Stability of arbitrary electron velocity distribution functions to electromagnetic modes

Abstract

The stability of general electron distribution functions to purely electromagnetic modes is considered, so as to generalize the well-known stability analysis for bi-Gaussian distribution functions. The expansion of an arbitrary nonrelativistic distribution function into a modified version of Hermite–Gaussian modes yields the dispersion relation for electromagnetic modes in a compact form that depends on the coefficients of the expansion as well as the well-known plasma dispersion function and its derivatives. The coefficients of the expansion that enter the dispersion relation depend only on the zeroth and second moments from the direction of high temperature. The general dispersion relation is solved analytically for the frequency in the low anisotropy (kinetic) limit. Purely imaginary solutions can be found for distribution functions symmetric in the direction of the wavenumber. If, in addition to being symmetric, the distribution function is separable, the only quantity from the high-temperature direction that enters the equation for the frequency of the electromagnetic wave is the variance.