Density jump as a function of the field for parallel relativistic collisionless shocks

Collisionless shocks are frequently analyzed using the magnetohydrodynamic formalism (MHD), even though the required collisionality hypothesis is not fulfilled. In a previous work (Bret & Narayan 2018), we presented a model of collisionless shock displaying an important departure from the expected MHD behavior, in the case of a strong flow aligned magnetic field. This model was non-relativistic. Here, it is extended to the relativistic regime, considering zero upstream pressure. The result agrees satisfactorily with Particle-in-Cell simulations.