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.     

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.     

An analytical benchmark for the calculation of current distribution in superconducting cables

The validation of numerical codes for the calculation of current distribution and AC losses in superconducting cables versus experimental results is essential, but could be affected by approximations in the electromagnetic model or incertitude in the evaluation of the model parameters. A preliminary validation of the codes by means of a comparison with analytical results can therefore be very useful, in order to distinguish among different error sources. We provide here a benchmark analytical solution for current distribution that applies to the case of a cable described using a distributed parameters electrical circuit model. The analytical solution of current distribution is valid for cables made of a generic number of strands, subjected to well defined symmetry and uniformity conditions in the electrical parameters. The closed form solution for the general case is rather complex to implement, and in this paper we give the analytical solutions for different simplified situations. In particular we examine the influence of different boundary conditions, the effect of a localised resistance in the middle of the cable such as in case of quench and the effects of localized time dependent magnetic fluxes acting on the cable.     

Investigation on AC loss of a high temperature superconducting tri-axial cable depending on twist pitches

High temperature superconductor (HTS) cables have been intensively studied because they are more compact compared with conventional copper cables. Since it is strongly expected that the HTS cables replace conventional power lines, some HTS cables are designed, manufactured, installed in power grids and tested to demonstrate full time operation. Recently, a tri-axial cable composed of three concentric phases has been developed, because of its reduced amount of HTS tapes, small leakage field and low heat loss when compared with single phase and co-axial HTS cables. The layers inside the tri-axial cable are subject to azimuthal fields applied from inner layers and axial fields applied from outer layers with different phase from their transport currents. These out-of-phase magnetic fields should be calculated under the condition of the three phase-balanced distribution of the tri-axial cable, and thereby AC losses should be evaluated. In this paper, the AC loss in the tri-axial HTS cable consisting of one layer per phase is theoretically treated for simplicity. The AC losses in the cable are calculated as functions of the twist pitches of HTS tapes. It is found that the AC losses rapidly decrease with increasing twist pitch.     

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.     

Mechanical properties of hybrid composites using finite element method based micromechanics

A micromechanical analysis of the representative volume element of a unidirectional hybrid composite is performed using finite element method. The fibers are assumed to be circular and packed in a hexagonal array. The effects of volume fractions of the two different fibers used and also their relative locations within the unit cell are studied. Analytical results are obtained for all the elastic constants. Modified Halpin–Tsai equations are proposed for predicting the transverse and shear moduli of hybrid composites. Variability in mechanical properties due to different locations of the two fibers for the same volume fractions was studied. It is found that the variability in elastic constants and longitudinal strength properties was negligible. However, there was significant variability in the transverse strength properties. The results for hybrid composites are compared with single fiber composites.     

CUDI: A model for calculation of electrodynamic and thermal behaviour of superconducting Rutherford cables

CUDI is the extended Fortran code to calculate the electrodynamic and thermal behaviour of any type of Rutherford cable subject to global and/or local variations in field, transport current, and external heat release. The internal parameters of the cable can be freely varied along the length and across the width, such as contact resistances, critical current, cooling rates etc. In this way, all the typical non-uniformities occurring in a cable, e.g. broken filaments, strand welds, cable joints, and edge degradation can be simulated. Also the characteristics of the strands in the cable can be varied from strand to strand. Heat flows through the matrix, through the interstrand contacts, and to the helium are incorporated, as well as the self-field and self- and mutual inductances between the strands. The main features and structure of the program will be discussed.     

Electromagnetic behavior of lap-joints for fusion magnet system

The joint between superconducting Cable-In-Conduit-Conductors (CICC) is a key technology in a magnetic confinement fusion apparatus. Several hundreds of joints are involved in one apparatus generally. DC resistance of the lap-joint is typically designed less than several n-ohms and the allowable joule loss is several watts. AC loss due to external magnetic field is also limited to less than several watts. Reduction of the AC loss and low joint resistance are required simultaneously and those are conflicting trade-off.The lap-joint had been examined under both self-field and external-transverse-field experimentally. In this study, we established a numerical model for the joint and analyzed for electromagnetic behavior of it numerically. In the simulation, modeling of contact resistances between twisted strands is important. Circuit constants, e.g., conductance between strands, were determined to reproduce the experimental results; those are the circuit constants and the DC joint resistance. The relation between the joint resistance and the AC loss was discussed. Constitution of the joint does not only influence on the joint resistance and the AC loss but also current distribution in the cable. Non-uniform current distribution among the strands is reported to result in the degradation of the stability. We successfully simulated mentioned phenomena and found our numerical model was useful in joint design to find a good compromise.     

Electro-mechanical modeling of Nb3Sn CICC performance degradation due to strand bending and inter-filament current transfer

Performance degradation of Nb₃Sn cable-in-conduit conductors (CICCs) is a critical issue in large-scale magnet design such as the International Thermonuclear Experimental Reactor (ITER) and the series-connected hybrid (SCH) magnets currently under development at the National High Magnetic Field Laboratory (NHMFL). Not only the critical current is significantly lower than expectations but also the voltage-current characteristic is observed to have a much broader transition from a single strand to a CICC cable. The variation of conductor voltage-current characteristic as a result of cable electromagnetic, mechanical and thermal interactions is challenging to model. In this paper, we use a new numerical model, called the Florida electro-mechanical cable model (FEMCAM) benchmarked against 40 different conductor tests, to study the influence of bending strain and current non-uniformity on the critical current and n-value of Nb₃Sn strands and CICC cables. The new model combines thermal bending effects during cool-down, electromagnetic bending effects during magnet operation and current transfer in strands with filament fracture. The n-value of a strand under bending is derived from integration of filament critical current over strand cross-section for full and no current transfer. The cable n-value is obtained from the power law relation of cable electric field and critical current curve. By comparing numerical results with measurements of advanced Nb₃Sn strands and various CICC cables, we demonstrate that FEMCAM is self-consistent in modeling inter-filament current transfer. The new model predicts that I_c degradation of bent strands initially follows closely full current transfer but starts deviating and falls between full and no current transfer with an increasing bending strain. The results agree with recent TARSIS measurements for less than 1% bending strain mostly interested in practice. The strand n-value degradation from FEMCAM with no filament current transfer agrees better with measurements than that from full current transfer. Finally, FEMCAM simulated cable n-values are compared with various CICC measurements. The results imply that FEMCAM is a useful tool for the design of Nb₃Sn-based CICCs and both thermal bending and electromagnetic bending play important roles in CICC performance.     

Circuit analysis model for AC losses of superconducting YBCO cable

Information about AC losses and electromagnetic behaviour is essential when designing superconducting cables. In this work, AC losses of coaxial YBCO cables are determined using circuit analysis based computational model tailored for the needs of the YBCO cable design work. In the equivalent circuit superconducting layers are connected in parallel, the layers have an inductive coupling between each other and AC loss within a layer generates an effective resistance. The layer currents can be solved from a set of circuit equations. The computational model takes into account that the current in the cable creates magnetic field, which generates magnetisation loss and affects strongly the critical current of the YBCO tapes. The model was applied on several coaxial superconducting YBCO cable designs, which had nominal currents of 1-10 kA (rms). Low AC loss values were predicted for these compact YBCO cable designs. For example, AC losses less than 4 W/m were predicted for 10 kA cables.     

Analysis of electrical coupling parameters in superconducting cables

The analysis of current distribution and re-distribution in superconducting cables requires the knowledge of the electric coupling among strands, and in particular the interstrand resistance and inductance values. In practice both parameters can have wide variations in cables commonly used such as Rutherford cables for accelerators or Cable-in-Conduits for fusion and SMES magnets. In this paper we describe a model of a multi-stage twisted cable with arbitrary geometry that can be used to study the range of interstrand resistances and inductances that is associated with variations of geometry. These variations can be due to cabling or compaction effects. To describe the variations from the nominal geometry we have adopted a cable model that resembles to the physical process of cabling and compaction. The inductance calculation part of the model is validated by comparison to semi-analytical results, showing excellent accuracy and execution speed.     

JackPot: A novel model to study the influence of current non-uniformity and cabling patterns in cable-in-conduit conductors

JackPot is a new model that is used to analyse how and to what extend current non-uniformity among strands in a cable-in-conduit conductor (CICC) affects its performance. The joints at the extremities of the CICCs in coils and short samples introduce a non-uniform current distribution among the strands. A detailed and quantitative study down to strand level is required to explain the involved phenomena, to understand their implications on short sample and coil tests and to provide adequate solutions for improvements. The model can be used to evaluate the influence of the joint design and to define its baseline requirements for short-sample qualification testing, and for optimum magnet performance of for example the ITER coils.JackPot is an electrical network model that simulates the interaction between the superconducting strands in the cable (following their precise trajectories), the interstrand contact resistances, the conduit, and the cable’s connection to the joints. The backbone of JackPot is its cable geometry model, from which all relevant properties are derived. All parameters are derived from well defined experimental measurements on conductor sections and joints, except the axial strain for Nb₃Sn strands, which is the only free parameter in the model.The simulations demonstrate that the current non-uniformity is the source for a number of observed phenomena. Another conclusion is that completely filling the bottom joints and upper terminations of a short sample with solder, opposed to only (partly) soldering the cable surface, improves short-sample testing significantly for qualifying the ITER type CICCs. This paper describes the model and gives a few examples of applications for its validation.     

Comparison study of cable geometries and superconducting tape layouts for high-temperature superconductor cables

High-temperature superconductor (HTS) rare-earth-barium-copper-oxide (REBCO) tapes are very promising for use in high-current cables. The cable geometry and the layout of the superconducting tapes are directly related to the performance of the HTS cable. In this paper, we use numerical methods to perform a comparison study of multiple-stage twisted stacked-tape cable (TSTC) conductors to find better cable structures that can both improve the critical current and minimize the alternating current (AC) losses of the cable. The sub-cable geometry is designed to have a stair-step shape. Three superconducting tape layouts are chosen and their transport performance and AC losses are evaluated. The magnetic field and current density profiles of the cables are obtained. The results show that arrangement of the superconducting tapes from the interior towards the exterior of the cable based on their critical current values in descending order can enhance the cable’s transport capacity while significantly reducing the AC losses. These results imply that cable transport capacity improvements can be achieved by arranging the superconducting tapes in a manner consistent with the electromagnetic field distribution. Through comparison of the critical currents and AC losses of four types of HTS cables, we determine the best structural choice among these cables.     

Simulation of quench for the cable-in-conduit-conductor in HT-7U superconducting Tokamak magnets using porous medium model

A cable-in-conduit-conductor (CICC) consists of superconducting cable, copper, supercritical helium and conduit. To keep the operating temperature of superconducting cable lower than its current sharing temperature, the supercritical helium is forced flow through the CICC. The supercritical helium through the cable bundle has the complex directional changes due to the interaction between the supercritical helium and strands. The structure of CICC is characterized with the porous medium. The quench characteristics of CICC are analyzed by the model which the temperature difference between the strands and helium is assumed to be very small due to the heating induced flow to generate high heat transfer coefficient of supercritical helium. A moving mesh method is developed for the numerical solution of the problem with the steep drop for temperature and density of supercritical helium in the short front region of the normal zone. The computational mesh is obtained by equidistribution of a monitor function tailored for the functional variation of the arguments for density, temperature and velocity of supercritical helium. Existence and uniqueness of the discretised equations using a moving mesh are also established. The coupled equation for porous medium is solved using the finite element method with the artificial viscosity term. The validation of the code is tested by comparing it with the other codes with good accuracy. The converged properties of numerical solution due to quench in CICC are studied. We present preliminary estimates of the maximum conductor temperature rise and helium pressure during a quench in the inner layer of toroidal field (TF) magnet for HT-7U. The quench scenarios with different dump time constants of 6.25, 12, and 21.1 s are considered. The goal of such work is to guide the protection scheme and a detailed prediction of the quench evolution of magnet.     

The Colossal Piezoresistive Effect in Nickel Nanostrand Polymer Composites and a Quantum Tunneling Model

A novel nickel nanostrand-silicone composite material at an optimized 15 vol% filler concentration demonstrates a dramatic piezoresistive effect with a negative gauge factor (ratio of percent change in resistivity to strain). The composite volume resistivity decreases in excess of three orders of magnitude at a 60% strain. The piezoresistivity does decrease slightly as a function of cycles, but not significantly as a function of time. The material's resistivity is also temperature dependent, once again with a negative dependence.
The evidence indicates that nickel strands are physically separated by matrix material even at high volume fractions, and points to a charge transport mechanism that causes a large change in conductivity for a small relative change in the distance between filler particles. Combined with the temperature dependence data, this suggests that conduction in this composite material may be dominated by quantum tunneling effects. Based upon a statistical model of junction character distribution, a quantum tunneling percolation model is applied that accurately reflects the mechanical and thermal trends.     

Measurement of time constants for superconducting cables with Hall probes

The time constants of coupling losses have been evaluated for the composite-type aluminum stabilized superconducting cables used for the pool-cooled helical coils of the Large Helical Device (LHD). A new method using Hall probes was incorporated to measure the local field change generated by the screening currents in the conductors. During an exponential discharge of the external magnetic field, the current decay was found to be well fitted according to a simple magnetic diffusion equation with a geometrical shape factor. Measurements in the magnetic fields both perpendicular and parallel to the wide surface of the flat cable were performed. The shielding effect of the pure aluminum stabilizer was confirmed by removing it from the cable, which then revealed a longer time constant.     

Effect of electromagnetic force on the pressure drop and coupling loss of a cable-in-conduit conductor

In the central solenoid (CS) insert experiment performed with the International Thermonuclear Experimental Reactor CS model coil, significant changes in the pressure drop and coupling losses were observed during coil energization. This phenomenon was quantitatively analyzed from the viewpoint of the deformation of the cable shape in the CS insert conductor due to an electromagnetic force acting on the cable. A new calculation model was proposed to provide the relation between the electromagnetic force and hydraulic characteristics of the conductor. Calculation results indicated that there seemed to be a gap of 1.3 mm between the cable and jacket created by the electromagnetic force when the CS insert was operated at 40 kA and 10 T, which can cause the decrease of the pressure drop by 12% and also the decrease of the local void fraction of the cable from 36.3% to approximately 34%. The latter well explained the increase of coupling losses. A local void fraction of 34.5% is suggested from the calculation in order both to reduce the amount of deformation and to maintain the coupling losses at acceptable level for this type of large current-carrying conductor.     

Thermal conductivity of nanocomposites with high volume fractions of particles

The model proposed by Ordonez-Miranda et al. [Appl Phys Lett 2001;98(233): 111], for the thermal conductivity of composites with low volume fractions of nanoparticles is extended for high volume fractions of spherical and cylindrical nanoparticles. In the dilute limit of macro/micro-sized particles, the obtained results agree with the ones previously reported. In contrast, when the radius of the particles is of the order of the mean free path of the energy carriers, it is shown that the dependence of the composite thermal conductivity on the collision cross-section per unit volume of the particles and the average distance that the energy carriers can travel inside the particles becomes stronger when the volume fractions of particles increases and is cancelled out for high enough interfacial thermal resistances. The predictions of the proposed analytical approach are in good agreement with reported experimental data and could be highly useful for guiding the design of particulate nanocomposites where the interactions among the particles and the interfacial scattering of the electrons and phonons need to be considered.     

A continuum theory of porous media saturated by multiple immiscible fluids: I. Linear poroelasticity

The mechanical behavior of porous media is largely governed by the interactions among coexisting components. These interactions occur through interfaces. In this paper, a continuum theory of multiphase porous media is developed that can be used to characterize the interactions among various components. Central to the theory is the implementation of the dynamic compatibility conditions microscopically representing the constraints on the pressure jumps across the interfaces. It is shown that capillary relaxation processes are thermodynamically associated with the changes in the volume fractions of fluids. A linear model is developed by a formal linearization of the proposed theory. For fully saturated conditions, the linearized theory reduces to the Biot's poroelasticity model. A procedure to evaluate the material constants is presented for the porous media with two fluids. The linear model is utilized to analyze the propagation of acoustic waves in an unsaturated rock. The theoretical results are compared with the experimental data available in the literature.     

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.