Demodulation of a positron beam in a bent crystal channel

The evolution of a modulated positron beam in a planar crystal channel is investigated within the diffusion approach. A detailed description of the formalism is given. A new parameter, the demodulation length, is introduced, representing the quantitative measure of the depth at which the channelling beam preserves its modulation in the crystal. It is demonstrated that there exist crystal channels with the demodulation length sufficiently large for using the crystalline undulator as a coherent source of hard X-rays. This finding is a crucial milestone in developing a new type of lasers radiating in the hard X- and gamma-ray range.