Simulating the kinetic ion response to magnetic islands in tokamak plasmas

In a tokamak, the conditions for fusion energy are achieved by confining a hot plasma using a toroidal configuration of magnetic field. Thus, the magnetic field lines lie on a set of toroidal flux surfaces that are nested like a set of Russian dolls. All magnetic field lines on a given flux surface are usually equivalent and, specifically, all carry the same current. However, under certain situations this state can bifurcate to one where some field lines carry more current than others. This filamentation of the current density effectively tears the flux surface apart, creating a chain of so-called magnetic islands. The instability responsible for this is called a tearing mode.

Such islands are detrimental to confinement, and therefore it is important to understand the physics of tearing modes. A particularly problematic instability is called the neoclassical tearing mode, or NTM. Small current filaments initially create small so-called "seed" islands. These seed islands reinforce the current filamentation, resulting in a positive feedback mechanism that causes the magnetic islands to grow extremely large. The degradation in confinement causes a drop in the core plasma pressure and a consequent loss in fusion power in a tokamak like ITER. However, this amplification mechanism is only observed when the initial seed island width exceeds a certain threshold of a few centimetres. Although we have ideas for the physics mechanisms that lie behind this threshold, there is no predictive quantitative model. This is largely because for small islands, the distribution of ions in both real and velocity space is important - a 6-dimensional problem. We have developed an expansion in the small ratio of the island width to system size that has enabled us to reduce the system to 4-dimensions - two spatial and two velocity components. Our initial studies indicate that this problem is tractable on modern high end computers, providing a predictive capability for the threshold for neoclassical tearing modes - a key ingredient for specifying the NTM control system on ITER, for example.

In a second application of the theory, we are interested in a situation where the magnetic islands are induced by the tokamak operator. This is achieved by applying so-called "resonant magnetic perturbations", or RMPs, to the plasma using a set of current-carrying coils. The motivation for this is to provide a control system for a repetitive sequence of tokamak plasma eruptions, called edge-localised modes, or ELMs. In an ELM, large filaments of plasma erupt from the surface in an event that is reminiscent of solar flares. We believe that these are driven by steep pressure gradients that form near the plasma edge. By driving small magnetic islands in this steep pressure gradient region with RMPs, it is expected that the pressure gradient can be reduced in a controlled way to just below that necessary to trigger an ELM. This is key for ITER, where uncontrolled ELMs will cause excessive erosion of its components at full fusion power. While the technique works on some tokamaks, it does not work on others. To understand this, we need improved models for how the plasma responds to magnetic islands that are driven externally - will it amplify them, as in the case of the NTM, or heal them? This understanding will help specify the ELM control system on ITER.

We will develop a new high end computing code to calculate the kinetic plasma response to both natural and driven magnetic islands, using the model we have derived by an analytic reduction of the so-called drift-kinetic theory. Knowledge of the plasma response will enable us to quantify the current filamentation, and hence identify the conditions for which the plasma tends to amplify magnetic islands and when it heals them. We will work with experimentalists to design tests for our predictions against data from today's tokamaks, and make predictions for the requirements of the instability control systems on ITER.

Identifying a solution to the energy problem would have a huge impact across the World - virtually everyone would be affected by it. While challenges remain, fusion energy has the potential to play a major role as part of a portfolio of possible sustainable energy solutions. The time to fusion energy depends on: (1) the construction time of ITER; (2) the time to ITER achieving full fusion performance and providing plasma physics data for the design of the demonstration fusion power plant, DEMO; (3) solving the remaining engineering and materials challenges in parallel with ITER, and (4) design, construction and operation of DEMO. The research proposed here as the potential to influence the second of these - the time to ITER achieving full performance. Understanding the neoclassical tearing mode (NTM) threshold physics will enable control systems to be optimised more efficiently, which will speed up the path to DT operation of ITER. Similarly, ITER must demonstrate an effective control system for the plasma eruptions called ELMs before it can be operated at full fusion performance. Our theoretical models will contribute to both of these issues, helping to ensure ITER achieves its full fusion power early, and starts to address the physics issues required for designing DEMO in a timely way. The PI already has strong, direct links to the ITER International Organisation through (1) a formal Memorandum of Understanding signed by both ITER and University of York, and (2) the PI is a member of one of the so-called ITPA groups, which operate under the auspices of ITER to coordinate international fusion research.

NTM and ELM control are important experimental research programmes on numerous tokamaks around the World. We anticipate that our theoretical developments and outputs will help to guide experimental programmes (e.g. through testing our theoretical predictions). This will enhance the impact of our theoretical research for ITER, but it will also benefit those experimental groups exploring the physics of ELMs and NTMs and testing/optimising control systems by helping to define a framework for their experimental programmes. Our partnership with leading experimentalists from CCFE and General Atomics will help us to maximise the impact of our research on the experimental tokamak programme (including tokamaks at other institutions).

This is a demanding research project, requiring advanced analytic skills and an ability to use the world's most powerful supercomputers effectively. High end computing is becoming increasingly important in a wide range of sectors (climate, financial, health, national security etc) so the skills that the research team will develop reach far beyond fusion plasma physics applications alone. To maximise the impact and opportunity, we will involve University of York undergraduates in the research programme through their final year projects. We would expect up to two or three undergraduate students per year to work with the PI and PDRA on different aspects of the programme. While we do not rely on their contributions to meet our objectives, this approach will nevertheless provide additional manpower to maximise the research outputs; however, the main benefit is likely to be the advanced training that these students will receive - skills that will benefit them and their future employers.