3-D SEEA charge analyses on surface of insulators in vacuum

In the bridged vacuum gaps, the secondary electron emission avalanche (SEEA) occurring along the surface of solid insulator and the resultant surface charging play a crucial role in the progress of surface discharge. In order to sophisticate the insulation design of high voltage vacuum devices, analysis and control of SEEA charging are of importance. Boersh et al. have proposed a boundary condition on the surface of an insulator to solve the charge distribution at an equilibrium state of SEEA charging. The boundary condition can be easily adopted for analyzing two dimensional SEEA charge distributions. However, the above condition by Boersh et al. cannot be applied in the case of three dimensional distributions. In this paper, the authors newly developed the boundary condition for three dimensional applications and created a numerical simulation code for analyzing three dimensional SEEA charge distributions. Two types of insulator were examined in this study; one was a solid cylinder and the other a hollow cylinder. In the case of the solid cylinder, electric field strength on the cathode was calculated and compared with the measurement. On the other hand, in the case of the hollow cylinder, the calculated result was compared with the charge distribution experimentally obtained by a movable electrostatic probe system. These calculation and measurement results have shown reasonable agreement and we have validated the newly developed numerical simulation method for three dimensional SEEA charge distributions.