Effective Demagnetization Factors of Diamagnetic Samples of Various Shapes

TL;DR

This paper numerically calculates effective demagnetizing factors for perfectly diamagnetic samples of various shapes, providing accurate formulas applicable to superconductors and conductors in AC fields.

Contribution

It introduces a numerical method to determine demagnetizing factors for non-ellipsoidal diamagnetic shapes, including practical approximate formulas.

Findings

Numerical values of demagnetizing factors for various shapes.

Approximate formulas for practical shapes.

Relevance to superconductors and conductors in AC fields.

Abstract

Effective demagnetizing factors that connect the sample magnetic moment with the applied magnetic field are calculated numerically for perfectly diamagnetic samples of various non-ellipsoidal shapes. The procedure is based on calculating total magnetic moment by integrating the magnetic induction obtained from a full three dimensional solution of the Maxwell equations using adaptive mesh. The results are relevant for superconductors (and conductors in AC fields) when the London penetration depth (or the skin depth) is much smaller than the sample size. Simple but reasonably accurate approximate formulas are given for practical shapes including rectangular cuboids, finite cylinders in axial and transverse field as well as infinite rectangular and elliptical cross-section strips.