Gamma-ray bursts and collisionless shocks
  Particle acceleration in collisionless shocks is believed to be responsible for the production of cosmic-rays over a wide range of energies, from few GeV to >10^{20}eV, as well as for the non-thermal emission of radiation from a wide variety of high energy astrophysical sources. A theory of collisionless shocks based on first principles does not, however, exist. Observations of gamma-ray burst (GRB) "afterglows" provide a unique opportunity for diagnosing the physics of relativistic collisionless shocks. Most GRBs are believed to be associated with explosions of massive stars. Their "afterglows," delayed low energy emission following the prompt burst of gamma-rays, are well accounted for by a model in which afterglow radiation is due to synchrotron emission of electrons accelerated in relativistic collisionless shock waves driven by the explosion into the surrounding plasma. Within the framework of this model, some striking characteristics of collisionless relativistic shocks are implied. These include the generation of downstream magnetic fields with energy density exceeding that of the upstream field by ~8 orders of magnitude, the survival of this strong field at distances ~10^{10} skin-depths downstream of the shock, and the acceleration of particles to a power-law energy spectrum, d\log n/d\log E ~ -2, possibly extending to 10^{20}eV. I review in this talk the phenomenological considerations, based on which these characteristics are inferred, and the challenges posed to our current models of particle acceleration and magnetic field generation in collisionless shocks. Some recent theoretical results derived based on the assumption of a self-similar shock structure are briefly discussed. 
E. Waxman (Weizmann Inst.)