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Relaxation oscillations in weak turbulence. The case of nonlinear wave-particle interaction

Published online by Cambridge University Press:  13 March 2009

C. Montes
C. Montes
Affiliation:
Observatoire de Nice, Le Mont-Gros, 06300 Nice
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Abstract

A model for nonlinear Landau stabilization of a linear instability is treated analytically. The model may apply to any dissipative system described by: (i) a linear dissipation function γ(k), of one degree of freedom k, which presents a limited unstable domain δK and a damped region for lower values of k, and (ii) a transition probability for the nonlinear Landau damping (nonlinear wave–particle interaction) proportional to k – K'. For a sharply pointed γ(k), the model leads to a kinetic regime presenting periodic relaxation oscillations of large and constant amplitude. Starting from weak turbulence, the system organizes itself into a periodic regime, which may be of interest in connexion with research in morphogenesis. For a smoothed γ(k), the relaxation oscillations damp, slowing down towards a turbulent energy level.

Type
Research Article
Information
Journal of Plasma Physics , Volume 11 , Issue 1 , February 1974 , pp. 141 - 158
Copyright
Copyright © Cambridge University Press 1974

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References

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