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- W2103548918 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." @default.
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- W2103548918 date "1980-02-01" @default.
- W2103548918 modified "2023-09-30" @default.
- W2103548918 title "Upper bound for the space-charge limiting current of annular electron beams" @default.
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- W2103548918 doi "https://doi.org/10.1017/s0022377800022194" @default.
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