Electron Acceleration and Efficiency in Nonthermal Gamma-Ray Sources
  In energetic nonthermal sources such as gamma-ray bursts, AGN or galactic jet sources, etc., one expects both relativistic and transrelativistic shocks acompanied by violent motions of moderately relativistic plasma. We present general considerations indicating that these sites are electron and positron accelerators leading to a modified power law spectrum. The electron (or $e^\pm$) energy index is very hard, $\propto \gamma^{-1}$ or flatter up to a comoving frame break energy $\gamma_\ast$, and becomes steeper above that. In the example of gamma-ray bursts the Lorentz factor reaches $\gamma_\ast\sim 10^3$ for $e^{\pm}$ accelerated by the internal shock ensemble on subhydrodynamical time scales. For pairs accelerated on hydrodynamical timescales in the external shocks similarly hard spectra are obtained, and the break Lorentz factor can be as high as $\gamma_\star \siml 10^5$. Radiation from the nonthermal electrons produces photon spectra with shape and characteristic energies in qualitative agreement with observed generic gamma-ray burst and blazar spectra. The scenario described here provides a plausible way to solve one of the crucial problems of nonthermal high energy sources, namely the efficient transfer of energy from the proton flow to an apropriate nonthermal lepton component. 
A. Bykov and P. Meszaros