Non-linear quantum regime of an X-ray wiggler laser

The scheme of X-ray coherent radiation generation in the non-linear quantum regime by means of a relativistic high-density electron beam in a wiggler is investigated. Due to the large wiggler parameter it is possible to achieve the quantum regime of an FEL at high harmonics of Doppler-shifted “wiggler frequencies”. The consideration is based on the self-consistent set of the Maxwell and relativistic quantum kinetic equations. Because of the non-equidistantness of the energy-momentum levels the probe wave resonantly couples only two electron states in the wiggler and the coupled equations are solved in the slowly varying envelope approximation.