A critical state model for a granular superconductor is employed to calculate the temperature and AC and DC magnetic field dependence of the complex susceptibility, χ = χ ′ + iχ ″, of a sintered bulk YBa 2 Cu 3 O 7- δ superconductor. Inter granular Josephson vortices are assumed to sweep in and out of the weak-link network while intragranular Abrikosov vortices move in and out of the superconducting grains, both causing bulk pinning hysteresis losses. The predictions of the model for χ′ and χ″ are consistent with experimental data and model parameters which characterize a high temperature granular superconductor can be determined. These parameters are the inter- and intragranular pinning force densities, the fraction of the superconducting grains, the grain size distribution and a London penetration depth which neglects grain anisotropy.

AC susceptibility of high temperature superconductors in a critical state model

Levitation and rotation of cylindrical rare‐earth magnets on yttrium‐barium‐copper‐oxide superconducting bearings has been sustained at speeds of up to 120 000 rpm with a surface speed of 40 m/s. The decay of the free rotation rate has been measured at both atmospheric pressure and a partial vacuum to 2.6 μm Hg. The decay measurements in vacuum indicate that the flux drag torques are constant and independent of speed. The magnetic shear stress on the rotor magnet is estimated to be 150 dyn/cm2. It is believed that drag torques on rotating magnets are related to asymmetry in the flux density pattern of the magnet.

High‐speed rotation of magnets on high Tc superconducting bearings

The rf residual surface resistance Rres is a figure of merit for superconducting microwave devices and for the homogeneity of superconducting surfaces. In granular superconductors not only high Rres values but also strong field dependencies Rres(T, ω, Hrf) at rather small fields Hrf ≤ 1 Oe are observed accompanied by penetration depth changes λres(T, ω, Hrf). These observations are explained by insulating and weakly conducting weak links causing additional degrees of freedom as strip line modes and fluxoids. This causes additional interaction mechanisms with rf fields:

rf Residual losses, surface impedance, and granularity in superconducting cuprates.

A double step characteristic is observed at 76 K in the transport critical current as a function of magnetic field (10 -4 T to 10 T) in bulk sintered Y-, Bi- and Tl-based high- T c superconducting materials. The low-field, step-like drop in the critical current density J c commences at magnetic fields B between about 0.3 and 2 mT. This is followed by a plateau region of relatively constant critical current extending from about 30 to 300 mT, and then a second drop at fields between about 0.3 and 10 T. These features occur for all three superconductor materials and are interpreted respectively as a self-field/weak-link regime, a remnant percolation path regime and a flux-flow/upper-critical-field regime. The sharpness of the transition of the voltage-current ( V-I characteristic, represented by the transition parameter n (i.e., V ∝ I n ), has a similar double-step shape as a function of magnetic field directly corresponding to the features of the J c ( B ) characteristic.

Double-step behavior of critical current vs. magnetic field in Y-, Bi- and Tl-based bulk high-Tc superconductors

The loss peak of the AC susceptibility in polycrystalline high- T c superconductors shifts slightly to higher temperatures with increasing frequency of the applied AC magnetic field It is shown that a flux creep term, added to the current density term in the critical state equation, can account for the observed frequency dependence The magnitude of the peak shift is predicted to increase with decreasing average grain size and decreasing grain boundary junction current density The model predictions are compared with the experimental data of Nikolo et al Some of the parameters used in the calculation are determined by fitting data for χ′ and χ″ over the full temperature range using a recently developed model for granular superconductors In addition, the relation between the intergranular pinning potential and the activation energy, which is extracted from log-frequency versus inverse χ″-peak temperature data, is clarified

Frequency dependence of AC susceptibility in high-temperature superconductors Flux creep and critical state at grain boundaries

We have investigated, experimentally and theoretically, the magnetic flux which threads a YBa 2 Cu 3 O 7− x cylinder sample at 77 K when a weak low frequency ac magnetic field is applied. We explain the highly nonlinear magnetic response in great detail quantitatively, using a critical state model where during each ac cycle, intergranular (Josephson) vortices sweep in and out of the cylinder. The Josephson vortex pinning force is found to be field independent and several orders of magnitude smaller than in conventional type II superconductors. This explains the weak shielding properties and low critical current density found in this material. At magnetic fields greater than about 50 Oe, vortices start to enter the superconducting grains.

Josephson vortices and flux penetration in high temperature superconductors

We have spectrum analysed the voltage induced in a pick-up coil wound around a cylindrical bulk sample of YBa 2 Cu 3 O 7−δ when driven by a weak low frequency AC magnetic field, superimposed on a weak DC magnetic field, at 77 K. The harmonics generated by the highly nonlinear response are explained quantitatively in great detail by employing a critical state model with a field independent pinning force density, where intergranular vortices sweep in and out of the Josephson weak link regions during each AC cycle. The symmetry relation for the local flux density, which relates the first and second half of an AC cycle, is broken in the presence of a DC magnetic field, causing even harmonics to appear. This suggests high-sensitivity applications in magnetometry.

Nonlinear magnetic flux response in high temperature superconductors

Electromagnetic shielding properties of yttrium barium cuprate superconductor

A critical state model has been employed with an intergranular pinning force density which is independent of the local magnetic field, to calculate the critical transport current and the ac susceptibility of sintered Y Ba Cu O as a function of temperature. The assumed temperature dependence of the pinning force density is consistent with measurements on long tubular samples. The flux creep term of the effective intergranular pinning force causes a weak frequency dependence of the ac susceptibility.

Intergranular flux pinning in high temperature superconductors

Measurements of the attenuation of alternating magnetic fields by disc-shaped samples of yttrium barium cuprate superconductor at 77K are reported. The effectiveness of this material in magnetic shielding applications is examined as a function of sample density, and its stability against atmospheric corrosion is demonstrated.

J.C. Macfarlane

Papers

Josephson vortices and flux penetration in high temperature superconductors

Nonlinear magnetic flux response in high temperature superconductors

Electromagnetic shielding properties of yttrium barium cuprate superconductor

Intergranular flux pinning in high temperature superconductors

Electromagnetic shielding properties of yttrium barium cuprate superconductor