Wakefield Acceleration by Radiation Pressure in Relativistic Shock Waves

A particle acceleration mechanism by radiation pressure of precursor waves in a relativistic shock is studied. For a relativistic, perpendicular shock with the upstream bulk Lorentz factor of $\gamma_1 \gg 1$, large amplitude electromagnetic (light) waves are known to be excited in the shock front due to the synchrotron maser instability, and those waves can propagate towards upstream as precursor waves. We find that non-thermal, high energy electrons and ions can be quickly produced by an action of electrostatic wakefields generated by the ponderomotive force of the precursor waves. The particles can be quickly accelerated up to $\epsilon_{\rm max}/\gamma_1 m_e c^2 \sim \gamma_1$ in the upstream coherent wakefield region, and they can be further accelerated during the nonlinear stage of the wakefield evolution. The maximum attainable energy is estimated by $\epsilon_{\rm max}/\gamma_1 m_e c^2 \sim L_{\rm sys}/(c/\omega_{pe})$, where $L_{\rm sys}$ and $c/\omega_{pe}$ are the size of an astrophysical object and the electron inertial length, respectively.