Practical theory of the multilayered transition radiation detector

Features of the multiplayered transition radiation detector for ultrarelativistic particles are studied, including especially details of: X-ray spectrum, gamma dependence, ( gamma =Lorentz factor) interference effects, saturation at high gamma , effects of irregularities, and multiple scattering. Three important dimensionless variables are introduced: a scaled Lorentz factor Gamma , a scaled frequency nu , and the ratio tau =foil spacing/foil thickness. One of the predictions is of large threshold effects due to interference, which can be exploited in a threshold detector for measuring a material's X-ray refractive index. Theoretical curves are given, along with a short discussion of photon statistics, optimisation of such a detector, and associated computational methods. (16 refs).