Maxwell's Equations for Magnets

Details Maxwell's Equations for Magnets Maxwell's Equations for Magnets

2011-03-03

arxiv.org/abs/1103.0713v1

Physics

Accelerator Physics

Presented at the CERN Accelerator School CAS 2009: Specialised Course on Magnets, Bruges, 16-25 June 2009

Scientific paper

Magnetostatic fields in accelerators are conventionally described in terms of multipoles. We show that in two dimensions, multipole fields do provide solutions of Maxwell's equations, and we consider the distributions of electric currents and geometries of ferromagnetic materials required (in idealized situations) to generate specified multipole fields. Then, we consider how to determine the multipole components in a given field. Finally, we show how the two-dimensional multipole description may be extended to three dimensions; this allows fringe fields, or the main fields in such devices as undulators and wigglers, to be expressed in terms of a set of modes, where each mode provides a solution to Maxwell's equations.

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