Return Currents in Collisionless Shocks

Collisionless shocks tend to send charged particles into the upstream, driving electric currents through the plasma. Using kinetic particle-in-cell simulations, we investigate how the background thermal plasma neutralizes such currents in the upstream of quasi-parallel non-relativistic electron-proton shocks. We observe distinct processes in different regions: the far upstream, the shock precursor, and the shock foot. In the far upstream, the current is carried by nonthermal protons, which drive electrostatic modes and produce supra-thermal electrons that move towards upstream infinity. Closer to the shock (in the precursor), both the current density and the momentum flux of the beam increase, which leads to electromagnetic streaming instabilities that contribute to the thermalization of supra-thermal electrons. At the shock foot, these electrons are exposed to shock-reflected protons, resulting in a two-stream type instability. We analyze these processes and the resulting heating through particle tracking and controlled simulations. In particular, we show that the instability at the shock foot can make the effective thermal speed of electrons comparable to the drift speed of the reflected protons. These findings are important for understanding both the magnetic field amplification and the processes that may lead to the injection of supra-thermal electrons into diffusive shock acceleration.