Analytical expressions of AC magnetic susceptibility for some critical state models of superconductor

Analytical expressions of AC magnetic susceptibility chi(AC) were given for some critical state models of superconductor, such as Rollins-Silcox, Kimishima, Bean, and Anderson-Kim models. From the AC field dependence of magnetization, the in-phase and out-of-phase linear chi(AC) of chi(0)' and chi(0)", and nonlinear third harmonic components of chi(2)' and chi(2)" are represented by the function of alpha. Here alpha is the (mean) penetration field normalized by the AC field amplitude H-AC, and it is proportional to the (mean) critical (surface) current density. The alpha(3/2)-dependence of chi(0)' against small a was obtained for each model, except for the A-K model with the alpha(3)-dependence of chi(0)'. It was found that the analytical expressions for chi(0)" were most simple and useful to estimate the (mean) critical (surface) current density from the experimental data, and the validity of each model should be confirmed by the behaviors of non-linear chi(2)' and chi(2)". (C) 1998 Elsevier Science Ltd. All rights reserved.