Alfven number for the Richtmyer-Meshkov instability in magnetized plasmas

TL;DR

This study uses 2D MHD simulations to analyze how the Alfvén number governs the suppression or amplification of the Richtmyer-Meshkov instability in magnetized plasmas, revealing a universal critical threshold.

Contribution

It introduces the Alfvén number as a key parameter to evaluate RMI behavior, providing a universal criterion independent of initial conditions.

Findings

Suppression of RMI occurs when Alfvén number < 1.

Magnetic field amplification is proportional to the Alfvén number.

The critical Alfvén number threshold is universal across various parameters.

Abstract

Magnetohydrodynamical evolution of the Richtmyer-Meshkov instability (RMI) is investigated by two-dimensional MHD simulations. The RMI is suppressed by a strong magnetic field, whereas the RMI amplifies an ambient magnetic field by many orders of magnitude if the seed field is weak. We have found that the suppression and amplification processes can be evaluated continuously along with the amplitude of the Alfv\'en number $R_A$, which is defined as the ratio of the linear growth velocity of the RMI to the Alfv\'en speed at the interface. When the Alfv\'en number is less than unity, the Lorentz force acting on the fluid mitigates the unstable motion of the RMI significantly, and the interface oscillates stably in this limit. If $R_A \gtrsim 1$, on the other hand, the surface modulation increases due to the growth of the RMI. The maximum strength of the magnetic field is enhanced up to by a factor of $R_A$. This critical feature is universal and independent of the initial Mach number of the incident shock, the Atwood number, corrugation amplitude, and even the direction of the initial magnetic field.