Step 1. Cycle Initiation

Figure below show the void space free from charges (dark red) and the initiation of a burst of 30V electrons at the 1 um cathode tip. The square wave puls is characterized by a very steep leading edge (high dV/dt), a short holding time at peak voltage, and a steep tailing edge, again at high dV/dt. 

Then there is a longer time period for next puls. This period allows remaining free electrons in the void space to find the way to the anode. The time period also helps thermal heat dissipation. A cycle time with today's fast MOSFET transistors can be made for 10 MHz.