Solution of space charge problems by conservation of momentum

The use of conservation of momentum makes it possible to solve space charge problems usually attacked by means of Poisson’s equation. The proposed method can be shown to be equivalent to Poisson’s equation but, in some types of problems, it appears easier to set up and the resulting equation is a first-order differential equation, rather than second order. Three problems are solved for which solutions have been previously found by Poisson’s equation. The solutions are more simply arrived at and are identical to those obtained via Poisson’s equation.