Numerical Study of the Shielding Properties of Macroscopic Hybrid Ferromagnetic/Superconductor Hollow Cylinders

Abstract

Abstract-We study the magnetic shielding properties of hybrid ferromagnetic/superconductor (F/S) structures consisting of two coaxial cylinders, with one of each material. We use an axisymmetric finite-element model in which the electrical properties of the superconducting tube are modeled by a nonlinear E-J power law with a magnetic-field-dependent critical current density whereas the magnetic properties of the ferromagnetic material take saturation into account. We study and compare the penetration of a uniform axial magnetic field in two cases: 1) a ferromagnetic tube placed inside a larger superconducting tube (Ferro-In configuration) and 2) a ferromagnetic tube placed outside the superconducting one (Ferro-Out configuration). In both cases, we assess how the ferromagnetic tube improves the shielding properties of the sole superconducting tube. The influence of the geometrical parameters of the ferromagnetic tube is also studied: It is shown that, upon an optimal choice of the geometrical parameters, the range of magnetic fields that are efficiently shielded by the hightemperature superconductor tube alone can be increased by a factor of up to 7 (2) in a Ferro-Out (Ferro-In) configuration. The optimal configuration uses a 1020 carbon steel with a thickness of 2 mm and a height that is half that of the superconducting cylinder (80 mm).Index Terms-Ferromagnetic/high-temperature superconductors (HTSs) hybrid structure, finite element, magnetic shield.

Finite-element simulations of hysteretic alternating current losses in a magnetically coated superconducting tubular wire subject to an oscillating transverse magnetic field

“…On the other hand, both sources favour a reduction of the hysteretic ac loss in the case of an outer paramagnetic support by depressing and guiding the magnetic flux, consistent with the findings of a previous analysis, which noted the factorization of the shielding effects of the superconducting and paramagnetic constituents before. [35] The decrease of the hysteretic ac loss in this configuration certainly involves a more subtle interaction between the two types of constituents. Shielding of the transverse applied magnetic field by the paramagnetic support alone would generate a homogeneous magnetic field inside the tube, like for a massive cylindrical set, the inverse of its reduced strength H a /H µ unfolding a nonlinear dependence on the permeability µ.…”

“…An elaborate numerical study of the shielding properties of such heterostructures, for example, assumes a nonlinear current-voltage characteristic of the superconductors and a reversible field-dependence of the permeability of the magnetic constituents µ, apart from including the fieldeffect on the critical current density j c . [35] Hence, configurations with the paramagnet layers placed outside the superconductor constituents exhibit much stronger shieldings than those with the respective layers placed inside. Based on an elegant analytical approach, [23,36] recent work probes the effect of outer magnetic supports on the hysteretic ac loss in a power transmission cable assembled from curved superconductor/soft-magnet tapes conforming to a cylindrical shape.…”

Numerical Method for Analyzing Shielding Current Density in HTS Film with Multiple-Layer/Multiply-Connected Structure

“…In HTS films, E p and j p are closely related to each other through the J-E constitutive equation. For the equation, we adopt the following power law [4][5][6][7]:…”

Accurate and Stable Numerical Method for Analyzing Shielding Current Density in High-Temperature Superconducting Film Containing Cracks

“…The relation is called the J-E constitutive relation. As the relation, we adopt the power law [2,3,6,7]:…”