Extended Gyrokinetic Modelling for Dynamic Flows

Lead Research Organisation: University of Warwick
Department Name: Physics


Plasma physics is the study of large collections of charged particles and their interactions. One key application of plasma physics is in magnetically confined nuclear fusion, where nuclei, typically of Hydrogen, are confined by a magnetic field, so that they can reach the high temperatures necessary to fuse together as they collide. A large research effort is underway to develop fusion reactors that exploit the energy release from fusion to produce electricity.
In a tokamak, which is a specific kind of fusion reactor design, the vacuum chamber containing the fusion fuel can be conceptually separated into a 'closed field region' where particles cannot escape along magnetic field lines, and an 'open field region' where they can stream along the field lines and hit the wall.

The quite sharp boundary between the open and closed field region is particularly interesting and important, because a strong additional 'transport barrier', called a pedestal, can develop there. A large difference in temperature and density is sustained across the narrow pedestal, allowing the core plasma to reach higher pressure, and leading to a major increase in fusion power. How the pedestal is formed, and when it breaks down, are questions of vital importance to fusion reactor operation, but these issues are quite poorly understood at present.

This proposal seeks to answer basic questions about the pedestal, and similar structures that develop in other laboratory and space plasmas. This is an investigation of the fundamental properties of magnetised plasmas. How do such structures evolve, and how does this interact with the plasma turbulence? What plasma instabilities develop in these plasmas?

To answer these questions, we need models of how the particles individually and collectively respond to electromagnetic fields, and for the hot plasmas of interest we usually need to keep track of the motion of particles, rather that just look at the overall fluid motion. In magnetised plasmas, the basic motion of plasma particles is a circular orbit, or gyration, perpendicular to the magnetic field, as well as a parallel motion along the magnetic field line. This can be formalized mathematically using a framework known as 'gyrokinetics', which has become the dominant way to understand the transport of hot plasma in tokamaks.

A new gyrokinetic formalism has been developed by the proposer which is designed to be more accurate in regions with large amplitude structures like the tokamak pedestal. It is based on a rethinking of the assumptions usually made, so that both short wavelength fluctuations and more global physics may be handled in a unified way. We relax the requirement that perturbations be small amplitude but instead require that the 'vorticity', which measures how rapidly blobs of plasma rotate, is relatively limited.

This proposal will develop and exploit this mathematical framework to solve a range of fundamental physics problems in magnetised plasmas with large perturbations. A computer code to embody this plasma model will be further developed, and this will require the development of new algorithms. This code will then be deployed to understand both fundamental physics problems of magnetised plasmas, as well as the specific applications to structured regions of tokamaks.

As well as computational work, physical understanding of these plasmas requires us to develop a deeper understanding of the mathematical framework. We will use limiting cases to determine how the physics relates to simpler formalisms, and determine the underlying conservation laws to tie the turbulent dynamics to the large scale physics of momentum and energy transport.

Planned Impact

This project forms part of long-term worldwide research program aimed at developing fusion power reactors. The pedestal and edge physics which this proposal will study is poorly understood, and critical to the success of tokamak-type fusion reactors. Standard modeling approaches are poorly justified in the pedestal, so confidence that larger devices will work as intended requires more powerful frameworks such as the one proposed here. The most important impacts of this work are indirect and long term, to address the crucial problem of reliable low-carbon energy production, in order to work towards energy-independence in the UK. The UK government has reaffirmed the importance of this objective in the 2015 Spending Review and Autumn Statement:
"The government will double its domestic energy innovation programme. In line with this, the UK will continue to play a leading role in international research efforts to reduce the costs of low carbon energy, working with other countries to strengthen international collaboration and transparency in clean energy research, development and demonstration."

Stakeholders include research organisations like the ITER collaboration and fusion research labs in the UK, EU, and worldwide, as well as companies like General Atomics in the US and Tokamak Solutions UK. One key stakeholder in the UK is the industrial partner at the Culham Centre for Fusion Energy UK, with whom the Proposer and the host institution have an established partnership. This research is of particular interest for the researchers of the MAST spherical tokamaks, where the impacts of strong rotation are known to be substantial, and Culham have offered support to apply this research to the MAST device. Via a joint CASE studentship, and through applications to the EURATOM Enabling Research fund, investigations of tokamak pedestals using the ORB5/NEMORB code are already underway, and this research will feed into that effort.

This project will exploit research linkages between the fusion community and the broader turbulence modelling and applied mathematics community, and in particular into an existing collaboration between the proposer and Sergey Nazarenko in the Mathematics Department at the University of Warwick. The project and the code to be developed have a broad range of applications in plasma physics beyond tokamak research, in areas like astrophysics, where strongly flowing magnetised plasmas are seen in accretion disks, and solar and space physics, where instabilities in the solar wind proceed via the physics to be examined in this proposal. The Centre for Fusion, Space and Astrophysics at the University of Warwick, where the candidate is employed, has an active research program in computational space physics and astrophysics, and plans exist to develop a comparison between gyrokinetic modeling and hybrid models more commonly used by space physicists.

Public engagement is supported by the communications office at Warwick, which promotes engagement with traditional and electronic media by offering technical support and facilities including a film studio. The Physics Department also has a dedicated outreach officer. Disseminating the results to the wider community will also proceed via events such as the 'Cafe' Scientifique' event in Birmingham where McMillan gave a talk and led a discussion on fusion with a general audience. Within academia, but outside of the fusion domain, a connection to the wider energy research program is provided by Warwick University's 'Global Research Priority' project for energy, where McMillan presented a talk on engineering-related challenges in the fusion program.

The PDRA will receive training in the application of numerical techniques, and the use of high performance computing. This will serve to broaden the UK skill base in these critical knowledge areas. Warwick university also supports staff personal development through several programs including the transferable skills award.


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Collier J (2016) Global gyrokinetic simulations with strong flows in Physics of Plasmas

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McMillan B (2016) A very general electromagnetic gyrokinetic formalism in Physics of Plasmas

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McMillan B (2019) Tokamak parameter regimes with low toroidal momentum diffusivity in Journal of Plasma Physics

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McMillan B (2019) Simulating background shear flow in local gyrokinetic simulations in Plasma Physics and Controlled Fusion

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Saarelma S (2017) Non-local effects on pedestal kinetic ballooning mode stability in Plasma Physics and Controlled Fusion

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Villard L (2019) Global turbulence features across marginality and non-local pedestal-core interactions in Plasma Physics and Controlled Fusion

Description We have shown that a theory that describes turbulent plasma motion on a small scale (the scale of the orbits charged particles make around a field line) can be unified with the theory that describes in on a larger scale. This means that two schools of thought on understanding how plasma moves can be reconciled with each other. Since large and small-scale plasma motion are tightly interlinked, this is a key advance in modelling plasmas. As well as this theory work, we have developed numerical algorithms and software to solve for the plasma motion. Plasma flow modelling is essential for understanding disparate phenomena such as space weather (important to military and commercial satellite users) and the behavior of tokamak magnetic confinement devices.
Exploitation Route The mathematical models and software developed here can be used by plasma physicists to understand and computationally model plasmas with large fluctuations: the software built during the course of this grant serves as proof-of-principle, but many disciplines, such as space science, astrophysics, and laboratory plasma physics could extend and specialise this research to correctly model highly dynamic plasma scenarios. In laboratory plasma physics, where the multi-scale flow dynamics are crucial but still poorly understood, this may allow the design of more efficient magnetic confinement devices, essential for the success of the fusion project. Some of the novel algorithms we have developed are appropriate for a very broad class of applications in numerical modelling (e.g., problems that appear in computational economics and biology).
Sectors Energy

Description Programme Grant
Amount £4,300,000 (GBP)
Funding ID EP/R034737/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 10/2018 
End 10/2023
Title Field-line map based mesh-free method 
Description A type of mesh-free element method for representing continuous functions has been found. This can be used in computational simulations of movement and transport in systems with elongated structures. It is particularly appropriate for describing turbulence in tokamaks, especially when the field topology is complicated beyond the X-point. 
Type Of Technology New/Improved Technique/Technology 
Year Produced 2017 
Impact A user-friendly software implementation of this newly developed software technique is under design: this has not yet been found end-user application.