Anisotropic critical-state model of type-II superconducting slabs

Abstract

We introduce a critical-state model incorporating the anisotropy of flux-line pinning to analyze the critical states developing in an anisotropic biaxial superconducting slab exposed to a uniform perpendicular magnetic field and to two crossed in-plane magnetic fields which are applied successively. The theory is an extension of the anisotropic collective pinning theory developed by Mikitik and Brandt. The anisotropic flux-line pinning enters into the critical states by generating the angular dependence of the critical current density and by deviating the direction of the electric field from the current in the plane perpendicular to the vortex line. Comparing to the isotropic case, the anisotropic flux pinning strongly influences the magnetic response in the slab. We also apply the critical-state model to predict the underlying physical phenomenon of a field-cooled slab in a rotating magnetic field. IntroductionThe critical-state model in Type-II superconductors is first introduced by Bean [1, 2]. The component J ⊥ of the current density J perpendicular to the magnetic induction B is restricted to the threshold c J ⊥ for flux depinning, c J J ⊥ ⊥ = . The vortex moves whenever the driving Lorentz L f J B ⊥ = exceeds the average pinning force c p f J B ⊥ = ,thus causing a local flux-transport electric field [3]. As it only contains physics of flux pinning, Bean model solves the critical states in a symmetric superconductor exposed to an external magnetic field that is applied along the symmetry axis [1] [4, 5] [6] [7-9]. The Bean critical states also describe the most cases of practical interest, such as in superconducting magnets where the self-field is generally perpendicular to the local current flow [10] and in HTS ac power cables [11]. If J is not perpendicular to the magnetic field H ( 0 µ = B H is a good approximation for high-κ superconductors [12]), as expected in the samples with nonsymmetrical geometry or excited by the magnetic field that varies in both magnitude and direction [13-16], the vortex lines may tilt each other. To avoid flux-line cutting, there is † Current address:a maximum gradient of the tilt angle α such that the component J  of J along H is constrained to the threshold c J  . The fundamental physics is the local helical instability in a vortex with a sufficiently large J  [17-19]. Flux-line cutting explains the first onset of a nonvanishing parallel component E  of the electric field at c J J ≥   [20]. This is put into the generalized double-critical-state model (GDCSM) by Clem and the coauthors [21-23], accounting for both flux cutting and flux transport in the critical states. Assuming uncoupled flux transport and flux cutting, GDCSM sketches a rectangular of c ( , ) J J J ⊥  in the J J ⊥ −  plane. GDCSM successfully predicts the experimental magnetic response of high-temperature superconducting plates [24] and YBCO thin film [25] in which B is inclined with J . In practical applications, this theory allows to calculate the AC loss in power transmission cables with second gene...

Critical states of a superconducting slab subjected to tension and bending

“…It is conventional to treat the three-dimensional case with the magnetic field in the direction z, on the basis of for the two-dimensional problem. The T-state equation (see equation (32) in [28]) in the GTP can be obtained. There are six unknowns H , P , y , j , q E y and E .…”

“…and t t t 0 ¢ = / are introduced, and the superscripts of z¢ and t¢ will be omitted below. The T-state equation (see equation (32) in [28]) in the GTP reduces to normalized one (see equation (33) in [28]). These equations can be solved by combining the boundary condition (see equation (15) in [28]).…”

“…The experimental magnetic response of YBCO thin film [26] and the high-temperature superconducting slab [27] was successfully predicted by GDCSM in the case of J inclined to B. GDCSM was extended by Brandt and Mikitik [16], who integrated the coupling effect of flux cutting and depinning into the critical-state model. The authors introduce anisotropy into the critical state [28], transforming a 2D critical current density ellipse into a 3D ellipsoid. A generalized phenomenological model is developed for the magnetic field parallel to the mixed state of type-II superconductors, with more in-depth simulations of flux penetration and hysteresis loops [29].…”

“…The critical current density J c given by the critical-state theory [24,25,28] is analogous to the plastic flow yield surface in mechanics. Both of J c and yield stress exhibit a variety of nonlinear electromagnetic constitutive relations.…”

“…The present model is used to describe the critical state evolution in a deformed superconducting slab. We introduce the concept of deformation into the original critical-state model [28], and work out how to describe the strain effects in the time evolution of critical states. Slabs subjected to bending and stretching are discussed in detail by the developed model, to show their profiles of the critical states at a particular time and strain and to determine the way in which the profiles evolve with time and strain.…”