Kim model for magnetization of type-II superconductors

Abstract

We have calculated the initial magnetization curves and complete hysteresis loops for hard type-II superconductors. The critical-current density Jc is assumed to be a function of the internal magnetic field Hi according to Kim’s model, Jc(Hi)=k/(H0+‖Hi‖), where k and H0 are constants. As is the case for other critical-state models, additional assumptions are that bulk supercurrent densities are equal to Jc, and that the lower critical field is zero. Our analytic solution is for an infinite orthorhombic specimen with finite rectangular cross section, 2a×2b (a≤b), in which a uniform field H is applied parallel to the infinite axis. Assuming equal flux penetration from the sides, we reduced the two-dimensional problem to a one-dimensional calculation. The calculated curves are functions of b/a, a dimensionless parameter p=(2ka)1/2/H0, and the maximum applied field Hm. The field for full penetration is Hp=H0[(1+p2)1/2−1]. A related parameter is H*m=H0[(1+2p2)1/2−1]. Hysteresis loops were calculated for the different ranges of Hm : Hm<Hp, Hp<Hm<H*m, and H*m<Hm. The equations for an infinite cylindrical specimen of radius a are the same as those for a specimen with square cross section, a=b. In the limit p≪1 and a=b, our results reduce to those of the Bean model (Jc independent of Hi) for cylindrical geometry. Similarly, in the limit p≪1 and b→∞, the results are the same as those for a slab in the Bean model. For H>1.5 Hp, or H>0 when p≪1, the width of the hysteresis loop ΔM may be used to deduce Jc as a function of H: Jc(H)=ΔM(H)/[a(1−a/3b)].

Synthesis of dense bulk MgB2by an infiltration and growth process

“…The magnetic moment of sample was measured using a superconducting quantum interference device (SQUID) magnetometer. Critical current density was calculated from the measured magnetic moment loop using the extended Bean model for a rectangular cross section in a perpendicular magnetic field [32]. Finally, a four-probe resistance technique was used to measure the resistivity of the sample under an applied external field of up to 9 T (applied perpendicular to the direction of transport current).…”

Tunability of the critical-current density in superconductor-ferromagnet hybrids

“…Many experiments are being carried out to study the effect of ferromagnetic parts on the J c of the SC, both in the transport case, that is, when a current is fed in the SC via an external source, [4][5][6] and in the magnetic case, in which current in the SC is induced by an external magnetic field H a . [7][8][9][10] Considering the magnetic case, it is known that in SCs the width of the hysteresis loop M͑H a ͒ is directly associated to the critical-current density J c ͑H a ͒ of the SC, 11,12 according to the critical-state model ͑CSM͒. 13 Obtaining a desired value of J c at a given field H a is, therefore, equivalent to finding a hysteresis loop with the adequate shape as to yield this J c value at H a .…”

Processing and Properties of Bar-Shaped Single-Seeded and Multi-Seeded YBCO Bulk Superconductors by a Top-Seeded Melt Growth Technique

“…A small sub-specimen of size 2.35 mm ×2.43 mm ×1.8 mm sliced and cleaved from each single grain sample was used to measure the transition temperature (T c ) and the critical current density (J c ) at 77 K using a superconducting quantum interference device (SQUID) magnetometer (Quantum Design MPMS-XL). Kim's extended model [27] was used to deduce the critical current densities from the measured magnetic hysteresis loops.…”