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.