= Superconducting depairing current density
{title2=$j_d=\Phi_0/(3\sqrt3\pi\mu_0\lambda^2\xi)$}
For uniform flow in local <Ginzburg-Landau theory of superconductivity>, a phase gradient $q$ suppresses the equilibrium condensate density by $1-\xi^2q^2$. Hence $j(q)=\Phi_0q(1-\xi^2q^2)/(2\pi\mu_0\lambda^2)$, maximized at $q=1/(\sqrt3\xi)$. This intrinsic local limit differs from vortex entry, depinning and the cross-section average in a thick wire. A Meissner surface shell has average-to-surface current-density ratio approximately $2\lambda/a$ for wire radius $a\gg\lambda$.
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