In general, generation of charged-particle transfer maps for conventional iron-pole-piece dipole magnets to third and higher order requires a model for the midplane field profile and its transverse derivatives (soft-edge model) to high order and numerical integration of map coefficients. An exact treatment of the problem for a particular magnet requires use of measured magnetic data. However, in initial design of beam transport systems, users of charged-particle optics codes generally rely on magnet models built into the codes. Indeed, if maps to third order are adequate for the problem, an approximate analytic field model together with numerical map coefficient integration can capture the important features of the transfer map. The model described in this paper is based on the fact that, except at very large distances from the magnet, the magnetic field for parallel pole-face magnets with constant pole gap height and wide pole faces is basically two dimensional (2D). The field for all space outside of the pole pieces is given by a single (complex) analytic expression and includes a parameter that controls the rate of falloff of the fringe field. Since the field function is analytic in the complex plane outside of the pole pieces, it satisfies two basic requirements of a field model for higher-order map codes: it is infinitely differentiable at the midplane and also a solution of the Laplace equation. It is apparently the only simple model available that combines an exponential approach to the central field with an inverse cubic falloff of field at large distances from the magnet in a single expression. The model is not intended for detailed fitting of magnetic field data, but for use in numerical map-generating codes for studying the effect of extended fringe fields on higher-order transfer maps. It is based on conformally mapping the area between the pole pieces to the upper half plane, and placing current filaments on the pole faces. An algorithm for computing the midplane field derivatives with the model is described. The model has been incorporated in the particle beam code Marylie/Impact as a special dipole-magnet type along with a tanh model with exponential falloff of the fringe field. Comparison of maps from the tanh model and the new model shows that significant differences in 3rd-order geometric terms can occur, apparently due to the extended fringe field in the new model.

• Received 24 August 2011

DOI:https://doi.org/10.1103/PhysRevSTAB.15.102401

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Published by the American Physical Society