Calculation of AC losses in ultra fine filamentary NbTi wires

The advent of Low loss Filamentary NbTi wires with very Fine Filaments, First developed hy Alsthom and the Laboratoires de Marcoussis, has led to the possibility of using superconductors in many AC 50/60 Hz applications. A computer program, based on the Bean Model, for any spacetime variation of the magnetic induction predicts losses successfully for filaments of diameter greater than
\sim 1 \mu
m. However, for filaments of diameter less than
\sim 1 \mu
m the theoretical calculation underestimates the losses dramatically. This is because the filament dimensions become comparable to ξ, the coherence length, λ the magnetic penetration depth, a
0
the flux line spacing and λ, the pinning penetration depth leading to electromagnetic coupling effects between filaments. In this paper these effects on loss calculations are investigated with a view to obtaining an improved prediction of the loss behaviour in these materials. The results are consistent with a model of flux penetration, whereby, due to proximity effects, the matrix is essentially behaving as a type II superconductor. The main effect of this is to strongly couple flux lines in the first compaction bundles so that hysteretic losses in A.C. fields are greater than those predicted by the Bean Model.