A new benchmark for electromagnetic modelling of superconductors: the high-Tc superconducting dynamo

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The high-Tc superconducting (HTS) dynamo is a promising device that can inject large DC supercurrents into a closed superconducting circuit. This is particularly attractive to energise HTS coils in NMR/MRI magnets and superconducting rotating machines without the need for connection to a power supply via current leads. It is only very recently that quantitatively accurate, predictive models have been developed which are capable of analysing these devices and explain their underlying physical mechanism. In this work, we propose to use the HTS dynamo as a new benchmark for the HTS modelling community. The benchmark geometry consists of a permanent magnet rotating past a stationary HTS coated-conductor wire in the open-circuit configuration, assuming for simplicity the 2D (infinitely long) case. Despite this geometric simplicity the solution is complex, comprising time-varying spatially-inhomogeneous currents and fields throughout the superconducting volume. In this work, this benchmark has been implemented using several different methods, including H-formulation-based methods, coupled H-A and T-A formulations, the Minimum Electromagnetic Entropy Production method, and integral equation and volume integral equation-based equivalent circuit methods. Each of these approaches show excellent qualitative and quantitative agreement for the open-circuit equivalent instantaneous voltage and the cumulative time-averaged equivalent voltage, as well as the current density and electric field distributions within the HTS wire at key positions during the magnet transit. Finally, a critical analysis and comparison of each of the modelling frameworks is presented, based on the following key metrics: number of mesh elements in the HTS wire, total number of mesh elements in the model, number of degrees of freedom (DOFs), tolerance settings and the approximate time taken per cycle for each model.

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Despite their proven ability to output DC currents of >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.
We report on the behavior of a high-Tcsuperconducting(HTS) homopolar dynamo which outputs a DC open-circuit voltage when the stator is in the superconducting state, but behaves as a conventional AC alternator when the stator is in the normal state. We observe that this time-averaged DC voltage arises from a change in the shape of the AC voltage waveform that is obtained from a normal conducting stator. The measured DC voltage is proportional to frequency, and decreases with increasing flux gap between the rotor magnet and the HTS stator wire. We observe that the DC output voltage decreases to zero at large flux gaps, although small differences between the normal-conducting and superconducting waveforms are still observed, which we attribute to screening currents in the HTS stator wire. Importantly, the normalised pulse shape is found to be a function of the rotor position angle only. Based on these observations, we suggest that the origin of this unexpected DC effect can be explained by a model first proposed by Giaever, which considers the impact of time-varying circulating eddy currents within the HTS stator wire. Such circulating currents form a superconducting shunt path which “short-circuits” the high field region directly beneath the rotor magnet, at those points in the cycle when the rotor magnet partially overlaps the superconducting stator wire. This reduces the output voltage from the device during these periods of the rotor cycle, leading to partial rectification of the output voltage waveform and hence the emergence of a time-averaged DC voltage.
Superconducting flux pumps enable large currents to be injected into a superconducting circuit, without the requirement for thermally conducting current leads which bridge between the cryogenic environment and room temperature. In this work, we have built and studied a mechanically rotating flux pump which employs a coated conductor high-Tc superconducting (HTS) stator. This flux pump has been used to excite an HTS double pancake coil at 77 K. Operation of the flux pump causes the current within the superconducting circuit to increase over time, before saturating at a limiting value. Interestingly, the superconducting flux pump is found to possess an effective internal resistance, Reff, which varies linearly with frequency, and is two orders of magnitude larger than the measured series resistance of the soldered contacts within the circuit. This internal resistance sets a limit for the maximum achievable output current from the flux pump, which is independent of the operating frequency. We attribute this effect to dynamic resistance within the superconducting stator wire which is caused by the interaction between the DC transport current and the imposed alternating magnetic field. We provide an analytical expression describing the output characteristics of our rotating flux pump in the high frequency limit, and demonstrate that it describes the time-dependent behavior of our experimental circuit. Dynamic resistance is highlighted as a generic issue that must be considered when optimizing the design of an HTS flux pump.
In many high-Tc superconductors the critical current density jc is an ill-defined quantity due to the smooth current-voltage characteristic. Since jc is the basic parameter entering the critical state model, its application to such materials becomes problematic. In this paper, a theory of magnetic properties and AC-losses in superconductors with smooth current-voltage characteristics is proposed. It is applied to superconductors with a power law characteristic, E ~ jalpha. The AC-losses are calculated analytically; simple scaling rules are obtained for their dependence on the frequency and the field amplitude. Moreover, it is shown that the normal ohmic conductor and the ``perfect'' type-II superconductor (critical state) emerge as limiting cases, alpha = 1 and alpha = ∞, from the theory.
This paper proposes a practical and memory efficient method to model YBCO coated conductors by commercial finite element software. This method uses the H formulation to directly solve a magnetic field in a two-dimensional space. This model has been successfully used for bulk materials and thick wires, and is extended in this article to solve geometries with high aspect ratios such as coated conductors. The effect of mesh quality and order of element on the performance and accuracy of the model is discussed. Amodel using 2nd order single layer elements is chosen as the optimal setting for solving AC loss in coated conductors. Based on this setting, a series of simulations with the thickness of the tape varying from 1μm (the actual thickness) to 120μm have been performed to investigate the effect of artificially expanding tape thickness. The results obtained from our FEM model are compared with the classical analytical solutions. The discrepancies between the two are discussed and explained. The model proposed in this paper is able to give an accurate solution of AC loss for simple geometry (such as a single tape with expanded thickness) within just a few minutes. Even in the case of dealing with complex problems (such as a tape in its actual dimension or a stack of tapes under complicated magnetic conditions), the model would only require a few hours to solve the problems with excellent convergence properties. KeywordsCoated conductor- H formulation-Critical state-AC loss-Finite element modelling
Although conventional transformers are ac, a device that may be termed a dc transformer has been constructed by using superconductors. To provide an understanding of how such a transformer would operate, some of the properties of type I and type II superconductors are reviewed. Since the dc transformer under discussion is constructed from thin superconducting films, the main emphasis is on these structures; the concept of flux motion is also explained. The result of the work described is a device in which a direct current or voltage can be transformed, and in which it is possible to extract power from the secondary circuit.
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