Heat Fluxes in Collisionless Magnetohydrodynamic Shock Waves

On the parallel shock waves in collisionless plasma with heat fluxes

“…The first condition in each of the above cases also defines a region on the plane of upstream parameters (M 1 , κ 1 ) while second condition defines a region on the plane of downstream parameters (M 2 , κ 2 ). Using the solution (13) of RH relations the reverse functions can be used to map the downstream state (and thus the second condition) into the upstream state: (M 2 , κ 2 ) → (M 1 , κ 1 ) [27]. The intersection of these two regions defines a region of evolutionarity although in some cases the intersection may be empty.…”