THEORETICAL CRITICAL-STATE SUSCEPTIBILITY SPECTRA AND THEIR APPLICATION TO HIGH-TC SUPERCONDUCTORS

The fundamental complex susceptibilities chi = chi' - j-chi" are calculated from the symmetric critical-state hysteresis loops M (H) for an infinitely long hard superconductor with a rectangular cross section 2a x 2b (a less-than-or-equal-to b). For the critical-state model, the Bean, the Kim, the exponential law, and the triangular-pulse local-internal-field-dependent critical-current densities J(c)(H(i)) are chosen. The results of chi' and chi" are given as functions of the field amplitude H(m) normalized to the full-penetration field H(p), the sample dimensional ratio a/b, and the p parameter that characterizes the H(i) nonuniformity in the sample at H = H(p) on the initial M(H) curve. chi"(- chi') curves are also given for the different functional J(c)(H(i)) and other conditions. These theoretical critical-state susceptibilities are particularly useful in the study of sintered high-T(c) superconductors. For these materials, the procedures to determine the effective grain volume fraction f(g)* and the averaged and the local intergranular critical-current densities <J(c)>acs and J(c)(H(i)) by means of ac susceptibility measurements using such theoretical critical-state-susceptibility functions are described. Related problems met in the high-T(c) superconductor study such as sample performance nonuniformity, frequency dependence, grain clusters, and susceptibilities for the grains are discussed.