Effective resistance of current-carrying superconducting wire in oscillating magnetic fields 1: Single core composite conductor

The influence of oscillating magnetic fields on the dc transport current in a single core superconducting wire has been studied by observing the terminal voltage of the wire. The voltage versus oscillating field characteristics can be explained quantitatively by a theoretical analysis based on the critical state model. The analysis shows that the voltage measurement gives detailed information on the change of the distribution of the magnetic induction inside the superconductor. An effective resistance appears in the transport current loop when the amplitude of the oscillating field exceeds a certain threshold value. The dependence of the effective resistance on the amplitude and frequency of the oscillating field and on the conductor diameter is discussed.     

Improved superconducting properties of multifilamentary niobium carbonitride wire

Transport and magnetization measurements have been made on 6μ, 720 filament niobium carbonitride yarn. The magnetization data is discussed in terms of the hysteretic loss, the temperature dependence of Jc, the matrix-superconductor bond quality and the doping effects on the high field Jc's. Transport properties are compared to properties obtained from magnetization data. In addition, weak coupling has been investigated in low conversion fibers. The V-I curves show numerous voltage steps, some corresponding to an order of magnitude increase in resistivity.     

Two methods of fabricating reliable superconducting joints with multifilamentary Nb-Ti superconducting wire

We describe two techniques for joining multifilamentary Nb-Ti superconducting wire. Both methods have achieved critical currents in vacuum at 4.2K comparable to the manufacturer's stated short segment rating. The techniques are simple and applicable to a wide variety of experimental apparati.     

Coupling losses in a rectangular multifilamentary superconducting composite

Coupling current losses between filaments of a superconducting multifilament composite subjected to a transverse varying field is highly dependent on the shape of the conductor. The ac loss is evaluated in a conductor of rectangular cross sectional area. It is shown that the loss per unit volume is somewhat different from the loss in an elliptical shaped composite of the same aspect ratio. In addition, the loss in the outer copper sheath is less sensitive to the aspect ratio than the inner filamentary region. Numerous experimental results are given on losses in as-received conductors and in conductors where the outer copper sheath has been partially removed. The anisotropy in the losses caused by a changing field perpendicular or parallel to the wide side of a conductor is in very good agreement with the theory.     

Losses in a multifilamentary superconducting wire caused by a simultaneous sweep of current and magnetic field

A theoretical discussion is presented on the energy loss in a multi-filamentary superconducting wire when an applied transport current and an external transverse magnetic field are varied simultaneously with a repeating pulsive wave form. In the present calculation, the effects of the ‘uniforming time constant’ which has been introduced by the authors as a characteristic time constant for the change in the transport-current distribution inside the wire is taken into account, together with the field dependence of the critical current density of superconducting filaments.Thus the present analytic expression for the energy loss of multi-filamentary wire is available to the whole range of the external magnetic field. It is shown that the contribution of the dynamic resistance loss to the total loss is strongly dependent on the position of the wire inside a coil.     

Coupling-current loss in a multifilamentary superconducting wire with a normal-metal core

Coupling-current losses in a multifilamentary superconducting wire with a normal metal core were calculated for the case of transverse magnetic fields. The results showed that the dependence of the coupling-current loss of such a wire on the rate of field variation is markedly different from that of a wire without the core, the former being characterized by two time constants while the latter by one. The theoretical result was confirmed experimentally. It was pointed out that in the case when a wire with Cu/CuNi matrices is to be used in a rapidly changing magnet field, Cu for a stabilization should be arranged at the centre of the wire rather than at the surface of the wire in order to reduce the loss.     

A low loss NbTi multifilamentary composite conductor for A.C. use

Investigations of a.c. losses and stability of a mixed-matrix NbTi multifilamentary conductor are presented. Fine filament size of 1.0 μm and a tight twist of 5.5 times the wire diameter 0.2 mm result in a time constant of the eddy current of 0.024 msec at 1.0 T. If this conductor is used in superconducting armature windings of rotating machines or in a.c. magnets, generating a maximum field of 1.0 T, economical benefits are expected at operation frequencies below 20 Hz.     

On the coupling current losses in a multifilamentary superconducting composite

The coupling current losses in a superconducting multifilamentary composite exposed to trapezoidally varying external magnetic field and carrying a small transport current are investigated for the volume pinning force density described with the dependence: F_v = α B^1?γ. Such a model allows estimation of the deviations from the solution based on Bean's (γ = 0) critical state model. Results indicate that there exists a region of small magnetic field amplitudes for which discrepancies are largest. They are also very sensitive to the rate of magnetic field change.     

Using magnetic field pulses with a slow sweep rate to produce uniform current distribution in multifilamentary superconducting wire

A detailed discussion is presented on the change in current distribution which takes place in a twisted multifilamentary superconducting wire induced by successive magnetic field pulses with a slow sweep-rate. The number of the field pulses required for a localized current-distribution to become uniform is estimated. Some modification of existing theories is necessary to describe the phenomenon. The results obtained are confirmed by systematic measurements of the net flux penetration into the wire during each cycle of field pulses.     

Alternating field losses in superconducting wires carrying dc transport currents. Part 2: multifilamentary composite conductors

Investigations of transient field losses in multifilamentary composite conductors carrying dc transport currents, I, are presented. As shown previously, the total loss is best characterized by a normalized transport current i = l/l_c and a dimensionless field-change rate β = τB_e/B_p, where τ is the relaxation time of the coupling current and B_p is the full-penetration field of a solid conductor equivalent to the multifilamentary composite. For β ? 1, the composite conductor behaves like a solid conductor and a saturation effect occurs in both the magnetization and the ac losses. The characteristic feature of the composite appears for β ? 1, and the total losses for transport currents below i < 1 ? β are almost independent of i. Beyond the limit given, losses rise sharply. Experimental results over a wide range of the field change rate and the transport-current level agree sufficiently with the calculations.     

On the distribution of a transport current inside a multifilamentary superconducting wire in a rapidly changing transverse magnetic field

For the current distribution inside a multifilamentary superconducting wire carring a dc transport current in a rapidly changing transverse magnetic field, inconsistencies with the existing models are shown by the following experimental evidence: when a transverse magnetic field is applied, the distribution of transport current is not unaltered but is forced to concentrate into the inner circular cross section region during a characteristic time constant τ_c, called the coupling time constant. Secondly, the characteristic time constant for the transport current distribution inside the inner region to approach a uniform distribution is not τ_c but a new time constant τ₁ called the ‘uniforming time constant’, though the variation in the distribution does not occur unless the external magnetic field changes with time.It is shown that the model of the current distribution based on the above experimental evidence exhibits a remarkable difference from the existing models, especially for the wires containing very fine superconducting filaments.     

Development of a Nb3Sn multifilamentary composite conductor for a.c. use

A Nb₃Sn composite conductor with ≈ 10 000 submicron diameter filaments has been manufactured using the external diffusion process. A.c. losses were greatly reduced by the use of a fine filament size (0.53 μm, design value), a tight twist pitch (0.87 mm) and a small wire diameter (0.153 mm) with a bronze matrix. In an a.c. field with a frequency of 50 Hz and amplitude of 2.0 T, the hysteresis loss and the coupling current loss were observed to be 465 kW m⁻³ and 26 kW m⁻³, respectively. A triplex conductor was constructed by cabling three strands at a twisting pitch of 3 mm, and a small coil was wound from this cable (i.d. 11 mm, o.d. 33 mm, axial length 19 mm). With d.c. the coil generated a field of 1.3 T at the critical current, l_c of 37.4 A. When the coil was operated at 50 Hz, with an exciting current of I_c, the observed loss averaged over the windings was 240 kW m⁻³. The quenching current for 50 Hz operation was 53 A at a maximum field of 1.8 T. This was considerably higher than the critical values under d.c. conditions. Preliminary studies have shown that, if this conductor is used in superconducting armature windings of rotating machines, economical benefits are obtained compared with the use of conventional armatures.     

Dissipation in current-carrying high-T c superconducting ceramics in applied magnetic field

The dissipation mechanism in high-T _csuperconducting ceramics was studied by analyzing the magnetic field dependence of the transport critical current and the form of the current-voltage characteristics. It was found that the actual magnetic field dependence of the transport critical current is significantly slower than that predicted by the weak-link-quenching model. The low-voltage-level current-voltage characteristics were described in terms of thermally activated flux creep at grain boundaries, taking into account collective pinning of intergranular Josephson vortices. For the investigated samples, a low-field, high-temperature mean pinning energy barrier of a few tens of meV was determined.     

Exact semiclassical resistance of thin superconducting wire

We give the exact analytic expression for the semiclassical rate of phase slips in a thin superconducting wire, thereby correcting earlier published results.     

Solenoids of composite conductor simulate ac losses in flexible superconducting cable

The complex current distribution on the individual strands of a flexible superconducting cable influences the ac loss. Hence reliable loss predictions cannot be made from previous measurements. It is shown that the required current patterns and losses can be simulated by winding the conductor into single or double layer solenoids. Both total and localized losses can be measured with suitably arranged voltage probes. Measurements have been made on five different strip conductors wound into single layer solenoids to simulate losses on the inner conductor of a flexible cable. Measurements on niobium clad copper composite conductor showed that edge losses contributed more to the total loss than had been predicted theoretically for an idealized case. Despite this the total losses averaged only 15 mW m^?2 at 40 A mm^?1 rms, at 4.2 K. Measurements were also made on a $\text{Nb}\text{Nb-25\%}$$\text{Zr}\text{Cu}$ conductor, developed to carry fault currents in the NbZr and fabricated by soldering together Nb clad NbZr and Nb clad Cu composites. At fields below about 100 A mm^?1 rms, currents were carried by the niobium surface layer and at higher fields flux penetrated into the NbZr underlayer. Thus losses were acceptably low over the entire field range.     

Superconducting materials in oscillating and rotating magnetic fields

The methods of measurement of the oscillating field threshold amplitude, ΔB_ϱ, are reviewed. As this quantity increases, an effective resistance occurs. The dependence of ΔB_ϱ upon current and frequency for monofilament and multifilament conductors is studied. A theoretical approach is suggested and similar effects are also shown to exist in rotating magnetic fields.     

Dynamics of vortices in current-carrying superconducting films

We study analytically and numerically the dynamics of vortices in current-carrying quasi-two dimensional superconducting films using the generalized time-dependent Ginzburg-Landau equations. The values of the mobility are determined analytically in the thin-film limit. The results are in quantitative agreement with numerical simulations.     

Losses in superconducting cables in pulsed magnetic fields

Measurements have been carried out of superconducting cables of different types in pulsed magnetic fields. Three types of samples have been made from multifilamentary Nb_0.5  Ti_0.5 superconductors: one, a cluster of isolated wires; two, a double-layer twisted flat cable; and three, one-layer twisted tube samples. Dependences have been studied of ac losses on the amplitude, direction and change velocity of the magnetic field as well as on the diameter of filaments and twist pitch. It is shown that the ac losses in unsoldered samples are close to those in the cluster of isolated wires.     

The temperature and magnetic field dependence of superconducting critical current densities of multifilamentary Nb3Sn and NbTi composite wires

Commercial NbTi and Nb3Sn multifilamentary superconducting wire is becoming increasing important for use in research and commercial magnet systems. In both materials the temperature dependence of Jcplays a major role in the determination of magnet system operating parameters and design stability margins. We report here critical current density measurements as a function of temperature from 4.2 to 19 K and of applied magnetic field upto 8 T for multifilamentary Nb3Sn wire and for 2 alloys of NbTi superconducting wire. From this data [partial J_{c}(H_{a})/partialT] and[partialH_{c2}/partialT]T=T_{c}can be obtained and stability criteria and other superconducting parameters of the wires may be extracted.     

Asymptotic study of transverse conductivity in superconducting multifilamentary composites

This paper deals with superconducting multifilamentary composites with periodic structure in the presence of a weak electromagnetic field. We study the magnetic induction and establish an approximation result when the period is small (in the framework of homogenization theory). Then we determine some physical constants of an “equivalent” homogeneous conductor, and thus transverse conductivity can be obtained. For various proportions of superconductor, we compute both the values of transverse conductivity proposed by different physicists and the mathematical value obtained in this paper (we use finite elements and an overrelaxation method); we compare them between themselves and with recent experimental results; we note that our results are in very good agreement with Carr's formula and with the experimental measures of Davoust.