  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.
