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Convergent Fourier–Bessel series to calculate potential and field strength in rotationally symmetric lens systems

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2 Author(s)
Simons, J. ; Delft University of Technology, Department of Applied Physics, P.O. Box 5046, 2600 GA Delft, The Netherlands ; Heerens, W.Chr.

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In this article a complete calculation strategy is given for potential and field strength in rotationally symmetric lens systems. The equations for these quantities are based on Fourier–Bessel series solutions. The series coefficients can be given analytically when simple boundary conditions are assumed, such as a rectangular cross section of the system and linear and logarithmic interpolation of the potentials on the walls between the points where this potential is given. It can be shown that with a continuous potential overlay on the walls the potential equations can be differentiated term by term and will also give convergent series. Methods to accelerate convergence of the calculations of the series are briefly discussed. Finally, some details are given on the calculation strategy of realistic lens systems, consisting of more than one rectangular element. The potential distributions on gaps or diaphragms, forming parts of the rectangular boundaries of one such element, are not exactly known in this case. It can be shown however that such potentials can be easily calculated with known finite‐difference techniques on the basis of the equations given.

Published in:

Journal of Applied Physics  (Volume:56 ,  Issue: 3 )