Rankine-Hugoniot Relations in Multispecies Plasma With Gyrotropic Anisotropic Downstream Ion Distributions

In the observed heliospheric shocks downstream distributions are usually measured in the regions where the kinematic relaxation has already happened but isotropy is not achieved. Rankine-Hugoniot relations, connecting the upstream and downstream plasma parameters, should be able to take into account the downstream ion anisotropy. In a multispecies plasma different species behave differently at the ramp crossing and when collisionlessly gyrating in the downstream region. The downstream density and pressure of each species can be expressed in terms of the magnetic compression and the cross-shock potential, which allows us to derive new Rankine-Hugoniot relations.