Congratulations to Michail Anastopoulos Tzanis, a York Fusion CDT student who successfully defended his thesis at viva in November 2019. Michail’s thesis is entitled “Beyond Axisymmetry in Tokamak Plasmas” and his supervisor is Professor Howard Wilson.  An abstract from Michail’s thesis is below. Well done Michail!

Michail is now working as a Post Doctoral Researcher at University of York.

H-mode tokamak plasmas are characterised by large plasma pressure in the core – a beneficial feature for fusion energy production – while still maintaining low pressure at the edge of the plasma. The transition from high to low pressure occurs in a narrow region, only a few centimetres wide, leading to steep pressure gradients and large current density at the plasma edge. However, both of features naturally lead to the destabilisation of edge localised instabilities, called ELMs. These transient events expel particles and heat from the confined plasma region to the exhaust region and plasma facing components of the tokamak device in a very short time scale. As a result, large heat fluxes develop and their extrapolation for large scale tokamaks, like ITER, is predicted to exceed the melting point of structural materials. 

One promising method that controls ELMs relies on the application of external non-axisymmetric magnetic perturbations (MPs). The MP field is characterised by a primary toroidal mode, a spectrum of poloidal harmonics, leading to a resonant or non-resonant perturbation, and an amplitude relatively to the axisymmetric confining field that is really low, typically δB/B~10-3. Its is experimentally proven that MPs can control the ELM frequency and expelled energy, called ELM mitigation, as well as leading to complete ELM suppression. However, complete physics understanding of the key mechanism that allows for mitigation or suppression is still not well understood. In this PhD work, the linear ideal non-axisymmetric MHD plasma response and global stability of peeling-ballooning modes was examined. 

For ELM related eigenmode perturbations, the poloidal and toroidal mode coupling in the non- axisymmetric geometry results in a large computational problem to be solved, for a such an analysis to not be usually performed. A framework was created that simplifies the numerical complexity of the non-axisymmetric stability of the system, using arguments that steam from non-axisymmetric perturbation and variational stability analysis, as well as physics considerations from local axisymmetric ballooning theory. These considerations lead to the use of unstable eigenmodes, obtained from the stability analysis of the original axisymmetric equilibrium, as trial functions for the minimisation of the non-axisymmetric energy functional. Since these eigenmodes are routinely computed with axisymmetric stability codes, the stability examination of the non-axisymmetric system becomes possible. 

The stability examination of plasma equilibria, which are ballooning unstable, resulted in further destabilisation and field-line localisation of the instability with an increasing MP field, as suggested by local non-axisymmetric ballooning stability analysis. Moreover, for D shaped high-β tokamak plasmas, which are kink-ballooning unstable, the most unstable kink-ballooning modes where highly destabilised with an increasing MP field. Finally, for a fixed MP field amplitude at the plasma edge, the MP poloidal spectrum configuration that had the stronger impact on stability, was the one where the MP field penetrated the most within the plasma.