  An extreme case of electron shock drift acceleration in low Mach number
collisionless shocks is investigated as a plausible mechanism of initial
acceleration of relativistic electrons in large-scale shocks in galaxy clusters
where upstream plasma temperature is of the order of 10 keV and a degree of
magnetization is not too small. One-dimensional electromagnetic full particle
simulations reveal that, even though a shock is rather moderate, a part of
thermal incoming electrons are accelerated and reflected through relativistic
shock drift acceleration and form a local nonthermal 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 has
well defined radio relics.
