Effect of magnetic sheath on filament AC losses and current distribution in MgB₂ superconducting wires: Numerical analysis

Finite element method (FEM) analysis is employed to study and compare AC losses in a wide frequency range in two MgB₂ superconducting wires in self-field and in the presence of external AC field. The modelled wires, of the same external dimensions, are mono- and 36-superconducting filaments embedded in either magnetic Monel or a nonmagnetic metallic wire sheath. We demonstrate that in a multifilamentary wire in self-field the Monel sheath serves as a 'pole piece' at the filament outer surface and alters local magnetic fields, current flow and AC losses distribution within the filament. In comparison with the nonmagnetic sheath with the same electrical conductivity, AC current in the wire with the magnetic sheath penetrates significantly deeper into the filaments and AC losses in the filament and in the magnetic sheath increase significantly. In contrast, the symmetry of the monofilament wire makes the current and loss distributions in the filament practically indifferent to the sheath composition. Still, losses in the magnetic sheath are much higher than in the nonmagnetic sheath due to increased flux dynamics. The application of DC current, on which the AC current is superimposed, sharply reduces the AC losses in the magnetic sheath material due to the drop in its permeability. Filament losses are also reduced in the presence of DC current, but to a much lesser extent. Results also show that in the kHz frequency range, the magnetic permeability of the sheath increases the skin effect in both the wire and filaments complex. As a result, at such frequencies, a significant portion of the current is carried by the metallic part of the wire instead of the superconductor, contributing to a further increase in losses. The analysis also shows that in the presence of external AC magnetic field, the Monel can provide magnetic shielding for inner filaments, thus reducing coupling effects between filaments. However, if magnetically saturated by the DC current, the Monel behaves quite similarly to a nonmagnetic sheath.