Superconducting critical current density ($J_c$)

A limiting transport current per conductor cross-sectional area for specified temperature, magnetic field and dissipation criterion. Local current distribution, flux motion and weak links can make it distinct from an intrinsic depairing limit. Its variation with the operating conditions is summarized by a superconducting critical surface.

For uniform flow in local Ginzburg-Landau theory of superconductivity, a phase gradient $q$ suppresses the equilibrium condensate density by $1-{\xi }^2{q}^2$. Hence $j(q)={\Phi }_{0}q(1-{\xi }^2{q}^2)/(2\pi {\mu }_0{\lambda }^2)$, maximized at $q=1/(\sqrt{3}\xi )$. 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 $a\gg \lambda$.

The boundary of a stated superconducting transport criterion in temperature, magnetic field and current-density space. A value measured under one combination does not specify a winding's usable current at another field or temperature. Strain and sample geometry can require further parameters.