Exact Solution of the One-dimensional Bunching Problem†
- 1 March 1961
- journal article
- research article
- Published by Taylor & Francis in Journal of Electronics and Control
- Vol. 10 (3) , 165-180
- https://doi.org/10.1080/00207216108937314
Abstract
A rigorous analytic solution has been derived for the bunching of an in finite electron beam modulated by an infinitesimal gap. The solution is valid as long as no overtaking occurs. The amplitude of the nth harmonic (for n=1, 2, 4, 8)is plotted for different values of beam density and modulation coefficient and the points where overtaking first occurs are noted. The solution contains previously derived ballistic and space-charge theories as limiting cases.Keywords
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