Space-charge-limited 2D electron flow between two flat electrodes in a strong magnetic field.
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.
Rokhlenko
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Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854-8019, USA.
Lebowitz
J L
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