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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

REFERENCES

Birkoff, G. & Rota, G. 1962 Ordinary Differential Equations. Ginn.Google Scholar
Bogdankevich, L. S. & Rukhadze, A. A. 1971 Soviet Phys. Uspekhi, 14, 163.Google Scholar
Brejzman, B. N., & Ryutov, D. D. 1974 Nucl. Fusion, 14, 873.Google Scholar
Genoni, T. C. & Proctor, W. A. 1977 Bull. Am. Phys. Soc. 22, 1085.Google Scholar
Haeff, A. V. 1939 Proc. I.R.E. 27, 586.Google Scholar
Reiser, M. 1977 Phys. Fluids, 20, 477.Google Scholar
Smith, L. P. & Hartman, P. L. 1940 J. Appl. Phys. 11, 220.CrossRefGoogle Scholar
Thode, L. E., Godfrey, B. B. & Shanahan, W. R. 1979 Phys. Fluids, 22, 747.Google Scholar
Thompson, J. R. & Sloan, M. L. 1978 Phys. Fluids, 21, 2032.Google Scholar
Voronin, V. S., Zozulaya, Yu. T. & Lebedev, A. N. 1972 Soviet Phys. Tech. Phys. 17, 432.Google Scholar