Bursty betatron acceleration of electrons at nonstationary quasi-perpendicular shocks

Energetic, non-thermal electrons with power-law energy spectra are directly observed in the vicinity of the Earth's quasi-perpendicular bow shock. However, the acceleration mechanism of these electrons remains unclear. Here we show, using 1D PIC simulations of a quasi-perpendicular collisionless shock (M_A~7.1, shock angle 70°, beta ~0.3), that bursts of energetic electrons are produced at a reforming magnetic overshoot by betatron acceleration in addition to the shock drift acceleration. The betatron acceleration occurs through efficient trapping in a thin magnetic trough formed by a phase-standing whistler wave, and achieves an energy gain larger than that obtained by the shock drift acceleration only. We also found that the shock potential works against the acceleration, but the accelerations are more efficient and leads to the net energy gain. We envision that this betatron acceleration process is an important component of the entire process of electron acceleration to non-thermal energies at a non-stationary, quasi-perpendicular shock.