Coherent bremsstrahlung in a bent crystal

At passage of an ultra-high-energy particle through a bent crystal coherent bremsstrahlung is emitted but with characteristic frequencies distributed continuously, in relation with the crystal bend profile. For practical crystals, such radiation can be calculated by the stationary phase approximation technique. The radiation spectrum averaged over the impact parameters is evaluated. Its characteristic feature is the presence of sharp breaks (or of the spectrum end-point) at photon energies proportional to frequencies of crystalline plane crossing at the edges of the crystal, but those features will smear out if the angular divergence of the beam is comparable to half the crystal bending angle.