Maximum synchrotron frequency for shock-accelerated particles

It is widely believed that the maximum energy of synchrotron photons when electrons are accelerated in shocks via the Fermi process is about 50 MeV (in plasma comoving frame). We show that under certain conditions, which are expected to be realized in relativistic shocks of gamma-ray bursts, synchrotron photons of energy much larger than 50 MeV (comoving frame) can be produced. The requirement is that magnetic field should decay downstream of the shock front on a length scale that is small compared with the distance traveled by the highest energy electrons before they lose half their energy; photons of energy much larger than 50 MeV are produced close to the shock front whereas the highest Lorentz factor that electrons can attain is controlled by the much weaker field that occupies most of the volume of the shocked plasma.