A theory for space-charge-limited currents with application to electrical precipitation

The flow of steady electric currents in the interior of any medium is governed by three laws 1. Poisson´s law which essentially relates space charge to potential. 2. Conservation of charge. 3. A law of the type of Ohm´s law connecting current flow and potential gradient. In most solid and liquid conductors of technical interest, Poisson´s law can be satisfactorily approximated by the simpler equation of Laplace, and Ohm´s law applies with the conductivity taken as constant. In gases, however, these simplifications cannot be made and hence the problem of calculating such electrical parameters as the current-voltage relationship, field strength, and charge density is much more difficult.