Hard Superconductors Research Articles

The influence of thermally activated flux creep on the ac response of a hard superconductor

A theoretical and experimental study is presented of the influence of thermally activated flux creep on the ac response of a type II superconductor in the mixed state. The theory describes the ac response of a cylindrical superconductor in the mixed state in an axial dc magnetic field and a superposed parallel ac field of low amplitude and low frequency. Thermally activated flux creep gives rise to flux motion at the peak and the valley of the sinusoidal ac applied field and a frequency-independent phase shift of the voltage induced in a pickup coil wound about the sample. The instantaneous voltage at the peak or valley of the ac applied field is related to the critical-current density J/sub c/ and the pinning-energy barrier normalized by the temperature U/kT. The ac loss voltage and the voltage waveform were measured for a cold-worked NbZr sample. For temperatures T below 4.2 K, the measured values of kT/U are nearly proportional to the temperature. Both J/sub c/ and U were observed to depend on magnetic field history.

Power losses in hard superconductors: An analysis using the critical state model

In this paper, power losses in a superconductive wire, carrying a time-varying current and embedded in an external magnetic field, are evaluated on the basis of an analytical approach, previously developed by the authors, to the computation of magnetic fields. Computation is carried out for a hard superconductor rectilinear wire of circular cross section, in the presence of an external magnetic field orthogonal to the wire axis. The hard superconductor is modelled according to critical state theory, which leads to a non-linear hysteretic formulation. An approximate analytical solution is obtained for the losses, in the case of steady-state ac currents, as a function of the superconducting material parameters as well as of field and geometrical quantitites. On this basis, an attempt can be made to evaluate and discuss the influence of the various loss terms of different origin, though under the rather restrictive conditions required by the analytical solution.

Magnetic instabilities in hard superconductors

This review treats magnetic instabilities in hard and combined Type II superconductors. We give and discuss in detail the criteria for stability of the critical state with respect to magnetic-flux jumps. We study the effect of magnetic and thermal diffusion, as well as that of the structure of a combined superconductor, on the magnetic-field value for a flux jump. The theoretical results are compared with the existing experimental data.

The influence of plastic deformation of the flux‐line lattice on flux transport in hard superconductors

AbstractIn 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.

Magnitnye neustoichivosti v zhestkikh sverkhprovodnikakh

Magnitnye neustoichivosti v zhestkikh sverkhprovodnikakh

The critical state stability

A review of the theory of flux jump nucleation in hard and composite superconductors is presented. Stability criteria for some special cases are established. The basic physical ideas and quantitative methods of stability investigation are outlined.

Pressure-induced semiconductor-metal transitions in amorphous InSb

Abstract Pressure-induced semiconductor-metal transitions, accompanied by a discontinuous decrease in the resistivity by a factor of 10−4, have been found at room temperature for amorphous InSb under pressures of 10 to 13 kbar. These transitions occur through a series of intermediate structural modifications which remain predominantly in the amorphous state, while the final stage partially transforms into a metastable crystal with a NaCl-type structure. The transformation to the NaCl type is irreversible on releasing the pressure. This material can be classed as a hard superconductor with a transition temperature Tc = 3·4±0·2 K and a critical magnetic field Hc = 9-10 kG.

On the theory of flux jumps in hard superconductors

The critical state stability against flux jumps in hard superconductors is considered by means of the WKBJ method. The universal stability criterion for an arbitrary critical state model is obtained.

Experimental investigation of the flux density profile in hard superconductors

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The Effect of Receiver Pressure on the Observed Flow Pattern in the Hydrostatic Extrusion of Bimetal Rods

An experimental study was conducted to determine the acceptable combinations of process variables for the production of a niobium-titanium superconducting alloy in a pure aluminum matrix by hydrostatic extrusion. Conditions for sound flow and defective flow are shown on plots of percent reduction in area versus die semicone angle. The superconductor used was a 56 percent Nb-44 percent Ti alloy surrounded by a matrix of 99.995 percent pure aluminum. The study was performed in three phases. Single-core billets were extruded into atmospheric pressure with reduction in area, die semicone angle, and the ratio of the volumes of the two phases being varied. Single-core billets were extruded into receiver pressure with reduction in area and die semicone angle being varied. Billets with three cores were extruded with reduction in area, die semicone angle, friction, and receiver pressure being varied. In all cases there was a light mechanical bond between the two materials produced by interference fitting of the cores into drilled holes. Experimental results showed that increasing the receiver pressure increases the range of acceptable process variables to produce sound flow. Although it was possible to produce sound flow, the results were not always consistent and repeatable. This is largely due to the great difference in strength between the soft aluminum and the hard superconductor and the difficulty in accurately controlling the bond strength. It is expected that the beneficial effect of receiver pressure will be even more pronounced with a tighter control on bonding.

Flux pinning in bronze-processed Nb3Sn

Superconducting critical currents have been measured at 4.2 K and applied magnetic fields up to Hc2 for a series of solid-state processed-Nb3Sn conductors. Variations were made in the alloy content of the matrix and core as well as heat-treatment times at 700 °C to produce a wide range of superconducting critical currents. The pinning-force density, Fp (=Jc×B), plotted as a function of reduced field, h (=H/Hc2), exhibits a peak, Fpmax, at a reduced field hp. Fpmax varies from 81×108 dyn/cm3 at hp=0.2 to 18×108 dyn/cm3 at hp=0.32. The high values of Fpmax for these samples are related to Nb3Sn grain sizes which are 1000 Å or less. At 2 kG the flux-line lattice spacing is approximately 1000 Å or nearly one flux line per grain. Kramer has proposed a model to account for flux pinning in such hard type-II superconductors, and while the pinning-site density in the present samples is near the upper limit to which Kramer’s model was meant to apply, it is possible to interpret the present data using his model. The dynamic pinning force fs (h) calculated by Kramer for flux-lattice shear around pinning sites too strong to be broken by the Lorentz force has the magnetic field dependence h1/2 (1−h)2. In the high pinning-density limit where √ρ=1/2a0, ρ being the pinning density and a0 the flux-line lattice spacing, the magnetic field dependence of fs (h) must be changed to h3/2 (1−h)2/(h1/2−n)2, where n equals (φ0ρ/Hc2)1/2, by incorporating the field dependence of a0. Using this new field dependence enables a prediction of Fpmax, and associated hp values, which fit the present data for bronze-processed Nb3Sn. It is concluded that near the upper limit of pinning density to which the theory applies a sharp increase in Fpmax may occur without significant shifts in hp to lower values. This result is added to the model’s prediction for lower pinning-density materials, i.e., when lower values of Fpmax increase there is a shift in hp to smaller values.

On the flux jumps in hard superconductors

An investigation is described of critical state stability against flux jumps in hard superconductors accounting the critical current density dependence on the temperature and magnetic field. A flat sample with finite thickness is considered. The stability criteria were found for the Kim-Anderson critical state model (1964) as well as for the region close to the upper critical field Hc2. It was shown that the stability diminishes near Hc2. The stability conditions were found for the total range of external fields below Hc2. It was found that under certain conditions the magnetic instabilities may develop in two isolated regions of the external fields.

Superconducting cavities

Superconducting cavities are characterized by extremely low rf losses. The best results have been obtained with niobium cavities, namely high field Q 0 values of 10 10 at rf flux densities up to 0.16 T (1 600 G) and low field Q 0 values of 10 11. Most important is the surface treatment, which is reported below. Hard superconductors with high critical temperatures, such as Nb 3Sn, have potentially even more favourable rf characteristics compared to niobium and a report is given on first measurements on Nb 3Sn cavities. As the rf losses of superconductor cavities are smaller by the factor of 10 6 than those of copper resonators, various potential applications are available, in particular with linear accelerators.

Electromechanical stresses in superconductors: An analysis using the critical state model

Abstract An analysis of the electromagnetic stresses on a hard superconductor wire has been performed by the critical state model. A theoretical approach has been carried out by taking into account both the field produced by the current flowing in the wire and an external field orthogonal to the wire axis. Owing to analytical difficulties, mainly depending on the non-linear hysteretical feature of the field penetration, a general solution cannot be found. Nevertheless, under some restrictive conditions, an approximate solution is obtained, allowing us to compare the various force components of different origin acting on the wire.

Microstructure-critical current relationships in hard superconductors

The pinning of the flux line lattice (FLL) by crystal lattice defects gives rise to a critical current density Jc for hard superconductors. The volume pinning force density Fp = ‖BXJc‖ however, depends both on the elementary interaction force fp between a single defect and the FLL and on the nature of the summation of these many fp’s. The latter will depend on the spatial arrangement of defects and on the elastic and plastic deformation properties of the FLL. For localized defects the fp is a strong function of defect “size”, reaching a maximum when the size is approximately the coherence length, and is approximately proportional to Hc 2(T) (1−h) where Hc is the thermodynamic critical field and h is the reduced magnetic field H/Hc2. The summation model must give a Fp which obeys the following empirical rules: 1) Fp has a maximum at a reduced field hp which decreases with increasing defect density ρ and f . 2) Fp at h > hp is structure insensitive while Fp at h < hp is structure sensitive. 3) A scaling law is obeyed if T is changed, i.e., Fp = Hc2(T)m .f(h), where m is ∿2.5 andf(h) is only a function of reduced field and microstructure. Experimental evidence for these generalizations is presented and a model which predicts these results is outlined and quantitatively tested.

The lower critical field H c1 of V 3Si

The temperature dependence of the lower critical field H c1 of V 3Si single crystals was investigated. Measurements were carried out using an alternating field method. Superposition of a small alternating field onto an outer magnetic field arising linearly in time makes it possible to detect flux changes in hard superconductors with a high degree of sensitivity.

The recovery current density of hard superconductors

In order to quantify stability in superconductors, the power supplied as external heat to drive the superconductor normal was measured. At constant current and temperature, it was found that the conductor could not be driven normal below a certain critical field, and likewise at constant field there was a threshold critical current I t. The threshold current density J t was found to correspond to the critical current density for the recovery of superconductivity after a disturbance, J r.

Calculation of the critical current density of hard superconductors from the magnetization of cylindrical samples

A new approximation formula for the critical current density is presented which is more exact than those proposed previously and allows the evaluation of the current density in the range of the initial magnetization curve. The relative error is calculated for one practical case and is plotted for the different branches of the magnetization curve.

The influence of plastic deformation on the peak effect in a type II superconductor

Abstract It is shown that the peak effect, a peak in the curve of critical current [Jc ] versus magnetic field [H], is due to the existence of a narrow peak in the pinning force density F p just below Hc2. The J c of a Nb-Ta alloy, which was progressively deformed by rolling to greater plastic strain, has been measured as a function of H. It is observed that plastic deformation shifts the peak in Fp to lower reduced field h, broadens it and increases it in height without markedly increasing Fp on the high-h side of the peak. The broadening of the peak in F p(h) with deformation gradually transforms the peak in Jc (h) into a plateau, and finally Jc(h) becomes a monotonically decreasing function of h. The results are in quantitative agreement with the predictions of a recent model of flux pinning in hard superconductors. It appears certain that the peak in Fp (h) in materials which exhibit the peak effect is caused by the same mechanism that causes the peak in Fp (h) at h × 0.3 to 0.5 in commercial superconductors.

Vortices in type-ll superconductors

The review is devoted to an investigation of the behavior of vortex filaments in hard superconductors. The analysis is carried out in the region of weak magnetic fields, where linear electrodynamics is applicable. This permits a simple physical interpretation of both the properties of isolated vortices and of interactions of vortices with one another and with the surface of the superconductor. A number of examples of the influence of the superconductor outer boundary on the vortex structure are analyzed. It follows from these examples that the vortex lattice is stable relative to a transverse transport current even in an ideally homogeneous sample. Estimates are presented of the maximum transport current at which the vortex structure still remains stable. The role played by the internal surfaces in a superconductor is also illustrated with the interaction of a vortex with a cylindrical cavity or with an interface between two different superconductors as an example.