Basic Studies in Plasma Physics
Abstract
We studied the spatial structure of the space charge limited current and electric field in a rectangle of arbitrary aspect ratio. The cathode and anode form two horizontal sides of the rectangle and a strong magnetic field forces the current to flow perpendicular to the electrodes. Using conformal mapping techniques we calculate the electric field outside this rectangle for any given potential distribution on its vertical boundaries. Inside the current rectangle we have a nonlinear Poisson equation with extra boundary conditions for two unknown functions: The potential and the current density. Both exhibit singular behavior at the edges of the rectangle. A semianalytic approximate method is developed for this unusual boundary value problem: We first match the boundary fields inside and outside the current region and then, using trial functions consistent with these matching conditions, we apply the least square technique and iterations to construct the solution in the current region. The analysis of the flow shows that the current wings are similar for all currents wider than one of the square cross noindent. There is also evidence that the total current does not vanish when the width goes to zero. The method of calculation appears generalizable to various geometries of vacuum and solid state devices.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 17, 2010
- Accession Number
- ADA515496
Entities
People
- Joel L. Labowitz
Organizations
- Rutgers University–New Brunswick