Finite-element modelling of no-insulation HTS coils using rotated anisotropic resistivity

The no-insulation (NI) winding method is an effective technique for winding coils from high-Tc superconductors (HTS). NI coils are electrically and thermally robust due to their ability to radially bypass current away from the fragile superconducting path when necessary. This avoids stored magnetic energy being entirely discharged on local defects in the HTS tape. However, the increased degrees of freedom for the current distribution makes finite-element modelling of these coils a complicated and multi-level problem. Here we present and validate a 2D axially symmetric model of an NI (or partially insulated) coil that captures all the inherent electromagnetic properties of these coils, including axial vs radial current flow and critical current suppression, and also reproduces the well-known charging and discharging characteristics. The model is validated against previously reported discharge measurements, and is shown to produce results consistent with the expected equivalent-circuit behaviour. Only by solving the NI coil problem with both axial and radial delity can the interplay of critical current anisotropy and turn-to-turn current be properly accounted for. The reported FE model will now enable coil designers to simulate key complex behaviours observed in NI coils, such as shielding currents, magnetic fi eld inhomogeneity and remnant fi eld effects

Numerical modelling of dynamic resistance in high-temperature superconducting coated-conductor wires

The use of superconducting wire within AC power systems is complicated by the dissipative interactions that occur when a superconductor is exposed to an alternating current and/or magnetic field, giving rise to a superconducting AC loss caused by the motion of vortices within the superconducting material. When a superconductor is exposed to an alternating field whilst carrying a constant DC transport current, a DC electrical resistance can be observed, commonly referred to as “dynamic resistance.” Dynamic resistance is relevant to many potential high-temperature superconducting (HTS) applications and has been identified as critical to understanding the operating mechanism of HTS flux pump devices. In this paper, a 2D numerical model based on the finite-element method and implementing the H-formulation is used to calculate the dynamic resistance and total AC loss in a coated-conductor HTS wire carrying an arbitrary transport current and exposed to background AC magnetic fields up to 100 mT. The measured angular dependence of the superconducting properties of the wire are used as input data, and the model is validated using experimental data for magnetic fields perpendicular to the plane of the wire, as well as at angles of 30° and 60° to this axis. The model is used to obtain insights into the characteristics of such dynamic resistance, including its relationship with the applied current and field, the wire’s superconducting properties, the threshold field above which dynamic resistance is generated and the flux-flow resistance that arises when the total driven transport current exceeds the field-dependent critical current, Ic(B), of the wire. It is also shown that the dynamic resistance can be mostly determined by the perpendicular field component with subtle differences determined by the angular dependence of the superconducting properties of the wire. The dynamic resistance in parallel fields is essentially negligible until Jc is exceeded and flux-flow resistance occurs

Numerical Modelling of Dynamic Resistance in a Parallel-Connected Stack of HTS Coated-Conductor Tapes

Dynamic resistance is observed in type-II superconductors carrying a DC transport current while simultaneously exposed to an alternating magnetic field. The appearance of a nonzero resistance is attributed to the interaction between the transport current and moving fluxons. This effect is relevant to many superconductor applications such as high-temperature-superconductor (HTS) flux pumps, DC / AC magnets, synchronous machines, and persistent current switches. Here, we present a finite element method (FEM) analysis of both the time averaged dynamic resistance and the instantaneous current sharing behaviour in a cable comprised of a stack of four YBCO thin films connected in parallel. Numerical modelling was performed using the H-formulation method implemented in the commercial software COMSOL. The model employs experimentally measured values of the angular dependence of the critical current Ic(B, θ) and the flux creep exponent n(B, θ). A single threshold field is observed, above which a finite dynamic resistance is observed in all tapes simultaneously. The time-averaged dynamic resistance of individual tapes tends to be larger for the exterior tapes than the interior tapes, but this difference decreases as the total transport current in the cable increases. We attribute this to shielding currents flowing in the exterior tapes during the majority of the cycle, which displace net DC current into the interior tapes. However, the relative proportion of DC transport current flowing in the exterior and interior tapes is also observed to vary periodically once per half cycle of the applied field. This is due to the periodic trapping of return screening currents in the interior tapes.New Zealand MBIE Endeavour Grant No. RTVU1707 and NZ Royal Society Marsden Grant No. MFP-VUW180

The transient voltage response of ReBCO coated conductors exhibiting dynamic resistance

Abstract: Dynamic resistance can be observed in a superconducting tape carrying a DC current which is exposed to an oscillating magnetic field. This effect is attributed to the interaction between the transport current and moving fluxons, and can occur in various superconducting components including high temperature superconducting (HTS) flux pumps, fast-ramping magnets and HTS rotating machines. Although conventionally expressed in terms of a DC ‘resistance,’ the phenomenon is inherently transient in nature, and the voltage drop across the superconductor follows a time-dependent periodic waveform. Here we present experimental measurements of the dynamic resistance of different REBCO tapes carrying a DC current and exposed to an oscillating perpendicular field. Measurements of both the transient voltage waveforms and the time-averaged DC resistances are compared with numerical finite element simulations obtained using the H-formulation. We observe clear variations between the voltage response from different tapes, which can be understood in terms of their differing Jc(B, θ) dependence. In particular, a key feature of the experimentally measured waveforms is the emergence of a split ‘double peak’ at higher applied fields. Graphical visualisations of the finite element data show that this coincides with a periodic increase in Jc(B, θ) throughout the tape. This occurs during each cycle at those times when the applied field falls below the shielding threshold of the tape (as the penetrating field within the tape then approaches zero). Our findings show that models which assume a constant Jc irrespective of local field strength cannot capture the full range of behaviour observed by experiment. This emphasises the importance of employing experimentally measured Jc(B, θ) data when simulating transient effects in HTS materials

Modeling of stator versus magnet width effects in High-T<inf>c</inf> superconducting dynamos

High-Tc superconducting (HTS) dynamos are simple devices for injecting and sustaining dc currents in superconducting coils/magnets. The simple geometry of these devices consists of a superconducting stator(s) and one or more rotor magnets arranged in identical fashion to a classical alternator. However, unlike the classical alternator, the HTS dynamo gives a self-rectified dc output. This somewhat anomalous result is caused by the non-linear resistivity of HTS materials and the large over-critical eddy currents that flow in the stator. As these overcritical currents must recirculate in the HTS stator, the stator's width becomes a key parameter in the physics of the device. In this work we explore the effect of increasing the stator width through using recent advances in modeling these systems. We find that given enough space in the stator, the total sum of circulating and transport currents do not drive the full width of the stator into the flux-flow regime. Operation of the device in this regime results in a non-linear I-V curve, a marked decrease in the internal resistance at open circuit R_oc, a saturation of the open circuit voltage V_oc, and a short-circuit current I_sc that approaches the in-field critical current of the stator itself I_c,min. These behaviors lead to the conclusion that optimal HTS dynamo design should ensure that the stator width be sufficient to avoid current saturation of the superconductor at the target operating current.New Zealand MBIE Endeavour contract no. RTVU1707 NZ Royal Society Marsden Award no. MFP-VUW180

Effect of Stack Geometry on the Dynamic Resistance Threshold Fields for Vertical Stacks of Coated Conductor Tapes

The expanding capabilities of HTS flux pumps and rectifiers to provide kA+ currents, necessitates the exploration of high current switching phenomenon. One such phenomenon, the dynamic resistance, occurs in type-II devices carrying dc transport currents while exposed to ac magnetic fields with an amplitude above some sample dependent threshold. In the following, finite element analysis of the threshold field for dynamic resistance in superconducting cables comprised of N tapes connected in parallel and stacked vertically is presented. Cables are modelled using the commercial software COMSOL and the H-formulation. The models employ Ic(B,θ) and n(B,θ) data obtained on short samples at 77K as inputs to more accurately reflect the variation in local properties within the superconductor. The finite element results are then compared with calculations made using analytical models assuming a critical state. The finite element data closely resembles that predicted for a strip for a single tape, rapidly tending towards the slab results as N increases.EPSRC Early Career Fellowship EP/ P020313/1 New Zealand MBIE Endeavour Grant no. RTVU1707 NZ Royal Society Marsden Grant no. MFP-VUW180

Modelling the Frequency Dependence of the Open-Circuit Voltage of a High-T<inf>c</inf>Superconducting Dynamo

A high-Tc superconducting (HTS) dynamo enables the injection of large DC currents into a superconducting circuit, without the requirement for current leads. In this work, we attempt to explain the frequency dependence of such dynamos/flux pumps reported in the literature, where it is observed that the rate at which the open-circuit DC voltage increases reduces with increasing frequency, in contrast to the expected linear behaviour. Heat generated in the HTS wire has been the common explanation given to date for this phenomenon. Here we offer an alternative explanation: the interaction between and current flow in the different layers of the HTS wire as the frequency of the dynamo increases. Our claim is based on numerical analysis using a segregated H-formulation finite-element model of the HTS dynamo benchmark problem that is extended to include the full HTS wire architecture and coupled with a thermal model. This framework enables us to efficiently model the relative movement between the rotating room-temperature permanent magnet and the stationary HTS wire and to study the impact of the frequency of rotation and temperature on the open-circuit DC voltage of the dynamo.- Engineering and Physical Sciences Research Council (EPSRC) Early Career Fellowship EP/P020313/1 - Royal Society of New Zealand Marsden Fund grant no. MFP-VUW1806 - EolSupra20 project ANR-10-LABX-0040-LaSIP

Origin of the DC output voltage from a high- T<inf>c</inf> superconducting dynamo

Despite their proven ability to output DC currents of &amp;gt;100 A, the physical mechanism which underpins the operation of a high-Tc superconducting (HTS) dynamo is still debated widely. Here, we show that the experimentally observed open-circuit DC output voltage, Vdc, is due to the action of overcritical eddy currents within the stator wire. We demonstrate close agreement between experimental results and numerical calculations, and show that large over-critical currents flow within the high-Tc stator during certain parts of the dynamo cycle. These overcritical currents experience a non-linear local resistivity which alters the output voltage waveform obtained in the superconducting state. As a result, the full-cycle integral of this altered waveform outputs a non-zero time-averaged DC voltage. We further show that the only necessary requirement for a non-zero Vdc output from any dynamo is that the stator must possess a non-linear local resistivity. Here, this is provided by the flux-flow regime of an HTS coated conductor wire, where conduction is described by the E–J power law. We also show that increased values of Vdc can be obtained by employing stator wires which exhibit a strong in-field dependence of the critical current Jc(B,θ). However, non-linear resistivity is the key requirement to realize a DC output, as linear magneto-resistance is not sufficient. Our results clarify this longstanding conundrum, and have direct implications for the optimization of future HTS dynamo devices.</jats:p

Modelling Parallel-Connected, No-Insulation High-T<inf>c</inf>Superconducting Magnets

The charging/discharging delays in superconducting coils wound without insulation (NI coils) are a major drawback of the technique. While removing the insulation improves safety margins, the increase in the characteristic time constant τ_c can make a coil unfit for a particular purpose. It is widely accepted for instance that NI coils will not be used in ac applications where τ_c ~ 1/f. To decrease τ_c of the NI coils, the same length of superconductor can be wound/connected in parallel rather than in series — decreasing the inductance L, and hence the time constant τ_c, while maintaining the number of amp-turns I_op*N. Here we investigate the effect of parallel connecting coils in a magnet using a 2D axially symmetric model which captures all the necessary electromagnetic properties of the HTS NI coils. These properties include: critical current anisotropy Jc(B, θ), turn-to-turn conductivity, as well as winding parallelism. Our modeling results show that the parallel connected magnet experiences magnet-wide shielding current effects. Whilst these shielding currents affect field homogeneity — the model enables this effect to be quantified. Furthermore, shielding currents are not an issue when running NI coils in saturated mode. The modeling work presented here provides a simple initial example of how magnet designers may approach designing, optimizing, and operating high current, HTS NI coils.New Zealand MBIE Endeavour grant no. RTVU1707; NZ Royal Society Marsden Grant no. MFP-VUW1806; EPSRC Early Career Fellowship EP/P020313/

Mid-infrared electroluminescence from coupled quantum dots and wells

The room temperature electroluminescence (EL) between 1.7-2.6 μ from coupled quantum dots and quantum wells in the InAs/InSb/GaSb materials system was investigated. The samples which were investigated consisted of a single narrow InAs quantum well grown below a layer of InSb quantum dots in a GaSb matrix. It was found that the thickness of the GaSb space layer lowers the energy from that of a quantum well alone. The results reveal the occurrence of a sharp transition after a single monolayer coverage of GaSb either due to structural changes in the quantum dots or from the shrinkage of the quantum well