Statistical Monitoring and Control of Nuclear Fusion Systems.

Statistical Monitoring and Control of Nuclear Fusion Systems.

My PhD is sponsored by Culham Centre for Fusion Energy (CCFE), the UK's national laboratory for fusion research, based in Oxfordshire and affiliated with UKAEA. The main scope of this company is to conduct research on magnetic confinement fusion, where plasma is shot inside a torus-like chamber named tokamak. Hence, my projects fall within the EPSRC energy and the mathematical sciences research area.

During the 80s, it was discovered that if the plasma is injected sufficient energy in the form of heating power, it spontaneously transitions into a high confinement state, the H-mode, during which more energy is produced than in standard L-mode. This better state of confinement is achieved consequently the formation of a transport barrier at the edge of the plasma. This new section of interest is typically several centimetres wide and here temperature, pressure and density profiles exhibit large gradients. In this H-mode regime it was observed the onset of a new instability, which had the highest amplitude and effect at the edge region. This was named edge-localised mode (ELM). ELMs can be described as repetitive bursts that cause emission of ionized particles coming from the edge of plasma, but sometimes more generally its outer area. This causes an obvious loss of energy in the plasma and, depending on its severity, it might affect the end result of the experiment. However, this does not always lead to a negative outcome as they control and eject impurities in the plasma, and, once the ELM event takes place, with the consequent pressure and temperature decrease, these quantities start to recover, until another ELM happens.

In the worst case scenario, an ELM event in a large tokamak, e.g. the future ITER, leads to extreme damage to the inner structure of the device following the expulsion of a great deal of particles and energy. Hence, due to costly implications of these occurrences, CCFE is interested in investigating properties of these events from a statistical point of view. What we are interested in is the real-time generation of predictive warnings, so that mitigation techniques can be deployed to proceed with the experiment, or alternatively, so that the complete interruption of the shot can be triggered, to prevent damage.

In terms of methodology, we are trying to model these events in a Bayesian framework, with the aim of making predictions and measure uncertainties about them. Since we want to allow for real time analysis and anomaly detection, inference will exploit the sequential nature of data: we centre our work around Sequential Monte Carlo approaches, thus facing common challenges related to these methods. We also faced the challenge of defining an appropriate model despite the quantity and quality of data that we were given access to. We are focusing on the field of Stochastic Differential Equations, in order to allow for an easy interpretation of the phenomenon under study. Given the high-data volume it is also plausible to investigate more data driven/machine learning approaches. Another method we are tackling this problem with, involves the development of surrogate models, in order to calibrate numerical codes which simulate reduced plasma physics, in order to improve the quality of our predictions.

The primary CDT impact will be training 75 PhD graduates as the next generation of leaders in statistics and statistical machine learning. These graduates will lead in industry, government, health care, and academic research. They will bridge the gap between academia and industry, resulting in significant knowledge transfer to both established and start-up companies. Because this cohort will also learn to mentor other researchers, the CDT will ultimately address a UK-wide skills gap. The students will also be crucial in keeping the UK at the forefront of methodological research in statistics and machine learning.
After graduating, students will act as multipliers, educating others in advanced methodology throughout their career. There are a range of further impacts:
- The CDT has a large number of high calibre external partners in government, health care, industry and science. These partnerships will catalyse immediate knowledge transfer, bringing cutting edge methodology to a large number of areas. Knowledge transfer will also be achieved through internships/placements of our students with users of statistics and machine learning.
- Our Women in Mathematics and Statistics summer programme is aimed at students who could go on to apply for a PhD. This programme will inspire the next generation of statisticians and also provide excellent leadership training for the CDT students.
- The students will develop new methodology and theory in the domains of statistics and statistical machine learning. It will be relevant research, addressing the key questions behind real world problems. The research will be published in the best possible statistics journals and machine learning conferences and will be made available online. To maximize reproducibility and replicability, source code and replication files will be made available as open source software or, when relevant to an industrial collaboration, held as a patent or software copyright.