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

Abstract

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/к 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.