Longitudinal Critical Current in Type-II Superconductors

The longitudinal critical current of a bulk type-II superconductor near the transition field $H_{c2\mathrm{}}$ has been calculated from the Ginzburg-Landau equations via a simple extension of Abrikosov's treatment of the mixed state, valid when the self-field of the current can be considered negligible compared with the external field. The critical current is given by $\left(\frac{4\pi J_c}{c}\right)={\left(\frac{2}{3}\right)}^{\frac{3}{2}}\left(\frac{H_{\mathrm{cb}}}{\lambda }\right)\frac{{(1-\frac{H}{H_{c2\mathrm{}}})}^{\frac{3}{2}}}{\beta (1-\frac{1}{2{\kappa }^2})}$