On the Saturation of the Magnetorotational Instability via Parasitic Modes

TL;DR

This paper analyzes how parasitic instabilities limit the saturation of the magnetorotational instability (MRI) in simulations, emphasizing the importance of domain size and mode compatibility for accurate modeling.

Contribution

It provides a detailed analysis of parasitic modes affecting MRI saturation, highlighting the critical role of domain size and mode fitting in numerical simulations.

Findings

Parasitic instabilities include Kelvin-Helmholtz and tearing modes.

Proper saturation requires domain sizes accommodating primary and parasitic modes.

The fastest parasitic modes have wavelengths twice as long as the primary vertical wavelength.

Abstract

We investigate the stability of incompressible, exact, non-ideal magnetorotational (MRI) modes against parasitic instabilities. Both Kelvin-Helmholtz and tearing-mode parasitic instabilities may occur in the dissipative regimes accessible to current numerical simulations. We suppose that a primary MRI mode saturates at an amplitude such that its fastest parasite has a growth rate comparable to its own. The predicted alpha parameter then depends critically on whether the fastest primary and parasitic modes fit within the computational domain and whether non-axisymmetric parasitic modes are allowed. Hence even simulations that resolve viscous and resistive scales may not saturate properly unless the numerical domain is large enough to allow the free evolution of both MRI and parasitic modes. To minimally satisfy these requirements in simulations with vertical background fields, the vertical extent of the domain should accommodate the fastest growing MRI mode while the radial and azimuthal extents must be twice as large. The fastest parasites have horizontal wavelengths roughly twice as long as the vertical wavelength of the primary.