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Peer reviewed: True, Over time, high-temperature superconductor (HTS)-coated conductors (CCs) have proven to be promising candidates for future high-efficiency and high-power density electrical machines. However, their commercialization is handicapped due to the AC dissipative loss that occurs upon exposure to external magnetic fields. In rotating electromagnetic devices, the external magnetic field is a combination of alternating and rotating magnetic fields. Most of the research is devoted to the effect of exposure of the superconductors to alternating magnetic fields only. This article presents an investigation to observe the behavior of HTSCCs under rotating magnetic fields, particularly the AC loss, using a finite-element-based homogeneous H-formulation technique. Our investigation shows that the AC loss could be considerably high when HTSCCs are exposed to rotating magnetic fields and, ultimately, could affect the cooling efficiency of future high-efficiency and high-power density electrical machines.

Peer reviewed: True, High-temperature superconductor (HTS) bulks have demonstrated extremely intriguing potential for industrial and commercial applications due to their capability to trap significantly larger magnetic fields than conventional permanent magnets. The magnetic field in electrical rotating machines is a combination of alternating and rotational fields. In contrast, all previous research on the characterization of electromagnetic properties of HTS have solely engrossed on the alternating AC magnetic fields and the associated AC loss. This research paper gives a thorough examination of the AC loss measurement under various conditions. The obtained results are compared to the finite element-based H-formulation. The AC loss is measured at various amplitudes of circular flux density patterns and compared with the AC loss under one-dimensional alternating flux density. The loss variation has also been studied at other frequencies. The findings in this research paper provide more insights into material characterization, which will be useful in the design of future large-scale HTS applications.

Funder: 2021 IEEE CSC Graduate Study Fellowship in Applied Superconductivity, Dynamic resistance is a time-averaged direct current (DC) resistance in superconducting materials, which typically occurs when a superconductor is carrying a transport DC while simultaneously subject to a time-varying magnetic field. Dynamic resistance has recently attracted increasing attention as it not only causes detrimental dynamic loss in superconducting devices such as the nuclear magnetic resonance magnets and superconducting machines, but on the other hand, the generated dynamic voltage can be exploited in many applications, e.g. high temperature superconducting (HTS) flux pumps. This article reviews the physical mechanism as well as analytical, numerical modelling, and experimental approaches for quantifying dynamic resistance during the last few decades. Analytical formulae can be conveniently used to estimate the dynamic resistance/loss of a simple superconducting topology, e.g. a single rare-earth-barium-copper-oxide tape. However, in a complex superconducting device, such as a superconducting machine, the prediction of dynamic resistance/loss has to rely on versatile numerical modelling methods before carrying out experiments, especially at high frequencies up to the kHz level. The advantages, accuracies, drawbacks, and challenges of different quantification approaches for dynamic resistance/loss in various scenarios are all inclusively discussed. The application of dynamic resistance in HTS flux pumps is also presented. It is believed that this review can help enhance the understanding of dynamic resistance/loss in superconducting applications and provide a useful reference for future superconducting energy conversion systems.

SiC/EP composites are promising insulating materials due to their high thermal conductivity, stable chemical properties, and nonlinear electrical conductivity. However, the compatibility of micron-sized SiC particles with the organic polymer matrix is poor, and defects such as air gaps may be introduced at the interface, which reduces the partial discharge resistance of the composite materials. In order to improve the partial discharge initial voltage (PDIV) of SiC/EP composites, in this paper, SiC/EP composites with different proportions were prepared by surface modification of filler and compound of micro/nano particles. Firstly, a method of secondary modification of SiC particles was proposed, which was first modified by alkali washing and then silane coupling agent KH560, and the effectiveness of the modification was verified. Therefore, the interface bonding ability between the filler and the matrix was improved, the air gap defects at the interface were reduced, and the PDIV of the composite material was improved. When the filling ratio is 10 wt%, the PDIV was enhanced by 13.75%, and when the filling ratio was further increased, the improvement was reduced. In contrast, the introduction of nanoparticles into the composites can effectively improve the PDIV of composite materials. In this study, nanoparticles were used to form a shell-core structure in epoxy resins to exert their huge specific surface area and active surface properties, thereby changing the overall crosslinking properties of the composites. Through experimental research, the optimal micro-nano particle compounding ratio was explored. Under the optimal mixing ratio, the PDIV of the composite material can be increased by more than 90%.

High-temperature superconductor (HTS) bulks have shown very promising potential for industrial applications due to the ability to trap much higher magnetic fields compared to traditional permanent magnets. In rotating electrical machines, the magnetic field is a combination of alternating and rotating fields. On the contrary, all studies on electromagnetic characterization of HTS presented in the literature so far have only focused on alternating AC magnetic fields and alternating AC loss due to the unavailability of robust experimental techniques and analytical models. This paper presents a numerical investigation on the characterization of HTS bulks subjected to rotating magnetic fields showing AC loss, current density distribution in three-dimensional axes, and trapped field analysis. A three-dimensional numerical model has been developed using H-formulation based on finite element analysis. An HTS cubic sample is magnetized and demagnetized with two-dimensional magnetic flux density vectors rotating in circular orientation around the XOY, XOZ, and YOZ planes.

The evolution from low-temperature superconductors (LTSs) to high-temperature superconductors (HTSs) has created a great amount of opportunities for superconducting applications to be used in real life. Dynamic voltage is a special superconducting phenomenon, and it occurs when the superconductor takes a DC transport current while simultaneously exposed to an AC magnetic field. The dynamic voltage is crucial for some superconducting applications as it is the energy source by which to energise the load, such as flux pumps. This article investigates the missing aspects that previous studies have not deeply exploited: the optimisation of energy efficiency for the dynamic voltage in an HTS tape with different working conditions (e.g., currents and magnetic fields). First, the mechanics of superconducting dynamic voltage were explicated by typical analytical solutions, and the modelling method was validated by reproducing the behaviours of the Bean model and analytical solutions of dynamic voltage. After the feasibility of the modelling was proved, in-depth modelling was performed to optimise the energy efficiency of an HTS tape with different DC transport currents and AC magnetic fields. Owing to the physical limitations of the superconducting tape (e.g., quench), a safe operating region was determined, and a more delicate optimisation was performed to discover the optimal operating conditions of the HTS tape. The novel conceptualisation and optimisation approaches for the superconducting dynamic voltage in this article are beneficial for the future design and optimisation of superconducting energy/power applications under complicated electromagnetic conditions.

The high-temperature superconductor (HTS) has been recognised as one of the most up-and-coming materials thanks to its superior electromagnetic performance (e.g., zero resistance). For a high-speed maglev, the HTS magnet can be the most crucial component because it is in charge of both the levitation and the propulsion of the maglev. Therefore, a fundamental study of HTS magnets for maglev is crucial. This article presents the fundamental design and modelling of the superconducting magnet for a high-speed maglev, including mechanics, electromagnetics, and loss analysis during instability. First, the measurements of the superconducting wire were performed. The HTS magnet was primarily designed and modelled to fulfil the basic electromagnetic requirements (e.g., magnetic field) in order to drive the maglev at a high speed. The modelling was verified by experimental tests on a scale-down HTS magnet. A more professional model using the H-formulation based on the finite element method (FEM) was built to further investigate some deeper physical phenomenon of the HTS magnet (e.g., current density and loss behaviours), particularly in situations where the high-speed maglev is in the normal steady state or encountering instability.

Peer reviewed: True, Various measures have been taken to improve ship energy efficiency while decreasing CO2 emissions. In this work, the navigation environment between Wuhan and Shanghai in China has been classified based on an improved K-means algorithm in order to realize route division. A fuel consumption prediction model considering the navigation environment factors has been established. Consequently, speed optimization models with multiple different optimization objectives have been constructed and tested based on an actual case using an artificial fish swarm algorithm. Finally, sensitivity analysis has been carried out focusing on the navigation time, fuel price, charter rate, free carbon credits, and carbon tax rate. The results show that the total shipping cost and CO2 emissions could be reduced by 0.94% and 0.38%, respectively, after the optimization. Considering a carbon tax policy with a tax rate of roughly 1300 RMB/t, the optimization result (including the carbon tax cost) is close to the compromised solution of multi-objective optimization, and the corresponding carbon tax rate can provide a useful reference for policymakers.

The dynamic voltage is a unique phenomenon of superconducting materials. It arises when the superconductor is carrying a DC transport current and spontaneously in subject to an AC magnetic field. This study excavates the aspects that previous studies have not comprehensively investigated: the dynamic voltage in a DC-carrying superconducting tape exposed to different oscillating AC magnetic fields. First, the fundamental physics of dynamic voltage/flux of superconductors is reviewed and further analysed in detail. We used the superconducting modelling method using the H-formulation merged into the finite-element method (FEM) software, to re-produce the typical dynamic voltage behaviour of a superconducting tape. The modelling was verified by both the analytical and experimental results, in order to precisely prove the reliability of the modelling. Afterwards, the modelling was performed for a DC-carrying superconducting tape under four different oscillating magnetic fields (sine, triangle, sawtooth and square), and their corresponding dynamic voltages and energy losses were analysed and compared. Results show the sinusoidal magnetic field can lead to the optimal combination of reasonable dynamic voltage but relatively lower loss, which is suitable for those superconducting applications requiring dynamic voltage as the energy source, e.g., flux pumps. This article presents novel investigation and analysis of the dynamic voltage in superconducting materials, and both the methodology and results can provide useful information for the future design/analysis of superconducting applications with DC transport currents and AC magnetic fields.

In this paper, in order to improve the electrical and thermal properties of SiC/EP composites, the methods of compounding different crystalline SiC and micro-nano SiC particles are used to optimize them. Under different compound ratios, the thermal conductivity and breakdown voltage parameters of the composite material were investigated. It was found that for the SiC/EP composite materials of different crystal types of SiC, when the ratio of α and β silicon carbide is 1:1, the electrical performance of the composite material is the best, and the breakdown strength can be increased by more than 10% compared with the composite material filled with single crystal particles. For micro-nano compound SiC/EP composites, different total filling amounts of SiC correspond to different optimal ratios of micro/nano particles. At the optimal ratio, the introduction of nanoparticles can increase the breakdown strength of the composite material by more than 10%. Compared with the compound of different crystalline SiC, the advantage is that the introduction of a small amount of nanoparticles can play a strong role in enhancing the break-down field strength. For the filled composite materials, the thermal conductivity mainly depends on whether an effective heat conduction channel can be constructed. Through experiments and finite element simulation calculations, it is found that the filler shape and particle size have a greater impact on the thermal conductivity of the composite material, when the filler shape is rounder, the composite material can more effectively construct the heat conduction channel.

Orderly arranged Silicon carbide (SiC)/epoxy (EP) composites were fabricated. SiC was made magnetically responsive by decorating the surface with iron oxide (Fe3O4) nanoparticles. Three treatment methods, including without magnetization, pre-magnetization and curing magnetization, were used to prepare SiC/EP composites with different filler distributions. Compared with unmodified SiC, magnetic SiC with core-shell structure was conducive to improve the breakdown strength of SiC/EP composites and the maximum enhancement rate was 20.86%. Among the three treatment methods, SiC/EP composites prepared in the curing-magnetization case had better comprehensive properties. Under the action of magnetic field, magnetic SiC were orderly oriented along the direction of an external field, thereby forming SiC chains. The magnetic alignment of SiC restricted the movement of EP macromolecules or polar groups to some extent, resulting in the decrease in the dielectric constant and dielectric loss. The SiC chains are equivalent to heat flow channels, which can improve the heat transfer efficiency, and the maximum improvement rate was 23.6%. The results prove that the orderly arrangement of SiC had a favorable effect on dielectric properties and thermal conductivity of SiC/EP composites. For future applications, the orderly arranged SiC/EP composites have potential for fabricating insulation materials in the power electronic device packaging field.

Orderly arranged Silicon carbide (SiC)/epoxy (EP) composites were fabricated. SiC was made magnetically responsive by decorating the surface with iron oxide (Fe3O4) nanoparticles. Three treatment methods, including without magnetization, pre-magnetization and curing magnetization, were used to prepare SiC/EP composites with different filler distributions. Compared with unmodified SiC, magnetic SiC with core-shell structure was conducive to improve the breakdown strength of SiC/EP composites and the maximum enhancement rate was 20.86%. Among the three treatment methods, SiC/EP composites prepared in the curing-magnetization case had better comprehensive properties. Under the action of magnetic field, magnetic SiC were orderly oriented along the direction of an external field, thereby forming SiC chains. The magnetic alignment of SiC restricted the movement of EP macromolecules or polar groups to some extent, resulting in the decrease in the dielectric constant and dielectric loss. The SiC chains are equivalent to heat flow channels, which can improve the heat transfer efficiency, and the maximum improvement rate was 23.6%. The results prove that the orderly arrangement of SiC had a favorable effect on dielectric properties and thermal conductivity of SiC/EP composites. For future applications, the orderly arranged SiC/EP composites have potential for fabricating insulation materials in the power electronic device packaging field.

© 2020 Elsevier B.V. The practical operation of a high-temperature superconducting (HTS) tape to form a HTS device is strongly related to the HTS tape electromagnetic environment in the device. With regard to the HTS tapes commonly stacked for practical applications, it is necessary to study the electromagnetic interaction of the proximity HTS tapes to design and optimize the HTS tapes and devices. This paper presents a numerical model of periodically arranged HTS tapes using the finite element method (FEM). The numerical method has been developed to build the equivalent periodical arrangement of infinite HTS tapes and applied to simulate two basic arrangements, horizontal and vertical periodical arrangements. The magnetic field and current distributions of HTS tapes by periodical arrangements have been investigated. The effects on critical current with different arrangements have been illustrated. It is found that the Y-stack can reduce the current carrying capacity while the X-array can increase that in comparison to a single tape. The differences between the FEM results and analytical models have been analysed and also compared with the Norris model. The two mathematical models derived for AC loss prediction have shown higher accuracy than the existing analytical models. This study presents an effective method to optimize the electromagnetic design by considering favorable structure or environment for the stacked HTS tapes and estimate the AC loss, shows the phenomenon of central tapes in an HTS array, which could be further used in performance analysis of superconducting devices, e.g. HTS transformers.

Due to the pressures caused by the energy crisis, environmental pollution, and international regulations, the largest ship-producing nations are exploring renewable resources, such as wind power, solar energy, and fuel cells to save energy and develop more environmentally-friendly ships. Solar energy has recently attracted a great deal of attention from both academics and practitioners; furthermore, the optimization of energy management has become a research topic of great interest. This paper takes a solar-diesel hybrid ship with 5000 car spaces as its research object. Then, following testing on this ship, experimental data were obtained, a multi-objective optimization model related to the ship’s fuel economy and diesel generator’s efficiency was established, and a partial swarm optimization algorithm was used to solve a multi-objective problem. The results show that the optimized energy management strategy for a hybrid energy system should be tested under different electrical loads. Moreover, the hybrid system’s economy should be taken into account when the ship’s power load is high, and the output power from the new energy generation system should be increased as much as possible. Finally, the diesel generators’ efficiency should be taken into consideration when the ship’s electrical load is low, and the injection power of the new energy system should be reduced appropriately.

This paper presents the measurement and simulation of Alternating Current (AC) losses on the Stabilizer-free and Copper Stabilizer High Temperature Superconducting (HTS) Tapes: SuperPower SF12100 and SCS12050. The AC loss measurement utilised electrical method to obtain overall losses with AC transport currents. The 2D H-formulation by COMSOL Multiphysics has been used to simulate the real geometry and multi-layer HTS tapes. Ferromagnetic AC losses of substrate have been assumed to be ignored as the substrates of SF12100 and SCS12050 are non-magnetic. Hysteresis AC losses in the superconducting layer, and eddy-current AC losses in copper stabilizer, silver overlayer and substrate were concerned in this investigation. The measured AC losses were compared to the AC losses from simulation, with 3 cases of different AC frequency 10, 100, and 1000 Hz. The eddy-current AC losses of copper stabilizer at frequency 1000 Hz were determined from both experiment and simulation. The estimation of AC losses with frequency at 10,000 Hz was also carried out using simulation method. Finally, the frequency dependence of AC losses from Stabilizer-free Tape and Copper Stabilizer Tape were compared and analysed.

© 2017 Elsevier B.V. This paper presents the optimization on the strength and homogeneity of magnetic field from superconducting Halbach Array magnet. Conventional Halbach Array uses a special arrangement of permanent magnets which can generate homogeneous magnetic field. Superconducting Halbach Array utilizes High Temperature Superconductor (HTS) to construct an electromagnet to work below its critical temperature, which performs equivalently to the permanent magnet based Halbach Array. The simulations of superconducting Halbach Array were carried out using H-formulation based on B-dependent critical current density and bulk approximation, with the FEM platform COMSOL Multiphysics. The optimization focused on the coils’ location, as well as the geometry and numbers of coils on the premise of maintaining the total amount of superconductor. Results show Halbach Array configuration based superconducting magnet is able to generate the magnetic field with intensity over 1 Tesla and improved homogeneity using proper optimization methods. Mathematical relation of these optimization parameters with the intensity and homogeneity of magnetic field was developed.

Lorentz Force Electrical Impedance Tomography (LFEIT) is a hybrid diagnostic scanner with strong capability for biological imaging, particularly in cancer and haemorrhages detection. This paper presents the design and simulation of a novel combination: a superconducting magnet together with LFEIT system. Superconducting magnets can generate magnetic field with high intensity and homogeneity, which could significantly enhance the imaging performance. The modelling of superconducting magnets was carried out using Finite Element Method (FEM) package, COMSOL Multiphysics, which was based on Partial Differential Equation (PDE) model with H -formulation coupling B -dependent critical current density and bulk approximation. The mathematical model for LFEIT system was built based on the theory of magneto-acoustic effect. The magnetic field properties from magnet design were imported into the LFEIT model. The basic imaging of electrical signal was developed using MATLAB codes. The LFEIT model simulated two samples located in three different magnetic fields with varying magnetic strength and homogeneity.

This paper presents the design and modeling of a second-generation (2G) high-temperature superconducting (HTS) magnet, which is suitable for Lorentz force electrical impedance tomography (LFEIT). The concept of constructing a superconducting magnet using the configuration of a Halbach array is proposed, which can achieve a favorable thin geometry for the LFEIT system, and is able to build a homogeneous magnetic field with high intensity. The modeling of this superconducting Halbach array magnet has been executed by COMSOL Multiphysics. H-formulation together with B-dependent critical current density and bulk approximation are used as the basic tools for modeling. Results reveal that this magnet can achieve over 1-T magnetic field in the cross section required. The optimization of HTS coils' location and different numbers of coils are carried out to balance the strength and homogeneity of magnetic field.

The application of resistive-type superconducting fault current limiters (RSFCLs) in electrical networks is very attractive due to their relative compactness, light weight, and good performance. However, this technology still has drawbacks: asymmetrical quench, uncertain limiting velocity, passive action, and incapability of enlarging capacity. Here, we present an active quenching technique which can potentially solve these problems. The quenching process is triggered using high frequency (HF) AC fields, which are generated by two coupled copper coils attached on both sides of the YBCO sample. Our experiments show that this approach is effective in guaranteeing uniform quench and therefore is expected to be able to significantly extend the service life of the device. Moreover, the quench speed can be considerably increased by the HF field. We find that the performance of acceleration is positively correlated to the transport current, intensity and frequency of the AC field. In addition, a DC magnetic field is added around the sample holder simultaneously with the AC field, to study the field-angular-frequency dependence of the quench time t(B_AC,f_AC,B_DC,θ_DC). Experimental results prove that the DC magnetic field can cooperate with the HF AC field to accelerate quench, which means better performance can be produced with lower costs with the two fields acting together. In all, this technique showed outstanding performance regarding quench acceleration and tape protection. We believe the HF-assisted quenching technology has a promising future in current limiting devices and hope our findings could be helpful for its potential applications.

Energy management strategy is a key technology of hybrid power ships. In recent years, renewable energy ship technologies have become a popular research field and one promising development direction to realize reasonable utilization of energy resource, as well as energy conservation and emission reduction. Among these technologies, the solar energy hybrid ship technology is currently attracting attention all over the word. In this paper, a 5000-car space solar energy hybrid ship is used as the research objective, and an energy management strategy that is based on fuzzy logic is proposed to distribute the ship power generation, solar energy, and battery output power according to the ship’s electrical load demand, and the fuzzification and stochasticity of solar energy. By comparing the simulation results with real ship testing results, it is identified that the proposed fuzzy logic energy management strategy can optimize the operation conditions of individual power generation sources, improve the overall performance of power system, and reduce the ship’s overall fuel consumption.

© 2002-2011 IEEE. Flux pumps are able to compensate slow current decay in high-T C superconducting (HTS) magnets through noncontact approaches. It is a promising alternative for power sources and thick current leads in operating HTS coils. Following the previous work of a rectifier flux pump, we developed a feedback control system to achieve flexible control of load current. Experimental results show that the flux pump can stabilize load current at a preset level with the help of the control system. Power loss of using the flux pump is also compared with that of using current leads.

This paper presents the concept of using horizontally parallel HTS tapes with AC loss study, and the investigation on possible wireless power transfer (WPT) applications. An example of three parallel HTS tapes was proposed, whose AC loss study was carried out both from experiment using electrical method; and simulation using 2D H -formulation on the FEM platform of COMSOL Multiphysics. The electromagnetic induction around the three parallel tapes was monitored using COMSOL simulation. The electromagnetic induction and AC losses generated by a conventional three turn coil was simulated as well, and then compared to the case of three parallel tapes with the same AC transport current. The analysis demonstrates that HTS parallel tapes could be potentially used into wireless power transfer systems, which could have lower total AC losses than conventional HTS coils.

© 2017 IOP Publishing Ltd. This paper presents an AC loss study of horizontally parallel HTS tapes. We proposed to use three parallel HTS tapes as an example. The AC losses of the middle and end tape of three parallel tapes have been measured using the electrical method and compared to those of an individual tape. The effect of the interaction between tapes on AC losses has been analysed, and compared with finite-element method (FEM) simulations using the 2D H-formulation implemented in COMSOL Multiphysics. By using FEM simulations, the cases of increasing number of parallel tapes have been considered, and the normalised ratio between the total average AC losses per tape and the AC losses of an individual single tape has been calculated for different gap distances. We proposed a new parameter, N s , a turning point for number of tapes, to divide Stage 1 and Stage 2 for the AC loss study of horizontally parallel tapes. For Stage 1, N < N s , the total average losses per tape increased with the increasing number of tapes. For Stage 2, N > N s , the total average losses per tape decrease with the increasing number of tapes. The analysis demonstrates that horizontally parallel HTS tapes could be potentially used in superconducting devices like HTS transformers, which could retain or even reduce the total average AC losses per tape with large number of parallel tapes.

Based on conventional approaches for the integration of resistive-type superconducting fault current limiters (SFCLs) on electric distribution networks, SFCL models largely rely on the insertion of a step or exponential resistance that is determined by a predefined quenching time. In this paper, we expand the scope of the aforementioned models by considering the actual behaviour of an SFCL in terms of the temperature dynamic power-law dependence between the electrical field and the current density, characteristic of high temperature superconductors. Our results are compared to the step-resistance models for the sake of discussion and clarity of the conclusions. Both SFCL models were integrated into a power system model built based on the UK power standard, to study the impact of these protection strategies on the performance of the overall electricity network. As a representative renewable energy source, a 90 MVA wind farm was considered for the simulations. Three fault conditions were simulated, and the figures for the fault current reduction predicted by both fault current limiting models have been compared in terms of multiple current measuring points and allocation strategies. Consequently, we have shown that the incorporation of the E-J characteristics and thermal properties of the superconductor at the simulation level of electric power systems, is crucial for estimations of reliability and determining the optimal locations of resistive type SFCLs in distributed power networks. Our results may help decision making by distribution network operators regarding investment and promotion of SFCL technologies, as it is possible to determine the maximum number of SFCLs necessary to protect against different fault conditions at multiple locations.

High-T$_{c}$ superconducting (HTS) flux pumps are capable of injecting flux into a superconducting circuit, which can achieve persistent current operation for HTS magnets. In this paper, we studied the operation of a rectifier-type HTS flux pump. The flux pump employs a transformer to generate high alternating current in its secondary winding, which is connected to an HTS load shorted by an HTS bridge. A high frequency ac field is intermittently applied perpendicular to the bridge, thus, generating flux flow. The dynamic resistance caused by the flux flow 'rectifies' the secondary current, resulting in a direct current in the load. We have found that the final load current can easily be controlled by changing the phase difference between the secondary current and the bridge field. The bridge field of frequency ranging from 10 to 40 Hz and magnitude ranging from 0 to 0.66 T was tested. Flux pumping was observed for field magnitudes of 50 mT or above. We have found that both higher field magnitude and higher field frequency result in a faster pumping speed and a higher final load current. This can be attributed to the influence of dynamic resistance. The dynamic resistance measured in the flux pump is comparable with the theoretical calculation. The experimental results fully support a first order circuit model. The flux pump is much more controllable than the traveling wave flux pumps based on permanent magnets, which makes it promising for practical use.

Superconducting flux pumps are the kind of devices which can generate direct current into superconducting circuit using external magnetic field. The key point is how to induce a dc voltage across the superconducting load by ac fields. Giaever (1966 IEEE Spectr. 3 117) pointed out flux motion in superconductors will induce a dc voltage, and demonstrated a rectifier model which depended on breaking superconductivity. van de Klundert et al (1981 Cryogenics 21 195, 267) in their review(s) described various configurations for flux pumps all of which relied on inducing the normal state in at least part of the superconductor. In this letter, following their work, we reveal that a variation in the resistivity of type II superconductors is sufficient to induce a dc voltage in flux pumps and it is not necessary to break superconductivity. This variation in resistivity is due to the fact that flux flow is influenced by current density, field intensity, and field rate of change. We propose a general circuit analogy for travelling wave flux pumps, and provide a mathematical analysis to explain the dc voltage. Several existing superconducting flux pumps which rely on the use of a travelling magnetic wave can be explained using the analysis enclosed. This work can also throw light on the design and optimization of flux pumps.