SIMULIA Opera Helps Understand Superconductivity Experiment at Oxford University 

Nuclear Fusion

Climate change is driving the need for scientists and engineers to develop green methods of creating energy to replace fossil fuel power generation. Wind, solar, tidal and wave energy can all help to meet that need but they have one major drawback – they are dependent on climatic and ocean conditions. On a still, cloudy day there could be a major problem for a power system that relied mainly on solar and wind. To provide a power grid with a continuous, controllable generation source, alternative methods must also be adopted. Nuclear fission, as used in conventional nuclear power stations, can be considered, but that has its own issues with storage or disposal of long term radioactive waste materials – maybe remaining dangerous for thousands of years.

One of the most promising alternative technologies that is currently being actively developed is nuclear fusion. The by-products of fusion are mostly harmless and even radioactive materials have a short half-life compared to fission waste. However, fusion – the same process as keeps our sun burning – has many challenges. The plasma that is created needs to be heated to around 100 – 150 million °C and confined within a small volume to ensure the fusion reaction is self-sustaining. Because of the extreme temperature, the plasma cannot be contained in a conventional vessel and must be held in place by extremely strong magnetic fields.

The magnetic configuration that has been most widely researched is the tokamak. The largest project currently in construction is ITER at Cadarache, France. An artist’s impression is in Fig 1 below – note the human figure standing at the base in the foreground! The coils that produce the magnetic field are made from low temperature superconductors (LTS) as these have zero resistance at temperatures close to absolute zero. Equivalent copper coils would probably use as much power as the reactor could generate to supply the resistive losses created by the necessary currents providing the required strength of magnetic field.

ITER was designed before a new generation of high temperature superconducting (HTS) materials became more readily available. The most important attribute of HTS materials is that they remain superconducting at higher magnetic fields than LTS, typically >20 T at 20 K. However, they can also operate as superconducting coils at temperatures up to 60 or 70 K, making the required cryogenics much simpler. These materials have produced a new wave of R&D into tokamaks, much of which is being conducted at smaller start-up companies with a view to having “off-the-shelf” designs that can be installed relatively quickly compared to large reactors like ITER. But there are also some larger projects, such as the proposed UK STEP tokamak, which will use HTS materials and is hoped to be generating power by 2040.

Neutron Bombardment

A significant unknown is how the HTS material will behave when it is continually subjected to bombardment by neutrons generated during the fusion reaction. It is expected that over time the performance of the coils (mainly their ability to carry very high currents without losses) will degrade, requiring the design to be capable of operating towards the end of its life as well as at the beginning.

The world-renowned Centre for Applied Superconductivity in Materials Science at Oxford University, led by Professors Chris Grovenor and Susannah Speller, is conducting experiments to investigate how the material will survive during operation. Samples of the HTS tape used to construct the coils are irradiated using a beam of ions to rapidly emulate the neutron damage in a fusion reactor in a safe, controllable way. The irradiation is performed in sequential steps, with the critical current (the current above which the sample will stop being superconducting) being measured during irradiation and after the ion beam is switched off. Kirk Adams, one of the PhD students at Oxford, has produced results that indicate that the ion beam is affecting the performance, as shown in Fig 2 below.

Fig 3 shows a view of the experiment and Fig 4 shows the equivalent CAD model with the ion beam entering through the aperture. The sample is contained just below the aperture in the top plate.

The dimensions of the sample are quite extreme. It is a 25 mm length cut from a typical 4 mm wide HTS tape, but the thickness is about 100 um. In the thickness direction, there are multiple materials, as shown in fig 5 at an exaggerated thickness scale. The layer of rare earth barium copper oxide high temperature superconductor (REBCO HTS) which carries the current in normal operation is only 2 um thick, while the barrier layer (buffer stack) is less than 0.1 um thick.

In the sample, a 5.8 mm length of the upper copper and silver have been removed to expose the HTS layer directly to the ion beam. The HTS has also been further etched to provide a narrow track of material to lower the input current needed to reach the critical current density, as shown in fig 6.

Effect of Temperature on Superconducting Capability

As can be seen in Fig 2, the experiment is also monitoring the temperature of the cold head on which the sample is mounted. This is nominally maintained at 40 K, and the measurements show that this is achieved. However, it is not directly possible to monitor the temperature in the sample, particularly where the ion beam is irradiating the HTS material (over the narrow track and substrate). Critical current density of HTS is also dependent on its temperature, with most REBCO having a critical temperature around 80-90 K.

Professor Speller approached the Opera team in SIMULIA, knowing of its many years of experience in simulating superconducting devices, to ask if it would be possible to model their sample to ascertain the peak temperature in the HTS material while the beam was switched on. The concern was that the heat deposited by the ion beam would be sufficient to lower the critical current density of the HTS during the beam on measurement (as shown in Fig 2), such that the in situ effect of the ion bombardment was not due to a physical reaction, but it was a thermal effect. The Oxford team also wanted to know the rate at which the temperature rose and fell when the ion beam was turned on and off.

Modeling in Opera-3d

Kirk Adams provided a CAD model of the outline shape of the sample but without any detail of the layer structure. The CAD was imported into the Opera-3d Modeler, and the dimensions were used to construct the whole model, as shown in Fig 7. As shown in Fig 7(c), the Modeler’s capability to scale the axes independently was very useful for visualization due to the high aspect ratio of the geometry. The Modeler was also used to remove two items of the geometry that had been included in the CAD model (highlighted in amber in Fig 7(a)) that were not in the experiment sample.

The thermal material properties as a function of temperature were also provided by Kirk and were imported into Opera-3d Modeler as functional tables, allowing the non-linear thermal diffusion Transient Thermal simulation to update the properties in each finite element to match the computed temperature. The heat from the beam was applied as a surface heat density switched on and off to follow the pattern of ion bombardment.

Producing a finite element mesh for such thin geometry (micron thicknesses) that will give accurate results without over-meshing in the other two directions is challenging. Conventional automatic tetrahedral meshing would give elements with very high aspect ratio and would probably give poor results. However, Opera-3d mosaic meshing is designed particularly to handle thin structures and the model only contains 22,718 elements (a mixture of 2^nd order hexahedra and triangular prisms) generated from a suitable 2-dimensional surface mesh that is adequate to capture the behavior in the length and width directions.

Fig 8 shows the temperature distribution in the etched section of the HTS after the ion beam has been applied for more than about 10 to 20 seconds for any pulse. By this time it has reached thermal equilibrium where the heat applied through the ion beam is being lost at the same rate through the contact between the underside of the copper and the cold head. As can be seen, the maximum temperature is just less than 60 K.

Fig 9 shows the profile of the maximum temperature during the whole of the transient simulation, while fig 10 shows the temperature rise and fall at each irradiation step. In fact, the results for all irradiation steps are almost identical, also showing that the sample is returning to the 40 K temperature of the cold head during the interval between ion beam pulses.

The time-stepping algorithm used in Opera-3d Transient Thermal is adaptive, ensuring that small enough steps are used to correctly capture fast transient behavior (such as when the ion beam is switched on and off) but increasing when there are stable periods of behavior. This ensures that the simulation runs with maximum efficiency without compromising accuracy. However, Opera-3d Transient Thermal allows the user to choose at what times to produce a complete set of results, rather than produce at every time-step used in the simulation. This can be seen in the traces in Fig 10 where the sampling times for the results relative to switch on and off have been changed for different pulses.

The modeling also gives insight into the factors that affect the behavior. It was found that the most significant effect was the amount of heat able to transfer from the base of the copper to the cold head. The results shown here used a value of 100 mW / mm² / K. If this is reduced by a factor of 2, the maximum temperature at each pulse will rise by about another 3.5 K. While the team at Oxford are happy that a maximum temperature of around 60 – 65 K is not going to degrade the HTS material, they will take extra measures in future experiments to ensure that good thermal contact is always maintained.

Kirk Adams said “Thank you again for the simulations you’ve provided. You’ve answered the key questions we had. I think we all came away with a better understanding of our work.” Prof Speller added “The modeling results are really helpful in interpreting our in situ experimental data and have informed modifications to our experimental setup that will enable us to mitigate the effects of beam heating”.

Chris Riley, Senior Consultant with the SIMULIA Low Frequency EMAG Applications Team, commented “It has been a real pleasure to work with such a highly respected team on an application that is important for future energy generation. The challenge of performing the simulation in a structure with such an extreme aspect ratio showed the value of offering different meshing techniques that best meet requirements. Although numerical results from simulations are always important, this example also shows how the Oxford University team has gained insight into the thermal behavior of the experiment.” The SIMULIA Opera team is currently in discussion about continuing to work with the HTS materials group at Oxford University as they realize the benefits that simulation can give. These are not only in terms of verification of experimental results but also the understanding of physical effects that are impossible to measure and the guidance on how future experiments should be conducted.

Acknowledgements

The experimental work conducted by the Centre for Applied Superconductivity in Materials Science at Oxford University was funded by the Engineering and Physical Sciences Research Council (EPSRC) grant EP/W011743/1.

Figures 2, 3, 4 and 5 are courtesy of the Centre for Applied Superconductivity in the Materials Department at Oxford University.

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