ELECTROHYDROSTATIC EQUILIBRIUM AND FIELD SOLUTIONS UNDER SPACE-CHARGE CONDITIONS

An examination is made, in terms of electrohydrostatic stress theory, of the restrictions placed on the solutions of the high-pressure space-charge equation in order to comply with the assumption of hydrostatic equilibrium, implicit in the equation's derivation. It is concluded that, except for the known elementary solutions, there are no solutions consistent with the equilibrium. The implication is that, except in the simple cases to which the elementary solutions apply, the space-charge situation is necessarily electrohydrodynamical and existing non-elementary solutions are acceptable only insofar as they are valid as approximations.