AC loss properties of elliptic superconducting wires exposed to a transverse magnetic field with an arbitrary angle

Analytical expressions of alternating current (AC) losses are derived in a superconducting wire with an infinite length and elliptic cross-section for limiting cases in which the amplitude of an external transverse magnetic field is much smaller or larger than the full penetration field. Since it is assumed that the superconducting wire is subject to Bean's critical state model, in which the critical current density is independent of the magnitude of the local magnetic field, the AC losses under consideration are completely hysteretic. The expressions obtained explicitly include the effects of the aspect ratio of the wire cross-section and the external-field angle with respect to the broadest face. An approximated curve of the AC loss, which becomes equal to the analytical results under the limiting conditions mentioned above, is also proposed for a wide range of external-field amplitudes. In order to validate the proposed curve, the AC losses in the elliptic wires are numerically calculated by means of the minimization of magnetic energy. It is concluded that the discrepancy between the approximated curves and the numerical results of the AC losses is less than 40%.