Self-heating in kinematically complex magnetohydrodynamic flows

TL;DR

This paper investigates how velocity shear in complex MHD flows causes self-heating through instabilities, with viscous and resistive dissipation contributing similarly, and finds exponential instability more efficient than parametric instability.

Contribution

It introduces a comprehensive analysis of self-heating mechanisms in kinematically complex MHD flows, considering both exponential and parametric instabilities with dissipative effects.

Findings

Viscous damping and magnetic resistivity contribute similarly to self-heating.

Exponential instability results in higher heating efficiency than parametric instability.

Both instabilities can significantly heat plasma through shear-driven mechanisms.

Abstract

The non-modal self-heating mechanism driven by the velocity shear in kinematically complex magnetohydrodynamic (MHD) plasma flows is considered. The study is based on the full set of MHD equations including dissipative terms. The equations are linearized and unstable modes in the flow are looked for. Two different cases are specified and studied: (a) the instability related to an exponential evolution of the wave vector; and (b) the parametric instability, which takes place when the components of the wave vector evolve in time periodically. By examining the dissipative terms, it is shown that the self-heating rate provided by viscous damping is of the same order of magnitude as that due to the magnetic resistivity. It is found that the heating efficiency of the exponential instability is higher than that of the parametric instability.