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 $J(B)$ determined only by the local magnetic field B, the magnetization can be predicted quantitatively from the critical current density $J(B)$. Using observed magnetization data, a critical current density relation $\frac{\ensuremath{\alpha}}{J}={B}_{0}+B$ is deduced for ${\mathrm{Nb}}_{3}$Sn and 3Nb-Zr. $\ensuremath{\alpha}$ 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 $JB=\ensuremath{\alpha}=\mathrm{const}$ for $B\ensuremath{\gg}{B}_{0}$, the Lorentz force plays an important role in determining the critical current density.

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