Consequences of electron reflection back upstream in oblique shocks

Astrophysical shocks are believed to efficiently accelerate charged particles, yet electrons need to undergo pre-acceleration to be energetic enough to cross the shock and join the game of acceleration. Understanding the mechanisms responsible for electron pre-acceleration is crucial to solving the shock injection problem. Here, we present PIC simulations of Oblique shocks of varying obliquity angle, using $\theta_{Bn} = 30^{\circ}, 45^{\circ}, 55^{\circ}, 63^{\circ}$ and $74.3^{\circ}$. Our analyses focus on the reflection of incident electrons back upstream, with these particles capable of generating upstream turbulence and transferring energy away from the shock itself and to the upstream plasma. In this work, we demonstrate that electron reflection initially occurs in the foot region of the shock, with upstream electrons trapped and accelerated by Buneman waves before being reflected. We show that while the proportion of reflected electrons is negligible for $\theta_{Bn} = 74.3$, but increases to $\sim 5\%$ for $\theta_{Bn} = 30$. We show that the most probable energy of reflected electrons is $\propto 1/\cos \theta_{Bn}$, but higher reflection rates at low $\theta_{Bn}$ mean in total reflected electrons here carry more kinetic energy back upstream, which produces turbulence. We show that reflected electrons generate electrostatic waves in the upstream region on length scales comparable to Buneman waves, and discuss how these waves interact with upstream electrons, and discuss whether they could compromise the efficiency of electron injection at the shock.