Paramagnetic Effect in Superconductors. I. Theoretical Aspects

Abstract

A theory for the paramagnetic effect is developed under the assumption that the ratio of the effective length to the effective diameter $\frac{l}{a}$ of the superconducting particles in the transition region is constant. While experiment shows that the relative apparent permeability ${\tilde{K}}_m$ is a function of $\gamma ={\varphi }_0(1-\frac{I_g}{I})$, where ${\varphi }_0=\frac{H_{\varphi 0}}{H_{z0\mathrm{}}}$, $H_{\varphi 0}$ is the circular and $H_{z0\mathrm{}}$ the longitudinal component of the field at the surface, $I_g$ is a limiting current, and $I$ the total current through the sample, this theory gives the permeability as a function of ${\varphi }_0$ only. Good agreement with the experimental range of ${\tilde{K}}_m$, however, is obtained when the theoretical value of ${\varphi }_0$ is replaced by $\gamma$. The experiments of the author et al. on solid and hollow mercury cylinders and recent experiments of Thompson and Squire on a solid tin cylinder are discussed. A reason why the theoretical value of ${\varphi }_0$ has to be replaced by $\gamma$ cannot be given at this time, although it is indicated where the present theory has to be amended.