Investigation of electrical breakdown properties in curved electrodes

Abstract

Properties of electrical breakdown in curved electrodes are investigated by making use of Paschen’s law. Simple analytical expressions for minimum breakdown voltage and its corresponding values of physical parameters are obtained for cylindrical and spherical geometries. The sparking criterion indicates that discharge properties are insensitive to the electrical field polarity inside a diode for both cylindrical and spherical systems, if the second ionization coefficient γ is constant. Due to the curvature effects, the minimum breakdown voltage in cylindrical and spherical geometries increases significantly from its planar value for a large aspect ratio of b/a, where a and b are radii of the inner and outer conductors, respectively. However, the optimum pressure parameter for minimum breakdown voltage in cylindrical geometry is identical to that in planar electrodes. The minimum breakdown voltage for spherical system increases continuously to a finite value, as the curvature aspect ratio b/a increases to infinity. Therefore, pressure for the minimum breakdown voltage may not be zero, even for the infinite aspect ratio. This means that an electrical breakdown with a minimum voltage may occur at surface of a spherical conductor immersed in a gas with an appropriate pressure.