Current distribution and coupling losses in superconducting cables being partially in magnetic fields

The diffusion equation for flux penetration into flat superconducting cables is derived, for magnetic fields changing along the cable and solved for cables exposed only partially to applied field. From these solutions, the current distribution in the strands, the AC losses and the corresponding time constants are determined. At low frequencies, the transverse losses inside the field region are enhanced due to currents induced outside this region, being negligible in field-free regions. At higher frequencies, both contributions are nearly the same of skin effect type, as in normal conductors The time constant for decaying the induced current is proportional to the cable length and can be much larger than calculated for spatially homogeneous AC fields. The result, analogous to those previously obtained for the EURATOM-LCT conductor 25 years ago, explain the existence of long living oscillatory currents (or super coupling currents) in some cables for accelerator magnets, as well as in some model cables.