Electric fields in stationary ion flows in symmetric geometries.

Abstract

A method is presented that yields exact closed-form solutions in curvilinear coordinates for the partial differential equations determining the electric field in a stationary flow of unipolar ions with constant mobility. The method is applied to the parabolic cylindrical, elliptic cylindrical, bipolar, parabolic, and spheroidal coordinates. The new solutions approach infinity roughly in the manner of the classical parallel-plate solution. They are expected to apply to analyses of non-self-sustained ion flows.