Under and over-adiabatic electrons through a perpendicular collisionless shock: theory versus simulations

Test particle simulations are performed in order to analyze in detail the dynamics of transmitted electrons through a supercritical, strictly perpendicular, collisionless shock. In addition to adiabatic particles, two distinct nonadiabatic populations are observed surprisingly: (i) first, an over-adiabatic population characterized by an increase in the gyrating velocity higher than that expected from the conservation of the magnetic moment μ, and (ii) second, an underadiabatic population characterized by a decrease in this velocity. Results show that both nonadiabatic populations have their pitch angle more aligned along the magnetic field than the adiabatic one at the time these hit the shock front. The formation of “under” and “over-adiabatic” particles strongly depends on their local injection conditions through the large amplitude cross-shock potential present within the shock front. A simplified theoretical model validates these results and points out the important role of the electric field as seen by the electrons. A classification shows that both nonadiabatic electrons are issued from the core part of the upstream distribution function. In contrast, suprathermal and tail electrons only contribute to the adiabatic population; nevertheless, the core part of the upstream distribution contributes at a lower percentage to the adiabatic electrons. Underadiabatic electrons are characterized by small injection angles θinj≤90, whereas “over-adiabatic” particles have high injection angles θinj>90 (where θinj is the angle between the local gyrating velocity vector and the shock normal).