Abstract
Hamilton’s principle, Liouville’s theorem, the Lagrange and Poincare invariants of classical mechanics, and the eikonal procedure are employed to charged-particle optics for describing the properties of ensembles of rays and the deviation of the trajectories from their course in paraxial approximation. In particular, the mixed eikonal is employed for deriving the Abbe sine condition and the Poincare invariant for elucidating the focusing properties of magnetic fields. Based on the eikonal method, integral equations are derived for the deviations of the trajectories from their paraxial course.
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References
P.A. Sturrock, Proc. R. Soc. A (London). 210, 269 (1951)
R.K. Luneburg, Mathematical Theory of Optics (University California Press, Berkeley, 1966)
M. Born, E. Wolf, Principles of Optics, 7th edn. (Cambridge University Press, Cambridge, 1999)
E. Plies, D. Typke, Z. Naturforsch. A 33, 1361 (1978)
H. Rose, Nucl. Instrum. Meth. Phys. Res. A 258, 374 (1987)
M. Berz, Modern Map Methods in Particle Beam Physics (Academic, San Diego, 1999)
W. Glaser, in Beiträge zur Elektronenoptik, ed. by H. Busch, E. Brüche (Barth, Leipzig, 1937), pp. 24–32
H. Rose, U. Petri, Optik 33, 151 (1971)
H. Rose, in High-Resolution Imaging and Spectrometry of Materials, ed. by F. Ernst, M. Ruehle (Springer, Berlin, 2002), pp. 189–270
H. Bruns, Abh. K. Saechs. Ges. Wiss., Math.-Phys. Kl. 21, 321 (1895)
E.H. Linfoot, Recent Advances in Optics (Oxford University Press, Oxford, 1955)
E. Zeitler, Nucl. Instrum. Meth. Phys. Res. A 298, 234 (1990)
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Rose, H. (2012). General Principles of Particle Motion. In: Geometrical Charged-Particle Optics. Springer Series in Optical Sciences, vol 142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32119-1_5
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DOI: https://doi.org/10.1007/978-3-642-32119-1_5
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