Effects of the passive voltage divider in a photomultiplier tube: Analytical model, simulations and experimental validation

The effects of the passive resistive voltage divider network in a photomultiplier tube (PMT) have been investigated by developing an in-house Monte Carlo simulation code and compared with experimental measurements and an analytical model. The simulation code follows an iterative procedure that takes into account the transport and amplification of the electrons within the device depending on the electrostatic fields produced by the electrode voltages. The PMT gain, dynode voltages, rise time and transit time have been studied as a function of the photocathode current and supply voltage. A good agreement between the analytical model, the simulations and numerous experimental measurements using a Hamamatsu R13408-100 PMT has been obtained. The simulation results endorse the use of logistic functions within the analytical model to account for the collection efficiency in the last dynode stages. This works deepens the understanding of passive voltage dividers and develops an advanced behavioral circuit model of photomultiplier tubes. Although validated for a single PMT, the proposed methodology is applicable to any PMT model. This aids in optimizing the design of fully active voltage dividers, to be applied in extremely pulsed applications with high count rates such as prompt gamma-ray imaging during proton therapy.