Modified jump conditions for parallel collisionless shocks

Within the context of Magnetohydrodynamics (MHD), the properties of a parallel shock do not depend on the field strength as the field and the fluid are disconnected for such a geometry. However, in the collisionless case, the field can sustain a stable anisotropy in the downstream, triggering a departure from the expected MHD behavior. In a recent work [A. Bret and R. Narayan, J. Plasma Phys. 84, 905840604 (2018)], a theoretical model was presented, allowing us to derive the density ratio of a non-relativistic parallel collisionless shock in an electron/positron plasma as a function of the field. Here, we derive the entropy, pressure, and temperature jumps stemming from this model. It is found to offer a transition between a 3D and a 1D downstream for the jumps in density, entropy, parallel temperature, and parallel pressure.