Hysteretic Losses Research Articles

Computational comparison of magnetization losses in HTS solenoids wound of tape conductors having different aspect ratios

In this paper a computational model for magnetization losses in HTS magnets is presented. The model is based on a semianalytical expression derived for the hysteretic energy loss density per cycle in HTS tapes due to changing external magnetic field. The real magnetic field dependent electric field-current density characteristic of HTS material, the geometry of the tape cross-section and the orientation of magnetic field are taken into account. Using the model the dependence of hysteresis losses on the orientation and amplitude of external magnetic field are studied. Furthermore, the model is applied to five solenoidal HTS coils which are wound of tape conductors having different aspect ratios. Special attention is paid to the differences in energy loss distributions between coils. The results show that in the coils wound of tape having aspect ratio higher than 3 the loss maxima are mainly caused by the radial component of magnetic field. Averaged losses in the magnet are investigated as a function of ramping frequency and the peak value of the operation current of coils.

Reconstruction of critical current density profiles from AC loss measurements

A method of reconstruction of critical current profiles from measurements of a hysteretic AC loss is proposed. As an example, we have applied this approach to study the degradation in the bulk melt-textured HTS sample with a resonance oscillations technique developed earlier for granular HTS samples and now modified to study HTS bulks. The critical current density profile was determined after the degradation in the thin undersurface layer of about 60 μm.

Frequency dependence of AC loss in Bi(2223)Ag-sheathed tapes

The AC self-field loss in Bi(2223)Ag-sheathed tapes with different number of filaments has been measured between 59 and 2500 Hz by means of a dual lock-in amplifier. Due to the wide frequency range of the measurements, we have been able to dissociate quantitatively the different self-field loss contributions: hysteretic, eddy current and resistive loss (near I c). This is an important advantage compared to single frequency measurements where such loss dissociation is only qualitative. The hysteresis losses of the different tapes fall between Norris' predictions for elliptical and strip cross-section. The relative weight of eddy current loss is found to be inversely proportional to the current ratio—the higher the i, the less is their contribution. Frequency-independent resistive loss due to flux-creep is observed for high currents at low frequencies; this loss becomes quickly negligible with the increasing frequency.

Experimental study on AC losses in Ag sheathed PbBi2223 tapes with twist filaments

Experimental measurements of AC losses were carried out on Ag sheathed PbBi2223 tapes with twisted and untwisted filaments. Losses were measured at 77 K as function of frequency and magnetic field parallel and perpendicular to the tape surface, using appropriate pick-up loops. Both the first and third harmonics of the signal were measured, in order to distinguish between the hysteresis loss and other types of loss. The effect of filaments uncoupling by twisting was clearly identified. For a tape with a twist pitch of 10 mm and I c=40 A (∼20 kA cm −2) operating at 43 Hz, the filaments are uncoupled in fields less than 40 mT, which is greater than the full penetration field for both the filaments and the tape. Hence, a reduction in the hysteretic loss of the superconducting core is realised at power frequency between 10 and 40 mT. Results form the self-field loss measurement implies the uncoupling of twisted filaments at relative low transport current ( I<0.5 I c)

Manifestations of damage to a silver–gold alloy sheathed Bi-2223 tape through the AC losses and V–I characteristics

AC losses are measured using the null calorimetric method on a silver–gold sheathed Bi-2223 tape. The dependencies on current and on frequency give the usual results, showing the predominance of hysteretic losses. After damaging the tape, the same measurements are repeated. Loss variations with current still follow a power law but with an increased coefficient. Furthermore, the loss now depends on the square root of the frequency. This result is attributed to the presence of cracks in the superconducting core. Some of them reduce locally the cross-section at a point where the transport current is shared nearly equally between the few remaining superconducting grains, and the silver–gold alloy. This explanation is supported by a micrograph of the peeled tape, which shows a thin layer of superconducting material adhering to the silver–gold alloy, even where large cracks are present. The comparison of critical current distributions, extracted from V–I characteristics of the tape before and after the damage, shows a broadening of the good condition peaks. Also a sharp peak at very low current appears and is attributed to a huge fracture in the core.

Contactless measurement of hysteretic transport AC losses in multifilamentary BiSrCaCuO-2223/Ag tapes

We demonstrate how the hysteretic transport AC losses in multifilamentary superconducting tapes can be determined in contactless way using a pick-up coil attached to the tape wide face. To transform the pick-up coil signal into the true loss signal, certain assumptions about the distribution of current in the tape section must be adopted. We show that the simple assumption of uniformly distributed current density gives results that are correct within 25%. A more complex model based on distribution of remanent currents brought the agreement between contactless and direct measurement to within 10%. Since the coil signal is directly proportional to the number of turns, the method provides increased sensitivity compared to that with voltage contacts. This can be helpful when investigating tapes with extremely low AC losses. Finally, we discuss how the comparison of direct and contactless methods can give information about filament nonuniformity.

Hysteretic energy losses in media described by vector Preisach model

Hysteretic energy losses which occur for arbitrary, not only cyclic, variations of the magnetic field are the subject of this paper. These losses are derived for the media which can be described by the vector Preisach model of hysteresis. An algorithm for computation of the losses is obtained based on the state diagram technique.

Nonequilibrium phase transition in the kinetic Ising model: Is the transition point the maximum lossy point?

The nonequilibrium dynamic phase transition, in the kinetic Ising model in presence of an oscillating magnetic field, has been studied both by Monte Carlo simulation (in two dimensions) and by solving the mean-field dynamical equation of motion for the average magnetization. The temperature variations of hysteretic loss (loop area) and the dynamic correlation have been studied near the transition point. The transition point has been identified as the minimum-correlation point. The hysteretic loss becomes maximum above the transition point. An analytical formulation has been developed to analyze the simulation results. A general relationship among hysteresis loop area, dynamic order parameter, and dynamic correlation has also been developed.

Tl 2Ba 2CaCu 2O 8− x superconducting films deposited by aerosol and their hysteretic ac losses

ac susceptibility measurements have been performed on Tl 2Ba 2CaCu 2O 8− x superconducting films. The films were grown in two steps: first Ba–Ca–Cu–Ag–O precursor films have been prepared by spraying an aerosol on MgO substrates and the Tl was then subsequently introduced by diffusion into the precursor films. The most favourable preparation conditions have been determined by comparing the structural and magnetic properties of the films. A detailed study of the ac susceptibility shows that the ac losses are due to intragrain bulk hysteretic pinning eventhough small geometrical barriers contributions could also be observed.

Magnetization curves and hysteretic losses in superconducting films with edge barrier

The influence of both bulk and edge pinning on the response of a thin-film superconductor to an oscillating magnetic field is considered. The magnetic-flux-defreezing field and the flux-exit field are defined. The hysteresis and magnetization curves of a sample are constructed for the entire cycle of the magnetic field. From this, we obtain the dependence of the hysteresis losses on the field amplitude.

Grain boundary contribution to the a.c. field behaviour of doped YBCO ceramics

The volume of the grain boundaries is a small percentage of the total volume of a polycrystalline superconducting material, but their contribution to the superconductor's properties is paramount. The present work analyses the influence of the variation of the relative fraction of the grain boundary volume, as well as the presence of alkaline additives (K and Rb) and CuO, on the hysteretic losses, the ability to screen low-frequency a.c. fields, the critical current density and the superconducting transition temperature. The data obtained are indicative of a strong dependence on the type of dopant accumulated on the grain boundaries and on the degree of recrystallization of the HTS. The influence of the internal grain pore boundaries caused by the intensification of the recrystallization process is discussed.

Experimental test of theories describing the magnetic ac susceptibility of differently shaped superconducting films: Rectangles, squares, disks, and rings patterned fromYBa2Cu3O7−δfilms

The magnetic ac response of rectangles, squares, disks, and rings patterned from ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ films (typical thickness 200 nm) was determined as a function of temperature for the case of the exciting external magnetic ac field being directed perpendicular to the film plane. For this geometry strong demagnetizing effects are expected and corresponding theories describing the resulting real $({\ensuremath{\chi}}^{\ensuremath{'}})$ and imaginary $({\ensuremath{\chi}}^{\ensuremath{''}})$ parts of the magnetic susceptibility $\ensuremath{\chi}$ on the basis of critical state models have only recently been developed. Plotting ${\ensuremath{\chi}}^{\ensuremath{''}}$ versus ${\ensuremath{\chi}}^{\ensuremath{'}}$ turns out to be useful in order to test these theories with respect to different sample shapes without invoking a specific temperature dependence of the critical current density ${J}_{c}(T)$. In this way, the following results were found. The shape dependent differences of the susceptibility are only small (of the order of %) with the smallest difference between squares and disks as predicted by theory. The recent theories yield an improved description of the experimental $\ensuremath{\chi}$ data as compared to a conventional Bean model neglecting demagnetization effects. At temperatures just below the superconducting transition, however, these theories based on purely hysteretic losses fail to be quantitative. A systematic change of symmetry of the ${\ensuremath{\chi}}^{\ensuremath{''}}$ versus ${\ensuremath{\chi}}^{\ensuremath{'}}$ curves is observed if rings of decreasing widths are patterned from a disk. For a diameter to width ratio $D/wg20$ the experimental susceptibilities, including the temperature dependence of the third harmonic, approach the behavior as calculated for an ideal thin narrow ring. This result allows a quantitative determination of ${J}_{c}(T)$ on such rings as is demonstrated by additional dc magnetization measurements using a SQUID magnetometer.

Hysteretic and ac dynamic losses of high T/sub c/ superconductors by numerical solution of the nonlinear magnetic diffusion equation

The complex ac susceptibility (/spl chi/) of high T/sub c/ superconducting materials has been described in terms of hysteretic and dynamic losses. By including both flux creep and flux flow resistivities in the expression of the flux flow resistivities in the expression of the flux diffusivity, induction profiles have been numerically calculated from the nonlinear flux diffusion equation. The imaginary part of /spl chi/ has been evaluated as function of temperature, frequency and amplitude of the applied magnetic field. The role of pinning and dynamic losses occuring in high T/sub c/ materials is discussed.

Analysis of optically and magnetically determined bridging in internal-tin process Nb/sub 3/Sn strands

An existing model for bridging induced magnetization and hysteretic loss has been extended to take into account the inhomogeneous morphology of metallurgical bridges. After an appropriate way of calculating the magnetization of a strand with a distribution of filament-bunch sizes had been devised some reasonable conformity between the results of optical image analysis and magnetization measurement was obtained. The previously developed anisotropic continuum model of bridging in multifilamentary (MF) strands led to a description of bridging intensity in terms of a dimensionless parameter /spl gamma//sub 2/ representing the area-fraction of bridged matrix material perpendicular to the filamentary axis. Based on measurements of variously heat treated (HT) internal-Sn ITER strands /spl gamma//sub 2/ was found to have values of 0.2 to 0.7%. At the same time saturation values of the length- and twist-pitch dependent magnetizations of the bridged samples were 3-6 times greater than the estimated un-bridged values. Some attention is also given to the influence of HT time and ramp-rate on the extent of bridging.

Magnetic processes in hysteresis motors equipped with melt-textured YBCO

Several hysteresis motors have been constructed with an output power up to 500 W at T=77 K. The rotors of these machines consist of melt-textured YBCO. In this work, the authors present detailed investigations on the magnetic processes in these rotors. Spheres were cut from melt-textured YBCO and investigated by rotating in vector-VSM. From these measurements, torque moments on the sample, hysteretic losses and the slip between external field and the sample can be calculated. The same dependence of the output power on the magnetic field for the samples as for the constructed motors can be derived. Influences of the critical current density and the domain size can be separated by changing the temperature.

The influence of granularity on dissipation in high temperature superconductor

We have investigated AC losses in high temperature superconductors. Granular YBCO samples were prepared by the conventional solid state synthesis process. Individual grains are anisotropic and these polycrystalline samples have randomly oriented c axes. Intrinsic and hysteretic losses were investigated using a Quantum Design PPMS magnetometer. AC susceptibility was measured as a function of magnetic field, frequency and temperature and field history. Three types of temperature dependent loss peaks, T/sub p/'s, were observed. The three peak types (in /spl chi/") are attributed to intrinsic (London theory), intergranular Josephson junction, and intragranular pinning loss mechanisms, respectively. They are observed to change systematically as temperature and magnetic field varies. We suggest physical models for the H, T and /spl omega/ dependence of the loss peaks.

Bi-2223 multifilament tapes and multistrand conductors for HTS power transmission cables

For application in high-power transmission cables, multifilamentary 2223 BPSCCO/Ag tapes have been prepared using the powder-in-tube (PIT) process. Critical current densities at 77 K of 33 kA/cm/sup 2/ in short samples and 22 kA/cm/sup 2/ over 400 m have been achieved. Machine stranded flexible cable conductors have been made with a length up to 10.5 m. The electrical performance has been evaluated at 77 K both under DC and AC conditions, yielding a current capacity up to 1420 A and purely hysteretic AC losses. Tests of the mechanical stability under bending conditions and repeated thermal cycling showed no serious degradation of the electrical performance.

Rolling resistance of articular cartilage due to interstitial fluid flow.

A mechanism which may contribute to the frictional coefficient of diarthrodial joints is the rolling resistance due to hysteretic energy loss of viscoelastic cartilage resulting from interstitial fluid flow. The hypothesis of this study is that rolling resistance contributes significantly to the measured friction coefficient of articular cartilage. Due to the difficulty of testing this hypothesis experimentally, theoretical predictions of the rolling resistance are obtained using the solution for rolling contact of biphasic cylindrical cartilage layers [Ateshian and Wang]. Over a range of rolling velocities, tissue properties and dimensions, it is found that the coefficient of rolling resistance microR varies in magnitude from 10(-6) to 10(-2); thus, it is generally negligible in comparison with experimental measurements of the cartilage friction coefficient (10(-3)-10(-1)) except, possibly, when the tissue is arthritic. Hence, the hypothesis of this study is rejected on the basis of these results.

Global ac susceptibility of low pinning high-T c crystals near T c

We have studied the hysteretic loss and the shielding capability of Bi2Sr2CaCu2O8and YBa2Cu4O8 crystals as a function of ac field (μ 0 H ≤ 1mT), frequency, and temperature at small dc fields (μ0 H a < 1 mT) near the critical temperature T c . We show that the global ac field dependence of the susceptibility can be described in terms of a geometrical barrier model in agreement with local permeability results. At temperatures very near T c , however, we observe a crossover to diffusive behavior. The frequency dependence of the temperature of the dissipation maximum at finite dc fields shows a thermally activated behavior.

Hysteretic losses at a gap in a thin sheet of hard superconductor carrying alternating transport current

Hysteretic losses at a gap in a thin sheet of hard superconductor carrying an alternating transport current evaluated by W.T. Norris [J. Phys. D, Vol. 3 (1970) p. 489] are reconsidered. An error overestimating the loss level by several times was found. Correct expressions are given and checked by numerical calculations.