On Magnetic Inhibition Theory in Non-resistive Magnetohydrodynamic Fluids

TL;DR

This paper explores the magnetic inhibition effect in non-resistive MHD fluids, explaining the physical mechanisms, energy dependence, and stability criteria, and extends the theory to stratified fluids and other instabilities.

Contribution

It introduces a new physical explanation for magnetic inhibition in non-resistive MHD fluids and extends the theory to stratified cases and other instability phenomena.

Findings

Magnetic energy depends on fluid particle displacement, acting as elastic potential energy.

The stability criteria can be explained via the minimum potential energy principle.

The magnetic inhibition theory applies to various instabilities like thermal and magnetic buoyancy.

Abstract

We investigate why the non-slip boundary condition for the velocity, imposed in the direction of impressed magnetic fields, can contribute to the magnetic inhibition effect based on the nonhomogeneous magnetic Rayleigh--Taylor (abbr. NMRT) problem in non-resistive magnetohydrodynamic (abbr. MHD) fluids. Exploiting an infinitesimal method in Lagrangian coordinates, the idea of (equivalent) magnetic tension, and the differential version of magnetic flux conservation, we give an explanation of physical mechanism for the magnetic inhibition phenomenon in a non-resistive MHD fluid. Moreover, we find that the magnetic energy in the non-resistive MHD fluid depends on the displacement of fluid particles, and thus can be regarded as elastic potential energy. Motivated by this observation, we further use the well-known minimum potential energy principle to explain the physical meaning of the stability/instability criteria in the NMRT problem. As a result of the analysis, we further extend the results on the NMRT problem to the stratified MHD fluid case. We point out that our magnetic inhibition theory can be used to explain the inhibition phenomenon of other instabilities, such as thermal instability, magnetic buoyancy instability, and so on, by impressed magnetic fields in non-resistive MHD fluids.