Current Density Scaling Expressions for a Bipolar Space-Charge-Limited Cylindrical Diode

Exact analytical solutions for the currents in a bipolar space-charge-limited (SCL) diode in cylindrical geometry do not exist. Expressions for the electron and ion current densities as functions of the diode cathode and anode radii and the applied voltage are developed and fit to numerical solution...

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Bibliographic Details
Published in:IEEE transactions on plasma science 2015-10, Vol.43 (10), p.3626-3636
Main Authors: Rittersdorf, Ian M., Ottinger, Paul F., Allen, Raymond J., Schumer, Joseph W.
Format: Article
Language:English
Subjects:
Anodes
Bipolar flow
Boundary conditions
Cathodes
Current density
cylindrical diodes
Diodes
Electric currents
Electrons
Geometry
Ion emission
Ions
space-charge limited (SCL)
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Summary:Exact analytical solutions for the currents in a bipolar space-charge-limited (SCL) diode in cylindrical geometry do not exist. Expressions for the electron and ion current densities as functions of the diode cathode and anode radii and the applied voltage are developed and fit to numerical solutions. The results are provided for nonrelativistic and relativistic electrons. These provide scaling relations for the diode, which were not previously available. They also converge to known planar diode expressions in the appropriate limit. The relativistic scaling relations are then combined with nonrelativistic results using a fit function technique to provide a general expression for the current densities valid for all values of the diode voltage. The results are presented for both negative and positive polarities. For completeness, single-species SCL flow results in cylindrical geometry are also developed using the same techniques presented here for bipolar SCL flow and are included in the Appendix.
ISSN:0093-3813
1939-9375
DOI:10.1109/TPS.2015.2471275