The effect of the production and loss reactions on the parametric instability

Abstract

In this paper, the effect of the loss and production reactions on the parametric instability in plasma is investigated. Based on the hydrodynamic equations, we derive the wave equations for the electron plasma oscillation and ion-acoustic oscillation and obtain the threshold and the growth rate for the parametric instability. It is shown that (1) there is no effect of production reaction on the parametric instability; (2) the effect of loss reaction on the parametric instability is a slight damping; (3) the higher threshold is needed to excite the parametric instability in plasma with the loss reaction; (4) if taking the loss reaction into account, the growth rate for parametric instability will decrease by one half of the loss rate; and (5) the growth rate increases as the external field increases.