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Upper bound for the space-charge limiting current of annular electron beams

Published online by Cambridge University Press:  13 March 2009

T. C. Genoni  and
W. A. Proctor
T. C. Genoni
Affiliation:
Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico 87117
W. A. Proctor
Affiliation:
Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico 87117
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Abstract

We report here on a two-dimensional analytical calculation of an upper bound on the space-charge limiting current for a relativistic electron beam in cylindrical geometry. Voronin and co-workers have previously obtained an analytical estimate for the maximum steady-state current that can be propagated in a solid, unneutralized electron beam which completely fills a drift tube immersed in an infinite magnetic guide field. We generalize their method to include annular beams of arbitrary thickness and length, specifying a rigorous upper bound on the limiting current in terms of an eigenvalue of Bessel' s differential equation and separated, homogeneous boundary conditions of the most general form. For the special cases of a thin solid beam in a drift tube of infinite length and a thin annular beam in a drift tube of finite length, we find closed-form analytical expressions for the upper bound which are in good agreement with numerical solutions for the actual space-charge limiting current.

Type
Research Article
Information
Journal of Plasma Physics , Volume 23 , Issue 1 , February 1980 , pp. 129 - 139
Copyright
Copyright © Cambridge University Press 1980

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References

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