AI 中文总结
该研究推导膨胀宇宙中带电费米子等离子体的相对论性手征MHD方程，通过坐标变换等使系统具闵可夫斯基度规形式，保留四项贡献产生新项，评估辐射主导时代系数，为数值实现做准备。
AI 中文摘要
我们给出了膨胀宇宙中带电费米子等离子体的相对论性手征磁流体动力学（MHD）方程的系统推导。通过坐标变换和动力学变量的重新缩放相结合，我们使整个系统具有与闵可夫斯基度规相同的形式，哈勃膨胀仅存在于手征翻转率和运动粘度中。保留对电流和轴向电流的所有四项贡献会产生标准手征MHD中不存在的项：化学势演化方程的电荷密度修正，以及与电荷化学势$\mu$和体速度成正比的电流。后者由电流守恒决定，不需要手征不平衡，并驱动了在另一篇论文中研究的电荷流不稳定性。对于辐射主导的时代，我们以物理单位评估所有系数，并用它们来估计磁雷诺数、可达到的磁场强度以及手征发电机运行的最低温度。所得方程具有可直接用于数值实现的形式。
英文摘要
We present a systematic derivation of the equations of relativistic chiral magnetohydrodynamics (MHD) for a plasma of charged fermions in an expanding universe. Through a combination of a coordinate transformation and a rescaling of the dynamical variables, we bring the full system to the same form as in the Minkowski metric, with the Hubble expansion surviving only in the chirality-flipping rate and the kinematic viscosity. Retaining all four contributions to both the electric and the axial current yields terms absent from standard chiral MHD: charge-density corrections to the evolution equations for the chemical potentials, and an electric current proportional to the charge chemical potential $μ$ and the bulk velocity. The latter is mandated by current conservation, requires no chirality imbalance, and drives the charge-flow instability studied in a companion paper. For the radiation-dominated era, we evaluate all the coefficients in physical units and use them to estimate the magnetic Reynolds number, the attainable magnetic field strength, and the minimum temperature at which the chiral dynamo can operate. The resulting equations are cast in a form ready for direct numerical implementation.
Comments14 pages
