A Paraxial Formulation of the Equations for Space-charge Flow in a Magnetic Field†
- 1 March 1960
- journal article
- research article
- Published by Taylor & Francis in Journal of Electronics and Control
- Vol. 8 (3) , 207-225
- https://doi.org/10.1080/00207216008937266
Abstract
The equations for irrotational, axially symmetric, laminar, space-charge flow are set op in a paraxial manner. To this approximation, the flow is specified by the magnetic field configuration, one trajectory, the potential along this trajectory, and the variation of beam thickness. Any three of these quantities may, within certain limits, be specified arbitrarily, and the fourth then computed by the formulae given. The method is directly applicable to flows in which the cathode is conical, and either the flow lines do not cut magnetic flux lines, or the magnetic field is tangential at the cathode. Numerical results are given for a beam from a cylindrical cathode, and extensions of the methods are discussed.Keywords
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