Size effect in AC losses of superconducting cables

We calculate the dependence of the transverse coupling losses in cables, the most important contribution to AC losses in cables without central insulating layer. Two effects cause differences with respect to the infinite samples: (1) changed area of the loops between the strands, and (2) increased resistivity between them. At low frequencies, the transverse losses P for finite samples of length l are well-described by the formula P/P/sub /spl infin//=1-C/sub 0/l/sub 0//l, where C/sub 0/ depends on the ratio b/c (b-cable width, c-thickness of normal layer between strands), l/sub 0/ is the cabling length and P/sub /spl infin// the losses for corresponding infinite sample. We obtain /spl alpha/=1/C/sub 0//spl ap/3 for b/c/spl ap/10 and /spl alpha//spl ap/2 for b/c>50. The same formula applies for higher frequencies, with frequency dependent correction factor C(/spl omega/). This correction factor decreases and becomes even negative at higher frequencies. Thus, the losses in finite samples are higher than in the corresponding infinite cables. This effect could be therefore called the inverse size effect, appearing above /spl omega//spl tau/>0.9 for b/c=10 and /spl omega//spl tau/>1.53 for b/c=50. It may explain some experimental results where size effect was expected but not found in the loss measurements.<
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