Particle Acceleration in Relativistic Collisionless Shocks: Fermi Process at Last?

Abstract

We present evidence that relativistic shocks propagating in unmagnetized plasmas can self-consistently accelerate particles. We use long-term two-dimensional particle-in-cell simulations to study the well-developed shock structure in unmagnetized pair plasma. The particle spectrum downstream of such a shock consists of two components: a relativistic Maxwellian, with characteristic temperature set by the upstream kinetic energy of the flow, and a high-energy tail, extending to energies >100 times that of the thermal peak. This tail is best fitted as a power law in energy with index -2.4+-0.1, modified by an exponential cutoff. The cutoff moves to higher energies with time of the simulation, leaving a larger power law range. The number of particles in the tail is ~1% of the downstream population, and they carry ~10% of the kinetic energy in the downstream. Upon investigation of the trajectories of particles in the tail, we find that the energy gains occur as particles bounce between the upstream and downstream regions in the magnetic fields generated by the Weibel instability. We compare this mechanism to the first order Fermi acceleration, and set a lower limit on the efficiency of shock acceleration process.