Differential Algebra based Magnetic Field Computations and Accurate Fringe Field Maps
AbstractFor the purpose of precision studies of transfer maps of particle
motion in complex magnetic fields, we develop a method for Differential
Algebra based 3D field computation and multipole decomposition.
It can be applied whenever a model of a magnet is given which consist
of line wire currents, and the wires are utilized to represent both
the coils and the iron parts via the so-called image current method.
Such a model exists for most modern superconducting magnets and a
large variety of others as well. It is stressed that it is the only
practically possible way to extract the multipoles and its derivatives,
and hence the transfer map of the particle motion, analytically to
high order. We also study various related topics like aspects of computational
complexity of the problem, Maxwellification of fields, importance
of vanishing curl, etc., and its applications to very accurate computation
of magnetic fields including fringe fields.
B. Erdelyi, M. Berz, M. Lindemann,
Vestnik Mathematica 10,4 (2015) 36-55
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