Parker Problem in Hall Magnetohydrodynamics

TL;DR

This paper investigates the Parker problem within Hall magnetohydrodynamics, revealing a complex triple-layer structure where magnetic field decay rates differ across regions due to Hall effects and shear flows.

Contribution

It introduces the Hall MHD framework to the Parker problem, demonstrating a triple deck structure with distinct magnetic decay behaviors in different regions.

Findings

Magnetic field decays as 1/x in the outer ideal MHD region.

In the Hall-resistive region, magnetic field decays more steeply as 1/x^3.

Hall effect and shear flow induce a triple-layer structure in the Parker problem.

Abstract

Parker problem in Hall magnetohydrodynamics (MHD) is considered. Poloidal shear into the toroidal flow generated by the Hall effect is incorporated. This is found to lead to a {\it triple deck} structure for the Parker problem in Hall MHD, with the magnetic field falling off in the intermediate Hall-resistive region more steeply (like \normalfont $1/x^3$) than that (like \normalfont$1/x$) in the outer ideal MHD region.