Possibilities and limits of controlling 3D electrostatic field distributions with insulator surfaces

Through optimization techniques it is possible to affect the field distribution of a given high voltage arrangement by modifying the shape of electrodes and insulators. When the modification of the shape of insulators is used to control the values of the total field strength intensity on their surfaces, the reduction in the field values that can be achieved is nor the same for every high voltage arrangement. In this paper, the theoretical and practical limits of such techniques are investigated. An axially symmetrical configuration that has been repeatedly used for optimization tasks has been extended adding a grounded electrode to obtain a 3D-Field. The surface of an insulator has been modified by taking as objective the reduction of the maximum total field strength intensity on its surface. The position of the grounded electrode and the way in which the insulator surface is modified are varied to study the influence of different parameters in the resulting field distribution. The possibility of fixing or freeing the end-points of the insulator is also studied