Superconducting dc transformer coupling

Measurements of the ratio of secondary voltage to primary voltage as a function of the secondary current allow a determination of the superconducting dc transformer coupling force. The force was measured for tin-film transformers. The primary film thickness and the thickness of the SiO insulating layer were varied. The maximum coupling force appears to be given approximately by $F_{\mathrm{cm}}\simeq \left(\frac{{\phi }_0^2}{8\pi {\mu }_0}\right)\times {\left[{\lambda }_{p}coth\right(\frac{d_p}{{\lambda }_p})+{\xi }_p+d_0]}^{-1\mathrm{}}$ ${\left[{\lambda }_{s}coth\right(\frac{d_s}{{\lambda }_s})+{\xi }_s+d_0]}^{-1\mathrm{}}$. Here $d_0$, $d_p$, and $d_s$ are the oxide thickness, primary thickness, and secondary thickness, and other symbols are standard.