Table of contents

The dependences of magnetic field penetration depth at zero temperature λ(0), microwave surface resistance R_s and π-band energy gap at zero temperature Δ_π(0) on the normal-state resistivity right above the critical temperature, ρ₀, were studied for MgB₂ thin films prepared by different techniques by employing a sapphire resonator technique. We found that the zero-temperature penetration depth λ(0) data could be well fitted by yielding a London penetration depth λ_L of 34.5 nm, where ξ₀ is the coherence length, and is the mean free path determined from ρ₀. The surface resistance R_s at 15 and 20 K increases roughly linearly with ρ₀. The observed increase of Δ_π(0) with ρ₀ and the decrease of T_c indicate the expected effects of interband impurity scattering within an extended BCS approach. The low values of R_s and λ(0) in conjunction with the large coherence length for epitaxial films are potentially attractive for applications in electronics and microwave technology.

Modern Nb₃Sn strands can now exceed 3000 A mm⁻² critical current density J_c at 4.2 K and 12 T within the non-copper area. However, the aggressive reaction used to achieve this performance causes the Nb₃Sn filaments to coalesce into a single large, continuous ring of superconductor, and also allows tin to penetrate through diffusion barriers and alloy with the copper stabilizer. This results in a lack of adiabatic stability, due to the combination of high J_c and large superconductor diameter, and a strong reduction of dynamic stability, due to the reduction of the copper's thermal conductivity. Under these circumstances, flux jumps at low fields are inevitable, and the associated heat release could propagate along the conductor in a quench. In magnets, this means that quenches could be initiated in low-field regions at currents well below the designed operating current. We show that by limiting the final reaction duration, it is possible to keep the quench current density above J_c, thus ensuring flux-jump recovery along the entire magnet load line. For the example studied, keeping the residual resistivity ratio above ensures safe operation. This was achieved for final reactions of 40 h or less, instead of the typical 72–200 h. Surprisingly, the performance penalty was small: a 24 h final reaction reached >90% of the highest J_c obtained. Energy-dispersive spectroscopy in a SEM did not reveal any detectable tin in the copper for stable strands, but in unstable strands as much as 4% Sn was found in the copper between sub-elements, suggesting that the contamination is rather local. The thermal conductivity of the stabilizer should then vary strongly with distance from the sub-element pack to the strand perimeter, complicating stability analyses.

Superconductivity in the simple elements is of both technological relevance and fundamental scientific interest in the investigation of superconductivity phenomena. Recent advances in the instrumentation of physics under pressure have enabled the observation of superconductivity in many elements not previously known to superconduct, and at steadily increasing temperatures. This article offers a review of the state of the art in the superconductivity of elements, highlighting underlying correlations and general trends.

We have investigated, in the framework of the proximity effect theory, the interface transparency between Nb and Cu in the case of high quality Nb/Cu trilayers fabricated by molecular beam epitaxy (MBE) and sputtering deposition techniques. The obtained values do not seem to be strongly influenced by the fabrication methods but more by the intrinsic properties of the two metals; a slightly higher value for has even been deduced for the MBE prepared samples. The proximity effect in these samples has also been studied in the presence of an external magnetic field. In the parallel configuration a significant shift towards lower values of the 2D–3D crossover temperature has been observed for MBE samples, in good agreement with very recent theoretical predictions. In the perpendicular case a positive curvature of the temperature dependence of the upper critical field has been detected, which was less pronounced for sputtered samples. Both the effects have been observed only for trilayers with low Nb thickness (<600 Å) which confirms the crucial influence of the interface transparency on the values of the upper critical field in such samples.

Biaxially cube textured polycrystalline Cu(200) substrate tapes were produced for high temperature superconducting (HTS) coated conductor applications. A comparison is made between Cu substrates fabricated by reverse cold rolling followed by recrystallization, from stock materials that were obtained in the form of extruded rod and rolled plate. Detailed x-ray diffraction (XRD) studies and orientation imaging microscopy (OIM) were performed to measure the in-plane alignment, out-of-plane alignment, and microtexture at various deformation levels and annealing temperatures. The rod starting geometry proved to have superior biaxial alignment with a predominant (220) deformation texture after rolling. Phi (Φ) scan and psi (Ψ) scan XRD reveals that the best in-plane and out-of-plane alignment, measured in terms of full width half maximum (FWHM) values of 5.4° and 5.8°, were obtained at 99.5% reduction in thickness and 750 °C annealing temperature. OIM microtexture results indicate that more than 97.5% of grains had less than 10° misorientation with no observable twinning.

We show that the magnetostriction hysteresis curves, measured at different temperatures by Chabanenko et al (1998 Supercond. Sci. Technol.11 1181) in a La_1.85Sr_0.15CuO₄ single crystal, can be well reproduced by exploiting the critical state framework proposed by Ikuta et al (1993 Phys. Rev. Lett.70 2116) to describe this phenomenon in high T_c superconductors, provided that the role of the Meissner current circulating at the surface of the crystals is taken into account.

Accurate data of complex permittivity of dielectric substrates are needed for efficient design of HTS microwave planar circuits. We have tested MgO substrates from three different manufacturing batches using a dielectric resonator with superconducting parts recently developed for precise microwave characterization of laminar dielectrics at cryogenic temperatures. The measurement fixture has been fabricated using a SrLaAlO₃ post dielectric resonator with DyBa₂Cu₃O₇ end plates and silver-plated copper sidewalls to achieve the resolution of loss tangent measurements of 2 × 10⁻⁶. The tested MgO substrates exhibited the average relative permittivity of 9.63 and tanδ from 3.7 × 10⁻⁷ to 2 × 10⁻⁵ at frequency of 10.5 GHz in the temperature range from 14 to 80 K.

Statistical thermodynamical and kinetically-limited models are applied to study the origin and evolution of space charges and band-bending effects at low-angle [001] tilt grain boundaries in YBa₂Cu₃O₇ and the effects of Ca doping upon them. Atomistic simulations, using shell models of interatomic forces, are used to calculate the energetics of various relevant point defects. The intrinsic space charge profiles at ideal surfaces are calculated for two limits of oxygen contents, i.e. YBa₂Cu₃O₆ and YBa₂Cu₃O₇. At one limit, O₆, the system is an insulator, while at O₇ it is a metal. This is analogous to the intrinsic and doping cases of semiconductors. The site selections for doping calcium and creating holes are also investigated by calculating the heat of solution. In a continuum treatment, the volume of formation of doping calcium at Y-sites is computed. It is then applied to study the segregation of calcium ions to grain boundaries in the Y-123 compound. The influences of the segregation of calcium ions on space charge profiles are finally studied to provide one guide for understanding the improvement of transport properties by doping calcium at grain boundaries in the Y-123 compound.

We report on the annealing effects on the microstructure, electrical, and magnetic properties of jelly-rolled Cu –xvol %Nb (x = 25, 33, 50, 63) composite wires, a promising material to be used in high-field magnets. During annealing at temperatures as high as 850 °C, noticeable changes take place in the microstructure, including recovery and recrystallization of copper and niobium, followed by partial spheroidization and further coarsening of niobium filaments. The influence of these microstructural changes on the electrical and magnetic properties of jelly-rolled Cu–Nb composite wires is discussed.

thin films have been grown on SrTiO₃ (STO) and yttrium-stabilized ZrO₂ (YSZ) substrates by pulsed laser ablation. The substrate temperature dependence of orientation and superconducting properties were systematically studied. Good quality c-axis and a-axis orientated films can be obtained on SrTiO₃ solely by changing the substrate temperature. On YSZ, films with good c-axis orientation can be grown, while it is hard to grow films with good a-axis orientation by changing substrate temperature alone. The highest T_{C 0} is about 37 K, which is found in the films grown on YSZ with a good c-axis orientation. For the films grown on STO, however, the highest T_{C 0} is about 35.6 K, with a mixed orientation of c-axis and a-axis. In most of the superconducting films, the weak temperature dependence of the normal state resistivity, as characterized by small ratios, together with a weak localization behaviour just above T_C, could be attributed to the essential scattering due to the localized electronic states. The superconducting transitions in a field up to 10 T along the c-axis have been measured on a c-axis oriented film grown on SrTiO₃. The zero-temperature in-plane upper critical field B_{C 2}^ab(0) is estimated from the resistivity transition data.

A 19 T cryocooled superconducting magnet with a 52 mm room temperature bore is currently under construction. The magnet consists of an outer NbTi section, middle Nb₃Sn section and innermost high-T_c section. The coils are exposed to an electromagnetic hoop stress following the magnetic field generation. In this 19 T cryocooled superconducting magnet, the high-T_c coil windings are Bi-2223 tapes with a low matrix ratio. Because of this, the mechanical characteristics, i.e., stress–strain characteristics, stress/strain dependence of the critical current and bending strain dependence of the critical current, were explored for the Bi-2223 tape. Furthermore, the small coil was wound with the superconducting tape. It was tested under magnetic fields to examine the stress–strain characteristics caused by the electromagnetic hoop stress.

The effect of annealing temperature for oxygenation (T_oxg) on grain boundary (GB) segregation and the distribution of calcium in the bulk was studied for Dy123/Ca_z (z = 0, 0.2) ceramics for T_oxg = 480 and 550 °C, where the first case corresponds to full oxygenation and the second to a little oxygen deficiency. Energy selective x-ray analysis techniques (with an ultra-fine probe) in field emission transmission electron microscopy were used for the characterization of the microstructure. It was found that Ca segregates at GBs in both cases, but the extent of such segregation strongly depends on T_oxg. The GB segregation for T_oxg = 550 °C was much lower than for 480 °C. For T_oxg = 480 °C, the calcium concentration was 1.5–3.5 times higher than in the bulk in 60% of the GBs, and segregation was absent in 40% of the GBs. For T_oxg = 550 °C, only 25% of the GBs showed Ca segregation, with a concentration 1.2–1.3 times exceeding that in the bulk. In both cases, the width of the segregation profile was about 10 nm. The change in T_oxg also affected the distribution of Ca in the bulk. In this way, the changes in the superconducting properties were directly correlated to the microstructure.

Irreversible fields B_irr of melt-processed (Sm,Eu,Gd)Ba₂Cu₃O_7−δ bulk superconductors with varying (Sm,Eu,Gd)₂BaCuO₅ concentrations have been measured with pulsed magnetic fields up to 28 T in a temperature range from 55 to 85 K. The temperature dependence of B_irr was studied by taking account of the effect of heat generation. In comparison with that including 5 mol% (Sm,Eu,Gd)₂BaCuO₅ phase the samples with 40 mol% (Sm,Eu,Gd)₂BaCuO₅ inclusion displayed a lower B_irr value for temperatures above 75 K, while B_irr was enhanced below 75 K. TEM observation unveiled a sharp contrast between a uniform nano-scaled compositional modulation in compositions with 40% (Sm,Eu,Gd)₂BaCuO₅ inclusion and an inhomogeneous distribution with very low (Sm,Eu,Gd)₂BaCuO₅ concentration. The present result could thus be understood in the context of different defect states induced by locally compositional fluctuation.

The effect of size, morphology and crystallinity of seed crystals on the nucleation and growth of melt processed Y–Ba–Cu–O (YBCO) during top seeded melt growth (TSMG) has been investigated. Conventional seeding of bulk YBCO with a small seed crystal of square planar or irregular geometry leads to point nucleation of the YBa₂Cu₃O_7−δ (Y-123) phase and a subsequent square planar c-sector growth habit. The use of seeds of triangular and round geometries, however, results in a deviation from this growth habit symmetry. The use of large surface area seed crystals of dimensions 20 mm × 10 mm, on the other hand, influences the growth of bulk YBCO in two significant ways. Firstly, rapid epitaxial nucleation of the Y-123 phase occurs beneath the seed crystal, followed by grain growth via the usual peritectic solidification in the incongruent melt. Secondly, a large area seed reduces the processing time of large single grains compared to that achieved by TSMG with small area seeds. The present study is particularly relevant to the fabrication of single-grain samples with controlled growth sectors, reduced processing times and the multiple seeding of large area bulk materials containing good grain boundaries.

The propagation of small amplitude (linear) electromagnetic waves in periodically spatially modulated finite Josephson junctions is studied using the transfer matrix approach. The transmittance of a finite length Josephson junction with thick, identical, periodic defects is presented. The linear wave spectrum consists of pass- and stop-bands, whose width may vary with the geometrical and/or the physical parameters of the junction. The band boundaries as a function of several junction parameters are also presented, and the possibility of creating mid-gap states of finite transmittance within the gaps by slightly disturbing the periodicity is demonstrated. The dependence of the plasma frequency on the parameters of the junction is also calculated using several simple approaches. The possibility of applying this approach to ϕ-junctions is briefly discussed. The knowledge of the mode spectrum may be useful in constructing elements of nonlinear systems for development of tunable superconducting resonators. It can also be useful in calculating the resonance voltages appearing in the current–voltage characteristics of a long periodically defected Josephson junction in a magnetic field, as proposed by Fistul et al.

Samples of YBa₂Cu₃O_7−δ, having about 30% Y₂BaCuO₅, were prepared with a melt-process method by adding B₂O₃ up to 0.5 wt% to the oxides. The structural and superconducting properties of the samples were studied by x-ray diffraction, x-ray fluorescence, scanning electron microscope, magnetization and magneto-optic techniques. B₂O₃ additions during the melt-processing enlarge intergrain regions that weaken the conduction links between the grains. T_c drops by 1.0–6.0 K, and at 50 K J_c decreases from about 1.6 × 10⁴ to 1.8 × 10³ A cm⁻² with B₂O₃ additions up to 0.5 wt%. A secondary peak was observed in the J_c versus field plot of the boron-free sample that decreases with boron additions. At 50 K the intragrain J_c values of the boron-free sample were about 12% higher than the intergrain J_c value, and such differences increase with B₂O₃ additions. These observations, together with the enlargements of the intergrain regions with B₂O₃ additions, suggest that most of the boron atoms take part and reside at grain boundaries.

Precursor materials for superconductors with nominal starting compositions of (Tl_0.6Pb_0.5)(Ba_0.2Sr_0.8)₂(Ca,RE)₂Cu₃O_y (RE: Y, La, Pr, Sm, Dy) were made via the evaporation of aqueous strontium–barium–calcium–copper–nitrate solutions followed by calcination at 900 °C in air. The stoichiometric amounts of the doping oxides were added by co-attrition. Sintering of the specimens was carried out inside a silver foil under flowing oxygen at 925 °C for 12 min and at 910 °C for 10 h. High quality Tl-1223 and Tl-1212 materials with well connected grains and T_{c (0)} values between 75 and 115 K were produced. The ΔT_(90−10%) values ranged from 2 to 18 K. Bulk phase j_c-values between 40 and 1400 A cm⁻² were obtained. Annealing improved the critical current densities. Two-step transitions were generally observed for samples containing rare earth cations.

Rare earth oxides favoured the formation of the Tl-1212 phase. Annealing at 750 °C for 50 h under flowing oxygen improved the transport properties of these samples.

Superconducting MgB₂ films were prepared on differently oriented α-Al₂O₃ substrates, C- and R-planes, which yielded superconducting transition temperatures of about 28 K. The electric resistivity of the MgB₂ film deposited on an R-plane substrate is 300 µΩ cm, six times larger than that on a C-plane substrate, 50 µΩ cm. To understand these differences in the electrical properties, various transmission electron microscopes were used to carry out a structural and the compositional analysis. It was shown from selected-area electron diffraction patterns that the microstructure consists of a mixture of columnar MgB₂ grains and amorphous phases in the case of the R-plane specimen, while no amorphous phase was present in the case of the C-plane specimen.

The mass attenuation coefficients for Y₂O₃, BaCO₃, CuO compounds, and solid-state forms of YBa₂Cu₃O₇ superconductor were determined at energies of 57.5, 59.5, 65.2, 74.8, 77.1, 87.3, 94.6, 98.4, 122, and 136 keV. The samples were irradiated using a ²⁴¹Am point source emitting 59.5 keV photon energies and a ⁵⁷Co point source emitting 122 and 136 keV photon energies. The other energies were obtained using secondary targets such as Ta, Bi₂O₃, and (CH₃COO)₂UO₂2H₂O. The gamma- and x-rays were counted by a Si(Li) detector with a resolution of 160 eV at 5.9 keV. Samples were selected on the basis of known composition and mass densities were measured using a densitometer. The experimental results obtained in this study are compared with theoretical values.

A sharp cube textured Ni overlayer on Cu substrates has been developed for the manufacturing of long-length RABiTS-based coated conductor tapes. Using a low-cost, non-vacuum and easily scalable technique of electroplating, smooth, crack-free and continuous Ni overlayers were deposited on cube textured Cu substrates without any intermediate layers. In addition, sharp cube textured Sm-doped CeO₂ buffer layers have been grown on the Ni-plated Cu substrates using pulsed laser deposition and found to exhibit in-plane and out-of-plane FWHM values of 6.50° and 5.25°, respectively. This electroplating process promises an efficient route for manufacturing Cu-based HTS coated conductors.

We have developed a high T_C SQUID probe microscope. A high permeability probe was used as a flux guide to improve its spatial resolution. The SQUID head with the flux guide makes it possible to measure samples with high spatial resolution in air at room temperature. The end of the flux guide and the SQUID were in vacuum with a 0.1 mm separation. The tip of the flux guide was in air. The rod diameter and length of the flux guide were 0.6 and 7 mm, respectively. The sharp tip of the flux guide required for high spatial resolution was prepared by microelectropolishing. Its tip radius was less than 1 µm. The static magnetic field pattern of magnetized toner particles was detected by this system and we obtained a high-resolution magnetic image with a spatial resolution of several microns.

MgB₂ bulks were synthesized by the solid-state reaction of Mg and B at 600 °C and their superconducting properties were compared with samples heated at 850 °C. The samples heated at 600 °C exhibited improved critical current properties up to high fields at 20 K. Poor crystallinity is found to contribute enhancement of H_c2, H_irr and J_c at high fields. On the other hand, the strongly grain connected network structure and smaller grain size are responsible for high J_c at low fields. Improved J_c up to 3.93 × 10⁵ A cm⁻² and a high μ₀H_irr of  T, as for undoped MgB₂ bulks, guarantees that low-temperature sintering is a promising way to fabricate MgB₂ conductors with high critical current performance.

AC losses of YBCO coated conductors are investigated by calculation and experiment for the higher frequency regime. Previous research using YBCO film deposited onto single-crystal substrates demonstrated the effectiveness of 'striping' or filamentary subdivision as a technique for AC loss reduction. As a result of these studies the idea of subdividing YBCO 'coated conductors' (YBCO, overlayer, and even underlayer) into such stripes suggested itself. The suggestion was implemented by burning grooves into samples of coated conductor using laser micromachining. Various machining parameters were investigated, and the striping and slicing characteristics are presented. Loss measurements were performed on unstriped as well as striped samples by the pick-up coil technique at frequencies from 50 to 200 Hz at field sweep amplitudes of up to 150 mT. The effect of soft ferromagnetic Fe shielding was also investigated. The results of the experiments form a starting point for a more general study of reduced-loss coated conductor design (including hysteretic, coupling, normal eddy current, and transport losses) projected into higher ranges of frequency and field-sweep amplitude with transformer and all-cryogenic-motor/generator applications in mind.

Contacts on high temperature superconductors have been fabricated using an electrodeposition process in non-aqueous media. This technique allows obtaining specific resistance values lower than 10⁻⁹ Ω cm² in a reproducible way. We have studied the differences in the silver grain morphology and metallic coating homogeneity depending on different electrodeposition parameters, such as deposition current density or different shaking techniques. The best results are obtained if the deposition process takes place in as-grown samples, before performing the required annealing to the superconducting material. The comparison between the predictions of the metallic layer thickness and the measured values indicates that the process is highly efficient and that the silver coating has a high density.

Several processing methods are under study for deposition of different layers of YBa₂Cu₃O_7−x- (YBCO-) coated conductors. The effect of these processing techniques on residual stress evolution in thin films of yttria-stabilized zirconia (YSZ) and YBCO was evaluated by measurement of the residual stresses using x-ray diffraction (XRD). The YSZ films (textured and nontextured) were deposited on Hastelloy C substrates by ion-beam-assisted deposition (IBAD), and the YBCO films were deposited on lanthanum aluminate (LaAlO₃) substrates by pulsed laser deposition (PLD) and sol–gel techniques. The measured residual stresses in the YSZ films (both textured and nontextured) were more compressive than the calculated thermal mismatch stress between Hastelloy C and YSZ, apparently due to intrinsic compressive stresses induced in the YSZ films during IBAD processing. In addition, a lower compressive residual stress was measured in the textured YSZ film compared to the nontextured film because of a reduction in the intrinsic compressive stress in the textured film. PLD processing of YBCO films on LaAlO₃ substrate resulted in a lower tensile residual stress (in the YBCO film) than the calculated thermal mismatch stress between YBCO and LaAlO₃. This difference is attributed to the generation of intrinsic compressive stresses in the YBCO film during PLD, in a manner similar to IBAD. In comparison to IBAD and PLD, sol–gel processing apparently generated negligible intrinsic stresses, resulting in a good agreement between the measured residual stress in the YBCO film and the calculated thermal mismatch stress between YBCO and LaAlO₃.

It is well known that MgB₂ tape conductors can be fabricated by the ex situ powder-in-tube (PIT) method with MgB₂ powder and without any heat treatment. We fabricated different A15-type superconducting tapes by applying this ex situ PIT method. Nb₃Sn, Nb₃Al, or V₃Si superconducting powder was tightly packed into a stainless steel (SUS316) tube or a Cu–10 wt% Ni tube. These tubes were cold rolled into tapes by using groove rolling and flat rolling. Rigid A15 superconducting cores were obtained after cold rolling. All the tapes showed substantial J_c values at 4.2 K without any heat treatment. The superior mechanical hardness of the sheath material was effective for obtaining a superconductor core of high density and realizing high J_c values. J_c increased with increasing degree of cold rolling. This J_c increase was also due to the increase in the density of the superconducting core. The highest J_c of at 6 T and 4.2 K was obtained for the Nb₃Al/(SUS316) tape. This J_c value was much higher than that of the ex situ-processed MgB₂/(SUS316) tapes. The temperature dependence of the B_c2 of the Nb₃Sn/(SUS316) tape, d B_c2/d T, was almost equal to that of the bronze-processed Nb₃Sn conductor. Annealing at after cold rolling considerably enhanced J_c values of all tapes.

Measurements of the critical current density dependence on the direction of the external magnetic field vector H have been performed on Nb/CuMn multilayers with and without a regular square lattice of submicrometre antidots. (i) At small angles between H and the surface of the sample, the presence of the antidot array strongly influences the topology of the flux lines. In the multilayers without the antidot array the vortex topology is mainly due to the anisotropy of the system with the formation of kinked vortices in the samples with higher values of the anisotropy parameter. In antidotted samples, the presence of kinked vortices is not related to the anisotropy of the system but to the geometry of the antidot array. (ii) At large angles between H and the surface of the sample, the dimensions of the antidots determine the pinning mechanism, with the prevalence of edge pinning when the antidot diameter is larger than the magnetic penetration depth λ and the presence of electromagnetic pinning when the diameter is comparable to λ. A phenomenological expression for the angular dependence of the pinning force at intermediate and large angles is proposed, satisfactorily describing the experimental data.

Pulse field magnetizing (PFM) using five successive magnetic pulses (Nos 1–5) with the same amplitude from 3.01 to 5.42 T has been performed for three types of cryo-cooled REBaCuO bulk superconductor discs (RE =  Gd, Sm, Y) with an identical size. The time evolution and spatial distribution of temperature T(t), the total trapped magnetic flux Φ_T^P and the trapped magnetic field B_T^P have been measured after applying the magnetic pulse. The total magnetic flux Φ_T^FC trapped by the field cooled magnetizing (FCM) is the largest for the Gd bulk and is the smallest for the Y bulk. The time and position dependences of T(t) during PFM show a characteristic behaviour depending on the species of bulks which results from the difference in the strength of the pinning force F_p. The generated heat Q(No  i) after the No  i pulse has been estimated based on the maximum temperature rise ΔT_max and the specific heat C. The ΔQ = Q(No 1)–Q(No 5) value, which is mainly contributed by the pinning power loss (Q_p) for pulse No 1, is the smallest for the Y bulk, and the Q(No 5) value, which is mainly contributed by the viscous flow loss (Q_v), is the smallest for the Gd bulk. These results suggest that the heat generation by PFM is closely related to the strength of F_p of the bulk crystal.

We theoretically investigate the spontaneous magnetization in double-junction and multi-junction π rings when the junctions' superconducting critical currents are not equal. The analytical solutions for the relations between the total magnetic flux Φ and the external magnetic flux Φ_x, the free energy f and the circulating current i, and the spontaneous magnetization conditions of the double-junction π rings are deduced. For the multi-junction π rings consisting of more than two junctions, mathematical computation is needed to analyse the Φ–Φ_x and f–i relations. In the conditions where the absolute critical current value of each junction is equal and there are hystereses on the Φ–Φ_x characteristic curve, the system has spontaneous magnetization solutions. However, the non-spontaneous magnetization state with zero circulating current is a metastable state with local minimum free energy; therefore, the multi-junction π ring system probably would not spontaneously magnetize.

Magnetization curves well below T_c of a lead nanowire array electrodeposited under pulsed voltage conditions are considered. Numerical simulations based on a two-dimensional resolution (2D model) of the Ginzburg–Landau (GL) equations for cylindrical configurations have also been developed. By freely adjusting the GL phenomenological lengths λ(T) and ξ(T), the experimental magnetization curves are reproduced to within a 10% error margin. The 2D model also allows us to check the cylindrical symmetry of the obtained configurations. Beyond the experimental–theoretical agreement, the question of whether the GL model remains valid far below T_c is also addressed. The temperature dependence of the adjusted characteristic lengths is compared with different theoretical and empirical laws. The most satisfactory agreement is achieved for the Gorter–Casimir two-fluid model. A comparison with a lead nanowire array electrodeposited under constant voltage conditions allows us to distinguish both samples in terms of their electronic mean free paths. The characterization of the latter quantities concurs perfectly with the experimental expectation given the different electrodeposition techniques.

The temperature dependence of the upper critical fields (H_c2(T)) of the two-gap superconductors Mg_1−xAl_xB₂ (x = 0, 0.1, 0.2, and 0.3) was obtained by resistivity measurements. The H_c2(T) values were analysed, within the dirty-limit two-gap model, using the calculated electron–phonon coupling constants and Coulomb pseudopotentials. As the Al contents increased, both T_c and H_c2(0) decreased, which was the direct manifestation of the increasing number of electrons. At the same time, the three-dimensional π bands became much dirtier when Al was doped. In contrast, the intraband scattering of the two-dimensional σ bands was relatively unaffected by the Al doping. These behaviours could be understood when the characters of both bands were considered. In all the samples that we investigated, the σ bands were dirtier than the π bands.

We calculate the total losses of flat cables with insulating central sheets by including all contributions to the coupling losses. For such structures, the currents between crossing strands are suppressed and the coupling losses between adjacent strands are decisive. The calculations are performed for two cable structures: strands soldered on the central layer and strands embedded in a normal conducting matrix. An additional conducting edge layer (occurring naturally or included artificially at the cable edges) increases the amount of current which can be transferred from one strand to another, thus increasing the coupling losses. We show that for both structures the additional losses created by current loops consisting of the same strand and the edge region are usually larger than the coupling losses between adjacent strands calculated without this contribution. This additional contribution also has to be taken into account in possible design of the tapes by segmenting the coated YBCO conductors in the form of stripes. In these designs, the conductance on the edges should be high enough to maintain high critical currents. On the other hand, the increased conductance would increase the coupling losses considerably.

This paper reports on 4.2 GeV Au ion irradiation of YBCO coplanar resonators aimed at controlling vortex-induced microwave dissipation and nonlinearity by means of a suitable distribution of columnar defects. Two procedures were used: (i) uniform irradiation at a given dose and (ii) non-uniform irradiation, obtained by means of a moving-target technique, producing a tailored profile of columnar defect density. The last configuration is needed in order to attain an optimal compromise between defect-induced enhancement of vortex pinning and increase of dissipative scattering. The resonators were characterized before and after irradiation in order to evaluate penetration depth and surface impedance, by means of a data analysis also suitable to account for the substrate properties. It turns out that in the case of uniform irradiation the induced damage, attributed to the addition of dissipative regions, always prevails over the improvement due to vortex pinning. In contrast, in the case of the tailored dose profile, significant damage is absent, while the onset of non-linearity is shifted towards higher circulating power. The need to control vortex-induced effects is confirmed by magneto-optical analysis that puts in evidence that vortex penetration occurs even at low values of transverse dc magnetic field and temperature.

Magnetic flux creep in a superconductor with large normal spherical defects is studied. The known coordinate dependence of the pinning energy allowed us to deduce the current dependence of the effective pinning barrier and the associated relaxation rate. A nonlinear differential equation governing the flux creep was derived. A macroscopic characteristic length determining the scale of the spatial flux changes was found. Magnetic flux density profiles during the penetration and relaxation processes were calculated for various mean defect size, R.