The Chern-Simons magnetohydrodynamics (CSMHD) is introduced using a Maxwell-Chern-Simons (MCS) Lagrangian including an axionlike field $\mathrm{\Theta }$. 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 $\mathrm{\Theta }$, and the latter arises from the spatial gradient of $\mathrm{\Theta }$. 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 Alfvén 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.

中文翻译：

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陈-西蒙斯磁流体动力学中的异常霍尔不稳定性

Chern-Simons 磁流体动力学 (CSMHD) 是使用 Maxwell-Chern-Simons (MCS) 拉格朗日量引入的，包括轴状场 $\mathrm{\Theta }$. 从这个拉格朗日量导出的 MCS 运动方程包含一个修正的电流，除了电阻磁流体力学 (MHD) 的普通欧姆电流之外，还包括一个手征磁 (CM) 和一个异常霍尔 (AH) 电流。前者由轴向化学势组成，它是根据时间共移导数给出的$\mathrm{\Theta }$，后者来自于空间梯度 $\mathrm{\Theta }$. 事实证明，轴向化学势的存在是一种非平衡效应，在线性稳定性分析中不起作用，而 AH 电流在热平衡的一阶线性扰动中出现。我们分析了 CSMHD 在电阻和手性介质中的线性稳定性和因果关系。我们表明，传播足够接近磁场方向的阿尔文模式是不稳定的，但具有因果关系。它们还伴随着真正的非水电模式。特定方向上的稳定模式可以对应于完全相反方向上传播的不稳定模式。AH 不稳定是奇偶校验崩溃的表现。相速度的数值分析证实了这些结果。