The Average Kinetic Energy of the Superconducting State

Isothermal magnetization curves are plotted as the magnetization times the magnetic induction, $4\pi M\cdot B$, versus the applied field, H. We show here that this new curve is the average kinetic energy of the superconducting state versus the applied field, for type-II superconductors with a high Ginzburg-Landau parameter $\kappa$. The maximum of $4\pi M\cdot B$ occurs at a field, $H^{\ast }$, 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 $T_c=8.5K$, and compare them.