Coherent synchrotron emission from cosmic ray air showers
  Coherent synchrotron emission by particles moving along semi-infinite tracks is discussed, with a specific application to radio emission from air showers induced by high-energy cosmic rays. It is shown that in general, radiation from a particle moving along a semi-infinite orbit consists of usual synchrotron emission and modified impulsive bremsstrahlung. The latter component is due to the instantaneous onset of the curved trajectory of the emitting particle at its creation. Inclusion of the bremsstrahlung leads to broadening of the radiation pattern and a slower decay of the spectrum at the cut-off frequency than the conventional synchrotron emission. Possible implications of these features for air shower radio emission are discussed. 
Qinghuan Luo