Critical state in thin anisotropic superconductors of arbitrary shape

Abstract

A thin flat superconductor of arbitrary shape and with arbitrary in-plane and out-of-plane anisotropy of flux-line pinning is considered, in an external magnetic field normal to its plane. It is shown that the general three-dimensional critical state problem for this superconductor reduces to the two-dimensional problem of an infinitely thin sample of the same shape but with a modified induction dependence of the critical sheet current. The methods of solving the latter problem are well-known. This finding thus enables one to study the critical states in realistic samples of high-Tc superconductors with various types of anisotropic flux-line pinning. As examples, we investigate the critical states of long strips and rectangular platelets of high-Tc superconductors with pinning either by the ab planes or by extended defects aligned with the c axis.

Flux cutting in high-Tcsuperconductors

“…It is expected that in a thin YBCO plate the current at the normal flux front can slightly increase due to the bending of vortices and enhanced pinning on the CuO planes [40]. In our case, the large fitting value of J M max is much higher than predicted in [40]. It corresponds to the observed strong current line at the boundary where the in-plane vortices meet the normal flux.…”

“…However, with our thin sample geometry, we assumed a simplified 2D current distribution that is homogeneous throughout the thickness (see Fig.14 [38][39]. It is expected that in a thin YBCO plate the current at the normal flux front can slightly increase due to the bending of vortices and enhanced pinning on the CuO planes [40]. In our case, the large fitting value of J M max is much higher than predicted in [40].…”

“…In the flux-free center zone, the current was approximated by the 1D Meissner solution for a long superconducting strip [38][39] with varying maximum current J M . A more accurate approach would use an elliptic 3D shape to model the flux front [40]. However, with our thin sample geometry, we assumed a simplified 2D current distribution that is homogeneous throughout the thickness (see Fig.14 [38][39].…”

3-D Finite-Element Modelling of a Maglev System using Bulk High-Tc Superconductor and its Application

“…www.intechopen.com Consequently, the critical current density J c of the high-Tc superconductor is anisotropic and strongly dependent on the orientation of the applied field (Mikitik & Brandt, 2000). Namely,the value of the critical current density flowing in the ab-plane J ab c is larger than that along the c-axis J c c (Matsushita, 2007).…”

“…Many methods have been proposed to formulate the dependence of the critical current density J c on the angle φ between the orientation of the local applied field and c-axis. However, a few of them are difficult to be employed in the present calculation due to its complexity in determining the parameters involved in the formulation (Mikitik & Brandt, 2000) or its applicable field range is beyond our focus (Sawamura & Tsuchimoto, 2000). Another model reported in (Yang, et al, 1999) is simple to be employed and has been valiadated in an axisymmetric levitation system.…”