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The AC losses, the current density and the magnetic field are important variables to design devices made of High Temperature Superconductors (HTS). These variables are often numerically computed using a transient finite element analysis even though the interest may lay in the steady-state regime of the device. The need for solving time-dependent variables has led to improve the computation time with efficient finite element models (FEM) relying on different formulations. These transient FEM are computationally slow and demanding in terms of resources. In the present work, an alternative path is taken with the development of a frequency-domain FEM using a phasor representation to alleviate the computation burden. This model does not have the versatility of the transient models. However, it can generate the initial steady-state conditions for a subsequent transient analysis. It is perfectly adapted to study the steady-state regime of HTS devices operated in AC conditions. In this phasor modelling approach, the Root Mean Square (RMS) resistivity of the superconductor is introduced. It is subsequently approximated by an exponential function introducing a factor to ease its implementation in the commercial software COMSOL Multiphysics with the most recent and fastest formulations T-A and J-A. The case studies encompass single BSCCO and REBCO tapes as well as a CORC cable or specifically, in the present work, a CORT (Conductor on Round Tube). The results of the time- and frequency-domain FEM simulations are compared against experimental data. The comparison of the models' results is carried out comparing the current density distributions as well as the AC losses. The comparison against experimental data is only conducted on the AC losses. In the present case, it is used to quantify thoroughly the accuracy of the numerical results compared to the measurements. A reasonable agreement between those results and the experimental data was found. 
The AC losses, the current density and the magnetic field are important variables to design devices made of High Temperature Superconductors (HTS). These variables are often numerically computed using a transient finite element analysis even though the interest may lay in the steady-state regime of the device. The need for solving time-dependent variables has led to improve the computation time with efficient finite element models (FEM) relying on different formulations. These transient FEM are computationally slow and demanding in terms of resources. In the present work, an alternative path is taken with the development of a frequency-domain FEM using a phasor representation to alleviate the computation burden. This model does not have the versatility of the transient models. However, it can generate the initial steady-state conditions for a subsequent transient analysis. It is perfectly adapted to study the steady-state regime of HTS devices operated in AC conditions. In this phasor modelling approach, the Root Mean Square (RMS) resistivity of the superconductor is introduced. It is subsequently approximated by an exponential function introducing a factor to ease its implementation in the commercial software COMSOL Multiphysics with the most recent and fastest formulations T-A and J-A. The case studies encompass single BSCCO and REBCO tapes as well as a CORC cable or specifically, in the present work, a CORT (Conductor on Round Tube). The results of the time- and frequency-domain FEM simulations are compared against experimental data. The comparison of the models' results is carried out comparing the current density distributions as well as the AC losses. The comparison against experimental data is only conducted on the AC losses. In the present case, it is used to quantify thoroughly the accuracy of the numerical results compared to the measurements. A reasonable agreement between those results and the experimental data was found. 
High-temperature superconducting coils are used in various large-scale
applications, like rotating machines and high-field magnets. However, modeling
these coils is a complicated and time-consuming process, especially due to the non-
linearity of the current-voltage characteristics of the superconductors and the complex
multiphysics involved. In this work, we used a fast homogenized method to model
the coupled electromagnetic and electrothermal properties of racetrack and pancake
coils for different applications. For this purpose, various formulations wielding
homogenization methods are used and benchmarked with each other, as well as with
models considering the detailed structure of the HTS tapes. We observe a very good
agreement between different models (homogenized and detailed), and we discuss the
pros and cons of the inclusion of insulating layers between the turns in homogenization.
This work was performed under the collaboration of the COST action modeling teams
and can be used as a review of the state-of-the-art superconductor modeling techniques,
and a source for the development and benchmark of future numerical methods.
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