xMHD Simulation of Instability Growth in Expanding Toroidal Plasmas

We investigate the growth of the magnetic Rayleigh-Taylor (MRT) instability in a compact toroidal plasma as it expands and propagates through an external magnetic field. This work supports the Plasma Bubble Expansion Experiment (PBEX), which aims to study the fundamental physics of interacting magnetized plasmas. Our approach employs 3D extended magnetohydrodynamic (xMHD) simulations using the PERSEUS code, with a focus on how Hall physics affect instability growth during expansion.

Simulations are initialized using self-similar solutions to the ideal MHD equations. These self-similar states represent the intermediate-asymptotic regime, where system behavior becomes independent of initial and boundary conditions but is not yet in equilibrium. This approach eliminates long transient phases and arbitrary initial guesses, allowing us to focus directly on the relevant plasma dynamics.

We then introduce Hall effects and external magnetic fields, thereby breaking the self-similarity and enabling the growth of instabilities. This framework offers a physically-grounded and computationally efficient method to study instability growth. The methodology is applicable to both laboratory and astrophysical plasmas, as long as self-similar expansion is a valid approximation.