Dead time effect on single photon counting for the longitudinal density monitor LHC

The longitudinal distribution of the protons in the two LHC rings needs to be known with high accuracy. This is required for both: the correct operation of the machine and the understanding of beam dynamics effects that can influence the performances of the collider. One possible way of achieving the required time resolution of 50 ps and dynamic range of 10.4 is single photons counting of the synchrotron radiation emitted by the beams using avalanche photo diodes (APDs). Although this kind of devices have very short rise times and allow precise time stamping of detected photons, they also have long recovery times (dead time) of the order of humdreds of nanoseconds, much longer than the bunch length of the LHC beams. For this reason it is important to evaluate the masking effect introduced by this dead time, where photons emitted by protons in different longitudinal positions will have different probabilities of being detected.