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5.—Adiabatic Motion in a Charged Particle Trap*

Published online by Cambridge University Press:  14 February 2012

J. Byrne
J. Byrne
Affiliation:
School of Mathematical and Physical Sciences, University of Sussex
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Synopsis

The adiabatic invariants associated with the motion of charged particles, trapped in electromagnetic fields with rotational and reflection symmetry, have been studied using classical methods based on the Hamilton-Jacobi equation. It has been shown that results, valid for trapping in purely magnetic configurations, may be applied in the analysis of electromagnetic charged particle traps, provided that suitably modified expressions are used for the angular frequencies in the various dynamical modes. Attention is drawn to circumstances in which the adiabatic conditions may be violated because of cancellation of electric and magnetic terms in the equations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 70 , 1972 , pp. 47 - 61
Copyright
Copyright © Royal Society of Edinburgh 1972

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References

References to Literature

[1]Rayleigh, Lord, 1902. Phil. Mag., 3, 338.CrossRefGoogle Scholar
[2]Ter Haar, D., 1961. Elements of Hamiltonian Mechanics, North Holland Publishing Co., Amsterdam.Google Scholar
[3]Littlewood, J. E., 1963. Ann. Phys., 21, 233.CrossRefGoogle Scholar
[4]Ehrenfest, P., 1916. Proc. K. Ned. Akad. Wet., 19, 576.Google Scholar
[5]McMillan, E. M., 1945. Phys. Rev., 68, 143.Google Scholar
[6]Veksler, V., 1945. Fiz. Zh., 9, 153.Google Scholar
[7]Van Allen, J. A., McIlwain, C. E. and Ludwig, G. H., 1959. J. Geophys. Res., 64, 271.Google Scholar
[8]Northrop, T. G. and Teller, E., 1960. Phys. Rev., 117, 215.Google Scholar
[9]Northrop, T. G., 1961. Ann. Phys., 15, 79.CrossRefGoogle Scholar
[10]Farago, P. S. and Siegmann, H. C., 1966. Phys. Lett., 20, 279.Google Scholar
[11]Gräff, G. and Klempt, E., 1967. Z. Naturf., 11, 1960.Google Scholar
[12]Cosslett, V. E., 1950. Introduction to Electron Optics, O.U.P.Google Scholar