Practical theory of the multilayered transition radiation detector

The transition radiation detector for ultrarelativistic particles with a multifoil radiator is studied in the following aspects: x-ray spectrum, $\gamma$ dependence, interference effects, saturation at high $\gamma$, effects of irregularities, and multiple scattering. The analysis is simplified by reducing the various parameters to essentially three dimensionless quantities: a scaled Lorentz factor $\Gamma$, a scaled frequency $\nu$, and the ratio $\tau =\frac{\mathrm{foil} \mathrm{spacing}}{\mathrm{foil} \mathrm{thickness}}$. Large threshold effects due to interference are predicted which can be used to build a threshold detector or to measure the x-ray index of refraction of a material. Theoretical curves are given. Photon statistics, optimization of the detector, and computational method are discussed briefly.