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An extreme case of electron shock drift acceleration in low Mach numbercollisionless shocks is investigated as a plausible mechanism of initialacceleration of relativistic electrons in large-scale shocks in galaxy clusterswhere upstream plasma temperature is of the order of 10 keV and a degree ofmagnetization is not too small. One-dimensional electromagnetic full particlesimulations reveal that, even though a shock is rather moderate, a part ofthermal incoming electrons are accelerated and reflected through relativisticshock drift acceleration and form a local nonthermal population just upstreamof the shock. The accelerated electrons can self-generate local coherent wavesand further be back-scattered toward the shock by those waves. This may be ascenario for the first stage of the electron shock acceleration occurring atthe large-scale shocks in galaxy clusters such as CIZA J2242.8+5301 which haswell defined radio relics.

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