Theory of electron holes in superthermal space plasma

The bipolar electric field structures associated with electron phase space holes (EHs) have been observed by many spacecraft in near Earth's space plasma environment. These structures are described as the stationary solutions of Vlasov-Poisson equations, obtained by adopting the Bernstein-Greene-Kruskal (BGK) approach. Through the literature survey, we find that the BGK EHs are modelled by using either thermal distribution function or any statistical distribution derived from particular spacecraft observations. However, Maxwell distributions are quite rare in space plasmas; instead, most of these plasmas are superthermal in nature and generally described by kappa distribution. We have developed BGK model of EHs for space plasma that follows superthermal kappa distribution. The analytical solution of trapped electron distribution function for such plasmas is derived. The trapped particle distribution of superthermal plasma is found to be steeper and denser as compared to that for Maxwellian distributed plasma. The width-amplitude relation of a perturbation for superthermal plasma is derived and allowed regions of stable BGK solutions are obtained. We find that the stable BGK solutions are better supported by superthermal plasmas compared to that of thermal plasmas for small amplitude perturbations. It is seen that increase in width and amplitude of wave potential cause an augmentation in the trapping of particles. The amplitude plays a dominant role in the trapping of maximum energetic particles whereas width plays role in deciding the density of particles at the center of the EHs. Furthermore, it is noticed that the superthermal space plasma does not impose restriction on the presence of electron hole with a width less than the electron Debye length.