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Chapter 3 covers various electromagnetic phenomena. These include geometrical effects and dynamic phenomena that were not treated in Chap. 2. The rectifying effect in the DC current-voltage characteristics in a superposed AC magnetic field, flux jumps, surface irreversibility, and DC susceptibility in a varying temperature are also included. In addition, it is shown that an abnormal reduction in losses occurs, deviating from the prediction of the critical state model when an AC magnetic field is applied to a superconductor smaller than the pinning correlation length called Campbell’s AC penetration depth. This is attributed to the reversible motion of flux lines limited within pinning potential wells. In high-temperature superconductors the superconducting current sustained by flux pinning appreciably decays with time due to the thermal agitation of flux lines. This phenomenon, which is called flux creep, is also discussed. In extreme cases the critical current density is reduced to zero at some magnetic field called the irreversibility field. The principles used to determine the irreversibility field are described, and the result is applied to high-temperature superconductors in Chap. 8.

Chapter 7 covers the summation theories that predict the global pinning force density as a function of the elementary pinning force and number density of pinning centers. First, the statistical theory of Labusch is discussed. This theory predicted that the pinning force density has non-zero value for the elementary pinning force above the threshold value. This condition is identical with the condition of the hysteresis loss, and this theory is consistent with the dynamic theory. However, this theoretical prediction is significantly contradictory to experiments. Although the fundamental threshold problem was resolved by Larkin and Ovchinnikov, who showed that a long-range order does not exist in the flux line lattice, quantitative disagreements are sometimes found between their theory and experiments. In the coherent potential approximation theory the statistical method is used with taking into account the lack of long range order, and the compatibility of the threshold problem and the instability of flux motion is obtained. A detailed comparison is made between the theories and experiments. The saturation phenomenon observed in metallic superconductors at high fields is also introduced. The pinning potential energy important for the analysis of flux creep is also derived.

Chapter 8 covers the various properties of high-temperature superconductors. These superconductors show significant anisotropy due to the two-dimensional crystal structure composed of superconducting CuO2 layers and insulating block layers. This makes the states of flux lines extremely complicated. Various phase transitions of the flux line system to be pinned and the mechanisms responsible are reviewed. In particular, the transitions in which the pinning plays an important role, i.e., the order-disorder transition associated with the peak effect of critical current density and the glass-liquid transition associated with the irreversibility field, are discussed in detail. The influences on these transitions, not only of the flux pinning strength and the anisotropy of the superconductor, but also of the electric field and the specimen size are discussed. Y-123, Bi-2212, and Bi-2223, which have been developed for applications, are at the focus of the discussion, and their pinning properties and recent progress are introduced. In particular, the effect of nanorods introduced into Y-123 coated conductors as artificial pinning centers is reviewed.

The main advantage of superconductors, that these materials can transport electric current without energy dissipation, is achieved by the mechanism of flux pinning. Quantized flux lines that contain superconducting structure inside do not move under interaction with defects in the superconductor, even when the Lorentz force is present due to the current. As a consequence, no electromotive force appears, resulting in no energy dissipation. The mechanism of flux pinning is, in principle, reversible with respect to the motion of flux lines. The observed results are commonly irreversible, however, as described by the critical state model, which assumes that there is a balance between the Lorentz force and the irreversible pinning force. In this Chapter, the summation theory is introduced, which is used to analytically determine the critical current density, i.e., the maximum non-dissipative current density. The reason why the resultant electromagnetic phenomena become irreversible is clarified, even though the fundamental flux pinning mechanism is reversible. The irreversibility in flux pinning phenomena does not originate from the breaking of time reversal symmetry, but is of another type, such as friction, that is non-dissipative in stationary condition, although it causes energy dissipation in motion due to the applied force.

The high upper critical field and low anisotropy of the 122-type iron-based superconductor BaFe2As2 makes it promising for use in superconducting high field magnets. However, its critical current density (J c) in high magnetic fields needs to be further improved. Here we show that for the film prepared by pulsed laser deposition method by controlling the deposition parameters (higher substrate temperature and lower growth rate), the crystallinity of BaFe2(As0.66P0.33)2 (Ba122:P) matrix is improved while maintaining a high density of incoherent BaZrO3 (BZO) nanoparticles (NPs) which together lead to significantly increased self field J c. Our Ba122:P nanocomposite films also exhibit increased in-field J c, reduced angular anisotropy of J c and reduced detrimental effects of thermal fluctuations (creep rate) over a wide range of temperatures and magnetic field strength. The BZO NP doped Ba122:P films show high in-field J c over 2.1 MA cm−2 even at 4 K and 9 T (μ 0 H∣∣c), which is significantly higher than that of standard Ba122:P films and conventional alloy superconducting wires. To understand the contribution of the various pinning centers, we applied a simple model, which was developed for cuprates, to Ba122:P film with all the parameters used derived by fitting to a limited set of experimental data (no free parameters) such that temperature, angle and field properties at other experimental conditions are then calculated. This simple model fits very well to the experimental results in these two very different material systems. We discuss the effectiveness of natural defect and BZO NPs on the ratio of J c to the depairing current density. The superconducting properties for 122-type iron-based superconductors obtained through this work are considered promising for high-field applications.

It is important to investigate condensation energy density of superconducting material, since it determines its pinning property. According to the heavy-ion irradiation, the columnar defects are introduced to the superconductor which act as the strong pinning centers, and the critical current density is enhanced by the new pinning centers. Since the number density and the size of the columnar defects can be observed, the condensation energy density is estimated by using the pinning summation theory. In the present study, we prepared Ba(Fe0.93Co0.07)2As2 (Ba-122) pnictide superconductors by self-flux method. 200 MeV Au ions were irradiated into the specimens along c-axis and the matching field was 2 T. After the irradiation, the critical current density was 6 times larger than that before the irradiation. The estimated condensation energy density is in the order of 104 J/m3 and is slightly smaller than those of cuprate superconductors. The temperature dependence is similar to that of YBa2Cu3Ox oxide superconductors, since the anisotropy parameter is small in Ba-122. Therefore, it is expected to use Ba-122 at high temperatures near the critical temperature., Superconductivity Centennial Conference 2011 - EUCAS–ISEC–ICMC, Sep 18 - 23, 2011, Hague, Netherlands

The improvement of critical current density properties of REBCO coated conductors for applications in superconducting power devices is desired. It is known that the critical current density Jc of REBCO thin films made by the TFA-MOD method in a magnetic field is greatly improved by the introduction of BZO-nanoparticles of a non-superconducting phase as artificial pinning centers. In addition, the field angle anisotropy can also be reduced by isotropic flux pinning interactions of nanoparticles. However, a detailed report on the mechanism of flux pinning with a quantitative investigation in such coated conductors has not been given. In this study, the field angle dependence of the critical current density is measured for TFA-MOD-processed YGdBCO coated conductor with a superconducting layer of 0.65 μm thick, and the results are theoretically analysed to clarify the flux pinning mechanism.

The upper limit of critical current density by the flux pinning mechanism is theoretically investigated by taking into account the influence of kinetic energy. The upper limit is estimated to be 67% of the depairing current density in the London limit, which is about 23% higher than the estimation by Tinkham. The reason for the higher value is attributed to the enhancement of the order parameter that reduces the kinetic energy caused by the current. The possibility of such a strong flux pinning is discussed for nano-rods introduced to REBCO coated conductors.

The flux pinning properties in a magnetic field of various directions are investigated for trifluoroacetates-metal organic deposition (TFA-MOD) processed Y 1− x Gd x Ba 2 Cu 3 O y (YGdBCO)-coated conductors with the superconducting layer of 0.5 μm thick with artificial BaZrO 3 (BZO)-nanoparticles. It is found that the critical current density is enhanced in a wide range of field angle except around the direction parallel to the a − b plane, resulting in low field-angle anistropy. The enhancement of J c in the wide range of field angle is attributed to the isotropic pinning of nanoparticles. The decrease in the critical current density in the field direction parallel to the a − b plane is considered to be caused by limitation of growth of stacking faults by distributed BZO nanoparticles. The observed results were theoretically explained by the flux creep-flow model and the above speculation of the pinning mechanism was confirmed.

Ion Beam Assist Deposition/Chemical Vapor Deposition(IBAD/CVD)-processed YBCO-coated conductors with high critical current density Jc at high magnetic fields are expected to be applied to superconducting equipments such as superconducting magnetic energy storage (SMES). For application to superconducting magnet in SMES one of the most important properties for superconductors is the relaxation property of superconducting current. In this paper, the relaxation property is investigated for IBAD/CVD-processed YBCO-coated conductors of the superconducting layer in the range of 0.18–0.90 μm. This property can be quantitatively characterized by the apparent pinning potential, U 0 ∗ . It is found that U 0 ∗ takes a smaller value due to the two-dimensional pinning mechanism at high magnetic fields for conductor with thinner superconducting layer. Although U 0 ∗ decreases with increasing thickness at low magnetic fields at 20 K, it increases at high magnetic fields. The results are theoretically explained by the model of the flux creep and flow based on the dimensionality of flux pinning. Scaling analysis is examined for the dependence of U 0 ∗ on the magnetic field, temperature and the layer thickness.

Critical current properties at high magnetic fields are analyzed using the percolation theory for polycrystalline MgB 2 superconductors. In the theory the effect of anisotropic irreversibility field of each grain due to random orientation is considered. Relatively low irreversibility field of this superconductor in spite of fairly strong flux pinning strength is attributed to the percolating nature for superconductor with low electrical connectivity. This theoretical approach explains the experimental result showing higher irreversibility field for samples with higher packing factor. It is concluded that the high packing factor is inevitable for high critical current density at high magnetic fields.

Flux pining properties of columnar defects nucleated by gold ion irradiation was investigated for DyBCO coated conductor. The energy of irradiated gold ions was 320 MeV and 200 MeV and the matching field was 1.0 and 2.0 T, respectively. It was found that the flux pinning strength was significantly enhanced at high magnetic fields. These experimental results were analysed using the summation theory of the elementary pinning forces with the theoretical model of flux creep and flow. It was found that the experimental results can be explained by the theories. The obtained result suggests that columnar defects with larger radius are more effective for pinning because of the larger probability of catching flux lines.

Flux pinning properties in high-temperature superconductors are significantly in fluenced by flux creep, especially at high temperatures and in high magnetic fields. One of the results of flux creep is an appreciable degradation of the maximum magnetic field for the non-resistive transport current from the upper critical field. This characteristic field, called the "irreversibility field", can be theoretically analyzed using the flux creep model. The important parameter that determines the creep phenomena is the pinning potential given by the product of the pinning energy density and the volume of the flux bundle. In this article, various dependencies of the irreversibility field on temperature, flux pinning strength anisotropy and size of the superconductor, and electric field at the time of measurement are reviewed according to the prediction of the flux creep model. These aspects are compared experimentally. An example of theoretical estimation of the irreversibility field is shown.

The saturation and non-saturation phenomena for pinning force density are described. Models for these phenomena are introduced and compared experimentally. It can be concluded that the non-saturation phenomenon observed in commercial Nb-Ti belongs to the pinning regime of higher pinning performance than the saturation phenomenon observed in Nb3Sn. Such classification is determined by the number density and elementary pinning force of the pinning centers. The peculiar behavior of flux lines in the saturation phenomenon can be clarified by a small AC ripple field measurement called Campbell's method. An avalanching flux flow model based on this experimental result explains the saturation and non-saturation properties well.

Electromagnetic phenomena in superconductors are reviewed. In superconductor in a transverse magnetic field, the electromagnetic phenomena are described by the critical state model assuming a balance between the Lorentz force and pinning force. In this case the Josephson equation for the induced electric field, E = B × v, holds for the motion of flux lines with velocity v. On the other hand, the electromagnetic phenomena in a longitudinal magnetic field of current-carrying superconductor are quite different from those in the transverse magnetic field. For example, the Josephson relation does not hold and even a negative potential drop is locally observed in the resistive state above the critical current. In this review it is shown that these peculiar phenomena are explainable using the flux motion driven by a force-free torque, a restoring torque against rotationally shearing deformation of flux lines due to the force-free current parallel to flux lines.

The relaxation properties were investigated for PLD processed YBCO coated conductors deposited on IBAD substrates in the region of 0.25–1.50 μm for the thickness of superconducting layer to clarify the thickness dependence of the relaxation of magnetization. The apparent pinning potential U 0 ∗ was estimated from the relaxation rate. It was found that U 0 ∗ increases with increasing temperature in the low temperature region. The weak thickness dependence of U 0 ∗ in this temperature region comes from the three-dimensional flux pinning mechanism. Then, U 0 ∗ has a peak followed by a decrease with increasing temperature. The peak value of U 0 ∗ increases with increasing thickness. Hence, the thicker superconductor is more advantageous for applications in the middle temperature range and higher. The flux pinning mechanism in the medium and higher temperature region is two-dimensional and the larger U 0 ∗ value in the thicker specimen originates mainly from the thickness. For the improvement of U 0 ∗ in the low temperature region, it is required to enhance the flux pinning strength and to increase the thickness without deterioration in the critical current density.

It seems to be believed that the critical current density is the essential factor which determines the pinning loss as described by the critical state model. However, this is not ture: the pinning loss is the essential factor which determines the critical current density in the dynamic pinning theory. The pinning loss of power is defined as an additional viscous loss of power due to the velocity fluctuation of the fluxons caused by pinning interactions. It is shown that the high velocity due to the unstable flux motion, which occurs when the fluxon drops in and jumps out of the pinning potential well, brings about the pinning loss power density that depends only on the pinning force density. This suggests that the flux motion is nearly reversible with extremely-low-loss power density deviating from the prediction of the critical state model if the flux motion is restricted within pinning potential wells. Such phenomenon is actually observed in multifilamentary wires with very-finr superconducting filaments thinner than the pinning correlation length.

Flux pinning interaction originates from the variation in the energy of a flux line during its displacement across inhomogeneous regions called pinning centers such as normal precipitates or grain boundaries. The flux pinning mechanism is classified according to the dominant energy involved in the interaction. Normal precipitates and grain boundaries work as strong pinning centers through a condensation energy interaction. The field-induced pinning resulting from a weak superconducting region is also classified in the condensation energy interaction. Magnetic interaction and kinetic interaction are also introduced. The pinning mechanism of artificially introduced Nb into Nb-Ti is considered to be a kinetic energy interaction.

Significant overestimation of the critical current density J c is found for the third harmonic voltage measurement method for thin YBCO superconductors. This is caused by a reversible flux motion in pinning potentials, which is known to be significant for superconductors of thickness comparable to or smaller than Campbell’s AC penetration depth. In this paper the effect of reversible flux motion on the estimation of J c by this method with different thicknesses is also theoretically investigated by using the Campbell model for the force–displacement characteristics of flux lines. Although the factor of overestimation can be approximately explained by the Campbell model, agreement is not satisfactory. It is considered that the variation in the flux motion from reversible to irreversible states seems to take place much faster than assumed in the Campbell model.

The hot topics of the critical current properties in YBCO coated conductors and Bi-2223 silver-sheathed tapes are discussed. The dependence of the critical current density in YBCO coated conductors on the superconducting layer thickness is partly associated with the defects nucleated in thicker films and is also caused by the thickness dependent influence of the flux creep. Experimental results on PLD processed conductors with different thicknesses are compared with the theoretical analysis based on the flux creep-flow model. A discussion will also be given for the optimum layer thickness for applications. In Bi-2223 tapes introduction of CT-OP (ConTrolled Over Pressure) process has significantly improved the critical current properties. This progress can be attributed to the improvement of the mean value of the flux pinning strength and the decrease in its distribution width. The possibility of further improvement of the critical current properties is discussed using the flux creep-flow model.

Investigation is done on the effect of ConTrolled Over Pressure (CT-OP) processes on the critical current properties in multifilamentary Bi-2223 tapes. It is found that the critical current density at low magnetic fields is remarkably improved by the new CT-OP process. This result with those on irreversibility field and n-value are compared with the numerical calculation based on the flux creep and flow model. The analysis reveals that the most probable value is increased, although the statistical distribution width is increased for the flux pinning strength. This result indicates that the critical current density at high magnetic fields is deteriorated by the widened distribution. If such an inhomogeneity can be reduced to the level of previous tapes by improving the CT-OP process, the high field performance is shown to be significantly improved.

The thickness dependence of pinning properties is investigated in detail under various conditions of temperature, magnetic field and electric field for IBAD/PLD YBCO-coated conductors. The thickness-dependent critical current density in the three-dimensional pinning regime at low magnetic fields is attributed to the change in the morphology of the superconducting layer. It is found that while the irreversibility field increases with the thickness at low electric fields according to DC magnetization measurements, it decreases at usual electric fields corresponding to resistive measurements. This can be explained by the theoretical model of flux creep and flow with the irreversible thermodynamic principle that the transverse flux bundle size is determined so that the critical current density under the flux creep is maximized. The former model assumes the limitation of the longitudinal flux bundle size by the superconducting layer thickness, while the latter principle assumes a change in the transverse one from the value expected from the elasticity of flux lines. The observed n-value, the parameter describing the relationship between the electric field (E) and the current density (J) as , increases monotonically with the thickness in both electric field regions. This can be simply attributed to the increase in the pinning potential with the thickness.

Flux pinning properties were investigated by focusing on the origin of the high peak critical current density and the high irreversibility field for Nd0.33Eu0.38Gd0.28Ba2Cu3Oy (NEG-123) bulk superconductors with the addition of 211 secondary phase particles of volume fractions up to 10 mol%. It was found that a negative correlation exists between the peak critical current density Jcp and the irreversibility field Bi for various fractions of added 211 phase. This suggests that the mechanisms that determine Jcp and Bi are different. The 211 particles do not contribute to the peak effect neither directly through the pinning mechanisms of the condensation energy interaction nor indirectly with the aid of the order–disorder transition of flux lines. Other possible defects are nano-lamella structures. Although these defects do not directly contribute to the peak effect through the pinning mechanism of the condensation energy interaction, they may contribute to it with the aid of the order–disorder transition of flux lines. On the other hand, as Bi deteriorates with the addition of 211 particles, it is not determined by the flux pinning of 211 particles. The decrease in Bi is considered to be caused by the proximity effect of nano-lamella structures.

The critical current properties of a superconducting Bi-2223 tape produced by the over pressure processing at the final heat treatment were investigated. The critical current density increased more than the factor of densification of the superconducting region. In addition, the irreversibility field also increased. This means that the quality of flux pinning is improved by the new process. From the numerical calculation based on the flux creep and flow model, it is speculated that the fraction of weakly pinning regions decreases due to the improved connectivity of grains.

Critical current properties in Bi-2223 superconductor were investigated in detail for silver-sheathed tapes fabricated by the usual process in a normal pressure, the previous controlled over-pressure (CT-OP) process and the recently improved CT-OP process at the final heat treatment. It was shown that the critical current density, the irreversibility field and the n-value were remarkably improved by application of the CT-OP process. The results were analysed using the flux creep-flow model to seek the reason for the improvements. It was found that the grain connectivity and the flux pinning strength were improved by the previous and recent CT-OP processes, respectively. The possibility of further improvements of the critical current properties in Bi-2223 tapes is discussed.

The critical current density J c and the apparent pinning potential U 0 ∗ in a single crystal NdBa 2 Cu 3 O y superconductor which shows a broad peak effect are investigated by measuring a DC magnetization and its relaxation. The field-induced pinning mechanism does not explain the temperature dependence of peak field B p and dip field B d . The experimental results of J c and U 0 ∗ are compared with the theoretical analysis based on the flux creep-flow model, taking the distribution of the flux pinning strength into account. The number of flux lines in the flux bundle ( g 2 ), the most probable value of pinning strength ( A m ) and distribution width ( σ 2 ) are determined so that a good fit is obtained between the experimental and theoretical results. The behavior of these parameters is discussed in correspondence to the disorder transition of flux lines.

A significant overestimation of the critical current density Jc is found for a measuring method of induced third harmonic voltage for thin superconductors of thickness less than 1 µm. This is speculated to be caused by a reversible motion of flux lines in a pinning potential which reduces the nonlinear properties such as AC losses or the third harmonic voltage. It is known that the effect of reversible flux motion is prominent for superconductors with a thickness comparable to or smaller than the pinning correlation length of the order of a sub-micrometre, the so-called Campbell's AC penetration depth. In this paper the effect of reversible flux motion on the estimation of Jc by this method is preliminarily investigated by using a simplified Campbell's model for the force–displacement characteristics of flux lines.

It is known that the critical current density vs. field angle of an Y-123 coated tape has a broad peak around the field direction normal to the tape surface. In this work, the angular dependencies of the irreversibility field and the critical current density are analytically investigated using the flux creep-flow theory with an assumption of the angular dependence of flux pinning strength, and these results are compared with the experimental results. The angular dependence of flux pinning strength obtained so as to get a good agreement between the experimental and theoretical results suggests an existence of long pinning centers along the c-axis.

The AC-current loss in a quench melt growth (QMG)-processed Y-123 bulk superconductor was found to fit well with the Norris’s formula for a superconductor with an ellipsoidal cross-section based on the Bean’s model, in spite of a rectangular cross-section and the magnetic field dependence of critical current density. The reason for this coincidence is generally argued by a theoretical analysis with respect to the effects of the magnetic field dependence of J c , the geometry of effect of superconductor and the effect of n -value on the AC loss. In this paper, finite element method is used for the numerical analysis of the AC-current loss of the QMG bulk sample with taking into account of the latter two effects. It is found that when the aspect ratio of rectangular superconductor increases, the loss becomes small. The AC loss takes on a larger value when the n -value decreases, suggesting a large effect of flux creep.

Size dependencies of the peak effect and irreversibility field in superconducting Sm-123 powder specimens were investigated. The peak effect was found to disappear in the two-dimensional pinning regime in which powder size is smaller than pinning correlation length. This shows that the peak effect does not originate directly from elementary pinning mechanisms, but from a cooperative phenomenon of flux lines, as proposed by the pinning-induced disorder transition model. In addition, when powder size is smaller than virtual pinning correlation length in the ideal creep-free case, irreversibility field decreases with powder size. This supports the hypothesis that longitudinal flux bundle size is given by this length, as predicted by flux creep theory. These findings indicate that pinning correlation length is a general parameter that determines various properties associated with flux pinning phenomena.

The E – J characteristics were measured for a YBCO-coated conductor by using the four probe method and the relaxation method of DC magnetization. The result on the latter measurement at extremely low electric fields was theoretically analyzed based on the flux creep-flow model. From the result on n -value the flux lines in YBCO are considered to be in the glass state even at high fields. The apparent pinning potential U 0 ∗ estimated from the relaxation of DC magnetization is much larger than that of Bi-2223. The present theoretical analysis clarifies a much stronger flux pinning and a higher dimensionality of YBCO in comparison with Bi-2223.

The critical current density and the irreversibility field were measured before and after nickel ion irradiation for Bi-2212 single crystals in an optimally doped or an overdoped state in a magnetic field parallel to the direction of irradiation. The critical current density was theoretically calculated by using the summation theory and the flux creep-flow model. From the comparison with experimental results the condensation energy density was estimated for each specimen. These results are compared with a similar analysis on three-dimensional Y-123.

We have investigated extended electric field-vs.-current density E-J characteristics in YBCO coated IBAD tapes. The results of a Monte-Carlo study on the depinning in a random pin medium were compared with measurements. Using a low temperature scanning laser microscope, we examined the percolative behavior of the local resistive transition in the YBCO tape. It was also shown that the depinning probability, which is proportional to the dynamic resistance of the E-J curves, is scaled as a function of reduced current density with the aid of a power index. Consequently, the E-J characteristics in the tapes can be described by the combination of the two kinds of scaling laws: one is the scaling law of the depinning probability predicted in a random network and the other is the scaling law for the flux pinning force. These properties agree well with the percolation model of depinned clusters.

Critical current properties in a YBCO coated tape have been studied as a function of temperature, magnetic field and field angle under high magnetic field up to 18 T. 1 μm thick YBCO film was deposited on a bi-axially aligned Y 2 O 3 /YSZ/Hastelloy substrate fabricated by the IBAD technique. The value of critical current, I c , of the 1 cm wide tape reached as high as 85 A at 77 K in self-field condition. After etching the tape into 100 μm wide and 1 mm long bridge, we measured extended E – J characteristics. The value of critical current density, J c , is maintained higher than 10 5 A/cm 2 at 70 K in 5 T perpendicular to the tape surface. Moreover, the power index n and the so called glass–liquid transition field, B GL , of the tape in perpendicular field are superior to those of epitaxial film deposited on a SrTiO 3 single crystalline substrate. J c vs. angle relationship shows broad peak around 90° where field is perpendicular to the tape surface, in addition to a sharp peak at 0°. These results suggest that the tape is highly uniform and correlated defects along c -axis direction contribute to flux pinning.

Extended E – J characteristics in a YBCO coated ion beam assisted deposition tape have been studied over a wide range of perpendicular magnetic field, B , and temperature, T . The statistical distribution of the critical current density, J c , and the magnetic transition field have been analyzed within the frame work of the percolation model. It has been shown that the distribution of pinning strength in the coated tape is much sharper than that in an epitaxial thin film deposited on a SrTiO 3 single crystalline substrate. This result suggests that effective pinning sites are introduced in the coated tape. Scaling behavior of the pinning force density will also be shown. The present analysis allows us to estimate the J c value quantitatively at an arbitrary B , T and electric field criterion.

The behavior of current–voltage ( I–V ) characteristics in Bi-2223 AgAgMg sheathed tape at various bending strain has been studied. The measured results were analyzed using the percolation model, and then the variation of critical current density, J c , has been analyzed. As increasing of bending strain, J c in the tape is reduced irreversible way. The irreversible degradation indicates that the J c reduction is caused mainly by crack formation. However, if we extract statistic J c distribution taking into account the cracking, it can be seen that the value of local J c is enlarged in the remained region as the strain is increased. Namely, the pinning strength in the remained region is enlarged as the bending strain is increased. Present analysis allows us to separate the influence on grain connectivity and pinning strength originated from the strain.

Pinning properties were investigated for bulk Y-123 superconductors in an underdoped condition by heat treatment at a high temperature. The critical current density was drastically decreased. It is ascribed to the weakened pinning strength of 211 phase particles resulting from a degradation of the superconductivity in the block layer. A decrease of g2, the number of flux lines in the flux bundle, was found to be stronger than that of the pinning strength. This indicates that an additional disorder because of the thermal activation of flux lines also makes g2 smaller. The present result shows that the disorder transition that causes the peak effect is more strongly affected by the elastic properties than by the pinning strength.

The E–J characteristics are measured for a Bi-2223 silver-sheathed tape wire using the four probe method and a relaxation method of DC magnetization in the high and low electric field regions, respectively. The obtained results in the two regions are approximately explained by a theoretical analysis based on the flux creep-flow model in which the distribution of flux pinning strength is taken into account. It was found that the value of the pinning force density and its peak magnetic field are largely different between the two measurements.

It is known that the peak effect in Y-123 superconductors is caused by oxygen deficient regions with lower T c . In order to study the flux pinning mechanism of these defects, the effect of addition of 211 particles on the peak effect was measured. It was found that the addition of 211 phase deteriorated the pronounced peak effect at medium magnetic fields. This shows that the pinning mechanism of the oxygen deficient regions is different from the condensation energy interaction known for 211 particles. The results on the critical current density and the irreversibility field were compared with the theoretical predictions of the flux creep-flow model.

It is known that the peak effect in Y-123 superconductors is caused by oxygen deficient regions with lower Tc. In order to study the flux pinning mechanism of these defects, the effect of the addition of 211 particles on the peak effect was measured. It was found that the addition of the 211 phase deteriorated the pronounced peak effect at medium magnetic fields. This suggests that the pinning mechanism of the oxygen deficient regions is repulsive and based on the kinetic energy interaction under the proximity effect. The peak effect itself is considered to be caused by a transitional variation in the elastic property of flux lines. In the low- and high-field regions, the dominant pinning centres are 211 particles. The observed results on the critical current density and the irreversibility field were compared with the theoretical predictions of the flux creep-flow model, assuming pinning by the 211 particles.

E – J curves in Bi-2223 Ag-sheathed tape have been analyzed within the framework of the percolation model proposed by the authors. It will be shown that a scaling holds for magnetic field ( B ) dependence in both field directions when we normalize B by the transition field at each temperature. Whereas, the temperature dependence can be described accurately by the prediction of two-dimensional d-wave symmetry. Using the present model, we can describe the nonlinear E – J characteristics quantitatively in a wide range of electric field, temperature, magnetic field and its angle.

Current-voltage characteristics in the range of very low electric field were analyzed from a relaxation of the magnetization using a SQUID magnetometer in a superconducting Bi-2223 tape. It was found that the observed current-voltage characteristics in this range were scaled well as predicted by the vortex glass-liquid transition theory. However, the obtained transition field was much lower than that obtained from a scaling in the higher electric field range. At the same time, the dynamic critical index, z, was much larger than usual values. Hence, it is concluded that these parameters are not uniquely determined independently of the level of electric field. The experimental result was compared with the theoretical analysis using the flux creep-flow theory in which the distribution of the effective flux pinning strength was taken into account. It was found that the theoretical result explains approximately the observed result. This shows that the essential mechanism which governs the transport property in the superconducting tape is the flux pinning.

The flux-pinning property in a melt-processed Sm-123 bulk superconductor was investigated and the observed irreversibility field was compared with the theoretical model of flux creep and flow assuming that the usual condensation energy interaction by 211 particles is dominant in flux pinning. The good agreement suggests that this hypothesis is valid. The pinning mechanism around the peak effect is discussed based on the results on scaling of the pinning force density.

The influence of flux pinning on the vortex glass-liquid (GL) phase transition and irreversibility in HTSs has been examined on the basis of systematic measurements of electric field (E) versus current density (J) curves in a YBCO thin film. It has been shown that the GL transition is identical to the thermal depinning determined by the minimum value of the macroscopic pinning strength. The isothermal scaling of the E-J characteristics is directly related to the nature of the pinning. The irreversibility line can be described as an iso-J line governed by the statistical pin distribution. If we determine the criteria for the irreversibility line, we can describe the irreversibility line based on the depinning line. The essential physical quantity, therefore, can be attributed to the flux depinning.

The energy loss density was measured for a Bi-2223 tape with superconducting filaments of average thickness 3 µm which were separated by about 40 µm so as to eliminate bridging of filaments. The result was compared with the prediction of the modified Kim model. Although it was lower than the prediction owing to the reversible fluxoid motion at temperatures above 77.3 K, it slightly increased at around 1 mT. It is considered that an increase in the pinning strength and a resultant shortening of the ac penetration depth suppressed the effect of the reversible fluxoid motion at such low ac magnetic field amplitudes.

The irreversibility field of superconducting Cu(Ba 0.8 Sr 0.2 ) 2 YbCu 2 O 6+ z (so-called Yb-123) powder was carefully measured as a function of temperature using a SQUID magnetometer. The DC magnetic susceptibility showed a gradual transition near the critical temperature, suggesting a wide distribution of the critical temperature. For a detailed characterization of the material, the evaluation of the mean critical temperature and its distribution width is important. These are estimated by fitting the theoretical result of the DC magnetic susceptibility in field cooled and zero field cooled processes to the experimental result. The obtained result proves that this material showed a superior irreversibility field than usual Y-123 superconductor.

The irreversibility line and the vortex glass-liquid transition line under a magnetic field parallel to the c-axis are investigated for silver-sheathed and dip-coated Bi-2212 tape wires. It is found that the two characteristic lines for silver-sheathed tape is well explained by the flux creep-flow model assuming the distribution of pinning strength with a single peak. On the other hand, general agreements are obtained for these characteristic lines and the critical current density between experiments and theory only when two peaks are assumed in the distribution of flux pinning strength for the dip-coated tape. The causative structure in the dip-coated tape for the peak at small strength in the distribution is discussed.

The vortex glass-liquid transition in pinned superconductors is studied theoretically from the viewpoint of thermal depinning of flux lines. It is clarified that this depinning phenomenon is a transition of the second order. This result is consistent with the fact that the scaling of the current-voltage curves is well explained by the theoretical model of flux creep and flow. It is also found that the degree of disorder of the flux line lattice decreases abruptly with elevating temperature above the transition temperature. This agrees qualitatively with the observation of flux lines using a Lorentz microscope.