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Reply to the ‘Comment on Negative Diffusion in Coefficients in Quasilinear Theory’ by David Montgomery and Stephen Bodner

Published online by Cambridge University Press:  13 March 2009

Ira B. Bernstein
Affiliation:
Yale University
J. P. Klozenberg
Affiliation:
Imperial College

Extract

The criticisms of Montgomery & Bodner (preceding paper) seem to stem from a misunderstanding of the claims in the paper of Klozenberg & Bernstein (1970) in part perhaps semantic. The derivation criticized was intended to apply only to those particle velocities v corresponding to the range in phase velocities βк for which there is an appreciable wave excitation. The term ‘resonant phase velocity’ was intended to mean those phase velocities in a small interval Δ such that ν − ½Δ < βк/к < ν + ½Δ, which interval in the integral determining the diffusion coefficients leads to the familiar expression involving δ(βк кν). When this contribution is non-vanishing it determines the lowest significant order contribution, in the small parameters of the problem, of ∂ƒ0/∂t, assuming that the wave excitation at the time in question is so large that effects associated with initial conditions are indeed negligible.

Type
Articles
Copyright
Copyright © Cambridge University Press 1971

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References

REFERENCES

Klozenberg, J. P. & Bernstein, I. B. 1970 J. Plasma Phys. 4, 595.CrossRefGoogle Scholar
Montgomery, D. & Bodner, S. 1971 J. Plasma Phys. 5, 131.CrossRefGoogle Scholar