Plasma Theory and Modelling Group
plasmas, fluids — complex physical systems
Bayesian Inference of Fusion Plasma Parameters
“In fact it’s the interaction between senses that often enables us to make sense of what’s in front of us. This is exactly the same situation with a confined plasma.”
Fusion power offers the promise of generating massive amounts of energy with essentially zero greenhouse gas emissions and few of the safety issues of conventional nuclear energy. But although huge progress has been made in the past 50 years, we are only just beginning to reach the elusive “burning plasma” condition, where output power of the confined products exceeds the input power required to heat the fuel.
The next step international fusion experiment ITER, is now under construction in France and is one of the world’s largest science experiments. ITER plasma temperatures will be exceed 100 million degrees C, with a plasma volume comparable to an Olympic swimming pool. The construction of ITER is only possible because physicists are able to model the behaviour of plasmas sufficiently well to enable engineers to construct a machine on this scale with confidence. However, there is still much work to be done before we have a complete understanding of the theory underlying plasma confinement.
The behaviour of all fluids is notoriously difficult to model. Even a simple fluid such as water exhibits a myriad of twists and turns as it flows from a tap. Plasma circulating within the magnetic confinement of a fusion reactor is far more complex because it has massive temperature gradients and is composed of charged particles that repel and attract each other as they circulate. This constantly moving charge also generates its own magnetic field which in turn, perturbs the flow of the plasma and disrupts the magnetic field used to confine it.
Australia’s contribution to the worldwide effort to develop fusion power centres on internationall collaborations, many of which harness the H1 National Plasma Fusion Research Facility at ANU. H-1 is a stellarator plasma confinement facility not designed to actually achieve fusion, but to conduct experiments on large scale confined plasmas. The relatively easy reconfigurability of the magnetic fields within H-1 makes it a particularly good tool for the development of diagnostic instruments to monitor the behaviour of confined plasma. However, Interpreting the gigabytes of data from the temperature, pressure and current sensors inside the plasma is a daunting task. Even more challenging is the globally consistent merging of this information into a cohesive picture that reflects the actual physics of a plasma confined in such extreme conditions.
Drs Matthew Hole and Greg von Nessi are part of the ANU Plasma Theory and Modelling group, who with collaborators in the Plasma Research Laboratory are focussing on interpreting data from the many sensors on H-1 and compiling a picture of the underlying physics.
“The different diagnostics on H1 are a lot like our own five senses,” Dr von Nessi says. “Data comes in from sight, sound smell, and often something we’re experiencing influences more than one sense. In fact it’s the interaction between senses that often enables us to make sense of what’s in front of us. This is exactly the same situation with a confined plasma. We have hundreds of variables and only a few measurements we can make. But if we can make better use of the interdependency of those measurements, then we can generate a far clearer picture of what’s going on.”
The way our brains work is hugely sophisticated and complex but because we’re part of the system we usually just take it for granted. But how do you go about building a rigorous mathematical model that in a sense, does the same thing?
Their model is compiled using a mathematical technique called Bayesian inference. The basic principle is that you begin with a scientific belief or expectation, add the observed data and then modify the extent of that belief to generate the next expectation. In effect as more and more data is added to the model the accurate predictions become reinforced and the inaccurate ones rejected. “It’s a lot like the way we learn things,” Dr von Nessi says, “We generate ideas based on experience then reinforce or reject them as more data comes in.”
“We wanted to ground our approach to modelling the behaviour of plasmas in sound physical theory such as Maxwell’s equations, but not to incorporate untested assumptions that might bias the outcome.”
The beauty of this approach is that you don’t have to deal directly with the hugely complex interdependencies within the data but those interdependencies are automatically incorporated into the model.
“By not building so many assumptions into the initial model, it’s possible to compare what’s going on in the data to various aspects of the physics” Dr Hole explains, “We can then use real data to give credence to, or reject proposed physical descriptions of the plasma.”
The Bayesian inference techniques being developed for this project are currently being used to help understand the theory of force balance on the higher temperature Mega Ampere Spherical tokamak, at UKAEA Fusion in the UK. But the underlying mathematics can be applied to many different complex systems and may even find applications in areas as diverse as climate change and global financial markets.
“It’s a lot like the way we learn things,” Dr von Nessi says, “We generate ideas based on experience then reinforce or reject them as more data comes in.”