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A retarded time superposition principle and the relativistic collision operator

Published online by Cambridge University Press:  13 March 2009

K. Hizanidis ,
K. Molvig  and
K. Swartz
K. Hizanidis
Affiliation:
Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
K. Molvig
Affiliation:
Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
K. Swartz
Affiliation:
Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
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Abstract

A retarded time superposition principle is formulated and proved for the two particle correlation function in a multi-species relativistic, and fully electro-magnetic, plasma. This principle is used to obtain the relativistic collision operator. Starting from the relativistic Klimontovich equation, the statistical (Liouville) average of the Klimontovich equation yields an expression for the collision operator in terms of the two-time two-point correlation function for two particles, G12(1, t12, t2). It is proved that G12(1, t12, t2) can be written in a retarded time superposition form in terms of the self-correlation W11(1, t12, t2) and the discreteness response function P(1, t12, t2). The equation for the pair correlation function G12(1, t12, t2), excluding triplet or higher-order correlations, is thus replaced by the simpler equation for P(1, t12, t2). This is the test particle problem which relates P(1, t12, t2) to the discreteness source term W11(1, t12, t2). The equations for P(1, t12, t2). and W11(1, t12, t2) are solved for stationary, homogeneous plasmas without external fields. With these solutions, the collision operator is expressed in terms of the relativistic dielectric properties of the plasma.

Type
Research Article
Information
Journal of Plasma Physics , Volume 30 , Issue 2 , October 1983 , pp. 223 - 248
Copyright
Copyright © Cambridge University Press 1983

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