Foxes, flowing tap water and nuclear fusion – these elements do not appear to have anything in common, right? You might be surprised, but there is a connection emerging. The familiar models of population dynamics might help researchers to tackle one of the most complex puzzles in fusion science.

A snapshot of simulated plasma turbulence. The red and blue structures are the turbulent fluctuations, while the green arrows indicate the flows preying on the turbulence. Illustration: Paavo Niskala

A snapshot of simulated plasma turbulence. The red and blue structures are the turbulent fluctuations, while the green arrows indicate the flows preying on the turbulence. Illustration: Paavo Niskala

As a fusion experiment, a tokamak is similar to a vacuum flask for coffee. It is not enough to heat the fuel so that it turns into a plasma. The performance of the device depends on its capability to keep the heat in. The fewer the particles, the less the heat leaks out of the machine, and the more energy can be produced. The usual rule of thumb is simple: bigger tokamaks with stronger magnetic fields ought to confine the plasma better thus resulting in improved performance. Researchers are working hard to understand the underlying processes in more detail. With the aid of advanced measurements, computer simulations, and inspiration from unexpected places, the European fusion scientists are definitely progressing.

Eddies everywhere

In the early days of fusion research, there was some overconfidence regarding the performance of the test devices. Simple calculations based on collisions in the plasma predicted that compact reactors would produce enough fusion power for commercial use. No ITER-size mammoths would be required. In reality, the performance has always tended to fall short of the expected. Even though the trajectory of a single particle in a magnetic field could be understood, the collective nature of plasma was not appreciated sufficiently.

The difference between simple estimates and experimental observations has been pinned on turbulence. The same phenomenon can be seen in smoke or flowing water, where eddies emerge like small hurricanes and break the nice and clean flow pattern. In fusion plasmas, the collective behaviour of charged particles creates analogous vortices that push the heat and the plasma towards the walls of the device. The size of the eddies is crucial: the larger the vortices, the bigger the losses tend to be.

Swirling eddies
Whenever water is flowing fast enough, there are small and large swirls that move the fluid transverse to the flow. The hot and fast flowing fusion plasmas have similar swirls, usually called eddies, that transport the otherwise well-confined plasma particles in unwanted directions. The bigger these eddies grow, the further and faster the particles are transported along them.

In the flow

cartoon_bild2_10_paavo_webPlasma turbulence is clearly suppressed in some situations. For example, the performance of a tokamak improves drastically and suddenly in the transition to the high confinement mode. This famous H-mode was first discovered by a team lead by Fritz Wagner in 1982. Now researchers achieve it regularly in their experiments. As the turbulence is suppressed on the edge of the plasma, a transport barrier is created. It acts like a dam and removes the leaks from the plasma. Temperature and the density start to rise dramatically in the core, which increases fusion power as well. While the exact mechanisms still elude researchers, they know that flows within the plasma play a key role in creating a transport barrier. The flows in the plasma limit the growth of turbulence. To be more precise, the plasma stream needs to change greatly in the direction perpendicular to the flow. When the variation in the flow is rapid, the turbulent eddies become distorted. If the shear is strong enough, the vortices are practically torn apart and turbulent losses are suppressed which leads to improved performance. This is immensely important for a fusion reactor, since it means increased power output.

Confinement with a capital H
Fusion power output depends on the temperature and the density of the plasma. This is where the high confinement mode or H-mode enters the picture. As the heat and particle losses decrease in H-mode, temperature and density increase and the fusion power increases rapidly. Accessing high confinement mode is thus crucial for the success of ITER and fusion power in general.

Not one direction

cartoon_bild1_10_paavo_webThe transition to high confinement has been a challenging puzzle to crack because the interaction of flows and turbulence is not only one-way. As a turbulence pushes the heat and the particles around, it also participates to create the flows. The two-way nature of the interaction makes plasma a self-organising system. It is a formidable beast for theoretical and computational researchers to tame. On the other hand, as our understanding deepens, experiments may take advantage of this feature by driving flows externally and creating optimal configurations for sheared flows to develop.

From rabbits to plasmas


Cartoon: Amita Joshi

One approach on modelling this highly nonlinear plasma behaviour draws its inspiration from familiar population dynamics. The predator-prey model has been used to study the dynamics of rabbit and fox populations, for example, using a simple set of equations. As the number of rabbits starts to increase, the fox population increases as well, but with a slight delay. Overgrowth of the predator population and overhunting of rabbits lead to depletion of both populations, and the cycle of growth and decline restarts. It is a classic example of nonlinear interactions in complex systems.

The predator-prey models have been successfully applied to neutral fluids to describe the transition from laminar to turbulent flows. Now the physicists are harnessing them to tackle the self-organisation of plasmas by replacing the rabbits with turbulence and the foxes with flows. This should help us to find conditions that force the turbulence to become extinct, so to speak. The simplicity of the equations appeals to our intuition but it is also deceiving. Reducing the complex behaviour into just a few crucial processes and nailing down the details is challenging to say the least.

Simply complex

The models require experimental validation like any theory. The predator-prey interaction has been seen in real plasmas, but the details are still fuzzy. Measuring the turbulent properties from blisteringly hot, rotating plasma needs innovative technological solutions and support from theory and modeling. Forging the path forward thus requires close collaboration between experimental, theoretical and computational researchers. They are doing just that at the European laboratories under EUROfusion.

Advanced computer models are developed next to the experimental fusion devices at EUROfusion’s Research Units CEA (Commissariat à l’Énergie Atomique et aux énergies alternatives) in France and at IPP (Max Planck Institute of Plasma Physics) in Germany, for example. The most taxing simulations require thousands of processors and days of computing.

EUROfusion’s supercomputer, Marconi-Fusion, will come in very handy for this work. It sounds like a far cry from the simple equations of predator-prey models. Familiar dynamics may yet emerge from the complex calculations, like they emerge from the collective behaviour of billions and billions of particles in the fusion experiments.

Paavo Niskala. Picture: privateI am working on my doctoral thesis on turbulence in fusion plasmas. It is an intimidating, but also inspiring puzzle, that requires active collaboration across the globe. EUROfusion enables these joint efforts, which is priceless when it comes to making fusion power a reality. As the organisation also helps us students, I could not pass an opportunity to give something back to the community by discussing my topic.

Paavo Niskala (28) from Finland is currently based at  Aalto University, Espoo (Finland).
Twitter: @Paavi
Instagram: @popelotto
(Picture: private)