Magnetic field distributions around superconducting strips on ferromagnetic substrates

Abstract

The complex-field approach is developed to derive analytical expressions of the magnetic field distributions around superconducting strips on ferromagnetic substrates ͑SC/FM strips͒. 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 1 Ј+i 1 Љ 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 strips͒. The real part 1 Ј for H 0 / j c d s → 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 strip͒ of a SC/FM strip is 3 / 4 of that of a SC/NM strip. The imaginary part 1 Љ ͑or ac loss Q͒ for H 0 / j c d s Ͻ 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 1 Љ ͑or Q͒ is due to the edge effect of the ferromagnetic substrate.

Hysteretic ac loss in a coated superconductor subjected to oscillating magnetic fields: ferromagnetic effect and frequency dependence

“…well reproduce the main features demonstrated in figure 5(b) of reference [9], particularly the excellent consistency in terms of the intersection between the curves for the superconductor strip sitting on a nonmagnetic substrate and a ferromagnetic substrate with identical width to the strip, 14 in the previous prediction [9], which may be considered as evidence to verify the present finite-element analysis and, on the other hand, to support the validity of the analytical model proposed in reference [9]. (The symbols used in reference [9] is cited in the Appendix for direct comparison) [9] and [39], were adopted in the present calculations.…”

“…Considering a bilayer heterostructure of a thin superconductor strip sitting on a ferromagnetic substrate and quoting the characteristics released in references [9] and [39], the hysteretic ac loss [9] with μ 0 H 0 representing the amplitude of the applied magnetic field, were plotted in figure A.1. Shown also in this figure is that of a nonmagnetic substrate and a widened ferromagnetic substrate to create the scenario addressed in reference [9].…”

“…However fundamental these results may be, further investigations at a more realistic level remain promising as a surplus adaption or hypothesis of the geometrical and material characteristics has been made in the existing models, e.g., the thickness of the superconducting layer being scaled due to the intractable aspect ratio of width/thickness of a real coated superconductor [10,14]; the ferromagnetic substrate being supposed as a linear media with constant or even infinite permeability [9,14,17]; the field-dependent feature of the critical current, which is found to be tangible at high applied magnetic fields [21], being neglected or silent in the literatures [9,[12][13][14]17]; the superconductor being described by exploiting the magnetostatic-electrostatic analogs in order to adapt to the commercial software ANSYS [17]. Motivated by the situation described above, this paper is dedicated to take a comprehensive examination of the ferromagnetic effect and frequency dependence on the hysteretic ac loss of a coated superconductor, with a pristine geometry and containing all electromagnetically critical constituents of a real one rather than the simplified version, i.e., a superconductor strip over a substrate [9,12,13,[15][16][17][18][19][20], by making use of the quasistatic approximation of a vector potential approach in conjunction with an elaborate description of the nonlinear behaviors in both the superconducting layer and ferromagnetic substrate.…”

Field-dependent critical state of high-Tc superconducting strip simultaneously exposed to transport current and perpendicular magnetic field

“…In fact, the magnetic field induced by the critical current and frozen flux obeys the generalized Biot-Savart law. 22,26 Then we can derive the solution of sheet current and flux-density distributions for the decreasing transport current, Figure 7 demonstrates the sheet current (top) and flux-density profiles (bottom) which can be calculated from Eqs. (13)- (15).…”

Numerical study of AC loss of two-layer HTS power transmission cables composed of coated conductors with a ferromagnetic substrate

“…The influence of the ferromagnetic (FM) material on the transport AC loss of HTS tapes, monolayer cables, and coils was extensively studied both experimentally and theoretically [17][18][19][20][21][22][23]. For the works on twolayer HTS cables made of coated conductors with a ferromagnetic substrate, Amemiya et al [24] performed numerical AC loss calculations of two-layer superconducting power transmission cables comprising coated conductors with a ferromagnetic substrate concerning the arrangement with respect to the cable axis.…”