Spectrum of Global Magnetorotational Instability in a Narrow Transition Layer

TL;DR

This paper explores the global magnetorotational instability in a narrow transition layer, revealing how growth rates and mode behaviors differ from local analyses, especially for non-axisymmetric and overstable modes.

Contribution

It provides a global analysis of MRI in a narrow transition layer, highlighting differences from local theory and identifying overstable modes with azimuthal dependence.

Findings

Growth rates differ from local analysis when the vertical wavelength is comparable to the transition width.

Non-axisymmetric spectrum includes overstable modes with azimuthal wavelength dependence.

In the limit of zero transition width, classical Rayleigh and Kelvin-Helmholtz instabilities are recovered.

Abstract

The Global Magnetorotational Instability (MRI) is investigated for a configuration in which the rotation frequency changes only in a narrow transition region. If the vertical wavelength of the unstable mode is of the same order or smaller than the width of this region, the growth rates can differ significantly from those given by a local analysis. In addition, the non-axisymmetric spectrum admits overstable modes with a non-trivial dependence on azimuthal wavelength, a feature missed by the local theory. In the limit of vanishing transition region width, the Rayleigh-centrifugal instability is recovered in the axisymmetric case, and the Kelvin-Helmholtz instability in the non-axisymmetric case.