Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T13:39:45.535Z Has data issue: false hasContentIssue false
  • English
  • Français

Kinetic theory of a two-dimensional magnetized plasma. Part 2. Balescu-Lenard limit

Published online by Cambridge University Press:  13 March 2009

George Vahala
George Vahala
Affiliation:
Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee
Get access Rights & Permissions [Opens in a new window]

Abstract

The kinetic theory of a two-dimensional one-species plasma in a uniform d.c. magnetic field is investigated in the small plasma parameter limit. The plasma consists of charged rods interacting through the logarithmic Coulomb potential. Vahala & Montgomery earlier derived a Fokker –;Planck equation for this system, but it contained a divergent integral, which had to be cut-off on physical grounds. This cut-off is compared to the standard cut-off introduced in the two-dimensional unmagnetized Fokker –;Planck equation. In the small plasma parameter limit, it is shown (under the assumption that for large integer n, γn/γn+1 = O(np), with p < 2, where γn = ωn −nΩ. with ωn the nth. Bernstein mode and Q the electron gyro frequency) that the Balescu-Lenard collision term is zero in the long time average limit if one considers only two-body interactions. The energy transfer from a test particle to an equilibrium plasma is discussed and also shown to be zero in the long time average limit. This supports the unexpected result of zero Balescu-Lenard collision term.

Type
Research Article
Information
Journal of Plasma Physics , Volume 8 , Issue 3 , December 1972 , pp. 357 - 374
Copyright
Copyright © Cambridge University Press 1972

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

Bernstein, I. B. 1958 Phys. Rev. 109, 10.Google Scholar
Haggerty, M. J. 1965 Canad. J. Phys. 43, 122, 1750.Google Scholar
Haggerty, M. J. & De, Sobrino L. G. 1964 Canad. J. Phys. 42, 1969.CrossRefGoogle Scholar
Joyce, G. & Montgomery, D. 1967 Phys. Fluids, 10, 2017.CrossRefGoogle Scholar
Montgomery, D. 1967 Kinetic Theory. Lectures in Theor. Phys. 9C (ed. Brittin, W., Barut, A. and Guenin, M.), p. 15. Gordon and Breach.Google Scholar
Montgomery, D. 1971 Theory of the Unmagnetized Plasma. Gordon and Breach.Google Scholar
Montgomery, D. & Tidman, D. A. 1964 Plasma Kinetic Theory. McGraw-Hill.Google Scholar
Rostoker, N. 1960 Phys. Fluids, 3, 922.CrossRefGoogle Scholar
Rostoker, N. 1961 Nucl. Fusion, 1, 101.CrossRefGoogle Scholar
Rutherford, P. H. & Frieman, E. A. 1963 Phys. Fluids, 6, 1139.CrossRefGoogle Scholar
Schram, P. P. J. M. 1969 Physica, 45, 165.CrossRefGoogle Scholar
Thompson, W. B. 1962 An Introduction to Plasma Physics. Pergamon.Google Scholar
Thompson, W. B. & Hubbard, J. 1960 Rev. Mod. Phys. 32, 714.CrossRefGoogle Scholar
Vahala, G. & Montgomery, D. 1971 J. Plasma Phys. 6, 425.Google Scholar
Watson, G. N. 1944 A Treatise on the Theory of Bessel Functions (2nd edn.) Cambridge University Press.Google Scholar