MAGNETIZATION OF TYPE-II SUPERCONDUCTORS IN THE KIM-ANDERSON MODEL

Within the construct of the complete Kim-Anderson model for the critical-current density, we have calculated the initial magnetization curves and full hysteresis loops of type-II superconductors immersed in an external field H = H(dc) + H(ac)cos(omegat), where H(dc) (greater-than-or-equal-to 0) is a dc bias field and H(ac) (> 0) is an ac field amplitude. We denote the maximum and minimum values of H by H(A) (= H(dc) + H(ac)) and H(B) (= H(dc) - H(ac)). According to the Kim-Anderson model, the critical-current density J(c) is assumed to be a function of the local internal magnetic-flux density B(i), J(c)(B(i)) = k/(B0 + \B(i)\), where k and B0 are constants. We consider an infinitely long cylinder with radius a, and the applied field along the cylinder axis. The field for full penetration is H(p) = [(B0(2) + 2mu0ka)1/2 - B0]/mu0. A related parameter is H* = [(B0(2) - 4mu0ka)1/2 - B0]/mu0. Magnetization equations for full hysteresis loops are derived for three different ranges of H(A): 0 < H(A) less-than-or-equal-to H(p), H(p) less-than-or-equal-to H(A) less-than-or-equal-to H*, and H* less-than-or-equal-to H(A). Each of these three cases is further classified for several ranges of H(B). To describe completely the descending and ascending branches of the full hysteresis loops for all cases, 58 stages of H are considered and the appropriate magnetization equations are derived. In addition to these equations for a cylinder, the corresponding equations for a slab are presented. Comparison with previous work by Ji et al. and by Chen and Goldfarb in the appropriate limits supports the validity of the present derivation.