Non-linear Weibel-type Soliton Modes

TL;DR

This paper investigates non-linear soliton modes in plasmas, emphasizing the importance of particle distribution functions and their dependence on transverse canonical momenta for the existence of solitons across different relativistic regimes.

Contribution

It demonstrates the critical role of distribution function dependence on transverse canonical momenta in enabling soliton solutions in various plasma relativistic conditions.

Findings

Soliton behavior requires dependence on transverse canonical momenta.

Coupled non-linear equations often need numerical solutions.

Examples cover non-relativistic to fully relativistic plasmas.

Abstract

Discussion is given of non-linear soliton behavior including coupling between electrostatic and electromagnetic potentials for non-relativistic, weakly relativistic, and fully relativistic plasmas. For plasma distribution functions that are independent of the canonical momenta perpendicular to the soliton spatial structure direction there are, in fact, no soliton behaviors allowed because transverse currents are zero. Dependence on the transverse canonical momenta is necessary. When such is the case, it is shown that the presence or absence of a soliton is intimately connected to the functional form assumed for the particle distribution functions. Except for simple situations, the coupled non-linear equations for the electrostatic and electromagnetic potentials would seem to require numerical solution procedures. Examples are given to illustrate all of these points for non-relativistic, weakly relativistic, and fully relativistic plasmas.