Electron Holes in a $\kappa$ Distribution Background with Singularities

TL;DR

This paper derives and analyzes electron hole structures in plasmas with nonthermal, superthermal electron distributions characterized by a $ppa$ distribution, highlighting the effects of singularities and the spectral index on wave properties.

Contribution

It generalizes the Schamel distribution to nonthermal plasmas with singularities, providing new insights into electron hole solutions in space plasma environments.

Findings

The spectral index $ppa$ significantly influences wave amplitude and dispersion.

Solutions include cases with no trapped electrons, non-analytic trapped electron distributions, and surplus trapped electrons.

Strong singularities in the distribution function affect the properties of electron holes.

Abstract

The pseudo-potential method is applied to derive diverse propagating electron hole structures, in a nonthermal or $\kappa$ particle distribution function background. The associated distribution function Ansatz reproduces the Schamel distribution of \cite{Schamel2015} in the Maxwellian ($\kappa \rightarrow \infty$) limit, providing a significant generalization of it for plasmas where superthermal electrons are ubiquitous, such as space plasmas. The pseudo-potential and the nonlinear dispersion relation are evaluated. The role of the spectral index $\kappa$ on the nonlinear dispersion relation is investigated, in what concerns the wave amplitude for instance. The energy-like first integral from Poisson's equation is applied to analyze the properties of diverse classes of solutions: with the absence of trapped electrons, with a non-analytic distribution of trapped electrons, or with a surplus of trapped electrons. Special attention is therefore paid to the non-orthodox case where the electrons distribution function exhibits strong singularities, being discontinuous or non-analytic.