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.     

Hysteresis losses in fine filament internal-tin superconductors

Hysteresis losses were measured on a series of fine filament Nb₃Sn superconductors made by the internal-tin process. Hysteresis was measured as a function of filament diameter and interfilament separation using a vibrating sample magnetometer in transverse magnetic field. Losses were greater than expected from the critical state model that expresses loss as a function of filament diameter. Micrographs of the reacted wire cross-sections showed some interfilament bridging for all wires. This gave rise to effective filament diameters that were greater than actual diameters. The critical interfilament separation, above which the losses would be expected to follow the critical state model, was determined.     

AC losses in multilayer superconducting tapes

ac losses have been investigated experimentally as well as theoretically in tapes having on the surface several normal conducting and/or superconducting layers. The superconducting layers under investigation have been Nb₃Sn on a niobium substrate and Nb₃Ge on a stainless steel substrate. It has been proved that the layered structure of the tapes is well reflected by the stepwise character of the ac losses dependence on the amplitude of the surface magnetic field. The magnetic flux passing through a surperconducting layer or surface barrier into the inside of the tape enhances the losses in the passed barrier or layer.     

Hysteresis in the phase-slip state of superconducting filaments

Recently some papers on measurements of the I-V characteristics (where V is the time-averaged voltage) of superconducting indium microbridges ¹ as well as tin and zinc whiskers ^2,3 driven by a dc current into the phase-slip state have appeared. Special emphasis was placed on a discussion of the hysteresis, which is well-known in such experiments (see, e.g., Refs.1–18 in Kramer and Rangel ⁴ ). The hysteresis was compared with the predictions of the generalized time-dependent Ginzburg-Landau (GTDGL) equations for dirty superconductors in local equilibrium. ^4,5 Unfortunately these predictions represent the only results in this context derived ultimately in a rigorous fashion from the standard microscopic theory of superconductivity. Comparison was also made with a model by Kadin, Smith, and Skocpol (KSS), ^6,7 which gives a much smaller hysteresis. The authors of Ref. 1 found good agreement with the KSS model. The authors of Refs. 2 and 3 found a hysteresis which is larger than that of the KSS model, but still considerably smaller than predicted by GTDGL theory. They proposed a generalization of KSS which can be fitted to the data.     

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.     

Coupling losses of finite superconducting cables

The calculations of coupling losses in superconducting cables are generalized for ac fields with time variations comparable with, or even larger than, the time cosntant τ of the coupling currents. The losses are calculated as function of the frequency ω and the cable length. At small frequencies, the losses are a monotonically increasing function of the cabling length, whereas for larger frequencies the losses reach a maximum at lengths about l₀/(1 + ωτ) (l₀ is the cabling length) and then they decrease with further increase of the length. Moreover, for systems with larger values of V = $\text{2 π}{}^2\text{(R + D)}{}^2\text{l>}{}_0{}^2$ (R is radius of the strand, D is the distance between them) the oscillations dependent on the cable length are more pronounced. For a given cable length, three characteristic forms of the frequency dependence of losses are found.The results can be important when comparing the losses from measurements on finite samples with the expected losses in larger systems (eg magnets for fusion reactors, generators, etc.).     

Electrocalorimetric apparatus for measuring losses in superconducting samples

We describe the improved version of a rather sensitive electrocalorimetric apparatus, particularly suitable to loss measurements of superconducting samples in various complex situations, like in the case of simultaneously variable transport currents and external magnetic fields. The new apparatus allows one to carry out loss measurements with a quite reasonable accuracy (about 10%) in the extended range of about 0.2 to 25 mW. The power dissipation due to the losses of a sample is detected by monitoring the capacitance-time variation of a condenser built into the system, its initial liquid helium dielectric being progressively replaced by a gaseous one during the measurement. The measuring procedure has been considerably speeded up by use of an automatic LCR meter and a microcomputer driven X-Y recorder.     

Magnetic hysteresis and dissipative losses in superconducting films

An analysis is made of the response of thin-film superconductors to an oscillating magnetic field. The field strengths for defreezing and expulsion of the flux are determined. A hysteresis curve is plotted for the sample over the entire oscillation cycle of the magnetic field. The dissipative loss power is determined as a function of the amplitude of the alternating field. Pis’ma Zh. Tekh. Fiz. 23, 27–33 (June 12, 1997)     

Hysteresis losses in superconductors of round cross-section with collective interaction

The paper presents the results of an experimental study of hysteresis losses in a transverse magnetic field by samples that represent small coils made of round wire of Nb-Ti alloy. The experimental results turned out to be considerably different from the values computed by the methods described in the literature. A theoretical analysis has been conducted of the effect of the demagnetization factors of the conductor and the field, associated with magnetization of other turns of the winding, and used as the basis for obtaining sufficiently general closed-form types of dependence which make it possible to compute the losses with a high degree of accuracy     

Induced circumferential currents and losses in flexible superconducting cables

In most designs for flexible ac superconducting cables each phase is carried by a co-axial pair of conductor tubes formed from a single layer of helically laid conductor strands. It is shown that the cable current would generate a net axial magnetic flux and hence an alternating circumferential electric field outside each co-axial pair. If, as in some cable designs, each conductor pair is to be contained in its own helium pipe, circumferential currents will be induced in the pipe wall. The losses depend on the pipe material but are typically three orders of magnitude too large. One solution is to line the pipe with superconductor, such as lead, but this could require more niobium in the conductor itself. Alternatively the co-axial pair could be redesigned so that there is no net axial flux. One possibility is to form conductor tubes from two layers of conductor strands laid in helices of opposite sense.The induced current problem is avoided if all three phase conductors are contained in a common helium pipe, provided that there are no zero sequence components to the phase currents. Losses from any zero sequence component could be readily reduced to an acceptable level, for example by laying a ferromagnetic strip alongside the conductors inside the helium pipe.Since circulating currents will also be induced in the electrostatic screens adjacent to the conductor strands the screens must be of semiconducting rather than metallic, tape.     

Iron losses calculation in non-oriented steel plate

This paper describes a method of calculating the iron losses from few macroscopic experiments, for non-oriented steel plate with sinusoidal magnetisation, taking into account saturation and hysteresis. With macroscopic considerations, iron losses are calculated using Poynting vector and Maxwell's equations, and can be separated into two components: hysteresis and eddy current losses. These losses are studied by resolution of the non-linear system equation associated to hysteresis simulation by the Preisach model. Calculations are applied to non-oriented Fe-Si steel plates and compared with experimental results obtained on Epstein apparatus for a wide range of frequencies and flux densities.     

A model for calculating a.c. losses in multistage superconducting cables

Superconducting magnets in tokamaks for fusion experiments are subjected to fast variations in magnetic field. As the high current conductors used in these magnets are made of multistage cables, these variations induce interstrand coupling currents that create losses. These losses are usually characterized by the so-called time constant of the conductor. A model is given to calculate this time constant. Working formulas are also proposed to calculate the current induced in the different cabling stages. This model takes into account the strand characteristics and the detailed cabling pattern. Using it, a method is also given to deduce the time constant from resistive measurements. The influence of the resistive barrier (chrome plating, CuNi shell, outer bronze matrix) is pointed out. Finally, this model is applied to a conductor that is foreseen for the toroidal coils of the International Thermonuclear Experimental Reactor (ITER).     

Dielectric losses in a polyethylene insulated superconducting cable between 4 and 22 K

The dielectric losses in a 5 m length of a superconducting cable, insulated with lapped polyethylene tape, have been determined between 4.3 K and 22 K with an inductively coupled ratio arms bridge which gave a resolution in tan δ of about 10^?6. The cable sample was built to a specification appropriate for power transmission at 132 kV and 6 kA; it was impregnated with helium at 0.4 MPa and cooled by a flow of cold helium circulated from a refrigerator.In the temperature range 4 to 5 K, applicable to a cable with niobium conductors, the dielectric loss increased slightly with electric field, and the observed tan δ (relative to tan δ of the reference capacitor) was 20 × 10^?6 at the maximum test stress of 7 MV m^?1. It is thought that a significant part of this loss can be attributed to the bedding layers and electrostatic screens between the dielectric and conductors.Tan δ showed a minimum at 18 K, which is encouraging for future developments of superconducting cables which might use hydrogen as a coolant and dielectric impregnant. The observed variation of tan δ with temperature is consistent with the existence of a low temperature relaxation mechanism with low activation energy.     

Temperature dependence of transport losses in multicored high-temperature superconducting composites

Measurements were made of the ac transport losses at temperatures T≥77K in silver-sheathed (Bi, Pb)₂Sr₂Ca₂Cu₃O_x composites with N=19, 61, and 127 filaments. It was observed that an increase in temperature causes an increase in the transport losses which depend on the amplitude of the working transport current. It is shown that the increase in the transport losses results from a reduction in the critical current of the composites. Pis’ma Zh. Tekh. Fiz. 25, 83–87 (June 12, 1999)     

Magnetic field dependence of ac losses in multi-filamentary superconducting wires

The magnetic field dependence of ac losses due to nonlinear flux penetration into superconducting filaments, ie, nonlinearity between an applied magnetic field and a penetrated flux, has been studied experimentally for multi-filamentary superconducting wires with Nb-Tl filaments and Cu matrix. In order to observe this effect, ac loss measurements were extensively carried out for the cases of applied transverse ac magnetic fields ranging from 0.06 to 50 Hz in frequency and from 10^?3 to 0.2 T in amplitude. Shifting of the frequency corresponding to the peak of the eddy current loss with the amplitude of applied magnetic fields was revealed experimentally. The results obtained were explained by taking into account the magnetic field dependence of the effective permeability of the wire originated from nonlinear flux penetration into superconducting filaments. The associated frequency dependence of the hysteresis loss is also discussed.     

AC losses in tubular superconducting composites with anisotropic surface structure

AC losses have been measured in prototype tubular composite conductors of a design proposed for superconducting ac power transmission lines. The conductors were of 15 and 19 mm diameter, with a niobium surface layer bonded to a copper substrate either directly or via an intermediate layer of niobium-titanium alloy. At a surface current density appropriate for the working conditions of a power transmission line (40 A mm^?1) the losses measured for current flow in the axial or circumferential directions differed by up to an order of magnitude, depending on details of the surface anisotropy of each sample.For purely topological anisotropy, manifest in practice as longitudinal corrugations, circumferential currents gave the lower losses. For largely compositional anisotropy, such as longitudinal welds or strips of degraded surface material, circumferential currents gave the greater losses. These results have been interpreted in terms of the surface current distribution in each case.     

Hysteresis losses of multifilament superconductors in superimposed dc and ac magnetic fields

Theoretical investigations, magnetization and calorimetric ac loss measurements have been performed on the problem, how the superposition of dc- and ac-magnetic fields influences the hysteresis losses of filamentary superconductors. For a given ac-field amplitude the maximum loss value as a function of the dc field can easily be predicted without knowledge of the superconducting properties.     

Hysteresis of critical currents of superconducting bridges in low perpendicular magnetic fields

Hysteresis of critcal currentsI _c of superconducting bridges with In, Nb, and NbN has been studied in low perpendicular magnetic fields. Influences of bridge geometry, small field sweep, trapped flux, and bombardment of argon ions on the hysteresis were made clear. The experimental results suggest that the edge pinning and trapped flux in the bank of bridges are associated with the hysteresis. The peak value ofI _c of NbN bridges, as well as granular Al and In bridges reported before, in decreasing fields agrees with the calculated pair-breaking current. The origin of the hysteresis is discussed.     

Modified boil-off method for measuring a.c. losses of superconducting composites

In this report the boil-off method for measuring a.c. loss in superconductors is developed, making it possible to conduct experimental measurements regardless of thermal equilibrium in the cryostat.