Shock waves in plasma are usually dealt with using magnetohydrodynamics (MHD). Yet, MHD entails the assumption of a short mean free path, which is not fulfilled in a collisionless plasma. Recently, for pair plasmas, we devised a model allowing one to account for kinetic effects within a MHD-like formalism. Its relies on an estimate of the anisotropy generated when crossing the front, with a subsequent assessment of the stability of this anisotropy in the downstream. We solved our model for parallel, perpendicular and switch-on shocks. Here we bridge between all these cases by treating the problem of an arbitrarily, but coplanar, oriented magnetic field. Even though the formalism presented is valid for anisotropic upstream temperatures, only the case of a cold upstream is solved. We find extra solutions which are not part of the MHD catalogue, and a density jump that is notably less in the quasi-parallel, highly magnetized, regime. Given the complexity of the calculations, this work is mainly devoted to the presentation of the mathematical aspect of our model. A forthcoming article will be devoted to the physics of the shocks here defined.
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Density jump as a function of magnetic field for switch-on collisionless shocks in pair plasmas
The properties of collisionless shocks, like the density jump, are usually derived from magnetohydrodynamics (MHD), where isotropic pressures are assumed. Yet, in a collisionless plasma, an external magnetic field can sustain a stable anisotropy. We have already devised a model for the kinetic history of the plasma through the shock front ( J. Plasma Phys. , vol. 84, issue 6, 2018, 905840604), allowing to self-consistently compute the downstream anisotropy, and hence the density jump, in terms of the upstream parameters. This model deals with the case of a parallel shock, where the magnetic field is normal to the front both in the upstream and the downstream. Yet, MHD also allows for shock solutions, the so-called switch-on solutions, where the field is normal to the front only in the upstream. This article consists in applying our model to these switch-on shocks. While MHD offers only one switch-on solution within a limited range of Alfvén Mach numbers, our model offers two kinds of solutions within a slightly different range of Alfvén Mach numbers. These two solutions are most likely the outcome of the intermediate and fast MHD shocks under our model. While the intermediate and fast shocks merge in MHD for the parallel case, they do not within our model. For simplicity, the formalism is restricted to non-relativistic shocks in pair plasmas where the upstream is cold.
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- Award ID(s):
- 1816420
- PAR ID:
- 10406750
- Date Published:
- Journal Name:
- Journal of Plasma Physics
- Volume:
- 88
- Issue:
- 3
- ISSN:
- 0022-3778
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/S0022377822000605
