A generalized effective potential for differentially rotating plasmas

TL;DR

This paper develops a generalized effective potential framework to analyze the stability of differentially rotating plasmas, encompassing various rotation profiles and modes, including MRI and non-axisymmetric instabilities, in the MHD regime.

Contribution

It introduces a comprehensive effective potential approach for plasma stability analysis, covering both axisymmetric and non-axisymmetric modes in differentially rotating systems.

Findings

Derived a general form of effective potential for non-axisymmetric disturbances.

Analyzed stability for various rotation profiles in the MHD regime.

Identified conditions for the onset of MRI and non-axisymmetric modes.

Abstract

Global stability of differentially rotating plasma is investigated using a generalized effective potential. We first, for a current-free system, obtain a general form of an effective potential in terms of the free energies of global curvature and gradients of rotation for non-axisymmetric disturbances. We then examine the stability of differentially rotating disks for several rotation profiles and present the associated effective potential for the onset of these instabilities in the MHD regime. In particular, results for global axisymmetric magnetorotational instability (MRI) as well as local and global non-axisymmetric modes are presented. The latter constitute two distinct non-axisymmetric modes, a high frequency local MRI and a global low-frequency non-axisymmetric mode (the magneto-curvature mode, introduced in Ebrahimi&Pharr, ApJ 2022), confined either between two Alfv\'enic resonances or an Alfv\'enic resonance and a boundary.