Hysteretic Losses Research Articles

Energy losses in mixed matrix superconducting wires under fast pulsed conditions

Energy losses have been measured on a set of mixed matrix (CuNi, Cu, NbTi) superconducting wires at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\dot{B}</tex> 's up to 1.5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sup> G/s. The losses have been measured as a function of wire diameter, twist pitch, maximum applied field, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\dot{B}</tex> . Both static and dynamic losses were measured for a field applied perpendicularly to the wire axis. The dynamic losses were measured by slowly applying an external field to a sample and then causing the field to decay exponentially in roughly 1 ms to 10 ms. Under low B (9 kG) and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\dot{B}</tex> (10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> G/s) conditions the hysteretic loss dominated. At high B (21 kG) and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\dot{B}</tex> (1.5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sup> G/s) the matrix losses became dominant. The systematic variation of the losses with the mentioned parameters will be presented and will be compared to theoretical predictions.

Ac losses and low-field superconducting behavior of Nb3Sn

Measurements have been made of the low-field ac and dc superconducting properties of thin films of electron-beam-evaporated Nb3Sn. Comparison of the 50-Hz hysteretic loss and flux entry waveforms with the measured field-dependent critical current indicates that a modification of the usual critical state model with a uniform surface barrier is necessary. A model based upon a nonuniform flux distribution, consistent with the observed morphology, is presented. Its success in describing the low-field properties of this sytem and its importance to related materials in which the superconducting properties are strongly dependent upon the microstructure are discussed.

Effect of Carbon Black on Hysteresis of Rubber Vulcanizates: Equivalence of Surface Area and Loading

Abstract We have developed an empirical correlation between the loss tangent (tan δ) and the product of the volume fraction (ϕ) of carbon black in the composite and the total filler-polymer interfacial area per unit volume of composite (ψ). This correlation was applied to vulcanizates based on SBR-1500, SBR-1712, and NR with various compounding procedures and under different deformation conditions, including forced vibration nonresonant dynamic test machines, and the Goodyear-Healey pendulum rebound. The functional form of the correlation was qualitatively similar in all instances ; however, quantitative aspects of the correlation are dependent upon the particular experimental conditions. Tan δ is a weak function of the deformation amplitude over the region of practical interest. This is in contrast to hysteretic energy loss, which is proportional to the square of the amplitude. The validity of the correlation over wide ranges of amplitude, temperature, and frequency indicates that the viscoelastic relaxation or loss processes are similar over the range of conditions studied. Since the combined parameter, ϕψ, is proportional to ϕ2 multiplied by the specific surface area of the carbon black, this relation implies an equivalence between surface area and loading, with regard to tan 5. It has previously been shown that the elastic modulus depends on structure and loading. Thus, the dynamic properties, including hysteresis under various conditions, can be predicted from the carbon black properties, and compounds can be designed for desired dynamic properties by independent adjustment of loading, structure and surface area.

Measurement of low hysteretic losses in CVD prepared Nb 3Ge

Very low hysteretic losses have been measured in CVD prepared Nb 3Ge. An apparent correlation between second phase content and low losses has been found as well as a reduction in hysteretic loss by appropriate surface treatment.

Experimental hysteretic loss for a series of superconducting filamentary NbTi wires and a field dependent critical state model

Analytic expressions for hysteretic loss have been developed for half-cycle and full-cycle field sweeps for rod geometries for a critical state model with critical current inversely proportional to field. Bulk effects with surface-like character are discussed along with surface shielding fields and the demagnetizing factor. The loss expressions of various models are compared to experimental loss data made on a series of NbTi superconducting wires. Universal loss curves constructed from experimental loss curves by appropriate normalization are obtained and used to predict loss accurately. Bias field ripple losses are also reported.

Flux Penetration into a Wire of a Nonideal Type II Superconductor in a Transverse Magnetic Field

The quasi-static flux-distribution in a wire of a nonideal type II superconductor induced by a transverse magnetic field is discussed in terms of the critical-state model with the pinning force of the Bean-London type. The hysteretic loss per cycle caused by the variation of the transverse magnetic field is also calculated from the obtained expression on the flux distribution. In the present configuration, the flux motion is two-dimensional and the value of the hysteretic loss is appreciably larger than that caused by the cyclic variation of a longitudinal magnetic field, where the flux motion is one-dimensional.

The frequency dependence of a.c. losses in type II superconductors

Abstract Energy losses occurring under the application of an alternating magnetic field were examined in type II superconductors representative of three different classes of material: (1) single-crystal niobium (elemental) in the Meissner state, (2) molybdenum-25 at.% rhenium (alloy) in fields both below and well above H C1, and (3) Nb3Sn (compound) principally in the mixed state. Losses were measured as a function of field amplitude and frequency in order to determine whether losses of other than hysteretic variety were present. The total loss per unit surface area per cycle associated with the superconductor was found to have the form W T(h 0, v) = W 0(h 0) + vF(h 0) where W 0(h 0) is identified as an hysteretic term, v is the frequency and h 0 the a.c. field amplitude. Only in the Mo-25 at.% Re alloy did the hysteretic term completely mask the frequency-dependent term. Hysteretic losses in the single-crystal niobium and two Nb3Sn specimens prepared by different solid state diffusion methods were strong...

Reduction of losses at low frequencies and large amplitudes in NbTi ribbons

The critical current density in NbTi ribbons increases considerably and hysteretic (A.C.) losses decrease by an order of magnitude when a magnetic field is present along the length of the ribbon. In our work, rather than feeding a current to the sample through leads connected to an external supply, we cause persistent transport currents to flow along the length of the ribbon by induction (by applying a magnetic field transverse to the ribbon axis and along its broad faces). The magnitude of the induced currents, their pattern of circulation and the hysteretic losses are determined by monitoring the evolution of the magnetic moment of the ribbon both along its length and along the wide faces as the transverse field is cycled. We observe that when a longitudinal field is present, the induced currents adopt trajectories which are "tilted" and tend to lie along the total magnetic induction <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\overrightarrow{B}</tex> along the flat faces of the ribbon, hence tend towards force-free configurations where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\overrightarrow{j} \times \overrightarrow{B} = 0</tex> .

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 J c , the matrix-superconductor bond quality and the doping effects on the high field J c '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.

The effect of cladding material on ac losses of commercial Nb3Sn tapes

ac losses of commercial Nb3Sn tapes have been measured before and after removal of the normal metal cladding which is used to stabilize the superconductor. It is shown that materials which are frequently used to assist in bonding the normal metal to the Nb3Sn surface give rise to hysteretic losses which are much larger than those of the Nb3Sn itself in the low-field region of interest for power transmission, below 1000 Oe. Examples of such materials are superconductive Pb–Sn solders used in cladding tin-diffused tapes and ferromagnetic nickel flashes used in silver plating vapor-deposited tapes. These lossy materials are not essential and can be eliminated in tapes which are properly designed for power transmission. It is also shown that eddy current losses are acceptably small for normal metal cladding thickness of the order of 25 μm (ρ∼10−8 Ω cm).

Variations in Tire Hysteretic Losses Due to Tire Design

Abstract The technique of analyzing energy losses of tires that have reached a state of thermal equilibrium has been applied to cross-ply and radial-ply passenger car tires and cross-ply truck tires. The derived formulations relating the tire energy losses to the viscoelastic properties of the tire components show the dependence of these losses on tire size and construction. The analysis was carried out by systematically varying tire tread compounds and operating parameters. This investigation of the energy losses experienced by tires operating in a state of thermal equilibrium, has enabled the losses due to the various stress-strain deformations to be characterized. In particular, the losses due to the strain deformation have been correlated with two mechanisms, which are outlined. The results described enable a better understanding of the mechanisms responsible for tire energy losses and allow the tire losses to be predicted at the design stage.

Some superconducting properties of multifilamentary niobium carbonitride

Superconducting properties of multifilamentary 10-μ niobium carbonitride fibers have been investigated. Niobium carbonitride has Tc's to 18 K and Hc2's to 120 kOe. Critical current densities and their temperature dependence and the magnetic field dependence of the hysteretic loss have been determined from magnetization measurements. The fibers had Jc's in the range of 104 A/cm2 for fields less than 50 kOe at 4.2 K. No flux jumping was observed, indicating that the fibers were intrinsically stable without a stabilizing matrix. The field dependence of the hysteretic loss was ∝ H2.4 for partial penetration.

High-field (5 T) pulsed superconducting dipole magnet

The paper is an account of the design, construction and testing of a pulsed superconducting dipole magnet of novel design known as AC4. It represents a stage in the development of very-high-field magnets for possible use in a super-high-energy proton synchrotron. Though the magnet does not quite attain the necessary field homogeneity, the extensive tests reported here provide confidence and much relevant information for future designs using saturated iron. From electrical measurements of total losses for unidirectional and bidi rectional pulsing, an estimate can be made of the contribution from the iron yoke and shows that the hysteretic losses in the superconductor are about as expected.

Hysteretic Losses in Rolling Tires

Abstract A relationship between the observed energy losses for a tire that has reached a state of thermal equilibrium when operating at a constant speed, and the viscoelastic properties of the tire components has been formulated. The analysis was carried out by systematically varying tire components and operating parameters, using the Vibron Viscoelastometer and tire test wheel dynamometer. The investigation was carried out for 6.95–14 cross ply passenger tires. From the derived dependence of the tire energy losses on viscoelastic properties, the effect of changes in tire tread compound, ply rubber and tire cord on the tire energy losses can be predicted. This enables the design of a tire with the properties to meet desired service characteristics.

Magnetization of hysteretic superconductors for complete field penetration and a critical-state model with Jc(H)=α/H

A critical-state model with Jc(H)=α/H has been developed for cylindrical geometries. It qualitatively describes the shape of magnetization curves obtained on multifilamentary superconducting wire and it accurately predicts the hysteretic loss. The size dependence of the hysteretic loss for this model is essentially the same as the Bean-London model result. However the maximum magnetization for this model is proportional to R1/2. The temperature dependence of the hysteretic loss and α have been determined from magnetization data for NbTi wire.

A linear theory for soft ferromagnetic elastic solids

A general theory of magnetoelasticity is developed for soft ferromagnetic materials of multidomain structure, for which the hysteretic loss and exchange effect may be neglected. The general equations are linearized by assuming infinitesimal strains, linear constitutive equations, and that all magnetic variables (magnetic intensity, induction and magnetization) in the deformed body may be divided into two parts: a rigid body state and a perturbation state. The former are the same as those in the magnetostatics for a rigid body and the latter which are the added corrections due to deformations, are coupled with strains and stresses in a set of linear differential equations and boundary conditions. Two versions of the linear theory are given for materials with isotropic, cubic or uniaxial symmetry. One of them is applied to investigate the buckling of an elastic, isotropic plate in a transversally applied uniform magnetic field. The calculated results agree with previous observations.

Induced ac losses in an enhanced Meissner state

Induced ac losses and magnetization curves measured at 4·2 K, are reported for a reversible supersaturated solid solution of Pb-11% Sn, and for the same material after the precipitation of pinning centres. The results show lower hysteretic losses in the precipitated material for peak applied fields up to Hfp, as defined by slow-swept magnetization measurements, but more significantly the losses up to this field are lower than in pure lead.

A.C. Losses in Superconducting Synchrotron Magnets

A.C. Losses of composite conductors and synchrotron magnets are given. A new equation based on a skin-effect assumption, is presented, which shows, that the generally accepted self field calculations yield too high values. Results from loss equations are compared to a few tests an small solenoids. Losses in superconducting coils, when exposed to time varying magnetic fields have several origins: Eddy current losses in the conductor matrix, self field, hysteretic and auxiliary losses in the superconducting coils and composite conductors, hysteretic and eddy current losses in the iron return path and eddy current losses in the metallic support structure, reinforcements and containers. As all losses including heat conduction and radiation have to be removed by the coolant, the major effort will be to limit these losses to manageable low values. Losses in superconductors and composits have been treated by Bean, Hancox, Wilson et al. and many others. Due to discrepancies between theory and experimental data specifically losses due to transport current (self field), the theory of loss generation is reexamined by Ries and Brechna. This paper summarizes the results of new investigations.

AC face field losses in a type II superconductor

The eddy current distribution in a thin superconducting strip subjected to an ac field perpendicular to its surface is derived for a critical-state model with constant critical current. From this, an approximate expression is obtained for the hysteretic loss per cycle. An approximate expression is also given for a field-dependent critical current.

Magnetization Studies in Nb 3Sn and Ti–Nb Alloys

Magnetization measurements were performed on commercial Nb3Sn and Ti–Nb alloy samples to determine hysteretic loss (magnetization vs magnetic field) and flux-jump stability at 4.2°K in magnetic fields up to 9.3 Wb/m2. The aforementioned superconducting properties were also observed and recorded with various geometries, field sweep rates and thermal environments. The samples consisted of ribbons and/or wires ranging in size from 1.0 to 0.1 cm wide and 0.1 to 0.0001 cm thick. The transport currents ranged from a few amperes to greater than a thousand amperes. These data were obtained utilizing an experimental setup similar to that described by Fietz. The shape and magnitude of the magnetization curves with and without the presence of transport current was not a function of frequency in the range employed, 0.012 to 3.0 Wb/m2·min, except for the multifilament composites. The magnetization and flux-jump stability was found to be a function of the sample dimensions, as would be expected with the earlier expressions given by Wipf, Hancox, Chester, and Stekly. The transport current density was not a function of the dimensions. These data on magnetization and transport current effects are in accord with earlier work by LeBlanc and co-workers on Nb–Zr. There is a first principle derivation of the flux-pinning effects that uses a Josephson junction tunneling model and results in the Kim-Anderson expression. The internal field distribution could be characterized by Hint(x)=(Ha−Hs exp(−x/λ)+Hs, λ=(Hs−Ha)/Jc(Ha). The exponential expression for Jc(Ha) vs Ha of Fietz et al. fits the sample data; however, the Kim-Anderson expression that would be the first term in the expansion of the exponential would also fit the observed data within the experimental error. The data concerning transport current and magnetization can be accurately accounted for (in the infinite sheet configuration) by expressions derived by Yasukochi. The thin plate geometry, with the proper demagnetization factor, is in agreement as well.