We investigate ion-scale kinetic plasma instabilities at the collisionless shock using linear theory and nonlinear particle-in-cell (PIC) simulations. We focus on the Alfvén ion cyclotron (AIC), mirror, and Weibel instabilities, which are all driven unstable by the effective temperature anisotropy induced by the shock-reflected ions within the transition layer of a strictly perpendicular shock. We conduct linear dispersion analysis with a homogeneous plasma model to mimic the shock transition layer by adopting a ring distribution with finite thermal spread to represent the velocity distribution of the reflected ions. We find that, for wave propagation parallel to the ambient magnetic field, the AIC instability at lower Alfvén Mach numbers tends to transition to the Weibel instability at higher Alfvén Mach numbers. The instability property is, however, also strongly affected by the sound Mach number. We conclude that the instability at a strong shock with Alfvén and sound Mach numbers both in excess of $\sim 20–40$ may be considered as Weibel-like in the sense that the reflected ions behave essentially unmagnetized. Two-dimensional PIC simulations confirm the linear theory and find that, with typical parameters of young supernova remnant shocks, the ring distribution model produces magnetic fluctuations of the order of the background magnetic field, which is smaller than those observed in previous PIC simulations for Weibel-dominated shocks. This indicates that the assumption of the gyrotropic reflected ion distribution may not be adequate to quantitatively predict nonlinear behaviors of the dynamics in high Mach number shocks.

中文翻译：

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无碰撞垂直激波中离子尺度动力学不稳定性的马赫数依赖性：Weibel 主导激波的条件

我们使用线性理论和非线性细胞内粒子 (PIC) 模拟研究了无碰撞冲击时离子级动力学等离子体的不稳定性。我们关注阿尔文离子回旋加速器 (AIC)、反射镜和韦贝尔不稳定性，这些不稳定性都是由严格垂直激波的过渡层内激波反射离子引起的有效温度各向异性引起的。我们使用均质等离子体模型进行线性色散分析，通过采用具有有限热扩散的环分布来表示反射离子的速度分布来模拟激波过渡层。我们发现，对于平行于环境磁场的波传播，较低阿尔文马赫数下的 AIC 不稳定性倾向于过渡到较高阿尔文马赫数下的韦伯不稳定性。不稳定性是，然而，声音也受马赫数的强烈影响。我们得出结论，阿尔文和稳健马赫数在强烈冲击下的不稳定性都超过$～20——40$可以认为是类 Weibel 的，因为反射离子基本上是未磁化的。二维 PIC 模拟证实了线性理论，并发现，利用年轻超新星残余冲击的典型参数，环分布模型产生背景磁场数量级的磁涨落，这比之前 Weibel PIC 模拟中观察到的要小- 主导的冲击。这表明回旋反射离子分布的假设可能不足以定量预测高马赫数激波中动力学的非线性行为。