Field Dependence Of Critical Current Research Articles

Measurements and analyses of hysteretic field dependences of critical currents in bicrystalline Nd1Ba2Cu3O7 films

Abstract We measured the critical current densities ( J cb ) of grain boundaries (GB) in the bicrystalline Nd 1 Ba 2 Cu 3 O 7 films of several misorientation angles under various applied fields. J cb ’s showed hysteresis curves as functions of fields. The main features of the data were qualitatively consistent with the calculation results. In the calculations, J cb ’s were expressed as functions of the densities of Josephson vortices, which were estimated from the field distributions around GB. We calculated the field distributions using the Brandt’s formula and expressed J cb by the modified Kim’s model.

Magnetic properties of finite superconducting cylinders. I. Uniform applied field

A model for the calculation of the magnetic levitation force for finite type-II superconductors in the critical state is presented in a series of two papers. In the first paper, we describe the main features of the model and understand the effect of demagnetizing fields in the magnetic properties of finite superconductors by considering the case of a superconducting cylinder in the presence of a homogeneous applied field. Field and current profiles are calculated from a minimization of the magnetic energy in the superconductor after a change in the applied field. Results are presented for both constant and field-dependent critical currents. The procedure is general enough to be applied to the case of nonuniform applied fields, as long as the cylindrical geometry is preserved.

Fabrication and critical currents of thin-film-type Bi 2Sr 2CaCu 2O x intrinsic Josephson junctions

We fabricated intrinsic Josephson junctions using Bi 2Sr 2CaCu 2O x thin films. High quality of the thin film is achieved by adjusting the composition of the thin films precisely using an atomic absorption spectroscopy system and by annealing the films at a high temperature. Current–voltage characteristics along the c-axis of the thin films show multiple branches of a series connection of Josephson junctions with large hystereses. Voltage jumps range from 24 to 36 mV and are comparable with those of bulk single crystals. The magnetic field dependence of critical currents was measured, and the results were compared with the numerical simulation using the Sakai–Bodin–Pedersen model. We found that 1 μm long intrinsic Josephson junctions with the current density of 1.2–3.0 kA/cm 2 exhibited critical currents smaller than those of the Fraunhofer type approximation because of the fluxon interaction among the junctions.

Magnetic behavior of thin superconducting disks with B-dependent Jc

The ac susceptibility, χ = χ′ + iχő, of a superconducting thin disk in a perpendicular magnetic field is calculated in the critical-state model assuming a field-dependent critical current, J c ( B). We find both analytically and numerically that the asymptotic behavior at large ac-field amplitudes B am changes from χ ′ ∝ B a m − 3 / 2 and χ ″ ∝ B a m − 1 for the Bean model, to χ ′ ∝ B a m − 3 and χ ″ ∝ B a m − 2 for J c decreasing with |B|as|B| −1 or faster. In the parametric χ″(χ′) plot the peak of χ″ increases in magnitude and shifts toward χ′ = 0. This allows an easy experimental discrimination between a Bean model behavior, one with J c( B), and one where flux creep is an ingredient. Account of the B-dependence of J c improves substantially agreement with available experimental χ″(χ′) data.

Thin superconducting disk with field-dependent critical current: Magnetization and ac susceptibilities

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.

Flux trapping and magnetic field dependence of critical currents in narrow YBCO step edge junctions

We have studied narrow (0.8-18 /spl mu/m wide) YBa/sub 2/Cu/sub 3/O/sub 7-/spl delta// step edge junctions in moderate applied magnetic fields as high as B/sub a//spl sim/25 mT. The magnetic field dependence of the junction critical current, I/sub c/, resembles a Fraunhofer diffraction pattern for all the junctions studied, although the field values of the pattern minima are modified due to the planar geometry. At 77 K these narrow junctions exhibit abrupt discontinuities in the I/sub c/(B/sub a/) pattern due to jumps in I/sub c/. These jumps are most likely due to sudden changes in the position of an individual vortex in close proximity to the junction. The I/sub c/(B/sub a/) patterns show hysteretic behaviour for applied fields B/sub a/>1-2 mT at 77 K, and the magnitude of this hysteretic behaviour appears to plateau for B/sub a/>/spl sim/12 mT, depending on junction width.

Critical current degradation caused by winding process of Bi-2223/Ag HTS wire in the form of a coil

High T/sub c/ superconducting (HTS) (Bi,Pb)/sub 2/Sr/sub 2/Ca/sub 2/ Cu/sub 3/O/sub 10+x/ Ag-clad wire has potential for practical applications in the form of a coil or a winding. This HTS wire has strong magnetic field-dependent and mechanical strain-dependent critical currents, consequently it has a severe problem of critical current degradation when it is used in the form of a coil. To design a winding with this conductor, the critical current degradation has to be identified with relation to the magnetic fields and the winding process. This is important to optimize an appropriate coil winding procedure using this HTS wire. A specially designed noninductive sample has been made with a (Bi,Pb)/sub 2/Sr/sub 2/Ca/sub 2/ Cu/sub 3/O/sub 10+x/ Ag-clad 27-filament wire, and the critical current degradation, which is caused by the magnetic field generated and the mechanical winding procedure used to form a coil, has been separated into two factors accordingly, and discussed in this paper.

On using tape to make a toroidal coil

High- superconducting (HTS) multifilamentary tape, was used to prepare an HTS toroidal coil. Magnetic field behaviour of the HTS coil is studied for this toroidal configuration. The magnetic field distribution of the HTS coil is investigated for use at 77 K and 4.2 K with the anisotropic HTS wire having a strong magnetic field dependent critical current. Since the magnetic field component along the HTS wire c-axis is significantly reduced in the form of a toroid, it is suitable to make a high-ampere-turn or high-inductance coil with the present HTS tape having an anisotropic transport property.

Critical state in thin superconductors: a Josephson junction array analogy

The Josephson junction array is numerically simulated to study the vortex dynamics in a thin superconductor in a transverse magnetic field. The non-local interaction between currents and fields is incorporated in the dynamics by considering the full inductance matrix of the array. The field and the current distribution in the array are obtained for various applied fields which shows striking similarity with that obtained in the critical state model for a superconductor in the 2D limit (thin film geometry). The cross-over from a non-linear distribution of the field for the 2D limit (demagnetisation factor N → 1) to a linear distribution for the 3D case (N = 0) is studied phenomenologically by increasing the thickness of the superconducting islands forming the array. Increasing the thickness of the array effectively reduces the strength of the non-local interaction between currents and fields. The M-H curve and the field distribution within the array are calculated for field independent and field dependent critical currents of the Josephson junction. We also probe in detail the evolution of the field and the current distribution towards their equilibrium values after an external field is applied. The results are discussed and compared with analytical results of the critical state model for a thin superconducting strip in a transverse magnetic field.

Bi-2223/Ag HTS coil magnetic field properties for magnet and bias winding

Ag-clad (Bi,Pb)2Sr2Ca2Cu3O10+x high-Tc supercondicting (HTS) multifilament wire, is used to prepare a HTS coil. The magnetic field behaviour of the HTS coil is studied with respect to its critical current and magnetic field properties. The anisotropic HTS wire has strong magnetic field dependent critical current, which causes critical current degradation when used in the form of a coil. The HTS coil magnetic field is measured and its distribution is investigated. The experimental results and analysis provide basic information for the design of a magnet or bias winding with the Ag-clad (Bi,Pb)2Sr2Ca2Cu3O10+x HTS wire.

Study of minor hysteresis loops in the usual and anomalous superconducting regime of (Ce 0.95Nd 0.05)Ru 2: evidence of a first-order transition

We present a detailed study of minor hysteresis loops (MHLs) in the usual and anomalous superconducting (SC) regime of (Ce 0.95Nd 0.05)Ru 2. MHLs in the usual SC regime follow the predictions of critical state models (CSM) for a hard type-II SC with field-dependent critical current ( J c). At the onset of the anomalous SC regime, the behaviour of the MHLs cannot be explained by CSM alone. Our results present strong evidence of a first-order transition from the usual to the anomalous SC phase. MHLs are used to track the growth of the domains or nuclei of the anomalous SC phase across this first-order transition. Well inside the anomalous regime where the first-order transition is complete, MHLs are again as expected from CSM and this behaviour persists until one reaches the reversible regime below H c2, indicating that the upper transition is of second order.

Phase sensitive measurements of the pairing state symmetries of cuprate superconductors using tricrystal microbridges

Measurements of the field-modulated critical currents of cuprate thin film microbridges on tricrystal substrates are reported. Two central peaks of equal height are observed in the field-dependent critical currents of YBCO tricrystal microbridges. However, the critical current is nonvanishing at zero field for YBCO, consistent with an orthorhombically distorted d-wave order parameter. An ion-irradiated YBCO tricrystal microbridge has also been measured, and has been found to exhibit more ideal dx2−y2-like behavior with increasing irradiation dosage.

Theory of flux penetration into thin films with field-dependent critical current.

A theoretical analysis is presented for the critical state of an infinitely long type-II superconducting strip characterized by an arbitrary critical current density ${\mathit{J}}_{\mathit{c}}$(B). An analytical framework is developed, and numerical solutions are presented for the quasistatic current-density and flux-density profiles, as well as the hysteretic magnetization curves. The field dependence of the critical current density significantly affects the shape of the magnetization curves.

Temperature and magnetic field dependence of critical currents in granular superconductors

We analyze the critical current density J/sub c/ of a two-dimensional granular superconductor by a Josephson junction network approach, taking into account shielding current effects. We show that the temperature and field dependence of J/sub c/ is not directly given by the corresponding dependences of the maximum Josephson current of a single junction. By a critical state picture we discuss the temperature and magnetic field dependence of the effective energy barrier U/sub /spl gamma// for flux motion in the array. From the knowledge of U/sub /spl gamma//, calculated in the presence of currents flowing through the junctions, the magnetic field and temperature dependence of the critical current is derived.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Magnetic self-field entry into a current-carrying type-II superconductor. II. Helical vortices in a longitudinal magnetic field.

The previous consideration of the irreversible magnetic self-field entry into a current-carrying type-II superconductor (SC) [Phys. Rev. B 49, 6950 (1994)] is extended to the case of an applied longitudinal magnetic field. The structure of the helical Abrikosov vortex is found exactly in the framework of the London approximation. The field-dependent critical current of a spontaneous entry of the right-handed flux helix against the surface Bean-Livingston barrier into the SC cylinder of arbitrary radius R is calculated, as well as the critical current of the flux-line instability with respect to the left-handed helical expansion. On the basis of these two mechanisms, a diagram of the resistive state in current-field coordinates is evaluated. The direction of the optimal helix for which the surface barrier is the least and which, hence, is the first to enter the sample turns out to coincide with that of the full magnetic field at the surface only in the case of a thick cylinder with R\ensuremath{\gg}\ensuremath{\lambda}, where \ensuremath{\lambda} is the magnetic penetration depth. For the latter case, the generalized Silsbee's rule of a breakdown of nondissipative state is formulated.

Field-dependent critical currents in thin Nb superconducting disks

Magnetic hysteresis loops were measured on thin Nb superconducting disks using a SQUID-based technique; field-dependent critical currents have been observed in thin superconducting disks at low magnetic flux trapping densities (⩽ 4 G). Such phenomena were found to exist over a wide range of temperatures below the transition temperature. The observed field-dependent critical current densities are attributed to long-range interactions between trapped vortices in a superconducting film whose thickness is much less than or comparable to the penetration depth. In the framework of Kim's critical state model, we developed a numerical method to calculate the field-dependent critical currents by fitting the measured magnetic hysteresis loops. Our experimental data were adequately explained by Kim's critical state model. Shielding currents and magnetic field patterns in thin superconducting disks were calculated.

Intergrain boundary asymmetry and the critical current of HTSC ceramics

he critical current of individual intergrain contacts in HTSC ceramics defining its transport critical current depends on the “construction” of these contacts and, in particular, on their geometry. We analyze the current-carrying properties of intercrystallite tilt boundaries in terms of the dislocation model of such boundaries, proceeding from the assumption of substantial suppression of the order parameter by local mechanical stresses arising in the vicinity of the boundary. The spatial distribution of stresses depends on the misorientation angle θ of adjacent grains and the orientation angle φ of the boundary. Calculations reveal mechanical stresses on the asymmetrical boundary ( φ≠0) to be on the average weaker than on the symmetrical one ( φ=0). It must lead to the increase of the current-carrying capacity of asymmetrical boundaries. The results obtained with regard to this circumstance describe much better the experimental dependences of the tilt boundary critical current on the misorientation angle θ. Another peculiarity of the asymmetrical boundary, that is a “random” character of the spatial distribution of stresses, leads to a random distribution of the critical current local density over the contact area. For such (Josephson) contacts the magnetic field dependence of the critical current is a double-step one which allows one to explain experimentally observable double-step magnetic field dependences of the transport critical current of a good number of HTSC ceramics.

Phase coherence in the hysteretic magnetic behavior of parallel Josephson-junction arrays.

We report on the hysteretic field-dependent critical currents of large inductance arrays with up to ten ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ grain-boundary junctions in parallel. A peak in the critical current, roughly equal to its initial zero-field value, is observed after each reversal of the field sweep. This behavior indicates that the junction phases become equal modulo 2\ensuremath{\pi} (self-organized phase coherence) as the system relaxes away from the critical state. The primary features can be modeled using a Frenkel-Kontorova model generalized to include global interactions due to mutual inductance.

Current-voltage characteristics of a Bi 2Sr 2Ca 2Cu 3O 8+δ ceramic superconductor

A special contactless technique in combination with the four-probe method allowed current-voltage characteristics in a very wide range of electric fields E∼10 -13÷10 -1 V/cm to be measured on a ring-shaped specimen of the Bi 2Sr 2Ca 2Cu 3O 8+δ ceramics at T=77 K and different magnetic fields. Experimental data are characterized with an S-like behavior that corresponds qualitatively to the characteristic of a single Josephson junction in the presence of thermal fluctuations. At low magnetic fields, a scaling behavior of magnetic field dependences of critical currents determined by different voltage levels has been revealed which fails on exceeding an intragrain lower critical field.

Critical state and AC loss of a granular superconductor in a superposed AC and DC field

When the loss factor μ″ of the dynamic permeability in granular superconductors is measured as a function of temperature in an applied DC bias field, the observed maximum in μ″ may reflect two quite different conditions at different temperatures. This is shown experimentally on granular YBCO, and it is argued to be a direct consequence of the critical state taking place in the sample with a field-dependent critical current. Measurements of μ″ as a function of AC field amplitude shows two intergranular loss peaks, in addition to the intragrain one. The locations of the two peaks shift in opposite directions with increasing DC field. The behavior is related to the so-called loss minimum in type-II superconductors. Model calculations based on a simplified Kim- Anderson functional for j c( B) are given to support the interpretation of the experimental results.