New Publication: “Combining Rankine–Hugoniot relations, ion dynamics in the shock front, and the cross-shock potential” by Michael Gedalin

RankineHugoniot relations (RH) connect the upstream and downstream plasma states. They allow us to determine the magnetic compression, the density compression, and the plasma heating as functions of the Mach number, shock angle, and upstream temperature. RH are based on the conservation laws in the hydrodynamical form. In collisionless shocks, the ion distributions behind the shock transition are determined by ion dynamics in the macroscopic fields of the shock front. The ion parameters upon crossing the shock are directly related to the magnetic compression and the cross-shock potential. For given upstream parameters, RH provide the magnetic compression. If there is no substantial overshoot, an analytical estimate provides the cross-shock potential as a function of the magnetic compression and the Mach number. Numerical tracing of ions across a shock profile with the derived parameters provides the ion pressure, which is in good agreement with the combination of the two theoretical approaches.

The normalized model magnetic field (black curve), the magnetic field derived from the pressure balance (blue curve), and the reduced distribution function (log scale), for M = 4.3, 𝜃=60°, and 𝐵𝑑/𝐵𝑢=3, with overshoot and undershoot added.

Full Article:
Gedalin, M. (SHARP) (2022), Combining Rankine-Hugoniot relations, ion dynamics in the shock front, and the cross-shock potential. Physics of Plasmas, 29, doi: 10.1063/5.0120578

License: CC BY 4.0