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The effect of ion production through ionizing collisions in a magnetically insulated crossed-field gap is studied by using one-dimensional particle-in-cell software. These results are compared with the predictions from previous efforts that assumed immobile sheets of positive charge at different positions within the gap. Our results with mobile ions created via collisions indicate that the diode can lose magnetic insulation of the electron flow at ion densities lower than that predicted from the immobile ion case. Furthermore, we observe that electron scattering plays a significant role in this gap closure. This loss of insulation depends on the background pressure and leads to time-dependent migration of charge across the gap. We characterize both the time-scale and the degree of current transport for cases relevant to the high-power microwave community.