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Differential Algebra-based Magnetic Field Computations and Accurate Fringe Field Maps

Abstract

Motivated by the dynamical studies of particle motion in magnetic fields, we develop the method of Differential Algebra (DA) based 3D magnetic field computation. It can be applied whenever an analytical model of a magnet is given, which usually consist of line wire currents. Such a model exists for most of the modern superconducting magnets. It is stressed that it is the only practically possible way to extract the multipoles and its derivatives, and hence the map, analytically to high order. We also elaborate on related topics like complexity of the problem, Maxwellification of fields, importance of vanishing curl, etc., and its applications to very accurate fringe field map computations.

B. Erdelyi, M. Berz, M. Lindemann

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