Abstract:
Several spacecraft missions have observed electron holes (EHs) in Earth’s and other planetary
magnetospheres. These EHs are modeled with 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 a one-dimensional 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
function in plasma following kappa distribution is found to be steeper and denser as compared to
that for Maxwellian distribution. The width-amplitude relation of 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.
