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Langmuir turbulence as a critical phenomenon. Part 1. Destruction of the statistical equilibrium of an interacting-modes ensemble

Published online by Cambridge University Press:  13 March 2009

Guy Pelletier
Physique des Milieux IonisésUnivorsité Scientifique et Médicale de Grenoble, B.P. 53 X-38041 Grenoble Cedex France


This paper is the first part of a work concerning a statistical theory of Langmuir turbulence in which the destabilization of an ensemble of plasmons by self- modulation is considered as a critical phenomenon. The first part is devoted to a discussion of the existence of a statistical equilibrium for the ensemble of modes. A transition curve, which separates equilibrium from non-equilibrium, is found. Several properties of the plasma, when the self-modulation instability is saturated, are derived in the neighbourhood of the critical Langmuir energy density Wc. In particular, the Langmuir energy spectrum is found to be proportional to kd-3, the correlation length is found to diverge as üW–Wcü–half, and the anomalous conductivity at the plasma frequency is found to diverge as üW – Wcü-1.

Research Article
Copyright © Cambridge University Press 1980

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