Structural optimization of vacuum insulator stack grading rings

The theories of secondary electron emission avalanche and anode-initiated flashover model are applied to optimizing the insulator stack grading rings. All results are calculated through the finite element method. Two methods are taken into account, one is to fit numerical results with analytic results, and the other is to refine those elements. Through comparing the results from the two methods, reasonable values of electric field intensity are confirmed. As for cathode, the value is the electric field at a distance of (0.005)(21/2d) from the junction (d is the thickness of the insulator), and for anode, it is the electric field at a distance of (0.008 5)(21/2d) from the junction. After the optimization, 5 bumps are selected for 10 grading rings. The largest electric field in the cathode triple junction reduces to 2.55 kV/mm, while that in the anode triple junction reduces to 23 kV/mm.