Rankine-Hugoniot Relations including Pickup Ions

The Rankine-Hugoniot relations are consequences of the global, magnetohydrodynamic conservation laws of mass, momentum, energy, and magnetic flux at shocks in plasma. They provide us with the boundary conditions, although these are insufficient to quantify the energy partition in substantially non-Maxwellian plasmas in the presence of nonthermal, pickup ions (PUIs). Ion dynamics inside the shock front is essentially nonadiabatic and gyrophase-dependent. The shock jump conditions are typically evaluated using the upstream and downstream distributions in the regions where they already become gyrotropic. The relation between the gyrophase-dependent motion inside the shock front and the gyrophase-averaged moments of the ion distributions is established using numerical ion tracing across a model shock profile, which includes the major basic features of a collisionless shock. The upstream distribution of PUIs is taken to be a filled shell. The obtained moments of the PUI distribution function are used to construct the Rankine-Hugoniot relations for a gyrotropic plasma regime. The quality of numerical ion tracing is checked by comparing it with full particle simulations. The moments of the distribution in the isotropic region are estimated.