On properties of Velikhov-Chandrasekhar MRI in ideal and non-ideal plasma

TL;DR

This paper analyzes the Velikhov-Chandrasekhar magneto-rotational instability (MRI) in ideal and non-ideal plasmas, exploring stability conditions, the transition to hydrodynamics, and effects of viscosity and magnetic diffusivity in accretion disks.

Contribution

It provides a detailed linear analysis of MRI properties in various plasma conditions, including the transition from magnetic to hydrodynamic regimes and the influence of plasma parameters.

Findings

MRI stabilizes in Rayleigh-unstable flows with decreasing angular momentum.

Magnetic fields suppress Rayleigh instability at small wavelengths.

Limits on ion mean free-paths for MRI operation in accretion disks.

Abstract

Conditions of Velikhov-Chandrasekhar magneto-rotational instability in ideal and non-ideal plasmas are examined. Linear WKB analysis of hydromagnetic axially symmetric flows shows that in the Rayleigh-unstable hydrodynamic case where the angular momentum decreases with radius, the MRI branch becomes stable, and the magnetic field suppresses the Rayleigh instability at small wavelengths. We investigate the limiting transition from hydromagnetic flows to hydrodynamic flows. The Rayleigh mode smoothly transits to the hydrodynamic case, while the Velikhov-Chandrasekhar MRI mode completely disappears without the magnetic field. The effects of viscosity and magnetic diffusivity in plasma on the MRI conditions in thin accretion discs are studied. We find the limits on the mean free-path of ions allowing MRI to operate in such discs.