetic equations of a stable or unstable plasma. They do not reduce to an equation for the one-body distribution function, but generally involve two coupled equations for the one-body distribution function and the spectral density of the fluctuating electric field. We study limiting cases where the Balescu-Lenard equation, the quasi-linear theory, the Pines-Schrieffer equations and the equations of weak turbulence in the random phase approximation are recovered. At last we generalise the H-theorem for the system of equations and we define conditions for irreversible behaviour. (authors) [French] Dans ce travail nous etablissons les equations cinetiques d'un plasma a partir des equations de la recurrence de Bogoliubov, Born, Green, Kirkwood et Yvon. Nous demontrons qu'entre les fonctions de correlation d'un plasma existent des relations qui permettent de justifier la troncature de la recurrence. Nous obtenons alors les equations cinetiques d'un plasma stable ou instable. En general elles ne se reduisent pas a une equation d'evolution pour la densite simple, mais se composent de deux equations couplees portant sur la densite simple et la densite spectrale du champ electrique fluctuant. Nous etudions le cas limites ou l'on retrouve l'equation de Balescu-Lenard, les equations de la theorie quasi-lineaire, les equations de Pines et Schrieffer et les equations de la turbulence faible dans l'approximation des phases aleatoires. Enfin, nous generalisons le theoreme H pour ce systeme d'equations et nous precisons les conditions d'evolution irreversible. (auteurs)}
place = {France}
year = {1968}
month = {Jul}
}