Over-cooled and Over-heated Electrons Through a Perpendicular Collisionless Shock : Theory Versus Simulations

Test particle simulations have been performed in order to analyze the time evolution of transmitted electrons dynamics through a supercritical perpendicular collisionless shock. In addition to the adiabatic transmitted particles, two distincts non adiabatic populations are observed. The first one suffers an "overheating" characterized by an increase of the gyrating velocity higher than that supposed by the conservation of the magnetic moment, and the second one suffers a "cooling" characterized by a deceleration of this velocity. a) Present simulations show that these two non-adiabatic populations, strongly depend on the particle injection parameters (both angles with respect to the shock front and initial gyrating velocities), at the beginning time of the ramp crossing. A single particle model is proposed and compared with these numerical results, and points out the key role of the DC electrostatic field at the shock ramp in the formation of non-adiabatic transmitted electrons. b) Moreover, a statistical analysis (electron heating) is performed with the use of a Lyapounov coefficient and a theoretical model including linearly varying profiles of the electric and magnetic fields. Numerical results are found in a good agreement with those issued from PIC simulations.