Effects of cold electron number density variation on whistler-mode wave growth

We examine how the growth of magnetospheric whistler-mode waves depends on the cold (background) electron number density N-0. The analysis is carried out by varying the cold-plasma parameter a = (electron gyrofrequency)(2)/(electron plasma frequency) 2 which is proportional to 1/N-0. For given values of the thermal anisotropy A(T) and the ratio N-h/N-0, where N-h is the hot (energetic) electron number density, we find that, as N-0 decreases, the maximum values of the linear and nonlinear growth rates decrease and the threshold wave amplitude for nonlinear growth increases. Generally, as N-0 decreases, the region of (N-h/N-0, A(T))-parameter space in which nonlinear wave growth can occur becomes more limited; that is, as N-0 decreases, the parameter region permitting nonlinear wave growth shifts to the top right of (N-h/N-0, A(T)) space characterized by larger N-h/N-0 values and larger A(T) values. The results have implications for choosing input parameters for full-scale particle simulations and also in the analysis of whistler-mode chorus data.