Antti Stenvall

Computation of Losses in HTS Under the Action of Varying Magnetic Fields and Currents

Numerical modeling of superconductors is widely recognized as a powerful tool for interpreting experimental results, understanding physical mechanisms, and predicting the performance of high-temperature-superconductor (HTS) tapes, wires, and devices. This is particularly true for ac loss calculation since a sufficiently low ac loss value is imperative to make these materials attractive for commercialization. In recent years, a large variety of numerical models, which are based on different techniques and implementations, has been proposed by researchers around the world, with the purpose of being able to estimate ac losses in HTSs quickly and accurately. This paper presents a literature review of the methods for computing ac losses in HTS tapes, wires, and devices. Technical superconductors have a relatively complex geometry (filaments, which might be twisted or transposed, or layers) and consist of different materials. As a result, different loss contributions exist. In this paper, we describe the ways of computing such loss contributions, which include hysteresis losses, eddy-current losses, coupling losses, and losses in ferromagnetic materials. We also provide an estimation of the losses occurring in a variety of power applications.

Accelerator-Quality HTS Dipole Magnet Demonstrator Designs for the EuCARD-2 5-T 40-mm Clear Aperture Magnet

Future high-energy accelerators will need very high magnetic fields in the range of 20 T. The Enhanced European Coordination for Accelerator Research and Development (EuCARD-2) Work Package 10 is a collaborative push to take high-temperature superconductor (HTS) materials into an accelerator-quality demonstrator magnet. The demonstrator will produce 5 T stand alone and between 17 and 20 T when inserted into the 100-mm aperture of a Fresca-2 high-field outsert magnet. The HTS magnet will demonstrate the field strength and the field quality that can be achieved. An effective quench detection and protection system will have to be developed to operate with the HTS superconducting materials. This paper presents a ReBCO magnet design using a multistrand Roebel cable that develops a stand-alone field of 5 T in a 40-mm clear aperture and discusses the challenges associated with a good field quality using this type of material. A selection of magnet designs is presented as the result of the first phase of development.

The EuCARD-2 Future Magnets European Collaboration for Accelerator-Quality HTS Magnets

EuCARD-2 is a project supported by FP7-European Commission that includes, inter alia, a work-package (WP10) called “Future Magnets.” This project is part of the long term development that CERN is launching to explore magnet technology at 16 T to 20 T dipole operating field, within the scope of a study on Future Circular Colliders. The EuCARD2 collaboration is closely liaising with similar programs for high field accelerator magnets in the USA and Japan. The main focus of EuCARD2 WP10 is the development of a 10 kA-class superconducting, high current density cable suitable for accelerator magnets, The cable will be used to wind a stand-alone magnet 500 mm long and with an aperture of 40 mm. This magnet should yield 5 T, when stand-alone, and will enable to reach a 15 to 18 T dipole field by placing it in a large bore background dipole of 12-15 T. REBCO based Roebel cables is the baseline. Various magnet configurations with HTS tapes are under investigation and also use of Bi-2212 round wire based cables is considered. The paper presents the structure of the collaboration and describes the main choices made in the first year of the program, which has a breadth of five to six years of which four are covered by the FP7 frame.

Comparison of three eddy current formulations for superconductor hysteresis loss modelling

As is well known, the superconductor hysteresis loss modelling problem may be formulated as an eddy current (EC) problem in which the resistivity of the superconducting region is modelled with a power law. We compare three EC formulations suitable for the modelling of superconductor hysteresis losses. Namely, the a?v?j-, T??- and h-formulations are discussed. We review these formulations, and through simulation results the properties of these formulations are discussed and their suitabilities for different modelling situations are compared. Special attention is paid to the h-formulation: we investigate the effects of the modelling decisions related to resistivity of the air region in an h-formulation based EC solver. According to the results, these decisions affect the energy distribution of the field solution and may even lead to seemingly contradictory behaviour.

Stability considerations of multifilamentary MgB2 tape

The risk of overheating arises if the stability of an MgB2 coil is lost. This is mainly due to the low thermal conductivity of the matrix metal, which is typically iron or nickel. Due to a strong chemical reaction, copper can be used in contact with MgB2 only in specific cases: in situ preparation route and low formation temperature. However, recent developments in the manufacture of MgB2 conductors have resulted in stabilized MgB2 tapes. In any case, the stability considerations of MgB2 conductors are of great importance. We studied computationally the stability of an MgB2/Ni/Fe/Cu tape manufactured by Columbus Superconductors. First, the effective material properties of the tape were computed. Based on these material properties, we computed the basic quench characteristics (minimum propagation zone, minimum quench energy and normal zone propagation velocities) for the tape at 15, 20 and 25 K. The tape unit cell model was used in computations. The computed stability results were compared with the measured ones of a monofilament MgB2/Cu/Ni tape and commercial LTS and HTS. According to the results, the basic quench characteristics computed fit between the ones of LTS and HTS materials.

An eddy current vector potential formulation for estimating hysteresis losses of superconductors with FEM

Many people these days employ only commercial finite element method (FEM) software when solving for the hysteresis losses of superconductors. Thus, the knowledge of a modeller is in the capability of using the black boxes of software efficiently. This has led to a relatively superficial examination of different formulations while the discussion stays mainly on the usage of the user interfaces of these programs. Also, if we stay only at the mercy of commercial software producers, we end up having less and less knowledge on the details of solvers. Then, it becomes more and more difficult to conceptually solve new kinds of problem. This may prevent us finding new kinds of method to solve old problems more efficiently, or finding a solution for a problem that was considered almost impossible earlier. In our earlier research, we presented the background of a co-tree gauged T– FEM solver for computing the hysteresis losses of superconductors. In this paper, we examine the feasibility of FEM and eddy current vector potential formulation in the same problem.

A checklist for designers of cryogen-free MgB2 coils

Intensive research has been directed at MgB2 since its discovery in 2001, focusing first on the material properties and conductor development and recently also on coil demonstrations. The relatively cheap and easy fabrication makes MgB2 a tempting material for superconducting applications. It can also be operated in the vicinity of 20 K, at which the commercial LTS materials are still in the normal state. However, commercial breakthrough requires practical applications and demonstrations. Therefore, we built a solenoidal react-and-wind MgB2 coil consisting of 46 m of commercially available MgB2 /Ni/Fe/Cu tape manufactured by Columbus Superconductors. We tested the coil in a cryogen-free environment and measured the effect of repeated cooldowns and current ramp rate on the coil critical current. Also, temperature homogeneity in the winding was studied. Based on the test results we point out features which should be checked when cryogen-free magnet systems are designed or their performance is discussed. For example, the coil critical current and n value can depend notably on the current ramp rate.

Programming finite element method based hysteresis loss computation software using non-linear superconductor resistivity and T ? phiv formulation

Due to the rapid development of personal computers from the beginning of the 1990s, it has become a reality to simulate current penetration, and thus hysteresis losses, in superconductors with other than very simple one-dimensional (1D) Bean model computations or Norris formulae. Even though these older approaches are still usable, they do not consider, for example, multifilamentary conductors, local critical current dependency on magnetic field or varying n-values. Currently, many numerical methods employing different formulations are available. The problem of hysteresis losses can be scrutinized via an eddy current formulation of the classical theory of electromagnetism. The difficulty of the problem lies in the non-linear resistivity of the superconducting region. The steep transition between the superconducting and the normal states often causes convergence problems for the most common finite element method based programs. The integration methods suffer from full system matrices and, thus, restrict the number of elements to a few thousands at most. The so-called T ? formulation and the use of edge elements, or more precisely Whitney 1-forms, within the finite element method have proved to be a very suitable method for hysteresis loss simulations of different geometries. In this paper we consider making such finite element method software from first steps, employing differential geometry and forms.

The 16 T Dipole Development Program for FCC

A key challenge for a future circular collider (FCC) with centre-of-mass energy of 100 TeV and a circumference in the range of 100 km is the development of high-field superconducting accelerator magnets, capable of providing a 16 T dipolar field of accelerator quality in a 50 mm aperture. This paper summarizes the strategy and actions being undertaken in the framework of the FCC 16 T Magnet Technology Program and the Work Package 5 of the EuroCirCol.

Quench analysis of MgB2 coils with a ferromagnetic matrix

If a superconducting wire includes a ferromagnetic constituent, then magnet design requires a novel approach. We have previously reported on computing the critical current of coils that include ferromagnetic matrix material. Now we introduce a quench analysis in MgB2 solenoid and racetrack coils that utilize conductors with a ferromagnetic matrix. The computer code that was developed uses the commercial software MATLAB and FEMLAB. The code is also capable of simulating quench with coils wound of low-temperature superconductor (LTS) and high-temperature superconductor (HTS). The enhancement to this code compared to the earlier reported quench programs is that the non-linear magnetic behaviour due to the ferromagnetic matrix is taken into account. So far, the code does not take into account the conductor AC losses during current decay and the possible quench back due to the thermal interface.