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.     

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.     

Experimental evidence for an interaction effect in the coupling losses of cabled superconductors

It is experimentally demonstrated on a series of one-stage superconducting cables, composed from multifilamentary superconducting wires, that the coupling current losses being induced in the wire and in the cable matrix, contain interaction loss terms directly proportional to the wire twist pitch I_w. This proves partly their theoretically expected l_c.l_w-dependence. Different twisting directions in a one or multistage superconducting cable increase the ac losses and should be avoided. The magnitude of the effect can become important.     

Hysteresis losses in a superconducting plate

On the basis of theoretical analysis expressions have been derived suitable for calculating the hysteresis losses in the presence of variable and constant components of both external magnetic field and transport current in a superconducting layer. The calculation scheme can be applied to any arbitrary shape of the field variation cycle, provided the variable components of the field and current are proportional. It has been assumed that the critical current density is dependent only on the external field. For the more common forms of this relationship the results have been expressed in an analytical form. Application of the results is illustrated by calculating the losses in a superconducting solenoid under variable current in the winding and the external field.     

AC losses of high-field superconductors

The Riemersma critical state model is applied to a long irreversible type-II superconductor carrying ac. Voltage waveforms, energy loss per cycle, and limiting values of effective resistivity are derived. For sinusoidal current of frequency f in 10-mil wire the critical current limit of resistivity is 4.06 × 10^-14f (ω.m). An equivalent circuit consisting of a variable inductance is proposed. Ex-perinlents at 4.2°K on bifilar windings of bare and copper-plated single-strand 10-mil nb-25Zr wire at 60, 400, and 800 Hz gave only fair agreement with the model with indications that the model can be improved by including surface hysteresis and eddy-current effects. Experimental values of resistivity agree more with Zar than with Wisseman, leading to the conclusion that continuous ac power applications of superconductivity are not attractive for the sake of efficiency. There remains some promise for dc energy storage for discharge into pulse power devices.     

A general treatment of losses in multifilamentary superconductors

Losses are calculated for a range of shapes of superconducting wire and cable. It is shown that the coupling losses can nearly always be expressed to a first approximation in terms of two parameters. One is the shape of the coil, the other (which contains most of the material parameters) is the time constant.The time constant is calculated for several cable types, including rectangular conductors, in which an exact solution for the field can be found at low frequencies. Maximum values for the loss are calculated and general conclusions for the design of cables are drawn.     

ac losses in cables of twisted multifilment superconductors

The losses due to coupling currents are calculated for a superconducting cable. The cable consists of multifilamentary superconducting wires which are twisted and surrounded by a material of different conductivity. It was found that if the wire twist pitch is different from the cable twist pitch, the losses diverge as 1/(1-f), where f is the volume fraction of wire in the cable. The time constant of the cable is increased by a similar factor. These large losses are caused by currents flowing between the wires of the cable and they can be minimized by choosing the correct ratio of cable pitch to wire pitch.     

60-Hz AC losses in Ag-doped high-temperature superconductors

60-Hz ac lossesP were measured at temperature 77 K for sintered powder (YBa₂Cu₃O₇)_1-x Ag _x samples as a function of applied magnetic fieldh. Rod-shaped samples were cut from pellets forx= 0 and 0.05. The losses were measured in a uniform ac magnetic fieldh applied parallel to the sample surface. Measurements were made in fields up toh= 1000 A/cm rms at temperature 4.2 K and up toh=600 A/cm rms at temperature 77 K. The results may indicate an increase of the intergranular current density and are discussed in relation to the grain size.     

Longitudinal dielectric function and collective surface oscillations in superconductors

The electrodynamic approach to the problem of collective oscillations in superconductors is considered. The kinetic equation for quasiparticles is used to find the longitudinal dielectric function ₁ (, k) of a pure superconductor at ( is the collision frequency). With the help of the evaluated ₁ (, k) the existence of collective oscillations localized near the boundary of the superconductor is investigated.     

Measuring a.c. losses of superconductors

A method is described to measure the a.c. losses of superconducting samples. The technique is similar to a thermal conductivity measurement. The sample is placed in a vacuum vessel and coupled to the helium bath by a thermal resistance. The stationary temperature increase of the sample in an a.c. field is a measure of the losses. Calibration is done with the pulse field off using an ohmic heater connected to the sample. There is no need for calibrated temperature sensors. Some results for the Euratom LCT conductor are included in this Paper.     

Electromagnetic interaction of quasiparticles in superconductors

We discuss the effect of superconductive Zitterbewegung on the electromagnetic interaction of quasiparticles in superconductors. We show that Zitterbewegung is responsible for the appearance, in the interaction Hamiltonian, of Darwin-like terms proportional to the divergence of the electric field strength. The appearance of these terms reflects the fact that in its interaction with the electromagnetic field the quasiparticle feels the averaged effect of the field over distances of the order of the Pippard coherence length 10^–4 cm.     

Influence of adiabatic conditions on the losses in composite superconductors

The losses in composite multifilamentary superconductors during a pulse of a transverse magnetic field under adiabatic conditions have been studied. A considerable difference in value and character of the loss dependences under adiabatic conditions, as compared to those under isothermal conditions, was found. The influence of various factors and conductor parameters on the losses was investigated.     

An apparatus for the measurement of ac losses in superconductors

An apparatus is described which can measure continuous alternating current losses on superconductor samples, or other heat loads, by the calorimetric helium boil-off technique over a range of 10 mW to 50 W. This apparatus has a modular design and is easily constructed from commercially available components. The construction and operation of this apparatus is described in detail and typical results presented.     

Scaling law for the ac losses of multifilament superconductors

It is experimentally and theoretically shown that the overall losses of a multifilament superconductor in an applied ac magnetic field can be described by a general scaling law. The losses depend only on a reduced frequency. This scaling law makes the prediction of the ac losses and the design of multifilament superconductors easier.     

ac Response and losses of differently pinned type-II superconductors

Measurements of the penetration of flux and losses in ac fields (20–2000 cps) at 4.2 K together with quasistatic magnetization curves on three samples of Ta ₉₂ Nb ₈ having different degrees of pinning are presented. The results are explained in terms of surface shielding currents taking into account both the pinning strength and the flux-flow resistivity exhibited by the bulk. A quantitative approach is used in which the concept of flux-flow resistivity proves applicable when the sample is subjected to an ac magnetic field.     

Experimental investigation of a.c. losses in cabled superconductors

A.c. losses in multifilamentary composite superconducting strands and cables have been measured in adiabatic conditions for transverse field sweep rates up to 50 T s⁻¹. Measurements were performed on NbTi and Nb₃Sn conductors of several configurations and surface preparations: single strands, soldered strands and cables of varying degrees of compaction composed of bare strands, strands with CuNi barriers and strands with chrome plating. The experimental data agree well with existing loss models. Loss data are characterized in terms of effective coupling current time constants. It has been determined that chrome plating on strands can reduce the coupling loss in highly compacted cables to as little as 20% of the coupling loss in similar cables composed of bare strands. In loosely compacted cables (down to ≈ 50% void) the strand-to-strand coupling loss was less than the filament coupling loss. As compaction is increased below 50% void the strand coupling quickly increases and becomes the dominant loss mechanism. The data suggest that the total cable loss grows as ≈ 1/(void)³ below void fractions of 40%. This observed cable loss dependence on void fraction does not agree well with a previously proposed model.     

Electric field induced by collective vortex creep in superconductors with fractal clusters of normal phase

The influence of the collective creep of magnetic flux on the electric field induced in a superconducting composite with fractal cluster structure is considered. Current–voltage (I–V) characteristics of these superconductors are determined with allowance for the influence of the fractal dimensionality of boundaries of the normal phase clusters and the height of pinning barriers on the nonlinearity of I–V characteristics at small transport currents. A relationship is established between the collective pinning and vortex glass state that is formed in superconductors with a fractal cluster structure. It is shown that the intensity of an electric field induced in the case of collective creep is smaller than that for Anderson–Kim creep.     

Hysteresis of the current-voltage characteristics and electric field effects in bulk YBCO superconductors

Some YBCO ceramics have been found to exhibit hysteresis of the current/voltage, I/V, characteristics, which reveals at a certain current I_f greater than critical current I_c a transition with switch from one branch of the I/V curve to another. In present work, the influence of an electric field at 77 K on hysteresis of I/V curves of ceramic YBCO/Ag and YBCO after hydrogen treatment has been studied. It was established that in strong electric field (120 MV/m) the conductivity increases at current I>I_c, the field effect being observed only in the upper branch of hysteresis loop. The electric field effect in YBCO after hydrogen treatment is reversible. The observed effects are assumed to be associated with a change of grain boundary weak links from S/I/S-to S/N/S-type in the course of hydrogen treatment or addition of silver into ceramics.     

Phenomenological theory of collective modes and relaxation effects in type II superconductors

The general phenomenological dispersion law for type II superconductors is presented. In addition to thermal conduction, charge fluctuation decay, and contact potential modes, it is shown that there in general exists a high-frequency propagating mode determined by the low-frequency resistance at super-normal junctions. This may be the mode observed by Carlson and Goldman.Supported in part by the NSF.     

Dielectric response functions in the problem of longitudinal collective mode excitation in superconductors

General methods of the electrodynamics of media with spatial and frequency dispersion are used to develop a formalism for the dielectric functions of the response of a superconducting metal to electromagnetic perturbations. The transformation of electromagnetic waves into long-wave oscillations of the longitudinal field in a superconductor is investigated. The temperature and frequency dependences of the collective mode contribution to the superconductor surface impedance are found. Resonant excitation of a collective mode in superconducting samples of finite size is predicted, which may result in selective transparency of superconducting films.