On the distribution function of suprathermal particles at collisionless shocks

The departure of particle distributions from the Maxwellian is commonly observed in space plasmas. These non-Maxwellian which are typical for plasmas that not thermal equilibrium, can be modeled with ?-distribution. Kinetic simulations quasi-parallel collisionless shocks show proton distribution a composite thermal, suprathermal, and non-thermal parts. By using particle-in-cell shock simulations, we ?-distribution adequately fits suprathermal parts together, as single continuous early spectra. We derive directly generalized entropy non-extensive statistical mechanics, populations both naturally embedded find index ? increases distance shock, following decrease part. non-equilibrium plasma continuously being enriched particles at reforming barrier, reaches equilibrium far downstream. part completely fades there, shape becomes emerges power-law.