Title :
On the solution of Langmuir´s spherical space-charge equation
Author :
Linson, L.M. ; Daugherty, J.D.
Abstract :
An analytic (parametric) integration of Langmuir´s equation for spherical space-charge flow has been obtained. The analytic expression for the voltage distribution is expanded for both large and small ratios of cathode to anode radius. The usefulness and form of the resulting precise expressions are compared with Langmuir´s empirical results.
Keywords :
Anodes; Boundary conditions; Cathodes; Convergence; Current distribution; Differential equations; NASA; Nonlinear equations; Poisson equations; Voltage;
Journal_Title :
Proceedings of the IEEE
DOI :
10.1109/PROC.1969.6882
