A 2D particle-in-cell code, including the space charge effects of insulator surface charge, is established to simulate the initiation of insulator surface flashover. The simulation is started with a field electron emission, which provides the seed electrons of the surface flashover discharge. Then the secondary electron emission is caused by the seed electrons on the insulator surface, gets into an avalanche, and saturates rapidly in a region between the cathode and anode. And the saturation region spreads to the anode at a speed of ∼107 m/s, which is coincident with the experiment measurement.
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Cai et al. (2012) studied this question.