Journal article
Magnetostatics of the uniformly polarized torus
We provide an exhaustive description of the magnetostatics of the uniformly polarized torus and its derivative self-intersecting (spindle) shapes. In the process, two complementary approaches have been implemented, position-space analysis of the Laplace equation with inhomogeneous boundary conditions and a Fourier-space analysis, starting from the determination of the shape amplitude of this topologically non-trivial body.
The stray field and the demagnetization tensor have been determined as rapidly converging series of toroidal functions. The single independent demagnetization-tensor eigenvalue has been determined as a function of the unique aspect ratio α of the torus. Throughout the range of values of the ratio, corresponding to a multiply connected torus proper, the axial demagnetization factor Nz remains close to one half.
There is no breach of smoothness of Nz(α) at the topological crossover to a simply connected tight torus (α=1). However, Nz is a non-monotonic function of the aspect ratio, such that substantially different pairs of corresponding tori would still have the same demagnetization factor. This property does not occur in a simply connected body of the same continuous axial symmetry.
Several self-suggesting practical applications are outlined, deriving from the acquired quantitative insight.
Language: | English |
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Publisher: | Royal Society |
Year: | 2009 |
Pages: | 3581-3604 |
ISSN: | 13645021 and 14712946 |
Types: | Journal article |
DOI: | 10.1098/rspa.2009.0355 |
ORCIDs: | Beleggia, Marco |