Maxwell's Equations for Magnets

Wolski, Andrzej

doi:10.5170/CERN-2010-004.1

Article
Report number	arXiv:1103.0713 ; CERN-2010-004 ; pp. 1-38
Title	Maxwell's Equations for Magnets
Author(s)	Wolski, Andrzej (Liverpool U. ; Cockcroft Inst. Accel. Sci. Tech.)
Publication	CERN, 2010
Imprint	04 Mar 2011
Number of pages	38
Note	Comments: Presented at the CERN Accelerator School CAS 2009: Specialised Course on Magnets, Bruges, 16-25 June 2009 Presented at the CERN Accelerator School CAS 2009: Specialised Course on Magnets, Bruges, 16-25 June 2009
In:	CAS - CERN Accelerator School: Magnets, pp.1-38
DOI	10.5170/CERN-2010-004.1
Subject category	Accelerators and Storage Rings
Abstract	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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