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Temporal evolution of reactive and resistive nonlinear instabilities

Published online by Cambridge University Press:  13 March 2009

D. B. Melrose
D. B. Melrose
Affiliation:
School of Physics, University of Sydney, Sydney NSW 2006, Australia
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Abstract

A kinetic theory for nonlinear processes involving Langmuir waves, developed in an earlier paper, is extended through consideration of three aspects of the temporal evolution, (i) Following Falk & Tsytovich (1975). the dynamic equation for the rate of change of one amplitude at t is expressed as an integral over T of the product of two amplitudes at t – T and a kernel functionf(T); two generalizations of Falk & Tsytovich's form (f(T) ∝ T) that satisfy the requirement f(∞) = 0 are identified, (ii) It is shown that the low-frequency or beat disturbance may be described in terms of fluctuations in the electron number density, and that its time evolution involves an operator that is essentially the inverse of f(t). (iii) The transition from oscillatory evolution in the reactive or ‘coherent-wave’ version of the three-wave instability to the secular evolution of the resistive or ‘random-phase’ version is discussed qualitatively.

Type
Research Article
Information
Journal of Plasma Physics , Volume 38 , Issue 3 , December 1987 , pp. 473 - 481
Copyright
Copyright © Cambridge University Press 1987

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References

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