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It is shown that, in some cases, the effect of discrete distributions of flux lines in quantum mechanics can be associated with the effect of continuous distributions of magnetic fields with special symmetries. In particular, flux lines with an arbitrary value of magnetic flux can be used to create energetic barriers, which can be used to confine quantum systems in specially designed configurations. This generalizes a previous work where such energy barriers arose from flux lines with half-integer fluxons. Furthermore, it is shown how the Landau levels can be obtained from a two-dimensional grid of flux lines. These results suggest that the classical magnetic force can be seen as emerging entirely from the Aharonov-Bohm effect. Finally, the basic elements of a semi-classical theory that models the emergence of classical magnetic forces from fields with special symmetries are introduced., Comment: 7 pages, 5 figures

To investigate the effect of discontinuity of 1-D pinning centers on the flux pinning in a wide range of magnetic field directions, discontinuous columnar defects (CDs) and continuous CDs were formed in GdBCO coated conductors using Xe-ion irradiations with 80 and 270 MeV, respectively. An overall shift upward in J c , for the 80-MeV-irradiated sample compared to the 270-MeV-irradiated one, can be observed in every direction of magnetic field, which is more remarkable as temperature decreases. This implies a synergetic effect of the pinning interaction between the linearity and the discontinuity for the discontinuous CDs. When the density of CDs is lower, however, the difference in Jc between the discontinuous and the continuous CDs becomes less at lower temperature, even in the magnetic field parallel to the c-axis. At lower density of CDs, the average spacing between CDs is wider, which would hardly lead to automatic entanglement of flux lines in the discontinuous CDs, i.e., to the synergetic effect.

An analysis of the interrelated changes in the material composition and the pinning strength in nanostructured Nb (1 1 0) thin films is presented. The nanopatterns were prepared by focused ion beam milling of an array of uniaxial grooves. They induce a washboard-like pinning potential landscape for vortices in the mixed state. By applying different magnetic fields, the most likely pinning sites along which the flux lines move through the samples have been selected. By this, either the background isotropic pinning of the pristine film or the enhanced isotropic pinning originating from the nanoprocessing has been probed. The enhanced pinning strength in the processed films has been found to correlate with the content of Ga implanted into the films during the nanopatterning.

This paper deals with electromagnetic actions that allow one to control the shaped-charge effect at different stages of shaped-charge operation. A decrease in penetration of the shaped-charge jet is attained by production of an axial magnetic field in the shaped-charge liner immediately before shot, and production of a magnetic field in the conducting target material that is transverse to the direction of jet propagation. The considerable decrease in the penetration capability of the charge observed in the experiments is attributed to a sharp amplification of the magnetic field in the jet formation region upon liner collapse. The effects accompanying the “field pumping” prevent the normal formation of a shaped-charge jet. A model of magnetic field generation in a conducting medium subjected to high-velocity deformation with particle elongation along the magnetic flux lines is considered. X-ray photographs of shaped-charge jets formed from a “magnetized liner” are given. Theoretical calculations have shown that deformation conditions that can provide for intense magnetic field generation also arise during high-velocity jet penetration into a conducting target across the flux lines of the initial magnetic field previously produced in the target.

Current–voltage ( I – V ) measurements were carried out for different current sweep rates (d I /d t ) of transport current at zero magnetic field ( H = 0) and H ≠ 0 in a polycrystalline sample of Bi 1.7 Pb 0.3 Sr 2 Ca 2 Cu 3 O x (BSCCO) with a macroscopic cylindrical hole (CH) drilled. Similar measurements were also performed in the same BSCCO sample without CH for a comparison before drilling CH. For the same values of H , T , and d I /d t taken for both samples, it was observed that hysteresis effects appear in I – V curves upon cycling of transport current in upward and downward directions which contain the increasing and decreasing current values, respectively. However these effects which are seen in I – V curves of BSCCO sample with CH is more prominent than that of the BSCCO sample without CH. Further, the irreversibility effects in I – V curves of the BSCCO sample without CH disappears for H ≠ 0 exhibiting nearly a linear behaviour, whereas the hysteretic behaviour in I – V curves of the BSCCO sample with CH is still observed. This interesting behaviour could be evaluated that macroscopic cylindrical hole improves pinning properties of sample acting as a macroscopic flux pinning center for flux lines.

In this paper, we suggest methods for calculating the magnetic conductivity of plane-paralle, planemeridian, and three-dimensional magnetic fields. The following assumptions are made: flux lines are replaced by straight lines and arcs or smooth lines constructed manually in scale pictures; a coil with current is considered to be an infinite thin wire or layer etc. Methods are recommended for use during the first steps of the design of a magnetic system.

We present strong evidence observed in a YBCO superconducting tube that helical flux lines can concurrently enter and leave across the inner surface of the wall of a hollow cylinder of sintered high-Tc superconductors at 77 K, and hence cut and traverse each other. The evidence for flux line cutting and cross-flow is examined in the perspective of basic concepts. The traffic of the flux lines is also described mathematically. The penetration fields across the wall and into the grains of the sintered ceramic tube are seen to correlate with salient features (peaks and valleys) of the flux line cutting and cross-flow phenomena. This enables us to claim that we are witnessing flux line cutting and cross-flow in the weak links as well as in the interior of the grains in the YBCO tube. The Clem/Perez-Gonzalez phenomenological theory is exploited in a simplified framework to describe the crucial features of the data semi-quantitatively. This analysis confirms the above conclusions and provides estimates of jc||m and jc||g, the critical current densities for intergranular and intragranular flux line cutting and their dependence on the magnetic flux density.

Current–voltage characteristics are investigated in Bi1.8Pb0.2Sr2CaCu2O8+δ single crystals irradiated by high-energy heavy-ions parallel and along the direction tilted by 45° from to the c-axis. The angular dependence of the resistance exhibits, in the vortex solid state and for T≥40 K, a usual unidirectional effect when a magnetic field is aligned to the columnar defects (CDs) for both samples. In the case of inclined defects two dips are available: one in the direction parallel to the tracks and the other perpendicularly. The melting transition for magnetic field applied parallely to the CDs and over a wide filling factor (f

We study the topologically protected Majorana zero modes induced by lattice dislocations in chiral topological superconductors. Dislocations provide a new way to realize Majorana modes at zero magnetic field. In particular, we study several different types of dislocations in the candidate material ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}.$ We also discuss the properties of linked dislocation lines and linked dislocation and flux lines. Various experimental consequences are predicted which provide an approach to determine the nature of the superconducting phase of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}.$

Microstructures of flux lines (FL) in Bi 2 Sr 2 CaCu 2 O 8 single crystals are observed by a high-resolution Bitter-decoration technique. Experiments were performed at low (4.2 K) and high (77 K) temperatures under a constant magnetic field of 20 G. We could observe the interaction between FL and defects of materials, such as growth steps and other planar crystal defects. FL near defects were remarkably different between low and high temperatures. We also found that planar crystal defects, which extended parallel to the a -axis, were only active at low temperatures.

We report muon spin rotation studies of the magnetic field distribution n ( B μ ) of the low-temperature ( T =5 K) vortex state of the high- T c superconductor Bi 2 Sr 2 CaCu 2 O 8+δ (Bi-2212) in an underdoped state ( T c =77 K). In agreement with previous reports we observe a pronounced change in n ( B μ ) with increasing field. The corresponding reorganization of the vortex structure with increasing vortex density is related to a disorder-induced destruction of the vortex lattice. Furthermore, we find evidence for a partial restoration of the vortex lines at higher fields, which may be related to the increase of the vortex–vortex interaction and the subsequent change from single-vortex pinning to collective pinning.

We have used scanning Hall probe microscopy to study the interaction between flux lines and a random array of precipitates in thin YBCO films. Pinning by precipitates has been demonstrated by measuring the distribution and magnetic field profiles of individual flux lines. Flux lines in the film with precipitates have strongly preferred locations as well as a much broader range of shapes and sizes compared to YBCO films without precipitates. We have also observed ``local magnetization'' anomalies, which appear at multiples of the matching field for the random array of pinning sites.

A new method to study the mixed state of high- T c superconductors by the relaxation of resistivity R ff ( t ) experiments is theoretically and experimentally discussed. The theoretical method about how to calculate the decayed magnetization current J i ( R ff ( t )) and the effective pinning energy of flux lines U ( R ff ( t ), J i ( t )) from R ff ( t ) is discussed. Two equations about J i ( R ff ( t ) and U ( R ff ( t ), J i ( t )), are obtained by the two-kind-of-flux-creeop model. R ff ( t ) experiments are performed at various temperatures and magnetic fields. U - J data are calculated. Reasonable physical parameters are derived by fitting the U - J data with two U - J relation models. Experiments and the U - J relation models support the new method and the two-kind-of-flux-creep model.

In order to increase the critical current density and trapped magnetic field in high Tc superconducting materials, various kinds of inhomogeneities were introduced and used as pinning centers of flux lines. A universal scaling behavior of the pinning force is observed in different high Tc cuprates. We show that this scaling law is a natural result of a unified materials equation for type-II superconductors. This equation agrees reasonably well with recently observed phenomena.

Ordered arrays of columnar defects have been fabricated by direct electron-beam writing on ${c}_{\ensuremath{\perp}}$-oriented $\mathrm{Ya}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}(\mathrm{YBCO})$ thin films. Serving as strong pinning sites, columnar defects cause a 70% enhancement of critical current density ${J}_{c}$ at $T=77$ K in magnetic fields parallel to the $c$ axis. The matching effect of the pinning force density has been observed, due to commensurability between flux lines and arrays of columnar defects. The pinning strength of columnar defects has been compared with that of point defects, and found to be greater than the latter in YBCO films. These results suggest that this way of pinning center fabrication could be a promising tool in studies of the pinning mechanism in high-temperature superconductors.

The longitudinal elastic correlation length, l 44 , of flux lines along the c -axis is measured using the Campbell method with the magnetic field parallel to the c -axis for a superconducting Bi-2212 single crystal. It is found that l 44 is of the order of 10μm and four orders of magnitude longer than the distance between the CuO 2 planes. In addition, l 44 increases with increasing magnetic field and/or temperature. These results agree well with the theoretical estimate of the pinning correlation length using the observed critical current density. The apparent pinning potential associated with the magnetic relaxation rate is calculated using these results and compared with the experimental result. Agreement is satisfactory. It is also found that the transverse flux-bundle size is as short as the flux-line spacing. It is concluded from these results that the flux lines are rather one-dimensional and strongly coupled along the c -axis.

The electrical resistance R in a superconducting Ba1−xKxBiO3 single crystal is studied as a function of the temperature T and the current I. The measurements performed without applied magnetic field indicate that the flux lines are generated by the self-field and that several transitions contribute independently to the R(T) and R(I) characteristics. A phenomenological expression of the R(T, I) dependence is proposed.

The pinning-force density and the irreversibility field are measured for Bi-2223 tape wires at various temperatures under the magnetic fields normal and parallel to the c -axis. It is found that the scaling laws of pinning-force density in the low- and high-temperature regions and the temperature dependence of the irreversibility field are formally the same between the two field directions in spite of some anisotropy factor, suggesting that the pinning mechanism is essentially the same for the two field directions. These results are compared with the numerical calculation based on the flux-creep model. The experimental results are well explained by the theory including the anisotropic property. The pinning potential estimated from the flux-creep theory at 80 K and 1.0 T is of the order of several 10 meV and the factor of the anisotropy is about 1.3. The value of the pinning potential under the magnetic field along the c -axis suggests that the flux lines are strongly connected along this direction. The longitudinal elastic correlation length of the flux lines is of the order of several μm and this supports the hypothesis. The pinning characteristics of a Bi-2223 tape wire to which the strong pinning centers are successfully introduced are discussed using the flux-creep theory for evaluating the potential of this material for application. The irreversibility field for the direction parallel to the c -axis is estimated to be sufficiently high even at 77.3 K and it is concluded that Bi-2223 has a sufficient potential for application.

Voltage-current characteristics were measured for Ag-clad (Bi, Pb)2Sr2Ca2Cu3O10 multifilamentary samples at 77 K, with magnetic field H parallel to the c-axis. The data were fitted by V=V0 exp[-(l*/l)mu ], where l is the critical current with no thermal excitations. The parameter mu was obtained from logd(In V)/d/3] versus log l plots, where the data give straight lines for each of the fields. The lines for the fields 30 mT

We studied YBa2Cu3O7−x ceramic samples during external magnetic field increase from 200 to 4000 Oe at 77 K using acoustic emission and magnetization methods. We observed a small magnetic anomaly near 2500 Oe. This observed magnetic anomaly was accompanied by acoustic emission impulses of activity equal to ~20 s−1. These impulses are thought to be Bean's mixed-state field Hs. Based on Bean's theory, the full penetration field H* has been calculated to be ~1200 Oe. The possible mechanism of acoustic emission signals due to interaction between flux lines during the formation of a mixed state inside a sample is discussed.

${}^{75}\phantom{\rule{-0.16em}{0ex}}$As NMR spin-lattice relaxation ($1/{T}_{1}$) and spin-echo decay ($1/{T}_{2}$) rate measurements were performed in a single crystal of Ba(Fe${}_{0.93}$Rh${}_{0.07}$)${}_{2}$As${}_{2}$ superconductor. Below the superconducting transition temperature ${T}_{c}$, when the magnetic field $\mathbf{H}$ is applied along the $c$ axes, a peak in both relaxation rates is observed. Remarkably that peak is suppressed for $\mathbf{H}\ensuremath{\perp}c$. Those maxima in $1/{T}_{1}$ and $1/{T}_{2}$ have been ascribed to the flux lines lattice motions and the corresponding correlation times and pinning energy barriers have been derived on the basis of a heuristic model. Further information on the flux lines motion was derived from the narrowing of ${}^{75}\phantom{\rule{-0.16em}{0ex}}$As NMR linewidth below ${T}_{c}$ and found to be consistent with that obtained from $1/{T}_{2}$ measurements. All the experimental results are described in the framework of thermally activated vortices motions.

Thermal motion of the flux lines (FL) gives rise to fluctuating magnetic fields. These dynamic fields couple to the nuclei in the sample and relax the nuclear spins. Based on a model of harmonic fluctuations, we provide a theoretical description of the nuclear spin-lattice relaxation (NSLR) process due to the fluctuating FLs in clean type-II superconductors. At low fields, the calculated longitudinal relaxation rate $T_1^{-1}$ is enormously enhanced at temperatures just below $T_c$. At intermediate fields, the resulting $T_1^{-1}$ exhibits a peak structure as a function of temperature, which is eventually suppressed as the field is increased. The vibrational modes which have components propagating along the FLs play an essential role in the $T_1^{-1}$ process.

The pinning force calculated from Larkin-Ovchinnikov collective pinning theory is used to determined the density profile (in one, two and three dimensions) of flux lines in the Bean critical state. In all cases one finds a result different from the conventional linear profile. The dependence of the corresponding magnetization on the external magnetic field is calculated. Strong single-particle pinning leads, in three dimensions, to a behaviour distinctly different from the collective pinning result.

The two distinct peaks observed as a function of temperature in the dissipation of vibrating superconducting slabs in a tilted magnetic field are explained by thermally activated flux diffusion across the thickness and width (or length) of the slab. These conspicuous peaks thus do not necessarily indicate multiple phase transitions of the flux-line lattice as proposed previously. Anisotropic mobility of the flux lines may increase or decrease the separation of the peaks.

The magnetic hysteresis curve of YBa2(Cu1-xFex)3Oy(0≤x≤0.08) prepared by two kinds of heat treatments was measured by SQUID magnetometer. YBa2(Cu1-xFex)3Oy was slowly cooled from 890°C in air, and a part of the samples was heated at 800°C in N2 gas. All products including those heated in N2 gas were annealed below 400°C in O2 gas. The measurements by SQUID were done at 5K and in magnetic fields up to 1T. Δ M, the difference in the hysteretic magnetization between the increasing and decreasing magnetic fields, of the samples prepared by heating in N2 gas followed by annealing in O2 gas shows the maximum value at x=0.02. This seems to indicate that the clustering of Fe atoms in the Cu1-O planes of the sample acts as effective pinning centers for flux lines.

The temperature dependence of the ultrasonic attenuation coefficient α ( T, H ) and sound velocity V s ( T, H ) were measured under magnetic fields for high- T c phase Bi-Pb-Sr-Ca-Cu-O ceramic samples aligned with the c -axis. In the case H · k , where k is the direction of sound propagation, a broad peak was observed in the α( T , 10T)-α( T , 0 T) versus T curve at T ∼ 65 K accompanied with a broad step in the V s ( T , 10 T) - V s ( T , 0 T) versus T curve. On the other hand, the peak and the step were also observed in the case of H | k , were the temperature position shifted down to T ∼50 K, and the width was narrower than in H · k . The behavior was explained in terms of thermally assisted flux flow in which flux lines are pinned by intrinsic pinning centers.

Current--voltage characteristics have been performed on an irradiated microbridged ${\text{Bi}}_{2}{\text{Sr}}_{2}{\text{CaCu}}_{2}{\text{O}}_{8+\ensuremath{\delta}}$ single crystal at low temperature $(T=5\text{ }\text{K})$ in a magnetic field applied parallel to the $c$ axis. The evolution of the I--V characteristics that leads to a peak in the differential resistance ${r}_{d}(I)=dV/dR(I)$ in the vicinity of the ``peak effect'' in the critical current was investigated. The analysis of the current-dependent differential resistance curves shows that the dynamics of the vortices in the vicinity of ${B}_{\ensuremath{\phi}}$ is dominated by the plastic flow of interstitially pinned vortex around regions of flux lines strongly pinned at the columnar defects. The pinning is found to be individual at low magnetic fields and collective when the vortex--vortex interactions are involved.

We derive a hydrodynamic model for a liquid of arbitrarily curved flux-lines and vortex loops using the mapping of the vortex liquid onto a liquid of relativistic charged quantum bosons in 2+1 dimensions recently suggested by Tesanovic and by Sudbo and collaborators. The loops in the flux-line system correspond to particle-antiparticle fluctuations in the bosons. We explicitly incorporate the externally applied magnetic field which in the boson model corresponds to a chemical potential associated with the conserved charge density of the bosons. We propose this model as a convenient and physically appealing starting point for studying the properties of the vortex liquid.

We performed a Monte Carlo simulation of current-driven flux-lines in an irradiated Bi2Sr2CaCu2O8+δ model. At a low temperature glassy phase, the applied current causes a rapid reduction of the c-axis coherence with decreasing temperature. We obtained a sharp peak effect in the critical current as a function of magnetic field B, when B increases towards the matching field. The current-induced non-equilibrium vortex state could explain the unusual critical state experimentally observed in the glassy phase.

Force-displacement characteristic of flux lines in a superconducting Bi-2212 single crystal was measured using the Campbell method at low temperatures and low magnetic fields where the peak effect of the critical current density was observed. It was found that the interaction distance, d i, had a peak around the peak field, while the Labusch parameter, α L, increased monotonously with increasing magnetic field. The peak of d i means an increment of the reversible limit of motion of pinned flux lines. This seems to be caused by an introduction of some disorder in the flux line lattice at the so-called 3-dimensional to 2-dimensional transition field. However, the characteristic length of the deformation along the c-axis is considered to be much longer than the distance between the CuO2 planes.

The pinning of flux lines by the twin planes is studied in bulk textured YBCO single domains using magnetic field angular measurements of c-axis critical current density J c (Φ). Above a matching field B M associated with the twin boundary network, J c (Φ) shows a fourfold peak structure related to the pinning by each variant of the twin plane (TP). Below B M , J c is angular and field independent, which is consistent with a complete adaptation of the flux lines to the twin planes network. In the direction of the TP, J c is independent of the field intensity up to 8 T suggesting that twin plane pinning might have a magnetic origin in addition to the core pinning effect.

Some of the properties of the low temperature vortex-glass phase of randomly-pinned flux lines in 1+1 dimensions are studied. The flux arrays are found to be sensitive to small changes in external parameters such as the magnetic field or temperature. These effects are captured by the variations in the magnetic response and noise, which have universal statistics and should provide an unambiguous signature of the glass phase., Comment: 11 pages and no figures; revtex 3.0

Made available in DSpace on 2022-04-29T08:47:22Z (GMT). No. of bitstreams: 0 Previous issue date: 1991-01-01 In this paper, we consider the extension of the Brandt theory of elasticity of the Abrikosov flux-line lattice for a uniaxial superconductor for the case of parallel flux lines. The results show that the effect of the anisotropy is to rescale the components of the wave vector k and the magnetic field and order-parameter wave vector cut off by a geometrical parameter previously introduced by Kogan. © 1991 The American Physical Society. Universidade Estadual Paulista Julio de Mesquita Filho, Campus de Ilha Solteira, Ilha Solteira Sao Paulo, Cep 15378 Universidade Estadual Paulista Julio de Mesquita Filho, Campus de Ilha Solteira, Ilha Solteira Sao Paulo, Cep 15378

We investigated the magnetization process of a Sm-Ba-Cu-O bulk superconductor induced by a pulsed magnetic field at 40 K by measuring the local magnetic flux density using several small Hall sensors that were mounted on the sample surface. We observed that the penetration of flux lines along the growth sector boundary (GSB) is more difficult than along the growth sector (GS) region. This can be attributed to the difference in the pinning strength of the two regions. When a relatively large magnetic pulse was applied, we found that the flux lines that penetrated along a weak region can reach the center of the sample first, and magnetize then the GSB region from inside. The reason of this interesting reversal in the magnetizing order can be attributed to the strong pinning effect of Sm-Ba-Cu-O.

Critical currents (I c ) of Bi-2223/Ag tapes were measured as a function of magnetic field (H) by a dc transport method, using 1μV/cm criterion. The field was perpendicular to the tape plane. Critical current at elevated fields can be expressed as I c =I c0 exp[- (H/H * ) a +1 ( a +1)]. Plots of log I c vs. H show downward curvature at elevated fields, which is defined by a and H * . It was shown that a generally increases with flux pinning. However, a also greatly depends on the grain alignment and quality of the links between the grains. The experimental findings support the suggestion that the origin of the downward curvature is entanglement of the flux lines.

The behavior of magnetic fields inside superconductors has implications for both technology and fundamental condensed matter physics. In his Perspective, Nori discusses results published in the same issue by Matsuda et al. (p. 1393) on the motion of magnetic flux lines in a high transition temperature superconductor. Video sequences show how the flux lines move around and are sometimes trapped by defects in the material.

High-Tc-superconductors are studied by measuring the ultrasonic attenuation and the relative change of the sound velocity in various applied magnetic fields. High sound amplitudes reveal nonlinear effects of the flux-line lattice. Due to the coupling of the flux lines to the sound waves, the occurring effects show the pinning behaviour of a high-Tc-superconductor. Especially the results for a textured ceramic Bi1.6Pb0.4Sr2Ca2Cu3Oy-superconductor are presented.

Since the 1986 discovery of high‐temperature superconductors, researchers have been struggling to understand the nature of the magnetic flux lines that thread through these copper‐oxide materials when the field is above a few tens of gauss. the flux lines take the form of vortices, swirling supercurrents that confine the magnetic field to a cylindrical region around a quiescent center. Understanding them is more than an academic exercise: Motion of the vortices, when pushed by a high enough current, introduces resistivity and limits the long‐sought high‐field applications. (See PHYSICS TODAY, October 1992, page 17.

The relationship between the NMR parameters and the motion of the flux lines (FL) in high-T c superconductors are discussed in the light of recent 89 Y NMR experiments in YBa 2 Cu 3 O 7 . In particular, novel experiments involving echo dephasing due to both thermal fluctuations of FL's and motion driven by pulsed magnetic fields are presented with preliminary results.

High-precision ultrasonic measurements of sound velocity and attenuation in magnetic fields up to 14 Tesla were carried out on a single-crystalline La 2-x Sr x CuO 4 with x =0.1, 0.14 and 0.19 to determine the depinning temperature of the flux lines as functions of doping. With decreasing Sr-content the depinning temperature, determined by the midpoint of the step in the sound velocity, decreases strongly. Furthermore, the angle dependence of the tilt modulus of the flux line lattice was studied by changing the orientation of the magnetic field with respect to the k-vector and to the displacement vector of the sound wave.

The behaviour of the irreversibility line is closely related to the flux line formation and pinning in high Tc superconductors. A relationship between magnetic field and temperature for the mixed state was obtained. It is suggested that on an irreversibility line the fraction transformed from superconducting state to normal cores as the flux lines pinned in the superconducting matrix is unchanged. The theoretical analysis is in agreement with experimental results.

Ultrasonic measurements are performed with sintered samples of (Bi 0.8 Pb 0.2 ) 2 Sr 2 Ca 2 Cu 3 O y and (La 1− x Sr x ) 2 CuO 4 changing temperature T under high magnetic fields H . Observed steps in sound velocity V s ( T , H ) versus T curves and the peaks in ultrasonic attenuation coefficient α ( T , H ) versus T ones are analyzed in terms of a flux-creep model. We showed that the phenomena obtained here can be explained quantitatively with the model in which flux lines are pinned by intrinsic pinning centers in low ( T , H ) region and activated thermally in high ( T , H ) region.

We give here a general formulation of statistical mechanics of an assembly of flux lines in oxide superconductors under magnetic field Hc1

The conductance of air-gaps with double-sided slotting is generally considered with the assumption that the flux lines are radially directed only. Calculations allowing for the two-dimensional nature of air-gap fields, however, show a different situation with regard to the effect of slotting, especially at the higher harmonic orders. Calculated curves and tables are presented to illustrate the correlation between these two ways of approach for two slot combinations under excitation by a single coil, and also to establish the way in which the harmonics vary with changing rotor position.

An experimental study has been conducted on flat sheets of vanadium single crystals. The critical current density Jc of the sample has been measured at temperatures of 1.8 ∼ 4.2 K in a magnetic field perpendicular to the broad surface of the sample. The dependence of the normalized pinning force density on reduced magnetic field has been expressed through an empirical form as J c /J c H( max ) = 4 (H/H c 2 ) 1 2 [1 — (H/H c 2 ) 1 2 ] . This expression is tentatively explained through the formulation of Jc based on the interaction between “flexible” flux lines and randomly distributed pinning centers.

A model of the magnetic pinning interaction (i.e., a system of N-curved flux lines (FLs) and a cylinderical inclusion) is developed. The field components inside and outside the inclusion are calculated. The energy of the system and the magnetic pinning force are completely determined from the field distribution inside the superconductor. The properties of the curved FLs near the surface of a type-II superconducting cylinder are established. The energy of the system as well as the magnetic field and the current density are calculated. The force on a flux line (FL) element is completely determined by the total current density at the element position. Es wird ein Modell der magnetischen Pinning-Wechselwirkung (d. h. ein System von N-formigen Fluslinien (Fls) und einem zylinderformigen Einschlus entwickelt. Die Feldkomponenten innerhalb und auserhalb des Einschlusses werden berechnet. Die Energie des Systems und die magnetische Anhaftkraft werden vollstandig aus der Feldverteilung im Inneren des Supraleiters bestimmt. Die Eigenschaften der gekrummten Fls in der Nahe der Oberflache eines supraleitenden Zylinders vom Typ II werden untersucht. Sowohl die Energie des Systems als auch das Magnetfeld und die Stromdichte werden berechnet. Die Kraft auf ein Fluslinien(Fl)-Element wird vollstandig bestimmt durch die gesamte Stromdichte am Ort des Elements.

Within the framework of the micromagnetic theory of superconductivity explicit expressions for the elastic stresses of flux lines are derived. The dependence of the stress tensor on the superconducting parameters λ, ξ, and χ is discussed. It is shown that the magnetic pressure associated with the magnetic field gives rise to elastic stresses of the same order of magnitude as the contribution from the Δ V/V effect of the order parameter. Explicit expressions are derived for the pinning forces exerted by dislocations on flux, lines. They are found to be approximately proportional to the condensation energy H/8π. Im Rahmen der mikromagnetischen Theorie der Supraleitung. werden explizite Aus-drucke fur die elastischen Spannungen der Fluslinien abgeleitet. Die Abhangigkeit des Spannungstensors von den supraleitenden Parametern λ, ξ und χ wird diskutiert. Es wird .gezeigt, das der Beitrag des magnetischen Druckes des Magnetfeldes zu den elastischen Spannungen von derselben Grosenordnung ist wie der Beitrag des.ΔV/V-Effektes des Ordnungsparameters. Die von Versetzungen auf Fluslinien ausgeubten Haftkrafte werden explizit berechnet. Sie ergeben sich als naherungsweise proportional zur Kondensations-energie H/8π.

By means of the magnetooptical method the intermediate-state structures of annealed polycrystalline lead foils having thicknesses between 40 and 120 µm have been investigated. The structures in increasing and decreasing magnetic field are qualitatively described. They mainly have laminar character, but above a critical thicknessd s , between 115 and 169 µm forT=4.2 K, structures are found which can be interpreted by branching of the normal domains. Rapid increasing of the applied magnetic field at the(SI) T transition favors the formation of macro flux lines. The period of laminar structures shows good agreement with the “nonbranching” model of Landau for values of the reduced applied magnetic fieldh=H/H c ≤0.6. A value of the surface energy parameter Δ=86±17 nm is calculated from the experimental data. In contrast to the model of Goren and Tinkham, the mean separation of macro flux lines in lattices of flux lines is proportional to $${1 \mathord{\left/ {\vphantom {1 {\sqrt h }}} \right. \kern-\nulldelimiterspace} {\sqrt h }}$$ for not too large values ofh.