Numerical Solutions of the Action Equation for Electrostatic Space-charge Flow, with Axial Symmetry

Two types of electron flow are described which are given by solutions of the fiction equation. The solutions ore of the form The coefficients S 0 , S 1 , S S 2 ., were obtained using a computer and the method used could be extended to include coefficients of higher powers of r. The flows, whoso shap...

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Bibliographic Details
Published in:International journal of electronics 1965-12, Vol.19 (6), p.577-586
Main Author: MAYO, B. J.
Format: Article
Language:English
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Summary:Two types of electron flow are described which are given by solutions of the fiction equation. The solutions ore of the form The coefficients S 0 , S 1 , S S 2 ., were obtained using a computer and the method used could be extended to include coefficients of higher powers of r. The flows, whoso shapes along the axis are initially prescribed, start off as wide spacc-charge-limited beams and are focused to narrow ones ; the area compression ratio is approximately 2500. One flow starts from a flat cathode and gives a transition from parallel to convergent flow ; the other has a curved cathode. In each case the axial potential rises to a maximum near the end of the flow and is zero at the end of the flow. As a result of the maximum nn aperture may be placed in the flow without disturbing the flow. As the beams progress, the current density tends to become more concentrated at the edge of the beam.
ISSN:0020-7217
1362-3060
DOI:10.1080/00207216508937844