The Rayleigh shearing instability limit of the magnetorotational instability

TL;DR

This paper derives stability criteria for Rayleigh shearing and magnetorotational instabilities using geometric optics, showing that weak magnetic fields favor Rayleigh shearing instability over magnetorotational instability.

Contribution

It introduces a unified approach to determine the dominant instability criterion based on magnetic field strength using geometric optics approximation.

Findings

Weak magnetic fields lead to Rayleigh shearing instability dominance.

The stability criteria depend on the magnitude of the magnetic field.

The analysis covers all orders of the small parameter in the characteristic equation.

Abstract

We use the geometric optics approximation to derive the stability criteria for the Rayleigh shearing instability and the magnetorotational instability. We examine the cases where each criterion is relevant by looking into the magnitude of the magnetic field using a small dimensionless parameter. Examining all the orders of this parameter in the characteristic equation we show that configurations with sufficiently small magnetic field are characterised by the Rayleigh shearing instability criterion rather than that of the magnetorotational instability.