Magnetic field distributions around superconducting strips on ferromagnetic substrates

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 χ₁^′+iχ₁^″ 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 χ₁^′ for H₀∕j_cd_s→0 (where H₀ 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 χ₁^″ (or ac loss Q) for H₀∕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 χ₁^″ (or Q) is due to the edge effect of the ferromagnetic substrate.