Parametric X-ray FEL operating with external Bragg reflectors

This report is devoted to the application of external Bragg reflectors in operating a volume parametric X-ray FEL. It is shown that external Bragg reflectors permit not only a reduction in electromagnetic energy losses through target boundaries but also a reduction in the radiation self-absorption inside the target by modifying radiation modes excited in the active medium containing a particle beam plus a crystal. As a result, the starting beam current can be reduced by more than a factor of ten. It is also shown that the best conditions for lasing are realized when the diffracted wave is reflected by the external Bragg reflector.