Towards Fusion Power: 3D Plasma Simulation in Stellarators and Tokamaks

Efficient plasma confinement is the main challenge that has to be solved on the way towards fusion power plants that work like miniature stars on Earth. The most common approach to do this is inside of a tokamak, torus-shaped devices with powerful magnet coils which have become ever more sophisticated and large, up to the enormous 20 billion dollar ITER project currently under construction. Scientists around the world are looking at multiple methods of bringing the stars down to earth, and one of the main alternatives is known as a stellarator. Algorithms and computer software to calculate the complex plasma behavior and optimize the configuration of the devices are required for both methods as well.

The stellarator, like the tokamak, uses magnetic fields to control hot plasmas in which fusion reactions can be created to produce energy. Where it differs is in the way these fields are created. To confine the plasma, it is necessary to put a twist in the magnetic field. The tokamak drives an electric current through the plasma to produce this twist. With the stellarator, the twist is provided by twisted magnetic coils outside of the plasma. Stellarators have actually been around for longer than tokamaks, dating back to the early 1950s, but the challenges of building such intricate machines have slowed progress. However, the construction of the advanced W 7-X stellarator at Greifswald in Germany is set to change all that, with assembly due for completion this year, first tests in 2014 and first plasma expected for 2015.

There is some crossover between the two paths. Both tokamaks and stellarators are part of the European Fusion Development Agreement's research programme. Physicists working on the compact MAST tokamak at Culham are now taking advantage of computer codes written by stellarator researchers to develop 3D plasma models. They explain that "computerized models allow scientists to match theories about plasma behavior to real experiments. The new 3D models give a much fuller understanding of what is happening inside the plasma than the 2D versions that have been used up till now, in analyzing the results of experiments where extra external magnetic coils are applied to the plasma." CCFE theoretical physicist Christopher Ham explains:

“MAST has a plasma with a ‘cored apple' shape. If you imagine slicing the apple open you can only see its condition at that one cross-section, and not in the rest of it. That is what it is like working with 2D codes. They are still essential for what we do and they have provided important insights, but now we need to look at 3D properties of the plasma too. The plasma isn't symmetrical the whole way round; it shifts and tilts in different points. Capturing these changes tells us more about how to keep plasma stable inside MAST. That's why 3D models are important.”

Luckily, it is not as difficult as you might think to transfer the complicated mathematics of stellarators to tokamaks. Once the differences in geometry have been accounted for, they translate well. Researcher Tony Cooper of Switzerland's CRPP institute has already adapted the VMEC stellarator code – which produces plasma models like the one opposite – to a number of tokamaks, including MAST.

“Stellarators are naturally 3D in nature, and codes like VMEC have been written to map this,” continues Christopher Ham. “So it makes sense to use these ready-made codes, which have been tried and tested over 30 years, for devices like MAST. Without them we'd be starting from scratch, which would be a massive effort. The expertise of our friends in stellarator research is saving us a lot of time and trouble.”

Christopher and colleagues Ian Chapman and Samuli Saarelma have taken on Tony Cooper's initial work and find it is already opening up new possibilities. One example is the study of Edge Localised Modes (ELMs), harmful instabilities that take energy out of the plasma, impeding the tokamak's performance. MAST has special magnetic coils that control ELMs by changing the magnetic field at the plasma edge. 3D modelling can show what effect the coils are having in all regions of the machine.

“Often we want to know why a particular coil configuration does what it does,” says Christopher Ham. “How does the edge of the plasma move in and out as you go around MAST? And how does this change the stability? These are questions we can only answer in 3D.”

An added benefit of the software project has been the chance to forge stronger links with the stellarator community – Christopher has been working particularly closely with counterparts in Germany and the United States.

“There is increasing interest in working together internationally,” he says. “I hope this continues – we can learn a lot from each other, and in the end fusion research will be the winner.”