Count-rate statistics for drift detectors

Synchrotron light sources are low-duty-cycle pulsed X-ray sources, a fact that is often neglected in estimating the count-rate capabilities of photon-counting detectors in synchrotron-based experiments. In this paper, we demonstrate the effect that this has on the pileup statistics of drift detectors. We derive expressions for the cases of continuous and pulsed X-ray sources. We consider a pulsed source with period that is either much less than the shaper support time or much less than the average drift time. We also consider a pulsed source with a period that is long or comparable to both the shaper support and the drift time. These conditions correspond to normal and reduced bunch fill patterns of synchrotrons.