Transmitted ions and ion heating in nearly perpendicular low-Mach number shocks

Nonadiabatic ion heating in low-Mach number shocks is only partially due to reflected ions, Directly transmitted ions contribute significantly into the downstream ion temperature and can be responsible for the whole heating even in the absence of reflected ions, due to insufficient and inhomogeneous deceleration in the cross-shock potential, As a result, the average ion velocity at the downstream edge of the shock ramp is significantly greater than the velocity required by the Rankine-Hugoniot relations, and the ion distribution gyrates as a whole. Because of the nonlinear dependence of the deceleration on the cross-shock potential and initial ion velocity, the gyrating ion distribution is also much more dispersed than the upstream distribution, Additional dispersion is caused by the increase of the vector potential across the shock ramp, The heating depends not only on the bulk shock parameters, as Mach number and beta, but also on the field profile, The ion distribution which leaves the ramp is gyrophase-bunched. Further downstream, strong spatially periodic heating occurs, because the initially gyrophase bunched ions become periodically gyrophase dispersed due to nonlinear dependence of the ion gyrophase on its coordinate and velocity.