Magnetron injection guns derived from theorectical space-charge flow solutions
During the past three years we have had occasion to design and build magnetron-injection guns for producing hollow beams. These guns have been designed both from a planar space-charge flow which has been described by Kino and Taylor  and more recently from one of the axially-symmetric flows described by Kirstein . Though these flows may be a gross simplification of what might actually occur in a crossed-field gun of this type wehave found that they enbale us to predict perveance and cathode current-density distribution to a most useful degree of accuracy.
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- K.J. HARKER, Determination of the El ec trode Shapes for Axially Symmetric Electron Guns, J. Appl. Phys., vol. 31, no.12, December 1960Google Scholar