Stability of Periodic-Field Beam Focusing
- 1 December 1956
- journal article
- Published by AIP Publishing in Journal of Applied Physics
- Vol. 27 (12), 1527-1532
- https://doi.org/10.1063/1.1722301
Abstract
By taking into consideration both the effects of space-charge and large-amplitude scalloping, an analytic solution for periodic-field beam focusing is obtained through use of successive approximation and Fourier series expansion. The stability limit is then determined by studying a perturbation of the obtained solution. The perturbation results in a Hill's differential equation for the incremental beam radius. This equation yields a stability criterion for periodic-field beam focusing. It is found that instability starts at some degree of beam scalloping and ends at a higher one, and thus forms an unstable band.Keywords
This publication has 7 references indexed in Scilit:
- Beam Focusing by Periodic and Complementary FieldsProceedings of the IRE, 1955
- Focusing of a Long Cylindrical Electron Stream by Means of Periodic Electrostatic FieldsJournal of Applied Physics, 1954
- Electron Beam Focusing with Periodic Permanent Magnet FieldsProceedings of the IRE, 1954
- Focusing of an Electron Beam by Periodic FieldsJournal of Applied Physics, 1954
- Spatially Alternating Magnetic Fields for Focusing Low-Voltage Electron BeamsJournal of Applied Physics, 1953
- Über die Stabilität der Lösungen Hillscher Differentialgleichungen mit drei unabhängigen Parametern. Erste Mitteilung: Über die Gleichung yn+(λ+γ1cosx+γ2cos2x)y=0ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1943
- Lösungen der inhomogenen Mathieuschen Differentialgleichung mit periodischer Störfunktion beliebiger Frequenz (mit besonderer Berücksichtigung der Resonanzlösungen)ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1943