Transition radiation (TR) X-rays are expected to he a highly brilliant X-ray source because the interference among TR X-rays emitted from many thin foils placed periodically in vacuum can increase their intensity and make them quasi-monochromatic. In order to study the interference (resonance) effects of TR, we measured the energy spectra of TR for several sets of thin foil stacks at various emission angles. It was found that the resonance effects of TR are classified into intrafoil and interfoil resonances and the intensity of TR X-rays increases nonlinearly with increasing foil number, attributed to the interfoil resonance. It became evident that the brilliance of TR is as high as that of SR.
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