Measurement of critical bulk and surface current densities in type-II superconductors in the mixed state

Abstract

We present an improved method for calculating from ac susceptibility measurements the critical current density Jc and the surface shielding parameter ΔH in bulk cylindrical type-II superconductors. As first developed by Bean, the method involves harmonic analysis of an expression for the voltage induced in a pickup coil around a specimen in an axial dc magnetic field with a small ac ripple field superimposed. Values of Jc obtained by Bean's analysis are suspect, in part because the analysis does not take account of surface shielding. Ullmaier modified Bean's calculation to remedy this defect. For simplicity he did not Fourier analyze the induced voltage, choosing instead to determine Jc and ΔH by comparing experimental waveforms with his calculated voltage. This procedure permits only a qualitative indication of whether the data are consistent with the model. For generality, we have modified Ullmaier's calculation by removing the approximation that the depth of penetration of the ac field is small compared to the sample radius. The resulting expression for the induced voltage V is a complicated function of Jc, ΔH, and the amplitude of the ripple field h0. A graphical procedure has been developed which not only extracts values of Jc and ΔH from plots of the amplitude of the third harmonic of V vs h0, but also provides a check for consistency of the data with the model.