Electron acceleration at nearly perpendicular collisionless shocks: 3. Downstream distributions

Abstract

Spacecraft observations at the Earth's bow shock and at interplanetary shocks have established that the largest fluxes of accelerated suprathermal electrons occur in so‐called shock spike events immediately downstream of the shock ramp. Previous theoretical efforts have mainly focused on explaining upstream energetic electron beams. Here we investigate the general motion and acceleration of energetic electrons in a curved, nearly perpendicular shock by numerically integrating the orbits of solar wind halo electrons in shock fields generated by a hybrid simulation (core electron fluid and kinetic ions). Close to the angle θBn = 90° between the upstream magnetic field and shock normal, the calculations result in a (perpendicular) temperature increase proportional to the magnetic field ratio and give the highest phase space densities in the overshoot. For a steep distribution, the temperature change can correspond to an enhancement of the distribution by several orders of magnitude. These results are in agreement with predictions from adiabatic mapping. With smaller angles θBn, the overshoot and downstream densities fall off quickly, because the adiabatic energy gain is less and fewer electrons transmit. The shock curvature also leads to an accumulation of electrons close to 90°. Without pitch angle scattering, energization is only significant within a few (∼ 5° to 10°) degrees of the point of tangency. However, shock spike events appear to be observed more easily and farther away from 90°. Given that over a region of several degrees around 90° the theory gives enhancements of up to ∼ 4 orders of magnitude, such electrons could in principle account for the typically observed enhancements of 1 to 2 orders of magnitude, if they were distributed over θBn. To test the idea that scattering could efficiently redistribute the energetic electrons, we have conducted test particle simulations in which artificial pitch angle scattering is included. We find that such a process can indeed be very efficient and can explain observations of shock spike events far away from θBn ∼ 90°. The scattering naturally leads to much higher phase space densities at smaller θBn than what a local one‐dimensional mapping would predict and thus can account for an observed discrepancy with adiabatic theory stated in the literature.