Relativistic Electron Shock Drift Acceleration in Low Mach Number Galaxy Cluster Shocks

An extreme case of electron shock drift acceleration (SDA) in low Mach number collisionless shocks is investigated as a plausible mechanism for the initial acceleration of relativistic electrons in large-scale shocks in galaxy clusters, where the upstream plasma temperature is of the order of 10 keV and the degree of magnetization is not too small. One-dimensional electromagnetic full particle simulations reveal that, even when a shock is rather moderate, a part of the thermal incoming electrons are accelerated and reflected through relativistic SDA and form a local non-thermal population just upstream of the shock. The accelerated electrons can self-generate local coherent waves and further be back-scattered toward the shock by those waves. This may be a scenario for the first stage of the electron shock acceleration occurring at the large-scale shocks in galaxy clusters, such as CIZA J2242.8+5301, which have well-defined radio relics.