A time-dependent model of partial discharges in voids

A time-dependent, hydrodynamic, model of partial discharges in voids in dielectrics is presented. The partial discharge is regarded as a space charge dominated electron avalanche. The model incorporates the relevant collisional and radiative processes in the void and at its boundary, and the field distortion due to the presence of space charge and void surface charges. Also the coupling with the external circuit is taken into account. Model simulations show that, as a result of field quenching, the associated charge versus applied field shows saturation above a certain threshold. The threshold field depends on geometry and initial electron number, but is higher than the inception values usually quoted. The saturation charge may deviate by a factor of 2-10 from values obtained with simplified models

Arbitrariness Of The General Solution And Symmetries

. The computation of the number of arbitrary functions in the general solution is briefly reviewed. The results are used to study normal systems and their symmetry reduction. We discuss the treatment of gauge systems, especially the analysis of gauge fixing conditions. As examples the Yang-Mills equations with the Lorentz gauge and Einstein's vacuum field equations with harmonic coordinates are considered. 1. Introduction If one can not determine the general solution of an equation, as it is usually the case with differential equations, one wants to know at least the dimension of the solution space. This is, however, not trivial for systems, especially if they are overdetermined. It turns out, that involution [10] provides the key. We showed in a recent paper [13], how to compute the number of arbitrary functions and their arity for closed representations of the general solution of an involutive system. The purpose of this paper is to provide more applications of these results. Normal..