An optimization model of targets for resonant transition radiation in the X-ray range

Generation of resonant transition radiation (RTR) is potentially a method to obtain useable fluxes of tuneable, relatively narrow-band soft X-ray radiation from compact (<10 MeV) electron accelerators. The RTR targets to be used are periodic multilayer structures of two materials with low absorption and high refractive-index contrast in the soft X-ray range. We present a model for optimizing the parameters of such targets. The model is based on an extension of the Ginzburg-Franck equation for transition radiation from a single interface. The model also accounts for absorption, elastic scattering, energy spread of the electron beam and inaccuracy in the foil thicknesses. Two examples are treated. First, a multilayer structure consisting of Mo foils and vacuum spacers is optimized for generation of 13.5 nm radiation by an electron beam with energy of 9 MeV. The model predicts a yield of up to 0.045 photons per electron per (eV sr). Second, a multilayer structure consisting of Al foils and vacuum spacers is optimized for generation of 0.83 nm radiation by 150 MeV electrons. For the latter case, the model predicts a yield of up to 3.7 photons per electron per (eV sr).