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