Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-24T03:56:26.808Z Has data issue: false hasContentIssue false
  • English
  • Français

Unified kinetic theory of plasma correlations

Published online by Cambridge University Press:  13 March 2009

Michael A. Guillen  and
Richard L. Liboff
Michael A. Guillen
Affiliation:
Schools of Electrical Engineering and Applied Physics, Cornell University, Ithaca, NY 14853, U.S.A.
Richard L. Liboff
Affiliation:
Schools of Electrical Engineering and Applied Physics, Cornell University, Ithaca, NY 14853, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

A unified approach to the kinetic theory of correlations in a plasma is presented, based on the BBKGY hierarchy. The theory is applied to a one-component plasma with the Coulomb interaction modified to include effects of the background. Closed integro-differential equations in space, momentum and time are obtained for the two-particle correlation function in both the strong and weak coupling limits. To corroborate the theory, the formalism is applied in the equilibrium limit. In the weak-coupling domain, γ ≪ 1, the time-independent analysis returns the well-known linearized Debye-Hückel result, where γ is the plasma parameter. In the strong-coupling domain with γ ≥ 1, the resulting two-particle ‘total’ correlation function exhibits decaying oscillatory behaviour for particle separation of the order of the effective interparticle range. Exponential behaviour of the correlation function found for small values of particle separation agrees with previous results of statistical mechanics.

Type
Research Article
Information
Journal of Plasma Physics , Volume 32 , Issue 1 , August 1984 , pp. 81 - 98
Copyright
Copyright © Cambridge University Press 1984

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. 1960 Phys. Fluids, 3, 52.CrossRefGoogle Scholar
Baus, M. & Hansen, J. P. 1980 Phys. Repts. 59, 1.CrossRefGoogle Scholar
Berggren, K. F. 1970 Phys. Rev. A 1, 1783.CrossRefGoogle Scholar
Bogoliubov, N. N. 1946 Problemi Dynamitcheskii Theorie v Statistitcheskey Phisike, OGIS, Moscow.Google Scholar
Bowers, D. L. & Salpeter, E. E. 1960 Phys. Rev. 119, 1180.CrossRefGoogle Scholar
Brush, S. G., Sahlin, H. L. & Teller, E. 1966 J. Chem. Phys. 45, 2102.CrossRefGoogle Scholar
Carley, D. D. 1963 Phys. Rev. 131, 1406.CrossRefGoogle Scholar
Caroff, L. J. & Liboff, R. L. 1970 J. Plasma Phys. 4, 83.CrossRefGoogle Scholar
Cauble, R. & Duderstadt, J. J. 1981 Phys. Rev. A 23, 3182.CrossRefGoogle Scholar
Cooper, M. S. 1973 Phys. Rev. A 7, 1.CrossRefGoogle Scholar
Debye, P. & Hückel, E. 1923 Phys. Z. 24, 185.Google Scholar
Dupree, T. H. 1961 Phys. Fluids, 4, 696.CrossRefGoogle Scholar
Frieman, E. A. & Book, D. L. 1963 Phys. Fluids, 6, 1700.CrossRefGoogle Scholar
Golden, K. I., Kalman, G. & Silevitch, M. B. 1974 Phys. Rev. Lett. 33, 1954.CrossRefGoogle Scholar
Goodstein, D. L. 1975 States of Matter. Prentice-Hall.Google Scholar
Gould, H., Palmer, R. G. & Estevex, G. A. 1979 J. Stat. Phys. 21, 55.CrossRefGoogle Scholar
Hirt, C. W. 1967 Phys. Fluids, 10, 565.CrossRefGoogle Scholar
Ichimaru, S. 1970 Phys. Rev. A 2, 494.CrossRefGoogle Scholar
Ichimaru, S. 1982 Revs. Mod. Phys. 54, 1017.CrossRefGoogle Scholar
Ichimaru, S. & Nakono, T. 1967 Phys. Lett. 25 A, 168.CrossRefGoogle Scholar
Ichimaru, S. & Nakono, T. 1968 Phys. Rev. 165, 231CrossRefGoogle Scholar
Ince, E. L. 1927 Ordinary Differential Equations. Longmans, Green and Co.Google Scholar
Ishihara, A. 1971 Statistical Physics. Academic.Google Scholar
Kalman, G., Datta, T. & Golden, K. I. 1975 Phys. Rev. A 12, 1125.CrossRefGoogle Scholar
Kalman, G. & Carini, P. 1978 Strongly Coupled Plasmas. Plenum.CrossRefGoogle Scholar
Kamke, E. 1943 Differentialgleichungen. Academische.Google Scholar
Krall, N. A. & Trivelpiece, A. W. 1973 Principles of Plasma Physics. McGraw-Hill.CrossRefGoogle Scholar
Kunkell, W. B. 1966 Plasma Physics in Theory and Application. McGraw-Hill.Google Scholar
Lamb, G. L. & Burdick, B. 1964 Phys. Fluids, 7, 1087.CrossRefGoogle Scholar
Landau, L. D., Lifshitz, E. M. & Pitaevskii, L. P. 1981 Physical Kinetics. Pergamon.Google Scholar
Lenard, A. 1960 Ann. Phys. 3, 390.CrossRefGoogle Scholar
Levitt, L. C., Richardson, J. M. & Cohen, E. R. 1967 Phys. Fluids, 10, 406.CrossRefGoogle Scholar
Liboff, R. L. 1963 Phys. Rev. 131, 2218.CrossRefGoogle Scholar
Liboff, R. L. 1979 Introduction to the Theory of Kinetic Equations. Krieger.Google Scholar
Liboff, R. L. 1981 Introductory Quantum Mechanics. Holden Day.Google Scholar
Liboff, R. L. & Perona, G. E. 1967 J. Math. Phys. 8, 2001.CrossRefGoogle Scholar
Liboff, R. L. & Merchant, A. H. 1973 J. Math. Phys. 14, 119.Google Scholar
Liboff, R. L. 1984 J. Math. Phys. (To be published.)Google Scholar
Mayer, J. E. & Mayer, M. G. 1940 Statistical Mechanics. Wiley.Google Scholar
McQuarrie, D. A. 1976 Statistical Mechanics. Harper and Row.Google Scholar
Pollock, E. L. & Hansen, J. P. 1973 Phys. Rev. A 8, 3110.CrossRefGoogle Scholar
Rosenfeld, Y. & Ashcroft, W. W. 1979 Phys. Rev. A 20, 1208.CrossRefGoogle Scholar
Rostoker, N. & Rosenbluth, M. N. 1960 Phys. Fluids, 4, 83.Google Scholar
Sandri, G. 1963 Ann. Phys. 24, 332.CrossRefGoogle Scholar
Slattery, W. I., Doolen, G. D. & DeWitt, H. E. 1980 Phys. Rev. A 21, 2087.CrossRefGoogle Scholar
Slattery, W. I., Doolen, G. D. & DeWitt, H. E. 1982 Phys. Rev. A 26, 2255.CrossRefGoogle Scholar
Whittaker, E. T. & Watson, G. N. 1952 A Course of Modern Analysis, 2nd ed.Cambridge University Press.Google Scholar
Widom, B. 1963 J. Chem. Phys. 39, 2808.CrossRefGoogle Scholar