Kinetic theory of $\mathrm{sech}^2x$ electron holes and applications to Kappa-distributed plasmas

TL;DR

This paper develops a kinetic theory for $ ext{sech}^2 x$ electron holes, analyzing their properties and applying the theory to Kappa-distributed plasmas, with theoretical results validated by numerical simulations.

Contribution

It introduces a new kinetic theory for $ ext{sech}^2 x$ electron holes and applies it to Kappa-distributed plasmas, including analysis of their amplitude and width.

Findings

Existence conditions depend on distribution derivatives at the separatrix.

Potential profiles are influenced by trapped and untrapped distribution derivatives.

Numerical calculations confirm the theoretical predictions.

Abstract

The kinetic theory of $\mathrm{sech}^2 x$-type electron holes is studied. The potential of the electron holes is solved in the weak amplitude limit by the pseudo-potential method. We investigate the existence condition of the $\mathrm{sech}^2 x$ electron holes. It indicates that the derivatives of trapped and untrapped distributions at the separatrix play significant roles in determining the potential profile. The theory is then applied to the Kappa-distributed plasmas. The amplitude and width of the $\mathrm{sech}^2 x$ electron holes are analyzed. Finally, the theoretical results are verified by numerical calculations.