Parallel whistler instability in a plasma with an anisotropic bi‐kappa distribution

Abstract

The parallel‐propagating whistler instability in a magnetized plasma of electrons and positive ions having bi‐kappa velocity distributions is investigated for a wide range of parameters. The threshold condition for instability does not depend on the index, κ e , of the electron bi‐kappa distribution, but the maximum growth rate depends strongly on this parameter. The functional dependence of the growth rate on κ e is strongly influenced by the value of the electron temperature anisotropy. For small anisotropies the maximum growth rate is enhanced by the presence of a low‐κ e power‐law tail, as is well known. At larger temperature anisotropies, however, the reverse applies. A hard tail on the electron velocity distribution is deleterious to the whistler instability in this parameter region. For electron temperature anisotropies intermediate between those described, the (maximum with respect to wave number) growth rate maximizes for a particular κ e value. The dependence of the maximum growth rate on κ e in this electron temperature anisotropy regime is non‐monotonic. For a fixed value of the electron temperature anisotropy, the growth rate is strongly controlled by the parallel electron beta. Larger values of this parameter increase the growth rate, and conversely. The parallel electron beta also governs the value of the electron temperature anisotropy that separates the different types of monotonic behavior of the growth rate described above. The instability is not very sensitive to the electron temperature, provided cases with similar parallel electron beta values are compared. It is pointed out that all whistler dispersion relations, regardless of the value of κ e used, pass through a common ( ω , k ) point. This point is closely related to the instability threshold condition. A novel application is suggested.