In the HTS/LTS high field magnet system, a sudden background LTS magnet quench was potential to destroy the double pancakes (DPs) of the insert HTS magnet. An equivalent circuit model and a finite element model were combined in this paper to simulate the hoop stress during the background magnet quench. A magnetic dam scheme to protect the insert magnet in this situation was proposed, simulated and test. According to the simulation results, magnetic dam can reduce the instantaneous stress rise by 83.5\%. The effect of the magnetic dam isolating the magnetic field changes was verified by experiments with a Bi2223 coil magnet. The magnetic dam parameters that could affect the isolating effect were also discussed in this paper. Magnetic dam could play a big role in quench protection as a passive protecting scheme.
REBCO insert magnet magnetic dam quench protection.
HTS magnet has achieved significant progress in recent years. A 26 T full REBCO magnet was developed by MIT and SuNAM in 2016. In 2017, National High Magnetic Field Laboratory (NHMFL) achieved a 32 T field with a 17 T REBCO insert and 15 T LTS background magnet. The Francis Bitter Magnet Laboratory, MIT has planned a new 1.3-GHz LTS/HTS NMR magnet. We, Institute of Electrical Engineering, Chinese Academy of Sciences (IEECAS) achieved 27.2T in 2017 and 32.35T in 2019, which was the world record DC magnetic field ever-achieved by all superconducting magnets. Many effective numerical models had been vital to study the electrical behaviors of HTS Magnets. These models can effectively analyze the self-protection ability, stress change and quench process of HTS magnets.
A variety of protecting methods have been adopted to protect the 32.35 tesla HTS/LTS system. Winding the insert magnet no-insulated (NI) could reduce the risk of quench. Special structure was designed to improved heat dissipation conditions. A parallel protecting circuit could convert the energy into external heat if the magnet quenched. In the whole 32.35T magnet system, the quenching propagation of the LTS magnet is fast. When background magnet quenches, the protecting system of the LTS magnet would cut off the current immediately. Mutual inductance coupling would transfer millions of joules of energy to the HTS insert. That would make REBCO insert magnet serious damaged. It is important to measure the influence of background magnet quench on the insert magnet. A scheme that can effectively protect the insert magnet in this situation is also necessary. Using additional coils to protect the coil from quench damage had been proposed recently. Yet, schemes protecting the insert magnet from the background field quench has not been promoted.
According to the simulation results, the magnetic dam scheme proposed in this paper can reduce the instantaneous stress rise by 83.5\%. In additional, a magnetic dam would not change the field shape considering the resistance itself.
In this paper, the current change of the insert magnet in the background field magnet quench was described by a circuit model. With the current data, the stress changes of the insert magnet were simulated by commercial finite element software. The isolation effect on changing magnetic field was verified by experiments with a Bi2223 isolating magnet.
An equivalent circuit model was used to simulate the current distribution of the insert magnet. The model of the insert magnet was shown in fig. Background magnet was shown in table and fig(gray parts).
Because of the massive induced voltage from magnet field change, the subdivision numerical model simulation got a poor convergence. A simplified circuit model was used to simulate the current change of the insert HTS magnet in the quenching progress of the background magnet.
In the circuit model, each single pancake was simplified as a unit. As seen in fig, where is the operation current; is the radial current; is the azimuthal current; is the equivalent radial resistance; is the stabilizer resistance; is the equivalent azimuthal superconducting resistance. The equivalent radial resistance was obtained by measuring the time constant which satisfies:
To get the equivalent circuit equation of a single element in the entire insert magnet, replace the with , where is the mutual inductance matrix of the insert magnet model, is the azimuthal current matrix. Decreasing the background magnet current from working current 225.5A to 0A in 2 seconds, there is another voltage part added:
where is the mutual inductance matrix between background magnet and the insert magnet, is the background magnet current. The critical current of a single pancake is determined by temperature and magnetic field.
As shown in fig, a model including background magnet (gray), a magnetic dam (dark green) and the insert magnet (orange) was constructed in COMSOL to analyze the protective effect of the magnetic dam. Current of insert magnet was given by the circuit simulation results. The stress of the insert magnet in background field magnet quenching can be obtained.
A magnetic dam can isolate the rapidly changing magnetic field. That is the reason it protects the insert magnet from background field magnet quench. The effect can be verified by a sudden discharge experiment. An insulating coiling Bi2223 magnet was used as the background field magnet (fig). Different types of magnetic dams were set in the Bi2223 magnet. Change of the central magnetic field was measured. The magnetic field isolation effect of the magnetic dam was characterized by the delay. The Bi2223 magnet in the experiment was an insulating magnet, whose magnetic field positively was correlated with the central magnetic field. The change of the central magnetic field characterized the entire magnetic field, thus reflecting the isolating effect of the magnetic dam.
Three different types of magnetic dams tested in the experiment were made of oxygen free copper, 1 mm and 2.5 mm enameled copper wire (fig). The inner diameter () of all 3 magnetic dams was 105 mm, outer diameter () about 120 mm, and the height was 360 mm. Their properties were shown in table. In fig, on the right side was the copper cylinder; in the middle was the 2.5 mm enameled wire coil; and the left was the 1 mm enameled wire coil.
Magnetic dam was set inside the Bi2223 magnet. A Hall probe was fixed on a rod to measure the central magnetic field (fig). The Bi2223 magnet connected with a 5.5 protecting parallel circuit was excited and discharged in liquid nitrogen.
To verify the experiment results and the influence, a simulation was established measuring the change of the central magnetic field. The structural optimization including different layers, magnetic dam thickness and material conductivity were also simulated. These simulation results could improve the design of the magnetic dam.
Current changes of half HTS DPs after background field magnet quench were simulated (fig). Current variation within 100 ms is shown in the figure, which is very representative. Most of the coil 1 DPs show little current changes because of the protection from coil 2, which has high electromagnetic margin designed. However, the azimuthal current of the single layer winded DP3 at the most ends quickly approached the critical current.
Decrease of the background magnetic field did not immediately influence most part of coil 1. However, the field deformation would result in screen current increase on the DPs at both ends of coil 1. The screen current could cause unbalanced stress to the REBCO tape.
After the background field magnet quench, the max hoop stress of the insert magnet would rise from 673 MPa to 788 MPa in 1 second (fig). Violent stress rose is potential to damage the insert magnet. If a magnetic dam was settled between the background and the insert magnet, the max hoop stress would only rise to 692 MPa (fig). That means magnetic dam can reduce the instantaneous stress rise by 83.5\%. %Meanwhile, the time of the maximum hoop stress is also delayed by about 0.5 second. In simulation, the 10 mm thick magnetic dam produces a deformation of 0.15 mm (fig). Researchers should not ignore the magnetic dam deformation in design.
In the central field simulation, the magnetic dam held the central field for a few seconds after the current of background magnet dropping (fig). Fig also shows that the protecting effect is not significantly improved after layering.
Curves in fig show the time required for the central magnetic field decreasing by 99\% and 90\%. The 99\% and 90\% lines are shown in fig. Fig shows that the effect of the magnetic dam is linearly related to its thickness. There is no marginal effect within the scope of feasibility.
Conductivity of the material would affect the protecting effect of the magnetic dam. The simulation results are shown in fig: the protecting effect is directly proportional to the conductivity of the material used.
Magnetic dam can also be an enameled coil. A simple calculation represents that the isolating effect of multi-turn coil type magnetic dam is not affected by wire diameter. That was also confirmed by simulation ().
On the other hand, the comparison between fig and fig shows that the protecting effect of the magnetic dam composed of multi-turn conductors is not as good as that of the whole block of the same material.
The results of the experiment were shown in fig. The Y-axis represents the normalized magnetic field, while the X-axis represents time. Data of several tests were aligned according to the current cut-off time, which can reflect the changes of the central magnetic field in different situations and the magnetic field change to delay caused by the existence of the magnetic dams.
The red line represents the central field change when the current of background field was cut off without a magnetic dam. The blue triangle corresponds to a magnetic dam with 10 mm thick, while the red rhombus represents the simulation result. The other 2 lines correspond to coil dams made by enameled wires with different radius.
The magnetic dam has remarkable isolation on the violent change of magnetic field, whatever the structure and diameter. The protecting effect of a magnetic dam made by pure copper is better than copper coils of the same size. Wire diameter difference has little effect on the magnetic field isolation effect.
With experimental results of good agreement with the simulation results, it can be positively concluded that the magnetic dam can play a big role protecting the insert magnet. We have planned to reserve a 15 mm space in the future 30T-series user magnets for magnetic dam as a passive protection.
In situation of background magnet quench, stress caused by unbalanced distribution of over current is more likely to damage the insert magnet than heating because of the self-protection mechanism of NI coils. To protect the insert magnet, a magnetic dam scheme can be used to reduce the over current in the DPs of the insert magnet by slowing down the magnetic flux changes. The magnetic dam performed well in simulation. A magnetic dam can reduce the instantaneous stress rise by 83.5\%. Simulation point out that magnetic dam made by integrated metal performs better than enameled coil. To improve the protecting performance, we can increase the dam thickness and use materials with higher conductivity. The magnetic dam might be deformed by 0.15 mm when the magnet quenches in simulation. The deformation which must be considered in the design. Experiments verified the results of analysis and simulation. Magnetic dam scheme is an attempt to combine the background field protection with the insert magnet protection. This combination is a fundamental way to establish the quench-protecting system of high field magnet systems.
The authors acknowledge the support of the National Natural Science Foundation of China under Grants 51777205, 51807191 and 11545004, the Bureau of Frontier Sciences and Education, Chinese Academy of Sciences under Grants QYZDJ-SSWJSC012, National Key Research and Development Project under Grants 2020-YFF-01014702, and China’s Synergetic Extreme Condition User Facility (SECUF) Project.