Extending the Lorentz Factor Range and Sensitivity of Transition Radiation with Compound Radiators

Transition radiation detectors (TRDs) have been used to identify high-energy particles (in particular, to separate electrons from heavier particles) in accelerator experiments. In space, they have been used to identify cosmic-ray electrons and measure the energies of cosmic-ray nuclei. To date, radiators have consisted of regular configurations of foils with fixed values of foil thickness and spacing (or foam or fiber radiators with comparable average dimensions) that have operated over a relatively restricted range of Lorentz factors. In order to extend the applicability of future TRDs (for example, to identify 0.5 - 3 TeV pions, kaons, and protons in the far forward region in a future accelerator experiment or to measure the energy spectrum of cosmic-ray nuclei up to 20 TeV/nucleon or higher), there is a need to increase the signal strength and extend the range of Lorentz factors that can be measured in a single detector. A possible approach is to utilize compound radiators consisting of varying radiator parameters. We discuss the case of a compound radiator and derive the yield produced in a TRD with an arbitrary configuration of foil thicknesses and spacings.