AIP Digital Archive
A method for constructing three-dimensional solenoidal magnetization distributions, with invariant magnitude of m, in arbitrarily shaped objects is presented. The formalism harks back to the theory developed by van den Berg for two-dimensional m distributions. The space within a general object Ω is partitioned into i subspaces Ωi, described by a family of surfaces to which the magnetization is tangent. A characteristic equation which defines the course of m at each of the surfaces is derived. A boundary condition for m arises naturally, or can be chosen to determine m at the surface. Within the above framework an infinite number of solutions are generated that, in general, exhibit singularities. Special attention, also from the topological point of view, is paid to the m distributions having point defects only.
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