  The effective bandwidth of an energy dispersive x-ray fluorescence
spectroscopy system is limited by the timing of incident photons. When multiple
photons strike the detector within the processing time of the detector photon
pile-up occurs and the signal received by the detector during this interval
must be ignored. In conventional ED-XRF systems the probability of a photon
being incident upon the detector is uniform over time, and thus pile-up follows
Poisson statistics. In this paper we present a mathematical treatment of the
relationship between photon timing statistics and the count rate of an XRF
system. We show that it is possible to increase the maximum count rates by
applying feedback from the detector to the x-ray source to alter the timing
statistics of photon emission. Monte-Carlo simulations, show that this
technique can increase the maximum count rate of an XRF spectroscopy system by
a factor of 2.94 under certain circumstances.
