Counterexample of the magnetorotational instability in two-dimensional axial symmetry

TL;DR

This paper demonstrates that under specific axial symmetry assumptions, the magnetorotational instability (MRI) is suppressed, showing that magnetic fields can stabilize plasma configurations in such symmetric conditions.

Contribution

It provides a counterexample showing MRI suppression in a two-dimensional axially symmetric plasma with specific magnetic and rotational assumptions.

Findings

MRI is suppressed under axial symmetry assumptions.

Magnetic fields stabilize plasma against hydrodynamical instabilities.

Azimuthal magnetic field component vanishes in the model.

Abstract

We analyze a linear perturbation scheme for a two-dimensional background plasma, which is rotating with a differential frequency and is embedded in a poloidal magnetic field. The main two assumptions of the present study, which in turn are related, are that the plasma profile is axially symmetric, both in the background and the perturbation approximation, where the azimuthal magnetic field is requested to vanish identically and secondly the angular frequency on the magnetic surface function only still holds in the non-stationary regime, which, on the steady background equilibrium, is ensured by the validity of the corotation theorem (Ferraro 1937). Indeed, such a restriction of the model is rather natural and it implies that the azimuthal component of the linear plasma shift is reabsorbed in the expression for the non stationary electric field (in principle, at any order of approximation) and can no longer provide a non-zero azimuthal component of the magnetic tension field. As a result, the Magneto-rotational instability is suppressed and the magnetic field has the effect to stabilize the plasma configuration with respect to the pure hydrodynamical case.