Relic gravitational waves (GWs) can be produced by primordial magnetic fields. However, not much is known about the resulting GW amplitudes and their dependence on the details of the generation mechanism. Here we treat magnetic field generation through the chiral magnetic effect (CME) as a generic mechanism and explore its dependence on the speed of generation (the product of magnetic diffusivity and characteristic wavenumber) and the speed characterizing the maximum magnetic field strength expected from the CME. When the latter exceeds the former (regime I), which is the regime applicable to the early universe, we obtain an inverse cascade with moderate GW energy that scales with the third power of the magnetic energy. When the generation speed exceeds the CME limit (regime II), the GW energy continues to increase without a corresponding increase of magnetic energy. In the early kinematic phase, the GW energy spectrum (per linear wavenumber interval) has opposite slopes in both regimes and is characterized by an inertial range spectrum in regime I and a white noise spectrum in regime II. The occurrence of these two slopes is shown to be a generic consequence of a nearly monochromatic exponential growth of the magnetic field. The resulting GW energy is found to be proportional to the fifth power of the limiting CME speed and the first power of the generation speed.

原始磁场可以产生遗迹引力波（GWs）。然而，关于产生的 GW 振幅及其对生成机制细节的依赖性知之甚少。在这里，我们将通过手性磁效应 (CME) 产生的磁场视为一种通用机制，并探讨其对产生速度（磁扩散率和特征波数的乘积）和表征 CME 预期的最大磁场强度的速度的依赖性. 当后者超过前者（适用于早期宇宙的制度）时，我们获得了一个具有中等 GW 能量的逆级联，该能量与磁能的三次幂成比例。当生成速度超过 CME 限制（规则 II）时，GW 能量继续增加，而磁能没有相应增加。在早期的运动学阶段，GW 能谱（每个线性波数间隔）在两种状态下都具有相反的斜率，其特征在于状态 I 中的惯性范围谱和状态 II 中的白噪声谱。这两个斜率的出现被证明是磁场几乎单色指数增长的一般结果。发现产生的 GW 能量与限制 CME 速度的五次方和发电速度的一次方成正比。这两个斜率的出现被证明是磁场几乎单色指数增长的一般结果。发现产生的 GW 能量与限制 CME 速度的五次方和发电速度的一次方成正比。这两个斜率的出现被证明是磁场几乎单色指数增长的一般结果。发现产生的 GW 能量与限制 CME 速度的五次方和发电速度的一次方成正比。