The pulse-pile-up tail artifact in pulse-height spectra

Pulse pile-up in pulse-height energy analyzers increases when the incident rate of pulses is comparable to or larger than the pulse pair resolving time of the detection system. Large changes in the observed energy distributions with incident rate and pulse shape then occur. In this paper we focus on the high energy tail of X-ray spectra, important for measurements on partially ionized, warm, pure-hydrogen plasma. A two-photon pulse-pile-up model is derived for trapezoidal-shaped pulses produced in Amptek Fast SDD detectors and quantitative agreement is found between the measurements and the model predictions. Further progress was made to extend the model to an arbitrary number of photon PPU by making use of Fourier transform on convolution terms which enabled the model to handle spectrum with arbitrary total count rate.