In tokamaks, the transition of low to high confinement mode, with improved energy confinement, has been offset by the emergence of Edge-Localised Modes (ELMs). These modes are a spectrum of magnetohydrodynamic (MHD) instability that can expel a significant fraction of the thermal energy of fusion plasmas to the walls of the tokamak. The energy is released in the form of magnetised plasma eruptions that eject filamentary structures from the edge plasma region to the low-density ‘scrape-off layer’. This phenomenon poses a major concern for ITER, since such releases of energy are likely to cause excessive erosion of plasma-facing wall components, significantly reducing their lifetime. As such, it is imperative that the physics underlying the emergence of ELMs during H-Mode operation is well-studied.

Edge Localised Modes are thought to be caused by a spectrum of MHD instabilities, including the ballooning mode. While ballooning modes have been studied extensively both theoretically and experimentally, the focus of the vast majority of this research has been on isotropic plasmas. The complexity of ELM dynamics means it is amenable to reduced “toy” models and phenomenological descriptions, such as sandpiles.

There are several possible projects in this topical area, which can be tailored to cater for special research projects, Honours, Masters or PhD.

• In recent work (https://doi.org/10.1088/13616587/aaba47) we have undertaken a numerical analysis of ballooning modes in anisotropic equilibria. The investigation was conducted using the ANU (co)developed codes HELENA+ATF and MISHKAA, which adds anisotropic physics to equilibria and stability analysis.  Our analysis found that the level of anisotropy had a significant impact on ballooning mode growth rates.  The project can be extended in a wide number of different directions.  These include:  extension of the MISHKAA stability code to include a vacuum, an exploration of the effect of anisotropy on a broader spectrum of peelingballooning modes, benchmarking and validating rotation and flow-shear into the MISHKA-A code, repeating the application of the code to non-circular boundary cross-sections, and application to experimental discharges on either MAST, JET or KSTAR plasmas.  
  

  Example of an n=30 ballooning mode (s is the minor “radial” coordinate).

• The full nonlinear evolution of ELMs as they linearly grow in the plasma, enter a nonlinear growth phase and ultimately erupt through the plasma separatrix is a complex physical problem.  A parallel path to modelling the nonlinear state of ELMS is to use reduced “toy” models such as an Abelian sandpile, which is an example of a dynamical system displaying selforganised criticality.  Variations on this model (http://dx.doi.org/10.1063/1.4964667, https://doi.org/10.1063/1.4998793)  have been able to explain the intermittency of ELMs, the probability distribution function of waiting times, the formation of a pedestal and the interdependency of ELM size. We have in mind exploring whether reduced dynamical “toy” models for the ELM dynamics can harness developments in stochastic programming.