Ac loss in two ac carrying superconducting concentric tubes--the duoblock model

The loss occurring in two concentric tubes carrying an alternative current is calculated. For currents below the critical current of the outer tube the loss is identical to the monoblock loss for that tube. If the current exceeds the critical current of the outer tube, some of the current is transferred into the inner tube leading to an extra term in the loss. For the case of very thin tubes (thin film conductor) separated by some gap much larger than the tube thickness, this leads to a linear dependence of the loss on current for currents above the critical current of the outer tube