### Abstract

Original language | English |
---|---|

Journal | Royal Society of London. Proceedings. Mathematical, Physical and Engineering Sciences |

Volume | 465 |

Issue number | 2112 |

Pages (from-to) | 3581-3604 |

ISSN | 1364-5021 |

DOIs | |

Publication status | Published - 2009 |

### Cite this

*Royal Society of London. Proceedings. Mathematical, Physical and Engineering Sciences*,

*465*(2112), 3581-3604. https://doi.org/10.1098/rspa.2009.0355

}

*Royal Society of London. Proceedings. Mathematical, Physical and Engineering Sciences*, vol. 465, no. 2112, pp. 3581-3604. https://doi.org/10.1098/rspa.2009.0355

**Magnetostatics of the uniformly polarized torus.** / Beleggia, Marco; De Graef, Marc; Millev, Yonko.

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - Magnetostatics of the uniformly polarized torus

AU - Beleggia, Marco

AU - De Graef, Marc

AU - Millev, Yonko

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

U2 - 10.1098/rspa.2009.0355

DO - 10.1098/rspa.2009.0355

M3 - Journal article

VL - 465

SP - 3581

EP - 3604

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

IS - 2112

ER -