Jorma Lehtonen

A numerical model for stability considerations in HTS magnets

We propose that in an HTS application, stability is lost more likely because of a global increase in temperature caused by heat generation distributed over the whole coil than because of a local normal zone which starts to propagate. For consideration of stability in HTS magnets, we present a computational model based on the heat conduction equation coupled with Maxwells equations, whereby analysis can be performed by using commercial software packages for computational electromagnetics and thermodynamics. For temperature distribution inside the magnet, we derive the magnetic field dependent effective values of thermal conductivity, specific heat, and heat generated by electromagnetic phenomena for the composite structure of the magnet, while cooling conditions and external heat sources are described as boundary conditions. Our model enables the magnet designer to estimate a safe level of the operation current before a thermal runaway. Finally, as examples, we present some calculations of the HTS magnet with ac to review the effects of slanted electric field-current density E (J ) characteristics and high critical temperature of HTS materials.

Effective thermal conductivity in HTS coils

Abstract We present a numerical model to determine the effective thermal conductivity in high- T c superconducting (HTS) coils. The model, based on the heat conduction equation solved with the finite element method, will help us to compute the temperature dependence of the effective thermal conductivity in coils with varying proportions of epoxy in the total winding volume. The conductor parameters in the coils correspond to those in a real Bi-2223/Ag multifilamentary composite tape, where the anisotropy of the Bi-2223 material has been taken into account. We will furthermore discuss about the effects of geometry of the composite structure on effective thermal conductivity. Our result shows that in epoxy impregnated HTS coils at temperatures below 60 K, the effective thermal conductivity is over two orders of magnitude higher in the parallel direction with the conductor axis compared to the perpendicular direction.

Computation of AC losses in high-temperature superconductors

Abstract A formulation for the computation of AC losses in technical HTS conductors by using commercial FEM packages developed for two-dimensional computation of electromagnetic problems is presented. The formulation takes into account the real current density–electric field characteristic of a conductor and the spatial dependence of the current density. Having presented the formulation, example runs comparing transport current loss behaviour between HTS and LTS conductors are given.

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.

Optimization of HTS superconducting magnetic energy storage magnet volume

Nonlinear optimization problems in the field of electromagnetics have been successfully solved by means of sequential quadratic programming (SQP) and the finite element method (FEM). For example, the combination of SQP and FEM has been proven to be an efficient tool in the optimization of low temperature superconductors (LTS) superconducting magnetic energy storage (SMES) magnets. The procedure can also be applied for the optimization of HTS magnets. However, due to a strongly anisotropic material and a slanted electric field, current density characteristic high temperature superconductors HTS optimization is quite different from that of the LTS. In this paper the volumes of solenoidal conduction-cooled Bi-2223/Ag SMES magnets have been optimized at the operation temperature of 20 K. In addition to the electromagnetic constraints the stress caused by the tape bending has also been taken into account. Several optimization runs with different initial geometries were performed in order to find the best possible solution for a certain energy requirement. The optimization constraints describe the steady-state operation, thus the presented coil geometries are designed for slow ramping rates. Different energy requirements were investigated in order to find the energy dependence of the design parameters of optimized solenoidal HTS coils. According to the results, these dependences can be described with polynomial expressions.

Superconducting power link for power transmission and fault current limitation

Abstract Superconducting power links (SUPERPOLI) will offer the opportunity for low-loss power transmission of high nominal currents and fault current limitation simultaneously in a single device. This paper presents the status of European SUPERPOLI project where the long term goal is to build a GVA class, 20 kV, three-phased, 200 m long superconducting power link. As a step towards the GVA-class application, a one-phase demonstrator of 2 m length for 20 kV, 2–5 kA rms operation has been designed and is now under construction. The project includes the development of two alternative low-ac-loss conductor designs suitable for current limitation: a tubular Bi-2212 bulk conductor with moderate J c and a tubular YBCO coated conductor with high J c .

Optimization of SMES magnet volume with electromagnetic and mechanical constraints

A tool for solving a nonlinear optimization problem by means of sequential quadratic programming (SQP) and finite element method (FEM) is presented. In this paper both the electromagnetic and mechanical design objectives are considered when optimizing the volume of a 0.2 MJ conduction cooled Nb/sub 3/Sn superconducting magnetic energy storage (SMES) magnet, which is under construction at Tampere University of Technology. The results show that the combination of SQP and FEM provides a useful computational tool for the design of the superconducting applications.

Stability and quench of a HTS magnet with a hot spot

Stability and quench experiments were performed on a cryocooler refrigerated Bi-2223/Ag magnet with an artificial hot spot. The hot spot was realized by making a poor, high-resistivity joint between the current terminal and the bottom pancake coil of the magnet. According to the experiments the magnet could tolerate considerable power dissipation at the hot spot for long times still avoiding a thermal runaway. Processes preceding the quench occurred much slower if compared to quenches in typical LTS windings. For a deeper understanding of the measured results computer simulations were done by using a model based on the heat conduction equation coupled with Maxwells equations and solved using the finite-element method. Simulated temperature distributions inside the magnet showed that considerable temperature differences exist between different parts of the magnet, despite the slowness of the processes. Before a quench there were no large temperature gradients around the hot spot. During the quench the hot spot temperature increased rapidly but the temperature of other parts of the magnet increased only with a delay.

Quench current in conduction-cooled HTS magnets

The quench current of a superconducting magnet, Iq, is the current at which a thermal runaway occurs. In trained LTS magnets Iq can be estimated from a short sample critical current, Ic, due to a steep electric field (E)–current density (J) characteristic. Anisotropy and the slanted E(J)-characteristic make the situation more complicated in HTS magnets. Furthermore, the Iq of a conduction-cooled magnet depends strongly on the geometry of the thermal interface. Several criteria, such as the average electric field of 0.1 μV cm−1 and the maximum electric field of 1 μV cm−1 have been suggested for Iq of an HTS magnet. However, in order to determine Iq accurately a detailed stability analysis is required. In this paper different Iq criteria for conduction-cooled HTS magnets are computationally compared at the operation temperatures of 4.2, 20 and 77 K. Computations are based on the Ic data measured with a Bi-2223/Ag tape. 150 different solenoidal magnets having the wire length of 2, 5 and 10 km have been studied. The effect of the thermal interface geometry on Iq has also been investigated. Rules of thumb for the quick estimation of Iq at the given operation temperature are suggested.

Mathematical model of voltage–current characteristics of Bi(2223)/Ag magnets under an external magnetic field

We have developed a mathematical model, which enables us to predict the voltage–current V(I) characteristics of a solenoidal high-temperature superconductor (HTS) magnet subjected to an external magnetic field parallel to the magnet axis. The model takes into account the anisotropy in the critical current–magnetic field (Ic(B)) characteristic and the n-value of Bi(2223)Ag multifilamentary tape at 20 K. From the power law between the electric field and the ratio of the operating and critical currents, the voltage on the magnet terminals is calculated by integrating the contributions of individual turns. The critical current of each turn, at given values of operating current and external magnetic field, is obtained by simple linear interpolation between the two suitable points of the Ic(B) characteristic, which corresponds to the angle α between the vector of the resulting magnetic flux density and the broad tape face. In fact, the model is valid for any value and orientation of external magnetic field, and is only limited by the validity of the electric field power law as a function of operating current. Electric fields of individual turns of the model magnet, which consists of 22 pancake coils, have been analysed for different values of operating current and external magnetic field. The voltage distribution on individual pancake coils and the overall voltage between the magnet terminals have also been analysed. Finally, the influence of external magnetic field on the V(I) characteristics of the magnet have been studied for different values of operating current. We report on a new and rather unexpected behaviour of the HTS magnets at different operating conditions, together with a theoretical explanation.