Magnetization and Critical Supercurrents

The magnetization in high-field superconductors has been investigated using tubular samples. When the sample assumes a critical state, wherein every region of the sample carries critical current density $J\left(B\right)\mathrm{}$ determined only by the local magnetic field B, the magnetization can be predicted quantitatively from the critical current density $J\left(B\right)\mathrm{}$. Using observed magnetization data, a critical current density relation $\frac{\alpha }{J}=B_0+B$ is deduced for ${\mathrm{Nb}}_3$Sn and 3Nb-Zr. $\alpha$ is a direct measure of the current carrying capacity of a sample, and $B_0$ coincides approximately with the thermodynamic critical field of the material. Since this relation implies $JB=\alpha =\mathrm{const}$ for $B\gg B_0$, the Lorentz force plays an important role in determining the critical current density.