Simple analytical model of gain saturation in microchannel plate devices

We derive, discuss, and test against experimental data an analytical model of the gain saturation in microchannel plate (MCP) devices. By introducing a simple recharging circuit for each dynode, we extend the well-known, unsaturated gain model of Eberhardt to a microchannel operating in condition of gain saturation and show that the amplification of a current pulse and the voltage drop along the channel can be described by a pair of coupled differential equations. Solutions of these equations are given in various conditions, including an approximate solution, valid in the case of weak saturation and a general solution in implicit form. The behavior of a microchannel operating in current mode is studied by finding the transient and steady-state solutions obtained with an input step current wave form. Exact solutions are given for the charge gain of pulses with a short duration, compared to the dynode recharging time, and for the gain recovery of a microchannel after the amplification of...