Modeling electron transport and multiplication in photomultiplier tubes using COMSOL Multiphysics®

Combining stochastic and finite element methods, a modeling approach was executed that will inform new photomultiplier tube and scintillation detector designs. Time-dependent signal formation within a commercially available photomultiplier tube was modeled including the release and transport of electrons from the photocathode through the dynode stages. An ET Enterprises 9214B photomultiplier tube was digitally reproduced using Computed Tomography, X-ray radiography, and SolidWorks solid-modeling software. Simulations were executed with COMSOL Multiphysics® finite element solving package. Stochastic models of electron emission from the photocathode and dynodes were integrated within the COMSOL framework. Photoelectron emission energy was modeled by combining NaI(Tl) spectral emission characteristics and K2CsSb photocathode quantum efficiency. Secondary electron emission yields were produced to follow nominal photomultiplier gain, while secondary electron energies were sampled from the Chung-Everhart distribution. Electron emission trajectories were sampled according to Lambert's cosine law. Coupling stochastic and finite element models, simulation reproduced signal formation for the commercial photomultiplier tube including timing characteristics within 9.5% and gain within 3% over a voltage range of 900–1250 V.