Local fields at the cathode-insulator junction as a cause of breakdown of shaped insulators in vacuum

High-voltage holdoff of solid insulators between electrodes in vacuum depends strongly on insulator shape. The angle between the applied field and the insulator interface is believed to be the fundamental dependence. A detailed calculation of the electric fields about solid insulators of various shapes is presented which gives an insight into the reason for this dependence. The breakdown field near the cathode-insulator junction appears to be constant if the enhancement of the applied field is considered. This enhancement is created not only by insulator geometry, but also by insulator surface charging effects.