Pedagogical review of the derivation of space-charge limiting current of an electron beam in a metal drift tube

B N Basu
Supreme Knowledge Foundation Group of Insttitutions, Mankundu-712 139, West Bengal, India

The expression for the space-charge limiting current of a hollow electron beam drifting through a metal drift-tube surrounding is derived from first principles for each of the two cases of (i) hollow, thin and (ii) thick, solid electron beams. The expression helps to appreciate the compromise on the requirements of large RF electric field for beam-wave interaction and, at the same time, large space-charge limiting current in gyrotron cavity. It also helps to appreciate why an electron beam should be placed far from the cavity wall of a virtual cathode oscillator for small space-charge limiting current. The derivation of the space-charge limiting current presented here is not easily available in published literature.
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Keywords: Space charge limiting current, Virtual cathode, Gyrotron, Virtual cathode oscillator.

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Method: Single- anonymous; Screened for Plagiarism? Yes
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