Global MRI with Braginskii viscosity in a galactic profile

TL;DR

This paper analyzes how Braginskii viscosity influences the magnetorotational instability (MRI) in galactic plasmas, revealing conditions where viscosity dampens or enhances MRI growth rates, with implications for astrophysical plasma modeling.

Contribution

It provides the first global-in-radius analytical solutions for MRI with Braginskii viscosity in galactic profiles, exploring different magnetic field orientations and regimes.

Findings

Braginskii viscosity dampens neutrally stable modes in azimuthal and vertical fields.

Viscosity can accelerate MRI growth up to 2√2 times in slightly pitched fields.

The effects of viscosity are characterized by a parameter linking rotation, viscosity, and magnetic field strength.

Abstract

We present a global-in-radius linear analysis of the axisymmetric magnetorotational instability (MRI) in a collisional magnetized plasma with Braginskii viscosity. For a galactic angular velocity profile $\Omega$ we obtain analytic solutions for three magnetic field orientations: purely azimuthal, purely vertical and slightly pitched (almost azimuthal). In the first two cases the Braginskii viscosity damps otherwise neutrally stable modes, and reduces the growth rate of the MRI respectively. In the final case the Braginskii viscosity makes the MRI up to $2\sqrt{2}$ times faster than its inviscid counterpart, even for \emph{asymptotically small} pitch angles. We investigate the transition between the Lorentz-force-dominated and the Braginskii viscosity-dominated regimes in terms of a parameter $\sim \Omega \nub/B^2$ where $\nub$ is the viscous coefficient and $B$ the Alfv\'en speed. In the limit where the parameter is small and large respectively we recover the inviscid MRI and the magnetoviscous instability (MVI). We obtain asymptotic expressions for the approach to these limits, and find the Braginskii viscosity can magnify the effects of azimuthal hoop tension (the growth rate becomes complex) by over an order of magnitude. We discuss the relevance of our results to the local approximation, galaxies and other magnetized astrophysical plasmas. Our results should prove useful for benchmarking codes in global geometries.