Unlimited relativistic shock surfing acceleration

Non-relativistic shock surfing acceleration at quasiperpendicular shocks is usually considered to be a preacceleration mechanism for slow pickup ions to initiate diffusive shock acceleration. In shuck surfing, the particle accelerates along the shock front under the action of the convective electric field of the plasma flow. However, the particle also gains kinetic energy normal to the shock and eventually escapes downstream. We consider the case when ions are accelerated to relativistic velocities. In this case, the ions are likely to be trapped for infinitely long times, because the energy of bounce oscillations tends to decrease during acceleration. This suggests the possibility of unlimited acceleration by shock surfing.