A Kinetic Foundation of the Theory of Parametric Instabilities in a Plasma

Abstract

This work is a first step in a long range programme on the foundation of the theory of parametric instabilities on a firm statistical mechanical basis. The present study is restricted to the parametric instabilities resulting from the coupling of plaoma- dynomioal modes through an external, time-dependent electromagnetic field. The plasmadynamical modes (P.D-modas) are defined, in absence of the field, to be the least damped collective excitations of the system, in the limit of small wave-vectors. In presence of the field, the coupling of these modes potentially leads to the instabilities with the lowest thresholds.