The modeling and analysis of superconducting coils is an essential task in the design stage of most devices based on high-temperature superconductors (HTS). These calculations allow verifying basic estimations and assumptions, proposing improvements, and computing quantities that are not easy to calculate with an analytical approach. For instance, the estimation of losses in HTS is fundamental during the design stage since losses can strongly influence the cooling system requirements and operating temperature. Typically, 2D finite element analysis is used to calculate AC losses in HTS, due to the lack of analytical solutions that can accurately represent complex operating conditions such as AC transport current and AC external applied magnetic field in coils. These 2D models are usually a representation of an infinitely long arrangement. Therefore, they cannot be used to analyze end effects and complex 3D configurations. In this publication, we use the homogenization of the T-A formulation in 3D for the analysis of superconducting coils with complex geometries where a 2D approach can not provide accurate analyses and verification of assumptions. The modeling methodology allows an easier implementation in commercial software (COMSOL Multiphysics) in comparison with the currently available 3D H homogenization, despite the complexity of the geometry. This methodology is first validated with a racetrack coil (benchmark case) by comparing the results with the well-established H formulation. Then, the electromagnetic behavior of coils with more complex geometries is analyzed.
Understanding the electro-thermal behavior of high temperature superconductor (HTS) materials is a critical aspect for designing efficient and reliable applications. In order to optimize cost and performance, one needs to understand the role played by the various layers of a HTS tape during a quench. On the one hand, the electrical and thermal properties of the materials used in the manufacturing of those tapes (e.g. alloy substrate, silver and copper) are well known. Knowledge of the functional dependence of the superconductor's resistivity ρ(J, T) above the critical current in 2G HTS CCs is very limited. In the flux creep or normal state regime, the resistivity can be approximated by empirical laws. In the flux-flow regime, it is difficult to extract ρ(J, T) due to the presence of Joule heating. In this contribution, using Finite Element Analysis (FEA), we present a method to retrieve the over-critical current resistivity, by estimating the amount of current, temperature and heat present in the various layers.
A detailed knowledge of the resistivity of high-temperature superconductors in the overcritical current regime is important to achieve reliable numerical simulations of applications such as superconducting fault current limiters. We have previously shown that the combination of fast pulsed current measurements and finite element analysis allows accounting for heating effects occurring during the current pulses. We demonstrated that it is possible to retrieve the correct current and temperature dependence of the resistivity data points of the superconductor material. In this contribution, we apply this method to characterize the resistivity vs. current and temperature of commercial REBCO tapes in the overcritical current regime, between 77 K and 90 K and in self-field conditions. The self-consistency of the overcritical resistivity model ρ OC (I, T) is verified by comparing DC fault measurements with the results of numerical simulations using this model as input. We then analyze by numerical simulation to what extent using the ρ OC (I, T) model instead of the widely used power-law model ρ PWL (I, T) affects the thermal and electrical performance of the tapes in the practical case of a superconducting fault current limiter. A remarkable difference is observed between the measured overcritical current resistivity model ρ OC (I, T) and the power-law resistivity model ρ PWL (I, T). In particular, the simulations using the power-law model show that the device quenches faster than with the overcritical resistivity model. This information can be used to optimize the architecture of the stabilizer in superconducting fault current limiters.
In recent years, the H formulation of Maxwell's equation has become the de facto standard for simulating the time-dependent electromagnetic behavior of superconducting applications with commercial software. However, there are cases where other formulations are desirable, for example for modeling superconducting turns in electrical machines or situations where the superconductor is better described by the critical state than by a power-law resistivity. In order to accurately and efficiently handle those situations, here we consider two published approaches based on the magnetic vector potential: the T -A formulation of Maxwell's equations (with power-law resistivity) and Campbell's implementation of the critical state model. In this contribution, we extend the T -A formulation to thick conductors so that large coils with different coupling scenarios between the turns can be considered. We also revise Campbell's model and discuss it in terms of its ability to calculate AC losses: in particular, we investigate the dependence of the calculated AC losses on the frequency of the AC excitation and the possibility of using quick one-step (instead of full cycle) simulations to calculate the AC losses.
The user has requested enhancement of the downloaded file.Abstract-The advanced telescope for high energy astrophysics (ATHENA) is an X-ray telescope of the European space agency which is planned to be launched in 2028. It will carry out observations in the X-ray band, exploiting two focal plane detectors where X-ray photons will be focused by silicon pore optics. Previous X-ray missions have shown a serious issue with soft protons and ions (below 150 keV/n), which could enter the telescope mirror aperture and be concentrated toward the focal plane. These particles must be blocked or diverted to avoid excess background loading on the detectors. The proposed solution is to deflect protons away from the instruments field of view by means of magnets located between the optics and the focal plane. A 160000 amp-turns HTS superconducting toroidal magnet, composed by three or four round coils located between 0.6 and 1.2 m from the focal plane, can efficiently deflect most of the incoming particles. The rejection rate for protons till 120 keV is better than 99%, to be compared with about 80% of a previously proposed diverter based on permanent magnets. The magnetic field requirement at the detectors level (B < 1 mT) is widely satisfied, as well as the mass budget of 110 kg. Challenging aspects related to the operation and reliability of the superconducting magnet will be discussed.Index Terms-Advanced telescope for high energy astrophysics (ATHENA), ESA, genetic algorithms, HTS, magnetic diverter, MgB 2 , superconductors. 1051-8223
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