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Josephson penetration depth

In superconductivity, Josephson penetration depth characterizes the typical length on which an externally-applied magnetic field penetrates into the long Josephson junction. Josephson penetration depth is usually denoted as λJ and is given by the following expression (in SI):

$\lambda_J=\sqrt{\frac{\Phi_0}{2\pi\mu_0 d' j_c}},$

$d'=d_I +\lambda_1 \coth\left(\frac{d_1}{\lambda_1}\right) +\lambda_2 \coth\left(\frac{d_2}{\lambda_2}\right),$