Estimation of the Spatial Extent of the Transient Gain Drop in a Microchannel Plate

The gain of the microchannel plate temporally drops after an ion initiates an electron avalanche. Electron multiplication was expected to deplete the charge from the microchannel wall and produce the depleted charge (wall charge). Moreover, it was reported that the gain drop occurred not only in the activated channels, where the electrons are multiplied, but also in the surrounding channels. One mechanism of the gain-drop spatial extension has been considered as that the wall charges in the activated channels change the electric field in the surrounding channels. Anacker et al. assumed that the wall charge is a uniform line charge; the gain-drop spatial extent should be proportional to the amount of the wall charges. We considered that the wall charges exponentially increased in the channel toward the exit. In this study, the electric field produced by the wall charges was calculated, considering the distribution of the wall charges. The transverse electric field generated by the wall charges was expected to disturb the electron trajectory near the channel exit and decrease the number of secondary electrons emitted per collision (gain per collision), resulting in a gain drop. The gain per collision was calculated to decrease by 22% for the position where the gain decreased significantly in the presence of the transverse electric field of 3×10⁵ V/m. In our model, the gain-drop spatial extent extended proportionally to the square root of the wall charges when the distance from the activated channel exceeded 50 μm.