Effects of cold electron density on the whistler anisotropy instability

Abstract

We confirm results from a previous derivation of the linear growth rate of the parallel propagating whistler wave instability when both cold and hot populations are present, and extend previous equations to describe the spatial growth rate. For moderate plasma beta, there is always a peak in the linear growth rate of the dominant mode with respect to the ratio of total plasma density to the hot plasma density. There is a similar peak in the linear convective growth rate for high anisotropy Ahot = T⊥ hot/T∥ hot − 1 but not for low anisotropy. We present these results for a large range of physical parameters. Our results can be used to quickly determine whether the growth rate will increase or decrease with respect to cold plasma density, and we demonstrate this for an event observed recently. We explain the observation that greater cold plasma density leads to a drop in the central frequency of the waves. Model equations can be used to predict the optimal cold plasma density for maximum temporal and spatial growth rate. A relativistic electromagnetic plasma dispersion code is used to show that the analytical formulas are roughly correct in the vicinity of the optimal cold density unless the thermal velocity is highly relativistic ∼0.5 c, where c is the speed of light. Comparison with the electromagnetic dispersion code WHAMP shows that our formulas are adequate for β∥ hot < 1 for realistic anisotropy.