Anomalous Hall instability in the Chern-Simons magnetohydrodynamics

TL;DR

This paper introduces Chern-Simons magnetohydrodynamics (CSMHD) with an axion-like field, analyzing its linear stability and causality, revealing anomalous Hall instability and mode behaviors in a chiral medium.

Contribution

It formulates CSMHD incorporating an axion-like field and studies its stability and causality, highlighting the role of anomalous Hall currents and parity-breaking instabilities.

Findings

Alfven modes near magnetic field direction are unstable but causal.

A genuine nonhydro mode accompanies unstable Alfven modes.

Parity-breaking leads to anomalous Hall instability.

Abstract

The Chern-Simons magnetohydrodynamics (CSMHD) is introduced using a Maxwell-Chern-Simons (MCS) Lagrangian including an axion-like field $\Theta$. The MCS equation of motion derived from this Lagrangian consists of a modified current, including a chiral magnetic (CM) and an anomalous Hall (AH) current, in addition to the ordinary Ohm current of resistive magnetohydrodynamics (MHD). The former consists of an axial chemical potential, which is given in terms of the temporal comoving derivative of $\Theta$, and the latter arises from the spatial gradient of $\Theta$. As it turns out, the existence of the axial chemical potential is a nonequilibrium effect that plays no role in the linear stability analysis, whereas the AH current arises as in the first-order linear perturbation of the thermal equilibrium. We analyze the linear stability and causality of the CSMHD in a resistive and chiral medium. We show that the Alfven modes propagating sufficiently close to the direction of the magnetic field are unstable but causal. They are also accompanied by a genuine nonhydro mode. A stable mode in a particular direction can correspond to an unstable mode propagating in the exact opposite direction. The AH instability is a manifestation of a breakdown of the parity. A numerical analysis of the phase velocity confirms these results.