Analytical, steady-state model of gain saturation in channel electron multipliers

By using the transmission line modeling (TLM) technique we derive a simple model describing the saturation of the gain in channel electron multipliers and show that it generalizes and extends a previous steady-state model due to Shikhaliev. Then by introducing a physically consistent rational approximation of the non-linear gain equation we derive an exact, steady-state, analytical solution in which, contrary to other authors, empirical assumptions about the functional dependence of the internal voltage are not required. The model is then used to simulate a multianode microchannel plate (MCP) photomultiplier, showing that the computed gain in saturated conditions is qualitatively in agreement with published experimental data. Finally, we discuss the general validity of our model, we suggest possible measurements and comment existing data relevant for its validation.