Recent kinetic simulations of supercritical, quasi-perpendicular shocks
yield time varying shock solutions that cyclically reform on the
spatio-temporal scales of the incoming protons. Whether a shock solution is
stationary or reforming depends upon the plasma parameters which, for SNR
shocks are ill defined but believed to be within thetime-dependent regime. We will first review the structure and evolution of
the time dependentsolutions, and the acceleration processes of the ions and electrons in
these time dependent fields, for a proton-electron plasma. We will then
present recent results for a three component plasma: background
protons; electrons; and a second heavier ion population. These acceleration
mechanisms may generate a suprathermal\"injection$quot; population - a seed population for subsequent
acceleration at the shock, which can in turn generate particles at cosmic
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