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

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 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> 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 ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ferro-In</i> configuration) and 2) a ferromagnetic tube placed outside the superconducting one ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ferro-Out</i> 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 high-temperature superconductor tube alone can be increased by a factor of up to 7 (2) in a <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ferro-Out</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ferro-In</i> ) 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).