Average kinetic energy of the superconducting state

Abstract

Isothermal magnetization curves are plotted as the magnetization times the magnetic induction, $4\ensuremath{\pi}M\ensuremath{\cdot}B,$ versus the applied field H. We show here that this curve is the average kinetic energy of the superconducting state versus the applied field, for type-II superconductors with a high Ginzburg-Landau parameter \ensuremath{\kappa}. The maximum of $4\ensuremath{\pi}M\ensuremath{\cdot}B$ occurs at a field ${H}^{*},$ directly related to the upper critical field ${H}_{c2},$ suggesting that ${H}_{c2}(T)$ may be extracted from such plots even in cases when it is too high for direct measurement. We obtain these plots both theoretically, from the Ginzburg-Landau theory, and experimentally, using a Niobium sample with ${T}_{c}=8.5\mathrm{K},$ and compare them.