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.     

Experimental setup for precise measurement of losses in high-temperature superconducting transformer

A simple cryogenic system for testing of the superconducting power transformer was constructed. Thermal shielding is provided by additional liquid nitrogen bath instead of super-insulation. The system, together with use of a precise nitrogen liquid level meter, permitted calorimetric measurements of losses of the 8 kVA HTS transformer with a resolution of the order of 0.1 W.     

A model for calculating a.c. losses in multistage superconducting cables

Superconducting magnets in tokamaks for fusion experiments are subjected to fast variations in magnetic field. As the high current conductors used in these magnets are made of multistage cables, these variations induce interstrand coupling currents that create losses. These losses are usually characterized by the so-called time constant of the conductor. A model is given to calculate this time constant. Working formulas are also proposed to calculate the current induced in the different cabling stages. This model takes into account the strand characteristics and the detailed cabling pattern. Using it, a method is also given to deduce the time constant from resistive measurements. The influence of the resistive barrier (chrome plating, CuNi shell, outer bronze matrix) is pointed out. Finally, this model is applied to a conductor that is foreseen for the toroidal coils of the International Thermonuclear Experimental Reactor (ITER).     

On the coupling current losses in a multifilamentary superconducting composite

The coupling current losses in a superconducting multifilamentary composite exposed to trapezoidally varying external magnetic field and carrying a small transport current are investigated for the volume pinning force density described with the dependence: F_v = α B^1?γ. Such a model allows estimation of the deviations from the solution based on Bean's (γ = 0) critical state model. Results indicate that there exists a region of small magnetic field amplitudes for which discrepancies are largest. They are also very sensitive to the rate of magnetic field change.     

A review of dielectrics for flexible superconducting cables

The tape materials for the dielectric of a flexible superconducting cable are discussed. The tape is wrapped around the superconductor and is impregnated with supercritical helium. Based on mechanical and electrical performance the most promising materials are Valeron, high density polyethylene, polypropylene, and nylon 11. A final assessment is made based on life expectancy and mechanism of electrical failure both of which are a function of discharge activity in the tapes.     

Uncertainty considerations in AC loss measurement of multifilamentary superconducting wires performed via a pickup coil method

The uncertainty of AC loss measurements for multifilamentary superconducting wires by a pickup coil method is evaluated on the basis of the law of propagation of uncertainty. In this evaluation, the effects of measurement conditions, signal processing, and the division of the AC loss into its components (hysteresis loss and coupling loss) are taken into account as elements of uncertainty. The effect of the measurement conditions is evaluated using theoretical expressions of the two main components. Additionally, the effect of signal processing is considered in accordance with the actual processes of the AC loss measurement using experimental outputs. The main factors that contribute to the uncertainty in the propagation process are discussed. The estimated resultant uncertainties are compared to experimental ones for round robin tests of AC loss measurement of Nb-Ti multifilamentary wires exposed to an alternating transverse magnetic field.     

Investigation of current distribution conditions in multiwire superconducting cables under the influence of self-magnetic field

The current distribution in a multi-wire round cable subjected to self-magnetic field is considered in this paper. A theoretical analysis of the current distribution process was made. The influence of layer parameters on the current distribution between the layers was determined. The theoretical analysis showed that it was necessary to twist two external layers into different directions with a minimum pitch to increase the current in the internal layers. It was shown that manufacturing round cable with more than two superconducting layers was unnecessary. Formulae are given allowing determination of the current in all layers. The theoretical conclusions were confirmed by the experimental results.     

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.     

Integration of superconducting magnets with cryogen-free dilution refrigerator systems

There has been much recent research interest into “cryogen-free” dilution refrigerators. Cryogen-free systems have some advantages from a safety and convenience point of view as liquid cryogens are unnecessary. However, this also makes integrating the low-temperature system with a high magnetic field environment much more challenging. Here we shall describe recent successes of integrating superconducting magnets and dilution refrigerators into one system requiring a single pulse tube cooler. The resulting environment provides experimental temperatures between 7 mK and 30 K and magnetic fields up to 12 T. We shall describe the effects of AC loss heating in such systems on the pulse tube refrigerator when the field is ramped and also the effects of eddy current heating on the mixing chamber in sweeping fields.     

Effect of the respective positions of filament bundles and stabilizing copper on coupling losses in superconducting composites

Superconductor stabilization is ensured by embedding filaments in a copper matrix. Calculations show that a central copper region always leads to an increase in loss in comparison with the case where the filaments are located in a central region surrounded by an outer copper sheath. Practical cases with a copper matrix and also mixed matrix conductors are discussed. Attention is drawn to the comparative roles played by the effective transverse resistivity of the matrix and the copper resistivity.     

Design parameter evaluation of a metal recoated Fiber Bragg Grating sensors for measurement of cryogenic temperature or stress in superconducting devices

There are plenty of complex physical phenomena which remain to be studied and verified experimentally for building an optimized superconducting magnet. The main problem for experimental validations is due to the unavailability of suitable sensors. This paper proposes a Fiber Bragg Gratings (FBG) sensor for this purpose which allows access to the local temperature/stress state. To measure the low temperature (20 K), FBG can be recoated with materials having high thermal expansion coefficient (HTCE). This can induce a thermal stress for a temperature change, which in turn increases the sensitivity of the sensor. The performance of such sensors has been experimentally studied and reported in earlier paper [Rajinikumar R, Suesser M, Narayankhedkar KG, Krieg G, Atrey MD. Performance evaluation of metallic coated Fiber Bragg Grating sensors for sensing cryogenic temperature. Cryogenics 2008;48:142-7]. This paper aims at evaluation and determination of different design parameters like coating materials, coating thickness, grating period and the grating length for design of better performance FBG sensor for low temperature/stress measurements.     

The influence of filament bundle location on coupling losses in superconducting composites. part i: mixed matrix conductor

The ac losses in mixed matrix multifilamentary superconducting composites with different superconducting filament bundle positions have been measured using the magnetization method to establish the relation between filament bundle position and coupling losses. Experimental results indicate that coupling losses between filaments in the composite with the filament bundle located in the central region is smaller than the composite with the filament bundle located in the outer region. It is also pointed out that a copper stabilizer, divided by the CuNi barrier into small regions, like a honeycomb, shows anomalous increase in its resistivity due to Ni duffusion during heat treatment.     

A novel high temperature superconducting magnetic flux pump for MRI magnets

This paper presents a kind of minitype magnetic flux pump made of high temperature superconductor. This kind of novel high temperature superconducting (HTS) flux pump has not any mechanical revolving parts or thermal switches. The excitation current of copper coils in magnetic pole system is controlled by a singlechip. The structure design and operational principle have been described. The operating performance of the new model magnetic flux pump has been preliminarily tested. The experiments show that the maximum pumping current is approximately 200 A for Bi2223 flux pump and 80 A for MgB₂ flux pump operating at 20 K. By comparison, it is discovered that the operating temperature range is wider, the ripple is smaller and the pumping frequency is higher in Bi2223 flux pump than those in MgB₂ flux pump. These results indicate that the newly developed Bi2223 magnetic flux pump may efficiently compensate the magnetic field decay in HTS magnet and make the magnet operate in persistent current mode, this point is significant to the magnetic resonance imaging (MRI) magnets. This new flux pump is under construction presently. It is expected that the Bi2223 flux pump would be applied to the superconducting MRI magnets by further optimizing structure and improving working process.     

Heat transfer performance of cryogenic oscillating heat pipes for effective cooling of superconducting magnets

The cryogenic oscillating heat pipe (OHP) for conduction cooling of superconducting magnets was developed and the function was demonstrated successfully. OHP is a highly-efficient heat transfer device using oscillating flow of two-phase mixture. The working fluids that are employed in the present research are Nitrogen, Neon and Hydrogen, and the operating temperatures are 67–91 K, 26–34 K and 17–27 K, respectively. The estimated effective thermal conductivities from the measurement data of the OHP were higher than one of the solids such as copper at low temperature. These results revealed that the cryogenic OHP can enhance the performance of cooling system for magnets.     

On conduction-cooling of a high-temperature superconducting cable

Current generation high-temperature superconducting (HTS) power transmission cables use liquid nitrogen as a coolant that circulates along the cable. In this work, the use of axial conduction-cooling in attaining HTS temperatures in transmission lines is proposed. Liquid coolant use is envisioned only at periodic length intervals along the transmission lines, in combination with insulation and copper. The proposed concept is feasible due to the high thermal conductivity of pure copper at cryogenic temperatures. A basic design for the insulated cable is proposed and a detailed numerical simulation of heat transfer in such a cable is carried out for various case studies considering the superconducting materials MgB₂ and BSCCO-2223.     

Finite element calculations on detailed 3D models for the superferric main magnets of the FAIR SIS100 synchrotron

The synchrotron SIS100 is one of the two basic accelerators of the future Facility for Antiproton and Ion Research (FAIR) at GSI in Darmstadt. This accelerator should provide high intensity U28+ and proton beams with a pulse repetition rate of 1 Hz (i.e. a ramp rate of 4 T/s). The magnetic system of the accelerator uses superferric 2.1 T dipoles of about 3 m length and 32 T/m quadrupoles of about 1 m length. The magnet coils are made of a hollow tube cable wrapped with Cu/NbTi composite wire cooled with two phase helium flow at 4.5 K. The bore dimensions were defined to 130 × 60 mm for the dipole and 135 × 65 mm for the quadrupole. We present the developed ANSYS models for different important aspects: AC loss, magnetic field quality and mechanical stability. Preliminary studies verified the approaches and these models were applied to calculate the effects for the coil, the yoke and the beam pipe structures. We outline further steps to fully describe the SIS100 magnets including mechanical and thermal 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.     

Prediction of transport properties of wood below the fiber saturation point - A multiscale homogenization approach and its experimental validation. Part II: Steady state moisture diffusion coefficient

In this publication a multiscale homogenization model for moisture transport in wood is developed and validated. The model aims at prediction of macroscopic transport properties of clear wood samples from their microstructure and the physical properties of a few microscale constituents. In the first part of this two-part paper, the theoretical background and fundamentals of the model were presented, and its specification for the estimation of macroscopic thermal conductivities was shown. In this second part the model is applied to steady state moisture diffusion below the fiber saturation point. The model starts on a scale of about 50 μm, where the wood cells form a honeycomb-like structure. In a first homogenization step the effective moisture transport behavior of the cell structure is determined from moisture diffusion properties of the cell walls and the (moist) air in lumens, respectively. Further homogenization steps account for the larger vessels that exist in hardwood species, the annual rings which are a succession of layers with different densities, and finally wood rays, that form pathways in the radial direction throughout the stem. The model validation rests on experiments as in the case of heat conduction: The macroscopic diffusion coefficients predicted by the multiscale homogenization model for tissue-specific composition data (input data set II) are compared to corresponding experimentally determined tissue-specific diffusion coefficients under steady state conditions (experimental data set). As for thermal conductivity, the good agreement of model predictions and test data underlines the suitability of the presented multiscale model.     

Multiplicities and thermal runaway of current leads for superconducting magnets

The multiple solutions of conduction and vapor cooled copper leads modeling current delivery to a superconducting magnet have been numerically calculated. Both ideal convection and convection with a finite heat transfer coefficient for an imposed coolant mass flow rate have been considered. Because of the nonlinearities introduced by the temperature dependent material properties, two solutions exist, one stable and one unstable regardless of the cooling method. The limit points separating the stable form the unstable steady states form the blow-up threshold beyond which, any further increase in the operating current results in a thermal runway. An interesting finding is that the multiplicity persists even when the cold end temperature is raised above the liquid nitrogen temperature. The effect of various parameters such as the residual resistivity ratio, the overcurrent and the variable conductor cross section on the bifurcation structure and their stabilization effect on the blow-up threshold is also evaluated.     

Maximum curvatures of 0/90 plates under thermal stress: Modelling and experimental validation

In this paper, special attention is paid to the maximum curvatures induced by uniform thermal fields in 0_m/90_n laminated square plates. The effects of the relative thickness of the 90° ply e₉₀ and of the elastic and thermoelastic anisotropy on the curvature tensor are then studied. The conditions for which the curvatures are maximum are established by adopting the polar method within the context of the classical lamination theory. It is found that the location of the maximum curvatures is influenced by the level of elastic anisotropy, defined by the polar parameter R₁, while the magnitude of the maximum curvatures is driven by the thermoelastic properties, that is, the coefficients of thermal expansion. The capabilities of a geometrical nonlinear model are explored and experimental evidence of maximum curvatures of glass/epoxy composite materials are provided.