A CRITIQUE OF THE DEUTSCH ASSUMPTION

The field equations of a small-scale point-plane negative DC corona discharge in air have been solved in a particular case by the authors. The technique was to use a finite-element method for solving Poisson's equation, and an algorithm for finding the charge density from a current-continuity relation. A single mobility coefficient was adopted and the methods were used alternately until convergence was obtained. Boundary conditions for this technique are the potentials of the electrodes and the measured current distribution. Geometric convergence occurs before arithmetic convergence, with the accuracy of the latter being better than 1% for the electric field (typically 0.5% everywhere except at the tip of the active electrode). The uncertainty in the solution because of the unknown charge distributions in the small glow region has been accurately quantified by using two extreme models. Geometrical and numerical differences between these models have been shown to be very small. The known accuracy of the solution has allowed a thorough appraisal of the Deutsch assumption which forms the basis of many approximate methods. The assumption is shown to be unfounded, and we conclude that it should be avoided if accurate numerical solutions are being sought for general electrode geometries.