High-gain FEL on the coherent Bremsstrahlung of a relativistic electron beam in a crystal

In this paper a possible way to achieve lasing in the X-ray domain due to coherent Bremsstrahlung of an electron beam in the crystal is considered. The high-gain regime is investigated when charged particles move close to the crystal lattice plane or axis. The consideration is based on the self-consistent set of the Maxwell-Vlasov equations. We illustrate the resulting formulae with some speculative examples