On the transient space-charge-limited current problem—a solution in Lagrangian mass variables

Abstract
Using a one-dimensional unipolar ion conduction model of the type originally studied by Many and Rakavy, the transient behavior of the electric field and space-charge distribution is studied in planar, cylindrical, and spherical geometries. A general solution in Lagrangian mass variables is obtained. We are able to recover the recent results of Hensen in planar geometry.