Parametric Instabilities in a Magnetized and Collisional Plasma

Abstract

The dispersion relation for a magnetized, collisional and hot plasma in the presence of a pump wave is developed for the case where the pump frequency Wo is large compared with the cyclotron frequency Wc and the plasma frequency Wp. Formulae for the growth rate, the damping rate for the free electron plasma wave and the threshold power are derived and discussed numerically under different conditions. It is found that in a hot plasma (for magnetic fields with wc/wp = 1 and 10) the threshold power PT is less than or greater than that in a cold plasma for the (Rew2)+ or (Rewz)_ modes respectively. In a weak magnetic field (wc/wp = 0·1), PT does not vary with the direction B of the magnetic field or the (Rewz)+ mode. However, PT for the (Rewz)_ mode is a minimum at B = 30° and 10° for c/wp = 1 and 10 respectively, and it becomes very large (105-107 times its value in a cold unmagnetized lasma) for wc/wp = 0·1. The results for the growth rate are found to be just the reverse of hose for the threshold power.