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

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

2003-02-14

arxiv.org/abs/physics/0302052v1

Physics

Plasma Physics

4 pages, LaTex, e-mail addresses: rokhlenko@math.rutgers.edu, lebowitz@sakharov.rutgers.edu

Scientific paper

10.1103/PhysRevLett.91.085002

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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