Xuv resonant transition radiations from periodic stratified media

General formulation of the xuv intensity emitted when relativistic electrons cross through any periodic stratified medium is presented in the framework of electromagnetism in continuous media. Application is made to the resonant transition radiation emitted in the geometries of both normal and oblique incidence. In the first case, agreement is found between our calculated results and published values. Intensity emitted by a periodic multilayer stack used in the Bragg conditions is determined and the practical interest of a such a radiation source is discussed.