title: Space-charge-limited 2D electron flow between two flat electrodes in a strong magnetic field.
abstract: An approximate analytic solution is constructed for the 2D space-charge-limited emission by a cathode surrounded by nonemitting conducting ledges of width Lambda. An essentially exact solution (via conformal mapping) of the electrostatic problem in vacuum is matched to the solution of a linearized problem in the space charge region whose boundaries are sharp due to the presence of a strong magnetic field. The current density growth in a narrow interval near the edges of the cathode depends strongly on Lambda. We obtain an empirical formula for the total current as a function of Lambda which extends to more general cathode geometries.
authors.affiliation: Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854-8019, USA.
authors.forename: A
authors.initials: A
authors.lastname: Rokhlenko
authors.forename: J L
authors.initials: JL
authors.lastname: Lebowitz