  Magnetization hysteresis loops and the ac susceptibility of a superconducting
thin disk are calculated in the critical-state model assuming a field-dependent
critical current density, Jc(B). The results are obtained by solving
numerically the set of coupled integral equations for the flux and current
distributions [PRB 60(17) p.13112 (1999)] for a disk placed in a perpendicular
applied field Ba. From the magnetization curves the range of fields where the
vertical width of the loop relates directly to Jc(Ba) is determined. Comparing
our results on susceptibility with experimental data for parametric plot
Im(chi) vs. Re(chi) shows that by taking the B-dependence of Jc into account
the agreement improves dramatically. We show that the asymptotic behavior for
large ac-field amplitudes Bam changes from Re(chi) ~ 1/Bam^{3/2} and Im(chi) ~
1/Bam for the Bean model, to Re(chi) ~ 1/Bam^3 and Im(chi) ~ 1/Bam^2 for Jc
decreasing with |B| as 1/|B| or faster. For small Bam the behavior can always
be described by an effective Bean model with a renormalized Jc. We also find
that in the Im(chi) vs. Re(chi) plot the peak of Im(chi) increases in magnitude
and shifts to lower |Re(chi)|. This allows an easy experimental discrimination
between a Bean model behavior, one with Jc(B), and one where flux creep is an
ingredient.
