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Space Charge Limited 2-d Electron Flow between Two Flat Electrodes in a Strong Magnetic Field

A. Rokhlenko·Joel L. Lebowitz
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Abstract

An approximate analytic solution is constructed for the 2-d space charge limited emission by a cathode surrounded by non emitting 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.

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A. Rokhlenko, Joel L. Lebowitz. 2003-02-14. Space Charge Limited 2-d Electron Flow between Two Flat Electrodes in a Strong Magnetic Field. https://doi.org/10.1103/physrevlett.91.085002

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