Axisymmetric Nonlinear Waves And Structures in Hall Plasmas

TL;DR

This paper derives a general evolution equation for axisymmetric magnetic fields in Hall plasmas, analyzes special nonlinear wave solutions, and discusses applications to astrophysical low-ionized plasmas such as protostellar disks and molecular clouds.

Contribution

It introduces a new generalized Grad-Shafranov equation for Hall plasmas and explores analytical and numerical solutions for nonlinear wave phenomena.

Findings

Derived a general evolution equation for axisymmetric magnetic fields in Hall plasmas.

Identified special solutions including whistler drift modes and soliton-like structures.

Applied results to astrophysical environments like protostellar disks and molecular clouds.

Abstract

In this paper, a general equation for the evolution of an axisymmetric magnetic field in a Hall plasma is derived, with an integral similar to the Grad-Shafranov equation. Special solutions arising from curvature -- whistler drift modes that propagate along the electron drift as a Burger's shock, and nonlinear periodic and soliton-like solutions to the generalized Grad-Shafranov integral -- are analyzed. We derive analytical and numerical solutions in a classical electron-ion Hall plasma, in which electrons and ions are the only species in the plasmas. Results may then be applied to the following low-ionized astrophysical plasmas: in protostellar disks, in which the ions may be coupled to the motion of gases; and in molecular clouds and protostellar jets, in which the much heavier charged dust in a dusty Hall plasma may be collisionally coupled to the gas.