Magnetization and Critical Supercurrents

TLDR

Magnetization of high‑field superconductors has been studied using tubular samples, and in a critical state the magnetization can be quantitatively predicted from the local critical current density J(B). By analyzing magnetization data, the authors deduced a critical current density relation α/J = B₀ + B for Nb₃Sn and 3Nb‑Zr. The study shows that α directly measures the current‑carrying capacity, B₀ approximates the thermodynamic critical field, and for B≫B₀ the product JB remains constant, indicating the Lorentz force governs the critical current density.

Abstract

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.