  The equations, which describe generation of coherent radiation by a
relativistic electron bunch moving in a photonic crystal, are obtained.
Spectral-angular distribution of radiation and intensity of radiation in
time-domain are derived. The interaction of the bunch electrons with the
electromagnetic field induced by bunch itself at the initial stage of producing
coherent radiation is shown contributing to the expression for the bunch
current with the terms proportional to particle acceleration (proportional to
interaction time and strength of electric field induced by bunch itself) along
with the terms proportional to velocity. Induced radiation produced by the
relativistic bunch is considered using the quantum physics approach.

Accelerator Physics