Analytical model of the response of a superconducting film to line currents

Abstract

We theoretically investigate the response of a superconducting film to line currents flowing in linear wires placed above the film, and we present analytic expressions for the magnetic-field and current distributions based on the critical state model. The behavior of the superconducting film is characterized by the sheet-current density Kz, whose magnitude cannot exceed the critical value jcd, where jc is the critical current density and d is the thickness of the film. When the transport current I0 flowing in the wire is small enough, |Kz| is smaller than jcd and the magnetic field is shielded below the film. When I0 exceeds a threshold value Ic0 ∝ jcd, on the other hand, |Kz| reaches jcd and the magnetic field penetrates below the film. We also calculate the ac response of the film when an ac transport current flows in the linear wires.

Magnetic field distributions around superconducting strips on ferromagnetic substrates

“…To analyze a two-dimensional magnetic field, H = H x ͑x , y͒x + H y ͑x , y͒ŷ, we consider the complex field [18][19][20][21][22][23][24][25][26][27] H͑͒ = H y ͑x,y͒ + iH x ͑x,y͒, ͑1͒…”

“…7 in Ref. 26. Substitution of H͑͒ → H ay + iH ax for ͉ ͉ → ϱ and H͑xЈ + i⑀͒ = H͑xЈ − i⑀͒ for ͉xЈ͉ Ͼ a into Eq.…”

Magnetic detectability of a finite size paramagnet/superconductor cylindrical cloak

“…(16) where Φ 0 is the magnetic flux quantum, ξ the superconductor coherence length and σ ∈ (ξ, λ) the typical defect size at the superconductor surface. On the other hand, for the case of multiple vortex penetration, the limiting field can be estimated within the critical state model 27 to be of the order of j c d S with j c the critical current density in the superconductor. The above consideration of cloaking is valid until the highest of these two fields is exceeded.…”

Influence of soft ferromagnetic substrate on magneto-elastic behavior in a superconducting coated conductor strip

“…In order to analyze the two dimensional magnetic field H ¼ H x x; y ð Þx þ H y x; y ð Þỹ , it is convenient to introduce the complex field [34][35][36] …”

“…Equations (31), (36), and (41) are analytical expressions from which the magneto-elastic response can be calculated once the force distribution f x x ð Þ is known.…”