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 $chi_1+ichi_1$ 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 $H_0/j_cd_sto 0$ (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.
Download