Analytical investigation of magnetic field distributions around superconducting strips on ferromagnetic substrates

TL;DR

This paper develops an analytical approach to study magnetic field distributions around superconducting strips on ferromagnetic substrates, revealing how ferromagnetic substrates influence ac susceptibility and losses compared to nonmagnetic substrates.

Contribution

It introduces a complex-field analytical method considering ideal soft ferromagnetic substrates and compares ac susceptibility of SC/FM strips with SC/NM strips under the critical state model.

Findings

Real part of susceptibility is 3/4 for SC/FM compared to SC/NM at low fields.

Imaginary part (loss) is higher in SC/FM strips for low field amplitudes.

Edge effects of ferromagnetic substrates enhance ac losses even without hysteresis.

Abstract

The complex-field approach is developed to derive analytical expressions of the magnetic field distributions around superconducting strips on ferromagnetic substrates (SC/FM strips). We consider the ferromagnetic substrates as ideal soft magnets with an infinite magnetic permeability, neglecting the ferromagnetic hysteresis. On the basis of the critical state model for a superconducting strip, the ac susceptibility $\chi_1'+i\chi_1''$ of a SC/FM strip exposed to a perpendicular ac magnetic field is theoretically investigated, and the results are compared with those for superconducting strips on nonmagnetic substrates (SC/NM strips). The real part $\chi_1'$ for $H_0/j_cd_s\to 0$ (where $H_0$ is the amplitude of the ac magnetic field, $j_c$ is the critical current density, and $d_s$ is the thickness of the superconducting strip) of a SC/FM strip is 3/4 of that of a SC/NM strip. The imaginary part $\chi_1''$ (or ac loss $Q$) for $H_0/j_cd_s<0.14$ of a SC/FM strip is larger than that of a SC/NM strip, even when the ferromagnetic hysteresis is neglected, and this enhancement of $\chi_1''$ (or $Q$) is due to the edge effect of the ferromagnetic substrate.