Collisionless shocks are frequently analysed using the magnetohydrodynamics (MHD) formalism, even though MHD assumes a small mean free path. Yet, isotropy of pressure, the fruit of binary collisions and assumed in MHD, may not apply in collisionless shocks. This is especially true within a magnetized plasma, where the field can stabilize an anisotropy. In a previous article (Bret & Narayan, J. Plasma Phys., vol. 88, no. 6, 2022b, p. 905880615), a model was presented capable of dealing with the anisotropies that may arise at the front crossing. It was solved for any orientation of the field with respect to the shock front. Yet, for some values of the upstream parameters, several downstream solutions were found. Here, we complete the work started in Bret & Narayan (J. Plasma Phys., vol. 88, no. 6, 2022b, p. 905880615) by showing how to pick the physical solution out of the ones offered by the algebra. This is achieved by 2 means: (i) selecting the solution that has the downstream field obliquity closest to the upstream one. This criterion is exemplified on the parallel case and backed up by particle-in-cell simulations. (ii) Filtering out solutions which do not satisfy a criteria already invoked to trim multiple solutions in MHD: the evolutionarity criterion, that we assume valid in the collisionless case. The end result is a model in which a given upstream configuration results in a unique, or no downstream configuration (as in MHD). The largest departure from MHD is found for the case of a parallel shock.

中文翻译：

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对等离子体中倾斜无碰撞激波的密度跳跃：物理解决方案

尽管 MHD 假设平均自由程较小，但经常使用磁流体动力学 (MHD) 形式来分析无碰撞冲击。然而，压力各向同性（二元碰撞的结果并在 MHD 中假设）可能不适用于无碰撞冲击。在磁化等离子体中尤其如此，其中磁场可以稳定各向异性。在上一篇文章中（布雷特和纳拉扬，J.等离子体物理学。，卷。 88，没有。 2022年6月乙，p。 905880615），提出了一个能够处理前方交叉口可能出现的各向异性的模型。该问题已针对任何相对于激波前沿的场方向进行了求解。然而，对于上游参数的某些值，找到了几个下游解决方案。在这里，我们完成了 Bret 和 Narayan 开始的工作（J.等离子体物理学。，卷。 88，没有。 2022年6月乙，p。 905880615）通过展示如何从代数提供的物理解决方案中挑选物理解决方案。这是通过两种方法实现的：(i) 选择下游场倾角最接近上游场倾角的解。该标准在并行情况下得到了例证，并得到了细胞内粒子模拟的支持。 (ii) 过滤掉不满足已调用的标准来修剪 MHD 中的多个解决方案的解决方案：进化标准，我们假设在无碰撞情况下有效。最终结果是一个模型，其中给定的上游配置导致唯一的或没有下游配置（如 MHD 中）。与 MHD 最大的偏离是在平行激波的情况下。