Low frequency impedance of a round superconducting wire

We calculated the electric field E on the surface of a straight superconducting wire with circular cross-section carrying AC transport current I = I(a)cos omega t. Performing the Fourier analysis of E, we found that both components of the first harmonic have the same form: the critical current I-c in prefactor and the rest depending on the ratio F = I-a/I-c. The in-phase component leads to the classical result of loss calculation, while the out-of-phase component was derived for the first time. Thus the wire can be symbolized by a complex self-inductance L-1(I) = L-1'(I) - jL(1)"(1) where L-1', represents the reactive power while L-1" the losses. When the lock-in amplifier, used to sort out the components of the first harmonic, is utilized in the wide-band mode, it allows one to determine the magnetic flux penetrated in the wire volume at two significant moments of the AC cycle: at zero current (remanent flux) and at the amplitude value of current. (C) 1998 Elsevier Science B.V. All rights reserved.