Relativistic collisionless shocks

I will present a summary of recent progress in theoretical modeling of relativistic collisionless shocks, focusing on the first-principles simulations of shocks using particle-in-cell codes. Such simulations allow self-consistent calculations of the structure of shocks and the generated turbulence. I will discuss the internal structure of shocks in different regimes of flow magnetization and composition, concentrating on the conditions necessary for particle acceleration. I will present simulations which show ab-initio Fermi acceleration of particles from the thermal pool to power-law distributions, setting constraints on the shock acceleration efficiency and geometry. Other results that will be discussed include the amplification of the upstream magnetic field by accelerated particles through streaming instabilities, and the electron-ion temperature equilibration in collisionless shocks. I will conclude with the applications of shock simulations to the physics of gamma-ray bursts, pulsar wind nebulae, and supernova remnants. (author)