A low loss NbTi multifilamentary composite conductor for A.C. use

Investigations of a.c. losses and stability of a mixed-matrix NbTi multifilamentary conductor are presented. Fine filament size of 1.0 μm and a tight twist of 5.5 times the wire diameter 0.2 mm result in a time constant of the eddy current of 0.024 msec at 1.0 T. If this conductor is used in superconducting armature windings of rotating machines or in a.c. magnets, generating a maximum field of 1.0 T, economical benefits are expected at operation frequencies below 20 Hz.     

Test results and analyses of conductor short samples for HT-7U

The experiments of Cable-in conduit conductor (CICC) short samples with high proportion of segregated copper strands have been carried out in SULTAN facility last September. These experiments aimed to investigate transient stability and AC losses of CICC conductor coated with different resistive barriers (Pb–30Sn–2Sb or Ni plating on strands) and to check the design of PF and TF CICC for HT-7U magnets. The resistive barriers’ influences on the stability and AC losses of CICC are evaluated. These experimental results are used for the choice of HT-7U TF and PF CICC design.     

An additional loss source in cabled multifilamentary superconductors

It is shown that irregularities in the twist rate of a multifilamentary superconducting strand, which may occur in the cabling or braiding process of a high current conductor, give rise to additional matrix currents and enhanced ac losses. Electrodynamic equations for matrix and filament currents in a strand with a sudden change in twist rate are derived and damped wave solutions are given for an external harmonic field as well as for a ramp field. Inder unfavourable conditions the associated loss enhancement may become comparable to the regular matrix losses. This is also verified experimentally by magnetization measurements. Some recommendations for cable design are given.     

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.     

NbTi superconductors with low ac loss: A review

Niobium titanium is still the superconductor of choice for magnets where the field changes rapidly with time. To keep the hysteretic ac losses within bounds, it must be finely subdivided. For practical handling and reliable performance in magnets, it is therefore made in the form of filamentary composite wires, with NbTi filaments embedded in a matrix of copper. Unfortunately, the copper matrix introduces eddy current coupling losses, which must be controlled by twisting and by resistive barriers. To date, the major applications have been in particle accelerators and fusion, where high operating currents are required. To achieve these high currents, the filamentary wires are made into cables. Eddy current coupling between wires within the cable can cause additional ac losses. Problems of non-uniform current distribution between the wires can prevent magnets from reaching their full current, particularly with the largest cables.     

A macroscopic model for coupling current losses in cables made of multistages of superconducting strands and its experimental validation

In a multistage cable the superconducting strands occupy the whole volume in a complex oscillatory pattern from the axis to the periphery. After considerations on the trajectories of the strands, it is shown that the cable can be organized in a multizone structure with time constants determined from the basic time constants of the various cabling stages. The effective volume fractions of the cable in which losses can be evaluated are also derived. The model is assessed by a fit of an experimental curve. In the case under consideration, the screening effects are relatively limited. Altogether, the cable is well characterized by very few parameters: a series of in sequence time constants associated to small fractions of volume. The model is then used to evaluate losses in various conditions of field variations.     

Dynamic Behavior of Torsional Eddy-Current Dampers: Sensitivity of the Design Parameters

Eddy-current devices are promising for the passive and semi-active control of vibrations. From the electromechanical point of view, their behavior is characterized by the torque-to-speed curve and the mechanical impedance. In this paper, we report an investigation of the electromechanical behavior of eddy-current dampers/couplers consisting of permanent magnets and a massive conductor. Our goal was to determine the influence of the main design parameters on the torque-to-speed characteristic and on the mechanical impedance. To this end, we studied the dependence of the electrical pole and static damping coefficient on the design parameters under a given current density distribution within the conductor. This approach is equivalent to the procedure used to characterize the inductance and the torque constant of a standard electrical machine and it allows us to show that the electrical pole is determined by the inductive and resistive nature of the conductive part. Even if the conductor is realized by a solid conductor, the approach allows us to determine its equivalent resistance and inductance as a function of the design parameters, such as the number of pole pairs and the thicknesses of the permanent magnets and the conductor. We validated the analytical expressions of the equivalent lumped parameters, of the electrical pole, and of the static damping coefficient by finite-element analysis. This analysis provides the guidelines to identify the project parameters that can be varied to optimize the performances of the device as a coupler, damper, or brake.     

Superconductor Stability Against Quench and Its Correlation with Current Propagation and Limiting

This paper presents a numerical (finite element) analysis of superconductor stability and current propagation under random variations of critical superconductor parameters. Instead of using singular (homogeneous) values, random variations potentially are appropriate to take into account any conductor inhomogeneity that can be considered as an obstacle to current propagation. Traditional assumptions like homogeneous current distribution, critical temperature, critical current density and critical magnetic fields are not justified in general; a local disturbance (for example, release of mechanical stress energy), if not immediately distributed by solid conduction, would generate a transient increase of local conductor temperature. Local critical current density and magnetic field then will be reduced, and current distribution will change. Disturbances may arise also from transport currents that locally exceed the critical current of the superconductor. Disturbances of all kinds may increase the conductor temperature above its critical value. A local analysis of all superconductor states thus is mandatory to safely avoid a quench. As an extension of standard stability models, also flux flow resistive states are taken into account. We will try to find a possibly existing correlation between current propagation and superconductor stability. Fault current limiting is discussed as a special case of current propagation. The analysis is applied to a bundle of high-temperature superconductor (HTSC) filaments. As will be shown, temperature profiles in a superconductor do not allow a clear distinction between Ohmic resistive or flux flow resistive fault current limiting. Though frequently made in the literature, this separation is highly questionable, because Ohmic resistive and flux flow resistive states may locally coexist, side by side, but are not very stable in the superconductor volume.     

The effect of interturn heat flow on the recovery currents of a superconducting magnet: A comparison of calculated and measured values

Cryostatic stabilization is appropriate for superconducting magnets producing steady fields over large volumes. The measured recovery currents for a 10 cm bore 6.4 T experimental solenoid are compared with values derived from a stability analysis which includes heat flow from the resistive region to adjacent conductors as well as to the helium coolant. Agreement is excellent despite some uncertainty in the helium heat transfer characteristic and in the thermal conductivity of the interturn insulation. Given good data for these it should be possible, using the method presented, to design cryostatically stabilized windings with precision just from basic data for the conductor and its intended environment.Details of the behaviour of large and small resistive regions in this solenoid are given. The critical currents are also accurately predicted from the performance of short samples of the conductor after taking account of anisotropy with respect to the direction of the ambient magnetic field.     

Optimization of conduction-cooled current leads with unsteady operating current

A generalized optimization method is presented for conduction-cooled or cryocooled current leads whose operating current may vary over a period of time. This study is part of our ongoing efforts to reduce the cooling load in HTS power applications, where the actual current level varies considerably over a day and over a year. The presented method is also applicable to superconducting magnets that are not always operational at full current. When the operating current is given as a function of time, the total or accumulated cooling load at the cold end is calculated by integrating the instantaneous load over the period. The optimal length-to-area ratio of conductor is determined to achieve a minimum in the total load. After an accurate procedure taking into full account the temperature-dependent properties of conductor is developed with numerical calculations, a simple and reasonably accurate method based on Wiedemann-Franz approximation is suggested for practical use.     

Analytical Computation of the Full Load Magnetic Losses in the Soft Magnetic Composite Stator of High-Speed Slotless Permanent Magnet Machines

This paper presents an analytical model for predicting the stator full load magnetic losses in high-speed slotless permanent-magnet machines with surface-mounted magnets on the rotor and a stator core made of isotropic and conductive soft magnetic composite material (SMC). The losses are derived from the computation of the two-dimensional magnetic field distribution created by the rotor magnets, the currents in the stator windings and the eddy currents that circulate in the SMC stator core, according to the time and space harmonics. Both eddy currents and hysteresis losses are computed. The model is cross-validated by 2-D FE analysis in terms of magnetic field distribution and eddy currents losses. 3-D FE simulations are also carried out to quantify the end-effect on the stator no-load eddy current losses. The developed model is an efficient machine design tool, used here to quantify the variations of both the eddy currents and hysteresis losses under full load operation when the control angle is modified.      

Simulation of the cabling process for Rutherford cables: An advanced finite element model

In all existing large particle accelerators (Tevatron, HERA, RHIC, LHC) the main superconducting magnets are based on Rutherford cables, which are characterized by having: strands fully transposed with respect to the magnetic field, a significant compaction that assures a large engineering critical current density and a geometry that allows efficient winding of the coils. The Nb₃Sn magnets developed in the framework of the HL-LHC project for improving the luminosity of the Large Hadron Collider (LHC) are also based on Rutherford cables. Due to the characteristics of Nb₃Sn wires, the cabling process has become a crucial step in the magnet manufacturing. During cabling the wires experience large plastic deformations that strongly modify the geometrical dimensions of the sub-elements constituting the superconducting strand. These deformations are particularly severe on the cable edges and can result in a significant reduction of the cable critical current as well as of the Residual Resistivity Ratio (RRR) of the stabilizing copper. In order to understand the main parameters that rule the cabling process and their impact on the cable performance, CERN has developed a 3D Finite Element (FE) model based on the LS-Dyna® software that simulates the whole cabling process. In the paper the model is presented together with a comparison between experimental and numerical results for a copper cable produced at CERN.     

Thermal stability of high current density magnets

The stabilization theories hitherto proposed for superconducting (SC) magnets are not fully developed for application to high current density magnets such as pulsed dipole magnets for a synchrotron. Hence, thermal stability in such high current density magnets is studied by obtaining a minimum energy of thermal disturbances which barely leads a magnet to quench. To find the minimum energy by calculation a dynamic simulation of temperature distribution along a conductor is carried out following an application of the disturbances on the conductor. The minimum energy is found to depend largely on time duration and spatial length of the disturbances. The values of the minimum energy given by calculation agree almost with the experimental results obtained for a coil which simulates a pulsed dipole magnet from the viewpoint of cooling. Discussion is also made in relation to the minimum energy on the performance of a pancake type solenoid magnet which has the same cooling as in the simulating coil.     

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.).     

Flux linkage areas of coupling current loops for different shape cable-in-conduit conductor

For large scale application such as fusion magnets, the cable-in-conduit conductor (CICC) is the most promising conductor because of its high mechanical strength under large electromagnetic force. However, there are still remained issues about degradation of critical current of Nb₃Sn conductor and unpredictable AC loss. With regard to the second item, inter-strand coupling current loss is dominant among the AC losses and unpredictable before fabricating large scale conductor. The strand displacements which are caused by the compaction of the conductor in order to increase its current density would cause the loss. In order to do quantitative investigation of the relation between the loss and the strand displacements, we measured strand traces for circular conductor and rectangular conductor. The evaluation of the flux linkage areas which are driving forces of the coupling current indicated that the flux linkage areas have strong dependence on the changing magnetic field only for the rectangular one. It also indicated that the loss should be large when the field is applied from the direction which is perpendicular to the wide surface of the conduit.     

The High Field Magnet Laboratory at Radboud University Nijmegen

The High Field Magnet Laboratory is dedicated to materials research in the highest continuous fields, up to 33 T, generated with resistive magnets. Circulating cold water evacuates the heat losses incurred when the coils are operating at a voltage drop of up to 500 V at the maximum current of 40 kA. There are three 20 MW resistive magnets with bore sizes of 32 and 50 mm, and a 50 mm bore hybrid magnet system allowing uninterrupted measurements at 30 T for many hours at a time. The infrastructure represents a major investment and has been in operation since 2003. At the moment HFML is extending its capabilities with the construction of a THz FEL. In this paper we will describe the facilities and the possibilities to perform a wide range of experiments in materials research, and show some highlights of the research performed. Even higher fields can be made with a background field provided by a large-bore superconducting magnet: in this paper we will also present the construction of a hybrid magnet system that will generate fields to 45 T.     

Nonlinear calculation of three-dimensional static magnetic fields

We present here the principle and structure of a method to calculate the three-dimensional (3-D) static magnetic fields which have already permitted us to study hybrid magnets for magnetic resonance imaging and ion confinement. Field sources can be issued from resistive or superconducting coils, permanent magnets, and other magnetic bodies such as soft iron. It can be extended to very low-frequency fields calculation as long as eddy current effects do not intervene. We call this method CALMAG3D     

Design of epoxy-free superconducting dipole magnets and performance in both Helium I and pressurized Helium II

Three model superconducting dipole magnet 1m long, without iron, having a bore diameter of 76 mm have been built without epoxy resins or other adhesives and tested in He I and He II. The conductor is the 23-strand Rutherford-type cable used in the Fermilab Doubler Saver magnets, and is insulated with Mylar and Kapton. The two-layer winding is highly compressed by a system of structural support rings and tapered collets. Little "training" was required to reach quench currents greater than 95 percent of "short sample" in Helium I. The maximum quench current in He II is increased 20 to 30 percent, compared with He I operation at 4.4 K. Test results are given on cyclic losses, heater-induced quenches, and charge-rate effects.     

AC losses in the SSC high energy booster dipole magnets

The baseline design for the SSC (Superconducting Super Collider) high energy booster (HEB) has dipole bending magnets with a 50-mm aperture. An analysis of the cryogenic heat load due to AC losses generated in the HEB ramp cycle is reported for this magnet. Included in this analysis are losses from superconductor hysteresis, yoke hysteresis, strand eddy currents, and cable eddy currents. The AC loss impact of 2.5 μm vs. 6 μm filament conductor is presented. A 60-mm aperture design is also investigated     

A physical model and numerical method for losses investigation in superconducting cable-in-conduit conductors (CICC)

A reliable prediction of losses in superconducting cable-in-conduit conductors (CICCs) is important for a successful application of fusion and SMES coils, given that every Watt dissipated at 4-5 K requires 400-800 W of electrical power to remove this heat load. There are also losses caused by field transients (like plasma disruption, plasma initiation and step discharge) that may influence the temperature margin in the conductor design. It is commonly supposed that the CICC losses are associated with the so-called coupling losses characterized by the nτ parameter. However, we would like to highlight the importance of the eddy current losses occurring in the external layers of the bundle: in some cases they are greater than the coupling losses. Therefore, the nτ parameter is a simplification and does not accurately describe the real physical processes taking place in a CICC. Also, we believe that the coupling currents (additional currents) generated in loops can either be added to or subtracted from the transport current flowing in superconducting strands, depending on mutual orientation of the varying magnetic flux density and transport current vectors. This can affect the stability margin and the ramp rate limitation of a conductor. The physical model and numerical method for estimating different kinds of losses in CICCs are proposed. The suggested physical model, albeit somewhat incomplete, allows an explanation of some experimental results obtained earlier. The purpose of this work is to develop a method for an independent numerical calculation of the eddy current and coupling current loss components and thereby avoid the costly experiments at the initial stage of the design work.