Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-07-01T11:02:36.873Z Has data issue: false hasContentIssue false

A retarded time superposition principle and the relativistic collision operator

Published online by Cambridge University Press:  13 March 2009

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

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
Copyright
Copyright © Cambridge University Press 1983

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Balescu, R.Phys. Fluids, 3, 52.CrossRefGoogle Scholar
Belyaev, S. T. & Budker, G. I. 1957 Soviet Phys. Doklady, 1, 218.Google Scholar
Bernstein, I. B., & Baxter, D. C. 1980 Science Applications Incorporated – Laboratory for Applied Plasma Studies, UC-20, G, Report no. LAPS-68 SAI-023–80–352–LJ.Google Scholar
Bezzerides, B. & DuBois, D. F. 1972 Ann. Phys. (N.Y.), 70, 10.CrossRefGoogle Scholar
Ichimaru, S. 1973 Basic Principles of Plasma Physics – A Statistical Approach. Benjamin.Google Scholar
Klimontovich, Yu. L. 1960 a Soviet Phys. JETP, 10, 524.Google Scholar
Klimontovich, Yu. L. 1960 b Soviet Phys. JETP, 11, 876.Google Scholar
Klimontovich, Yu. L. & Temko, S. V. 1958 Soviet Phys. JETP, 6, 102.Google Scholar
Landau, L. D. 1936 Phya. Z. Sowjetunion, 10, 154.Google Scholar
Landau, L. D. 1937 Zhur. Eksptl. Teoret. Fiz. 7, 203.Google Scholar
Lenard, A. 1960 Ann. Phys. (N.Y.), 10, 390.CrossRefGoogle Scholar
Møller, C. 1931 J. Physik, 70, 786.CrossRefGoogle Scholar
Rostoker, N. 1964 Phys. Fluids, 7, 479.CrossRefGoogle Scholar
Silin, V. P. 1960 Soviet Phys. JETP, 11, 1136.Google Scholar
Silin, V. P. 1961 Soviet Phys. JETP, 13, 1244.Google Scholar