Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-29T18:14:58.295Z Has data issue: false hasContentIssue false
  • English
  • Français

Extension of Doughterty's model Fokker–Planck equation for a plasma

Published online by Cambridge University Press:  13 March 2009

Robert J. Papa
Robert J. Papa
Affiliation:
Air Force Cambridge Research Laboratories, L. G. Hansom Field, Bedford, Massachusetts
Get access Rights & Permissions [Opens in a new window]

Abstract

A generalization of the Appleton–Hartree equation is made to include the effects of energy-dependent electron-neutron collisions, Coulomb encounters and spatial dispersion. The frequency of electromagnetic waves propagating in a magneto-plasma is sufficiently high that the ion motion may be neglected compared with the electron motion. The present analysis extends Dougherty (1963, 1964) to include the simultaneous effect on wave propagation of Coulomb forces, spatial dispersion and energy-dependent electron-neutral collisions, where one or more of these effects can have a significant influence on circularly polarized waves propagating at frequencies near electron cyclotron resonance. The electrical conductivity tensor is expressible in terms of appropriate velocity moments of the electron distribution function. The electron velocity distribution function is determined by expanding the inverse of the differential operator of the linearized kinetic equation in a small parameter ε2', where in one case ε2 is the ratio of Coulomb collision frequency to signal frequency, and in the second case ε2 is the ratio of electron-neutral collision frequency to signal frequency. For wave propagation along the magnetic field, the dispersion relations for right-hand and left-hand circularly polarized waves, and also the dispersion relation for longitudinal waves, are solved numerically, and graphs are presented to show the effects of collisionless damping, velocity dependent electron-neutral collisions and Coulomb collisions.

Type
Research Article
Information
Journal of Plasma Physics , Volume 11 , Issue 1 , February 1974 , pp. 11 - 35
Copyright
Copyright © Cambridge University Press 1974

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

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. National Bureau of Standards.Google Scholar
Bachynski, M. P. & Gibbs, B. W. 1966 a Phys. Fluids, 9, 520.CrossRefGoogle Scholar
Bachynski, M. P. & Gibbs, B. W. 1966 b Phys. Fluids, 9, 532.CrossRefGoogle Scholar
Bakshi, P. M., Haskell, R. E. & Papa, R. J. 1968 Canadian J. Phys. 46, 1547.CrossRefGoogle Scholar
Bernstein, I. B. 1958 Phys. Rev. 109, 10.CrossRefGoogle Scholar
Bhatnagar, P. L., Gross, E. P. & Krook, M. 1954 Phys. Rev. 94, 511.CrossRefGoogle Scholar
Derfler, H. 1962 Proc. 5th Int. Conf. on Ionization Phenomena in Gases, p. 1423.Google Scholar
Dougherty, J. P. 1963 J. Fluid Mech. 16, 126.CrossRefGoogle Scholar
Dougherty, J. P. 1964 Phys. Fluids, 7, 1788.CrossRefGoogle Scholar
Ewald, H. N. 1968 Sperry Rand Res. Center Sci. Rep. 1.Google Scholar
Goldman, M. V. & Dubois, D. F. 1972 Nonlinear laser heating of a plasma. AFWL TR 72–101.Google Scholar
Holt, E. H. & Haskell, R. E. 1965 Foundations of Plasma Dynamics. Macmillan.Google Scholar
Kaw, P. K. & Dawson, J. 1969 Phys. Fluids, 12, 2586.CrossRefGoogle Scholar
Meservey, E. B. & Schlesinger, S. P. 1965 Phys. Fluids, 8, 500.CrossRefGoogle Scholar
Papa, R. J. 1970 Air Force Cambridge Res. Labs. 70–0613.Google Scholar
Papa, R. J. 1971 Ph.D. thesis, Harvard University.Google Scholar
Phelps, A. V. & Pack, J. L. 1959 Phys. Rev. Letters, 3, 340.Google Scholar
Poirier, J. L., Rotman, W., Hayes, D. T. & Lennon, J. F. 1969 Air Force Cambridge Res. Labs. 69.0354.Google Scholar
Sen, H. K. & Wyller, A. A. 1960 J. Geophys. Res. 65, 3931.CrossRefGoogle Scholar
Shkarofsky, I. P 1961 a Canadian J. Phys. 39, 1619.CrossRefGoogle Scholar
Shkarofsky, I. P. 1961 b Proc. IRE, 49, 1857.CrossRefGoogle Scholar
Simonen, T. C. 1967 Landau waves. Aerospace Res. Lab. Res. Rep. 67−0012.Google Scholar
Stix, T. H. 1962 Theory of Plasma Waves. McGraw-Hill.Google Scholar
Whitmer, R. F. & Herrmann, G. F. 1966 Phys. Fluids, 9, 768.CrossRefGoogle Scholar