ABSTRACT The chiral magnetic effect (CME) is a quantum relativistic effect that describes the appearance of an additional electric current along a magnetic field. It is caused by an asymmetry between the number densities of left- and right-handed fermions, which can be maintained at high energies when the chirality flipping rate can be neglected, for example in the early Universe. The inclusion of the CME in the Maxwell equations leads to a modified set of magnetohydrodynamical (MHD) equations. The CME is studied here in numerical simulations with the Pencil Code. We discuss how the CME is implemented in the code and how the time step and the spatial resolution of a simulation need to be adjusted in presence of a chiral asymmetry. The CME plays a key role in the evolution of magnetic fields, since it results in a dynamo effect associated with an additional term in the induction equation. This term is formally similar to the α effect in classical mean-field MHD. However, the chiral dynamo can operate without turbulence and is associated with small spatial scales that can be, in the case of the early Universe, orders of magnitude below the Hubble radius. A chiral effect has also been identified in mean-field theory. It occurs in the presence of turbulence, but is not related to kinetic helicity. Depending on the plasma parameters, chiral dynamo instabilities can amplify magnetic fields over many orders of magnitude. These instabilities can potentially affect the propagation of MHD waves. Our numerical simulations demonstrate strong modifications of the dispersion relation for MHD waves for large chiral asymmetry. We also study the coupling between the evolution of the chiral chemical potential and the ordinary chemical potential, which is proportional to the sum of the number densities of left- and right-handed fermions. An important consequence of this coupling is the emergence of chiral magnetic waves (CMWs). We confirm numerically that linear CMWs and MHD waves are not interacting. Our simulations suggest that the chemical potential has only a minor effect on the non-linear evolution of the chiral dynamo.

中文翻译：

---

高能等离子体模拟中的手性费米子不对称性

摘要 手性磁效应 (CME) 是一种量子相对论效应，它描述了沿磁场的附加电流的出现。它是由左手和右手费米子的数密度不对称引起的，当手性翻转率可以忽略时，例如在早期宇宙中，这种费米子可以保持在高能量下。麦克斯韦方程中包含 CME 导致了一组修改后的磁流体动力学 (MHD) 方程。此处使用铅笔代码在数值模拟中研究 CME。我们讨论了如何在代码中实现 CME 以及如何在存在手征不对称性的情况下调整模拟的时间步长和空间分辨率。CME 在磁场的演化中起着关键作用，因为它会导致与归纳方程中的附加项相关的发电机效应。该术语在形式上类似于经典平均场 MHD 中的 α 效应。然而，手征发电机可以在没有湍流的情况下运行，并且与小空间尺度有关，在早期宇宙的情况下，可以低于哈勃半径几个数量级。在平均场理论中也发现了手性效应。它发生在存在湍流的情况下，但与动力学螺旋度无关。根据等离子体参数，手性发电机不稳定性可以将磁场放大多个数量级。这些不稳定性可能会影响 MHD 波的传播。我们的数值模拟表明，对于大手征不对称性，MHD 波的色散关系发生了强烈的修改。我们还研究了手性化学势和普通化学势演化之间的耦合，这与左手和右手费米子的数量密度之和成正比。这种耦合的一个重要后果是手性磁波 (CMW) 的出现。我们从数值上确认线性 CMW 和 MHD 波没有相互作用。我们的模拟表明，化学势对手性发电机的非线性演化只有很小的影响。