Global axisymmetric Magnetorotational Instability with density gradients

TL;DR

This paper investigates the global axisymmetric magnetorotational instability in rotating MHD plasmas with density gradients, revealing limitations of local criteria and identifying localized unstable modes influenced by rotation and density profiles.

Contribution

It introduces a global analysis approach for MRI with density gradients, showing the inadequacy of local criteria and characterizing localized unstable modes.

Findings

Standard MRI criterion can be misleading in global settings.

Unstable modes are localized by rotation and density profiles.

The problem with Keplerian profiles is mathematically ill-posed.

Abstract

We examine global incompressible axisymmetric perturbations of a differentially rotating MHD plasma with radial density gradients. It is shown that the standard magnetorotational instability, (MRI) criterion drawn from the local dispersion relation is often misleading. If the equilibrium magnetic field is either purely axial or purely toroidal, the problem reduces to finding the global radial eigenvalues of an effective potential. The standard Keplerian profile including the origin is mathematically ill-posed, and thus any solution will depend strongly on the inner boundary. We find a class of unstable modes localized by the form of the rotation and density profiles, with reduced dependence on boundary conditions.