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More uniform perturbation theory of the Vlasov equation

Published online by Cambridge University Press:  13 March 2009

G. J. Lewak
G. J. Lewak
Affiliation:
Department of Applied Electrophysics and Institute for Pure and Applied Physical Sciences, University of California, San Diego, La Jolla, California 92037
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Abstract

The Vlasov—Poisson equations are reformulated by applying an arbitrary transformation to the velocity variable in such a way that perturbation theory of the transformed equations does not exhibit the customary secularity in time (or space) in second or higher order. The lowest order approximation of the new formulation is discussed and compared with conventional results. The source of the non-uniformity appears to be the divergence of Particle trajectories as calculated by perturbation methods, from the exact ones after long times. The transformation which allows one to follow the particle trajectories is a transformation to a frame of reference moving with a plasma test particle in the self-consistent field.

Type
Research Article
Information
Journal of Plasma Physics , Volume 3 , Issue 2 , May 1969 , pp. 243 - 253
Copyright
Copyright © Cambridge University Press 1969

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References

REFERENCES

Backus, G. 1960 J. Math. Phys. 1, 178.CrossRefGoogle Scholar
Drummond, W. F. & Pines, D. 1962 Nucl. Fusion, suppl. p. 1049.Google Scholar
Dupree, T. H. 1963 Phys. Fluids 6, 1714.CrossRefGoogle Scholar
Hirschfield, J. L. & Jacob, J. H. 1968 Phys. Fluids 11, 411.CrossRefGoogle Scholar
Klimontovich, Y. L. 1958 JETP 6, 753.Google Scholar
Landau, L. D. 1946 J. Phys. U.S.S.R. 10, 25.Google Scholar
Montgomery, D. C. & Tidman, D. A. 1964 Plasma Kinetic Theory. McGraw Hill.Google Scholar
O'niel, T. M. & Gould, R. W. 1968 Phys. Fluids 11, 134.CrossRefGoogle Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics, p. 101. Academic Press.Google Scholar