Paraxial Solutions for Accelerated and Decelerated Axially Symmetric Space-Charge Flow
- 1 March 1963
- journal article
- research article
- Published by AIP Publishing in Journal of Applied Physics
- Vol. 34 (3) , 692-702
- https://doi.org/10.1063/1.1729333
Abstract
Particle trajectories in the presence of space charge are calculated for prescribed axial potential variations, including linear, parabolic, and sinusoidal variations, using the paraxial‐ray equation including space charge for axial symmetry. Solutions are also presented for the potential as a function of distance corresponding to prescribed hyperbolic and parabolic trajectories. The off‐axis equipotentials are calculated for some representative cases. These two‐dimensional results are interpreted in the light of one‐dimensional space‐arge theory in which exact solutions can be obtained for the potential as a function of distance. Some of the limitations of the present theory in which either the potential or the trajectory is prescribed are pointed out.This publication has 9 references indexed in Scilit:
- Space-Charge Instabilities in Electron Diodes and Plasma ConvertersJournal of Applied Physics, 1961
- Transient Space-charge Flow†Journal of Electronics and Control, 1960
- Paraxial Formulation of the Equations of Electrostatic Space-Charge FlowJournal of Applied Physics, 1959
- Some calculations of transients in an electronic valveApplied Scientific Research, Section B, 1950
- Congruent Space Charge FlowProceedings of the Physical Society. Section B, 1950
- On the Theory of Space Charge Between Parallel Plane ElectrodesBell System Technical Journal, 1938
- Die Raumladegleichung für Elektronen mit Anfangsgeschwindigkeit. II. TeilThe European Physical Journal A, 1937
- Die Raumladegleichung für Elektronen mit AnfangsgeschwindigkeitThe European Physical Journal A, 1936
- LXXX.Dispersion of an electron beamJournal of Computers in Education, 1927