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International audience; This work validates a posteriori the use of the theory developed ca. 40 years ago by Amatore and Savéant for regular arrays of electroactive band or disk electrodes. This theory has been profitably used and widely applied in more than 900 research papers for the treatment of the voltammetric responses of arrays of nanoelectroactive objects that were necessarily random by construction. In this work we show that competitive diffusion interaction between the active sites enforce redistribution of individual diffusion layer which homogenize dimensions of the solution volumes 'feeding' each active site. For arrays of nanodisk electrodes, it also validates the corresponding approximation assuming that its voltammetric behavior is to that afforded by identical independent cylindrical unit cells performing in parallel.

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.

Flux-reversal machine (FRM) is a new doubly salient stator-permanent magnet (PM) machine with flux linkage reversal in the stator concentrated windings. It can operate in both motoring and generating modes. Its simple structure makes it cost effective and suitable for mass production. However, there is notable permanent magnet flux leakage which deteriorates the torque ability of the FRM. In this paper, a novel design to improve the performance of an FRM is proposed. The proposed FRM has permanent magnets parallel to the stator magnet flux lines and thus is much more difficult to demagnetize. To analyze the characteristics of the proposed FRM, a two-dimensional finite-element method (2-D FEM) is used. The prototype FRM is also built to prove the advantage of the new design method. From the analysis and experimental results, it is shown that the proposed FRM has an improved performance.

We present a Hamiltonian for the boson–boson interaction, based on elastic coupling through flux lines. This Hamiltonian may be used to study polaritons and plasmons and likewise the cohesive energy in crystals of noble gases. The presented results for crystals of noble gases are in a good agreement with experimental data.

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.

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.

Using the Lagrangian formalism we attempt to calculate the interaction energy between the two bodies, nonconnected and connected, in a linear lattice. The obtained results show that the interaction is dependent on the dispersion relation ω (q). On this basis we calculate the binding energy of an ionic lattice and we have found a good agreement with experimental data.

The creep motions of flux lines in both Bragg glass (BrG) and vortex glass (VG) are studied. The power-law dependence of the creep activation barrier on the driving force is obtained. Two universal classes of creep motion are found with the exponent μ=0.5±0.02 for the BrG and μ=0.28±0.02 for the VG. The former is in good agreement with the prediction by the scaling theory and the functional-renormalization-group theory on creep, while the latter is a new estimate. The different dynamics of flux lines in the VG and in the BrG are investigated accordingly.

It is well known that the point charge, line charge and homogeneously charged plane of infinite extent are sources of electrostatic fields with straight flux lines. It is proved in this note that provided these flux lines occupy all of three-dimensional space, then these charge configurations and appropriate variants of them are the only sources of straight-line electrostatic fields in R 3.

Fluctuation in the distance between flux lines in a superconductor is calculated in a fractal dimension and from that using Lindemann criterion of melting, a field versus temperature phase boundary is deduced for the dendritic phase of a superconductor. This phase boundary is predicted to be B−4∝(1−T FM /T c ) where T FM is the flux-lattice melting temperature. When both the fractal as well as the spectral dimensionalities are considered the phase boundary is predicted to be determined by B8/5∝(1−T FM /T c ).

We consider a model of oriented, non-intersecting flux lines on the lattice Zd, where each flux line is assigned a Boltzmann factor omega per unit length and a fugacity y. We prove the existence of free energy, both for y>0 and for y=-1, and show that it is independent of y for y>0. Using upper and lower bounds in terms of exactly solvable models, we rigorously establish that, for all y>0, the model has a phase transition at omega =1/d. For omega

A model of a type-II superconducting cylindrical shell is established to verify the properties of distorted flux lines using the London theory. The field distributions inside and outside the superconducting region are determined. Moreover, the current density and the forces on the vortex segments are calculated using these field distributions. Finally, the Gibbs free energy of the system is obtained in compact form which can be easily applied to real-life application. As the shell tends to a rigid cylinder agreement with previous results is achieved.

Clebsch potentials are of tremendous value in visualizing the flux lines of a three-dimensional solenoidal vector field. Unfortunately, only a local theory of Clebsch potentials exists, and their use in visualizing arbitrary three-dimensional solenoidal vector fields requires a global theory. Furthermore, such a global theory must be built on constructive techniques which yield practical algorithms. The virtues of Clebsch potentials are reviewed and a question about their global existence is formulated. The subtlety of this question is illustrated through an analogy with micromagnetic theory. A formalism for addressing questions about Clebsch potentials is presented. >

Slits patterned into a YBa2Cu3O7−δ thin film were observed to obstruct Meissner sheet currents leading to an imbalance in the local Meissner screening properties. The new phenomenon was studied with magneto‐optic imaging where twin lobes of opposite flux polarity were seen to form near the slits and inside the Meissner region. The lobe closest to the sample edge is always polarized opposite to the applied field. At weak fields, the anomalous flux generation is reversible. At higher fields, but still sufficiently small to keep the vortex penetration front away from the slits, the anomalous current starts nucleating flux lines which become trapped when the field is removed.

The dynamics of vortices near depinning transition is studied in terms of a three-dimensional flux-line model with point-like pinning centers. The zero-temperature critical depinning force F c 0 is determined with two methods consistently. We find two universal exponents β ≈ 0.64 and δ ≈ 2.3 which characterize the critical behaviors of depinning transition of Bragg glass (BrG). The dynamical modes of flux lines near F c 0 are also discussed.

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.

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.

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.

We explore the magnetization pattern of Co and permalloy disks with diameters between 80 nm and 1 μm by using two complementary experimental techniques: Lorentz microscopy and magnetic force microscopy (MFM). By means of Lorentz microscopy we show that the dominating magnetization pattern of the disks is a vortex structure with closed flux lines in the plane of the disks. Complementary MFM measurements demonstrate that the magnetization in the center of the disks is tilted out of the plane of the disk. The experimental findings closely agree with corresponding micromagnetic calculations.

In low-x type II superconductors there exists a long range attractive interaction between flux lines. This leads to a step B0 in the magnetization curve at Hc1. Experimental results frequently deviate from the ideal behaviour. The deviations are caused by the necessity to perform a plastic deformation of the intruding flux line lattice in order to accommodate the specimen geometry, and by flux line pinning. It is shown that both mechanisms lead to a finite slope of the magnetization curve near Hc1. The flow stress of the FLL and the volume pinning force may be obtained from magnetization measurements. In Supraleitern II. Art mit kleinem Ginsburg-Landau-Parameter existiert eine anziehende Wechselwirkung der Fluslinien. Deshalb wird bei Hcl ein sprunghaftes Fluseindringen bis zur Flusdichte B0 erwartet. Experimentelle Ergebnisse zeigen haufig Abweichungen vom idealen Verhalten. Diese Abweichungen werden verursacht durch auf die Fluslinien ausgeubte Haftkrafte und durch plastische Verformungen des Flusliniengitters, die durch die Probengeometrie bedingt sind. Beide Mechanismen geben Anlas zu einer endlichen Steigung der Magnetisierungskurve bei Hcl. Die Fliesspannung des Flusliniengitters und der Beitrag der Haftkraft werden abgeschatzt.

The scattering of cold neutrons from an imperfect flux line lattice (FLL) is analysed. It turns out to be possible by suitable experiments to distinguish between distortions due to pinning centres and those of grown-in intrinsic defects of the FLL, and thus to obtain valuable information on the interaction forces between pinning centres and flux lines from the shape of the scattering intensity profiles. Es wird die Streuung thermischer Neutronen an einem gestorten Flusfadengitter analysiert. Dabei stcllt sich heraus, das es durch geeignete Experimente moglich ist, zwischen Verzerrungen, die durch Verankerungszentren entstehen, und solchen, die zu eingewachsenen Eigenfehlern des Flusfadengitters gehoren, zu unterscheiden. Aus den Profilen der Streuintensitat ergeben sich damit wertvolle Informationen uber die Wechselwirkungskrafte zwischen Flusfaden und Verankerungszentren.

The pinning forces exerte dby a planar imperfection on the flux lines in a type-II superconductor are calculated from the Ginzburg-Landau theory. The elastic strains caused by this imperfection in the flux line lattice are found to diverge at large inductions. As a consequence, even rather thin planar inclusions or grain boundaries lead to a breakdown of elastic linearity and to a trapping of flux lines by the imperfection as the induction is increased. This result does not require a vanishing shear modulus of the flux-line lattice but is due entirely to the nonlocal character of the elastic behaviour of the lattice. It may explain in certain cases the observed peak in the volume pinning force at large inductions. Mit der Ginzburg-Landau-Theorie werden die Haftkrafte berechnet, die von einem ebenen Defekt auf die Fluslinien in Supraleitern II. Art ausgeubt werden. Es wird gefunden, das die durch diese Defekte im Flusliniengitter verursachten elastischen Verzerrungen bei grosen Induktionen divergieren. Als Konsequenz fuhren sogar ziemlich dunne ebene Einschlusse oder Korngrenzen zu einem Zusammenbruch der elastischen Linearitat und zum Einfangen der Fluslinien durch die Defekte, wenn die Induktion erhoht wird. Dieses Ergebnis erfordert nicht ein Verschwinden des Schermoduls des Flusliniengitters und wird vollstandig durch den nichtlokalen Charakter des elastischen Verhaltens des Gitters verursacht. Es konnte in bestimmten Fallen den beobachteten Peak in der Volumenhaftkraft bei grosen Induktionen erklaren.

The interaction of straight or curved flux lines with the boundaries of a type II superconducting slab, ellipsoid, and sphere is considered. The surface barrier opposing the entry of the vortices into the sample shows to be of different values depending on the place of entry into the sample with iespect to the boundary. The force on different elements of the flux lines is completely determined in terms of the total current density at the position under consideration. Es wird die Wechselwirkung einer geraden und gekrummten Fluslinie mit den Begrenzungen eines stabformigen, elliptischen und kugelformigen Supraleiters II. Art betrachtet. Es wird gezeigt, das die Oberflachenbarriere, die den Eintritt der Wirbel in die Probe hindert, einen von dem Ort des Eintritts in die Probe bezuglich der Begrenzung abhangigen unterschiedlichen Wert besitzt. Die Kraft auf die verschiedenen Elemente der Fluslinien ist mit der Gesamtstromdichte am betrachteten Ort vollstandig bestimmt.

Gravity profiles can be computed by summing flux lines uniformly radiating from source elements within a density distribution. Digital computations are performed efficiently, irregular density distributions modeled, and alterations easily made to the model to alter the profile by recomputation of only the altered elements. The concept applies to both two- and three-dimensional models and the corresponding datum plane contours. Two-dimensional computations are described and illustrated.

In hard type-II superconductors flux lines may overcome pinning obstacles by plastical flow of the flux-line lattice around the pinning centres. The conditions for this process to occur are investigated. The results for the volume pinning force obey a scaling law and show a specific dependence on the anisotropy of the pinning obstacles and on the Ginsburg-Landau parameter. #In harten Supraleitern zweiter Art erfolgt der Flustransport moglicherweise nicht durch Losreisen der Fluslinien von den Haftzentren, sondern durch Umgehung der Haftzentren unter plastischer Verformung des Flusliniengitters. Die Bedingungen fur das Auftreten dieses Vorgangs werden untersucht. Die Ergebnisse fur die Volumenhaftkraft gehorchen einem Masstabsgesetz und zeigen eine spezifische Abhangigkeit von der Anisotropie der Haftzentren und vom Ginsburg-Landau-Parameter.

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.

A model for thermal fluctuations of the Abrikosov flux lattice is considered which describes the continuous phase transition from the flux lattice to the Meissner phase. We calculate the density of flux lines, the characteristic decay length of the longitudinal density correlations and the characteristic oscillations of the transversal density correlations near the phase transition point.