On the Efficiency of Fermi Acceleration at Relativistic Shocks

Abstract

We show that Fermi acceleration at an ultrarelativistic shock wave cannot operate on a particle for more than 1 Fermi cycles (i.e., u → d → u → d) if the particle's Larmor radius is much smaller than the coherence length of the magnetic field on both sides of the shock, as is usually assumed. This conclusion proves to be in excellent agreement with recent numerical simulations. We thus argue that efficient Fermi acceleration at ultrarelativistic shock waves requires significant nonlinear processing of the far-upstream magnetic field with strong amplification of the small-scale magnetic power. The streaming or transverse Weibel instabilities are likely to play a key role in this respect.