Diffusive Shock Acceleration by Multiple Shocks

Diffusive shock acceleration produces a power law momentum distribution f(p)α p −b , with b ≥ 4 for a single shock, and b = 4 for a single strong shock. It has been shown that the distribution for acceleration at a sequence of identical shocks is flatter, approaching f(p)α p −3 below a high energy knee, for an arbitrarily large number of shocks. We show how this flatter distribution arises and discuss the range of momenta over which it extends after a finite number of shocks.