Thin superconducting disk with B-dependent Jc D.V. Shantsev, T.H. Johansen, Y.M. Galperin University of Oslo, Norway     &     Ioffe Institute, St. Petersburg, Russia Online presentation

Part I: Flux and current distributions Phys. Rev. B 60, 13112-13118 (1999) [PDF] Advances in Superconductivity XII: pp. 416-418 (2000) eds. T. Yamashita and K. Tanabe (Springer-Verlag, Tokyo) [Proc. of ISS'99; get Zipped PS file or Tex & Eps files]. Highlighted in 99Aug01 issue of  High Tc-Update Abstract.  The critical state in a superconducting thin circular disk with an arbitrary magnetic field dependence of the critical sheet current, Jc(B), is analyzed. With an applied field Ba perpendicular to the disk, a set of coupled integral equations for the flux and current distributions is derived. The equations are solved numerically, and flux and current profiles are presented graphically for several commonly used Jc(B) dependences. It is shown that for small Ba the flux penetration depth can be described by an effective Bean model with a renormalized Jc entering the leading term.We argue that these results are qualitatively correct for thin superconductors of any shape. The results contrast the parallel geometry behavior, where at small Ba the B-dependence of the critical current can be ignored.

Part II: Magnetization and ac susceptibility Phys. Rev. B v. 61, p. 9699-9706 (2000) [PDF]. (Also TeX file and eps figures) Physica C 341-348, pp. 2045-2046 (2000) [PDF] [Proc. of M2S-HTSC-VI] (Also TeX & Eps files). Highlighted in 99Nov15 issue of  High Tc-Update Abstract.   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 [Part I: 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 of susceptibility (chi) for large ac-field amplitudes Bam changes from Re(chi) ~ Bam-3/2 and   Im(chi) ~ Bam-1 for the Bean model, to Re(chi) ~ Bam-3 and  Im(chi) ~ 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.