Production of X-ray transition radiation with relativistic electrons propagating at grazing incidence

This paper is concerned with the production of X-ray transition radiation when a relativistic electron crosses the interface between two media of different permittivities at the grazing incidence. The production yields are derived analytically when a thick interface is considered and are compared with those obtained when the electron crosses the interface at normal incidence. The production of X-ray photons having an energy between two photoabsorption edges or close to a photoabsorption edge is also investigated. The main features of the transition radiation produced are then exhibited and it is shown that the intensity can be increased by many orders of magnitude. We also show that, at grazing incidence, the backward transition radiation has an intensity close to the forward emission one, contrary to the normal incidence case. The production of quasi-monochromatic radiation is also presented. Finally, the production of X-ray transition radiation using a multilayer radiator is considered and compared in both geometries.