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Higher order approximations in the theory of longitudinal plasma oscillations. II

Published online by Cambridge University Press:  13 March 2009

F. Einaudi
Affiliation:
Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado 80302, U.S.A.
W. I. Axford
Affiliation:
Department of Applied Physics and Information Science, University of California at San Diego, La Jolla, California 92037, U.S.A.

Abstract

In this note we comment and extend the results of a previous analysis in which the non-linear behaviour of one-dimensional electrostatic oscillations in a homogeneous, unbounded, collisionless and fully ionized plasma was considered. The evolution of a monochromatic wave of small, but finite amplitude is studied by expanding the dependent variables as well as the independent variable tin the form of asymptotic series; an ordering parameter e proportional to the initial amplitude of the electric field is introduced. The expansion of the independent variable in such a series allows us to eliminate secular terms from the part of the distribution function which does not depend on the free-streaming terms. This, in turn, allows us to determine corrections to the complex frequency a. Results of a previous note on non-linear Landau damping for an initially Maxwellian. distribution function are confirmed, but it is indicated that they apply to values of time up to a value τ1 rather than for all times. One can proceed to larger values of time in the manner of the multiple time-scale method. In particular it is found that the Landau damping is increased with respect to the linear value only initially during the first time scale.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1970

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References

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