The mathematics of fusion plasmas

If realised on Earth, fusion power offers a near unlimited supply of clean, sustainable power. The newest research activity addition to MSI: “Plasma Theory and Modelling”, uses reduced models to capture the configuration and phase-space complexity of high performance fusion experiments.

The mathematics is congruous with the complexity of experiments. The world’s next generation leading experiment, the International Thermonuclear Experimental Reactor (ITER) will explore the hitherto uncharted physics of burning plasmas.

We use kinetic theory to determine new fluid moments (e.g. anisotropy), whose physics in turn can change the magnetic configuration, wave stability, and wave-particle interaction dynamics. At extremis, energetic particle populations can create new modes whose time evolution is extremely nonlinear - so called Bernstein Greene Kruskal modes. Although notionally a 2D axisymmetric toroidal device, in practice, ITER will depend critically on symmetry-breaking external coils to suppress performance-limiting instabilities which erupt explosively through the plasma separatrix.

The ANU has developed a new formulation, Multiple Relaxed region MHD (MRxMHD), that is able to capture the full complexity of equilibrium fields in both real tokamaks (including those with symmetry-breaking external coils), and stellarators, which deliberately break toroidal symmetry. MRxMHD is able to resolve the fractal mix of islands, chaotic field lines and magnetic flux surfaces, and is the basis of a recently awarded high profile Simon’s grant led by Princeton University in collaboration with the ANU.

Several other drivers shape the mathematics of fusion plasmas. Reduced models such as sandpiles have surprising capacity to describe the evolution and dynamics of a fusion plasma. At the other extreme, fusion is a canonical big data field: ITER will generate up to 2 PB of data per day when operational. Much of this data has intricate dependency with other parameters through complex models, and so is a driver for model-data fusion (e.g. Bayesian) techniques, integrated modelling and ultimately real-time plasma control.

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