Flux-line cutting in rotating type-II superconductors in parallel geometry

Abstract

Experimental results of a type-II superconductor, undergoing slow oscillations in a static magnetic field, have been theoretically investigated. The theoretical description considers the occurrence of flux-line cutting since the critical currents have a parallel component to the magnetic induction B. For this purpose, the elliptic flux-line-cutting critical-state model has been employed to calculate the magnitude B and orientation α(x) of the magnetic induction. Hysteresis loops, at different initial magnetic states and, at relatively small and large amplitudes of oscillation, are calculated numerically and compared with experimental data of a Nb disk. The complex behavior of the hysteresis loops is associated with the magnetic induction consumption. Our results are compared with those obtained employing the generalized double critical-state model. Our elliptic model is not restricted by the isotropic condition, that establishes that the electric field E is parallel to the current density J, but considers an induced anisotropy by flux line cutting. The limits of applicability of the elliptic model are discussed.

Bianisotropic-critical-state model to study flux cutting in type-II superconductors at parallel geometry

“…Therefore, in general, none of the principal axes lies on the magnetic induction vector B. The latter result differs from the ECSM, where the curve traced by J in the - J J plane is an ellipse whose major axis  J c always coincides with the direction of B [21][22][23].…”

“…The ECSM, introduced by Romero-Salazar and Pérez-Rodríguez, is valid for isotropic superconductors under rotating or crossed magnetic fields [20][21][22][23]. They postulated a constitutive equation J E ( ) similar to those used for anisotropic materials, see equation (2), except that the diagonal tensor J c ˆhad the principal values J c⊥ and J cP .…”

Smooth double critical state theory for type-II superconductors

“…In addition, the minimization is performed with the local distribution of currents constrained by the law J ∈ r . Notice that either material or extrinsic anisotropy can be easily incorporated by prescribing r to be the appropriate region: for instance, by modeling r as an elliptical [4,[18][19][20]22] or a rectangular [4][5][6][7][8][9][10][11][12]30] region oriented over selected axes. Mathematically, such kinds of regions are hosted as limiting cases of a smooth expression defined by the two-parameter family of superelliptic functions:…”

“…Notice that, either material or extrinsic anisotropy can be easily incorporated by prescribing ∆ r to be the appropriate region. For instance, by modeling ∆ r as an elliptical [4,[18][19][20]22] or a rectangular [4][5][6][7][8][9][10][11][12]30] region oriented over selected axes.…”

Flux-cutting and flux-transport effects in type-II superconductor slabs in a parallel rotating magnetic field

“…Furthermore, as it is shown in Refs. [19,27], the elliptic critical-state model successfully describes the magnetic response of superconducting disks undergoing oscillations in a magnetic field of fixed magnitude for nonmagnetic, paramagnetic, and diamagnetic initial states [11].…”