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Electron focusing in magnetic fields of the form z n

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We describe an investigation into the focusing properties of magnetic fields of the form kz n for all integer n. With two exceptions, the trajectories can be expressed as a linear sum of Bessel functions of the first and second type, of order 1/2 (n + 1) and with argument ±kz n + 1/2(n + 1). The coefficients in this linear sum can be determined from the initial conditions. Numerical ray tracing calculations confirm these trajectories and this method is to be preferred for determination of the lens parameters. The properties of these lenses are very simple, the focal length and the two principal aberration coefficients are proportional to the value of z at the focus. For this reason only one trajectory is needed in order to describe these properties (say k = 1). All other trajectories can be scaled from this one. The two exceptions are n = –1 and n = 0 and these are considered separately.

Document Type: Research Article


Affiliations: The Enrico Fermi Institute and the Department of Physics, The University of Chicago, 5640 S. Ellis, Chicago, Illinois 60637, USA

Publication date: May 1, 2004

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