Multiscale turbulent dynamics of tokamak plasmas

Lead Research Organisation: University of York
Department Name: Physics


Plasma turbulence underpins a wide range of phenomena, including the formation of stars and galaxies; the properties of the solar wind, and - the focus of this programme - the confinement of plasmas in tokamaks. It is complicated by feedback mechanisms that couple space and time scales spanning several orders of magnitude. The full problem is extremely challenging, and so to make progress for real world applications we must develop reduced models that capture the essential physics. The goal of our proposed programme is to address this by advancing our understanding of these multi-scale interactions at a fundamental science level. This will be achieved by coupling analytic theory, advanced computation and experimental capabilities, including the newly upgraded MAST-U tokamak.

Plasma turbulence is complicated by the fact that there are at least two types of interacting "fluids" - electrons and ions - and these are charged. Fluctuations in density therefore drive charge separation and hence fluctuations in the electrostatic field, while fluctuations in velocity drive currents and hence fluctuations in the magnetic field. These fields then couple the relative motions of the electron and ion "fluids". The situation is further complicated by the rich variety of waves that a magnetised plasma supports, and the resonances that exist when the phase velocity of a wave matches the particle velocity. To properly treat these resonances requires knowledge of the particle velocity distribution; this, in turn, requires either a kinetic or an advanced fluid approach - a daunting task.

Turbulence, typically at the millimetre-centimetre scale in tokamaks, interacts in a complex way with the global equilibrium profiles (density, temperature and flow gradients, for example), which are on the metre-scale. To quantify the complex, multi-scale feedback mechanisms between tokamak plasma turbulence and profiles, and so provide a predictive capability for the quasi-steady final states, we will address and integrate a number of topics. We will first learn how mean flows interact with electrostatic turbulence (ie neglecting fluctuations in the magnetic field), requiring coupling between fluctuations with characteristic scales ranging from the electron Larmor radius (sub-mm) through to the ion Larmor radius (few mm) and beyond (cm), to the system length scale of the profiles (m). Our new theory and simulations will inform experiments on MAST-U, exploiting two diagnostic instruments already planned for the device (beam emission spectroscopy and doppler back-scattering). It is likely there will be gaps in the wavelength range that these instruments can measure, so we anticipate a need to develop and install a new microwave imaging system. This will be designed using knowledge gained from the early phase of the programme, and deployed for further experiments towards the end.

Understanding of electromagnetic turbulence is less developed and new theoretical models will be required. Building on the knowledge gained from the electrostatic turbulence, we will seek to again understand the multi-scale interactions and feedbacks, including flows. However, now the situation is more complicated as electromagnetic turbulence can drive large scale currents, modifying the magnetic field which confines the plasma, and coupling into large scale electromagnetic modes.

A key motivation is to optimise tokamak plasmas for fusion performance, and this requires us to understand the impact of fast particles. These can drive turbulence directly through the instabilities they excite, or influence the turbulence driven by the thermal particles. Our simulations will assess the impact of the fast particles created by the neutral beam heating systems on MAST-U, and also the impact of energetic alpha particles from fusion reactions on future devices like ITER, as well as experiments planned on JET with the deuterium-tritium mix fusion fuel.

Planned Impact

The largest impact will be on the fusion programme. This impact will occur at several levels, as follows.
(1) A greater understanding of turbulence and confinement on MAST-U will enable us to identify a wider range of plasma scenarios on MAST-U. These, in turn, will broaden the range of plasma parameters achievable on MAST-U, further extending its flexibility for a wide variety of plasma science experiments. This will benefit many UK researchers, but will also make the device even more attractive for international participation which will increase opportunities for international funding for MAST-U operations (EUROfusion, and the wider international community).
(2) Our improved understanding will feed into the development of operational scenarios for the DT operation of JET and ITER. This will, in turn, help maintain UK influence in ITER, and contribute towards ITER meeting its fusion objectives in a timely way. This is important, as the design of the first demonstration power plants, and hence the commercialisation of fusion energy, cannot be finalised until the first results are obtained from burning fusion plasmas in ITER.
(3) The size and capital cost of a tokamak fusion power plant depend to a large extent on the effectiveness of the confinement which, in turn, depends on turbulence. We will exploit our improved understanding of turbulence to seek techniques to further enhance tokamak confinement, and feed these results into the integrated design studies of fusion reactors which are presently under way (e.g. at UKAEA). If we are successful, our research results will underpin designs for more compact fusion reactors, that could form the basis for small modular fusion power plants, or for a fusion components test facility that would be valuable for mitigating risks of delays to commercial fusion power.

The main pathway to realising the above impacts will be through our close links with the UK national fusion programme led by UKAEA. However, we also have close collaborative links with international programmes, including those in Europe, USA, S Korea and China. These collaborative links will provide us with a broader range of fusion facilities and expertise to help meet our research objectives, but also provide a pathway to international impact. We will, of course, seek to strengthen our impact via high profile presentations at international conferences and publications in high impact journals. While our research has a clear application, it is also developing fundamental plasma science. As such, there is potential for publications in journals with a wider readership, beyond the fusion community, such as in Nature and Science.

Turbulence is a feature of most magnetised plasma systems, and plays a role in many solar and astrophysical phenomena, as well as laser-produced plasmas. We have contacted key individuals from astrophysics groups from 14 UK universities, asking about their interest in a 'National Centre for Turbulence in Magnetised Plasmas' that would cut across astrophysical and laboratory plasmas. The fundamental science has similarities across the disciplines, so the different systems, when brought together, could provide opportunities to advance the field beyond the capabilities of the individual communities. We will launch this new Centre as a key part of our Programme, organising three national meetings which, we anticipate, will act as a platform on which to build a strong interdisciplinary plasma turbulence community that will last well beyond the term of the Programme Grant.

A sustainable, cost-effective source of energy is fundamental to our standard of living and the national economy. We will ensure that the general public, industrialists and policy makers are kept aware of the significant contribution that fusion energy can make as a key part of a portfolio of possible solutions through public lectures and targeted events at our universities.
Description This programme provides underpinning research for the UKAEA STEP programme, which seeks to build a fusion reactor by 2040 that will deliver net electricity. The effectiveness of the confinement system is a key driver for the design of the STEP fusion reactor, and this confinement is determined by plasma turbulence. Team members have been funded by STEP to provide expertise on the micro-instabilities responsible for driving turbulence in STEP plasmas. In addition, our expertise in the interaction of microwaves in plasmas has been employed to understand the issues related to current driven by microwaves in STEP.
First Year Of Impact 2019
Sector Energy,Environment
Impact Types Societal,Policy & public services

Description EPSRC studentship
Amount £50,000 (GBP)
Funding ID 1991712 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 10/2019 
End 03/2023
Description SAMI-2: two-dimensional Doppler imaging of tokamak plasmas
Amount £213,056 (GBP)
Funding ID EP/S018867/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 01/2019 
End 06/2020
Description STEP Plasma Modelling Lot 1: Gyrokinetic plasma modelling for STEP
Amount £97,781 (GBP)
Funding ID CMF/11441 
Organisation UK Atomic Energy Authority 
Sector Public
Country United Kingdom
Start 07/2019 
End 03/2020
Description STEP Plasma Modelling Lot 3: Simulations of non-inductive plasma start-up and non-inductive current drive using waves in the electron cyclotron range of frequencies
Amount £168,402 (GBP)
Funding ID CMF/11441 (Lot 3) 
Organisation UK Atomic Energy Authority 
Sector Public
Country United Kingdom
Start 07/2019 
End 03/2020
Description General Atomics - extensions to TGLF to tight aspect ratio, high beta equilibria 
Organisation General Atomics
Department Fusion Theory and Computational Sciences
Country United States 
Sector Private 
PI Contribution Howard Wilson and Colin Roach of TDoTP, together with a PhD student linked to the programme (Bhavin Patel) have been extending the TGLF tokamak plasma transport model to high beta equilibria characteristic of tight aspect ratio. Bhavin has visited General Atomics (funded from elsewhere) during 2019 to develop the extended model in collaboration.
Collaborator Contribution Expertise of Gary Staebler on TGLF transport model, and also Jeff Candy on Gyro code. Gary Staebler has visited the team in the UK two times, funded from outside the programme)
Impact Still early - an abstract has been submitted to 2020 EPS plasma physics conference on the work
Start Year 2019
Description Gyrokinetic analysis of JET ILW shots 
Organisation EUROfusion
Country European Union (EU) 
Sector Public 
PI Contribution We have analysed the stability of JET ILW pedestals. Pedestals are regions of reduced turbulence with large temperature and density gradients. Pedestals are considered to be crucial to achieving fusion energy, but are poorly understood. We have conducted a careful stability analysis of the experimental profiles, discovering a new type of mode. The results will be submitted to publication in the next month.
Collaborator Contribution EUROfusion funded 5 researcher-days and provided the data that was used for the gyrokinetic analysis.
Impact The outcome of the collaboration is an article to be submitted shortly.
Start Year 2019
Description Modelling of the Doppler-Back-Scattering Diagnostic in MAST-Upgrade 
Organisation Culham Centre for Fusion Energy
Country United Kingdom 
Sector Academic/University 
PI Contribution We have developed a model to interpret the data obtained with a Doppler-Back-Scattering (DBS) system. This diagnostic is a non-perturbative method to measure turbulence in tokamaks. Previous analyses of DBS made assumptions about the magnetic field that are not valid for spherical tokamaks such as MAST-Upgrade, and hence needed upgrading.
Collaborator Contribution The Culham Centre for Fusion Energy (CCFE) provided time of one of his researchers, Dr. Jon Hillesheim, and promised run time in MAST-Upgrade in 2020 to check the model. The estimated value of CCFE's contribution does not include the MAST-Upgrade run time yet.
Impact A publication on the model is being written and will probably be submitted for publication before the summer of 2020.
Start Year 2019
Description Partnership on high frequency circuits and components 
Organisation Rutherford Appleton Laboratory
Country United Kingdom 
Sector Academic/University 
PI Contribution Strathclyde have been involved in designing novel high frequency waveguides for many years, and in the measuring of these waveguides in both cold and hot tests. In the context of TDoTP Strathclyde (with York and others) are actively developing a new microwave diagnostic. We believe RAL Space expertise will be important in delivering this diagnostic.
Collaborator Contribution RAL Space's precision machine shop have made critical contributions to the fabrication of the novel waverguides. They have expertise in high performance sources and detectors in the sub-mm wave range that will be vital for future microwave diagnostic developement.
Impact There have been many successful outcomes from this partnership between Strathclyde and RAL Space in the past, including a world leading result in fast wave microwave amplifiers at W band. In the context though of the TDoTP project the outcomes are envisioned for the future.
Start Year 2019
Description Research Collaboration on Microwave emission due to kinetic instabilities in an overdense mirror-confined plasma (supported by Royal Society in UK and RFBR in Russia) 
Organisation Russian Academy of Sciences
Department Institute of Applied Physics
Country Russian Federation 
Sector Academic/University 
PI Contribution Strathclyde are contributing the simulations of complex microwave emissions from overdense mirror confined and microwave driven plasma
Collaborator Contribution IAP are undertaking experiments driving plasma in a mirror confined plasma volume using microwaves, studying the micorwave emissions
Impact A joint conference paper has arisen from bilateral visits.
Start Year 2018
Title GS2 
Description GS2 is a physics application, developed to study low-frequency turbulence in magnetized plasma. It is typically used to assess the microstability of plasmas produced in the laboratory and to calculate key properties of the turbulence which results from instabilities. It is also used to simulate turbulence in plasmas which occur in nature, such as in astrophysical and magnetospheric systems. 
Type Of Technology Software 
Year Produced 2020 
Open Source License? Yes  
Impact GS2 is a vital tool for a large fraction of the simulations performed under this project, as well as work at labs across the world, including the USA (PPPL, University of Maryland), Japan (NIFS, SOKENDAI), and the UK (CCFE, University of Oxford, University of York). 
Title stella gyrokinetic code 
Description stella is a piece of software that simulates the turbulent dynamics of small 'flux tubes' encompassing magnetic field lines in magnetic confinement fusion plasmas. 
Type Of Technology Software 
Year Produced 2019 
Open Source License? Yes  
Impact This software is still in its infancy but is being used by students and researchers at Oxford, as well as researchers at the national fusion laboratories in Spain (CIEMAT) and Germany (Max Planck Institute for Plasma Physics in Greifswald). This software is enabling a reduction in computation time for micro stability calculations in 3D magnetic field by greater than an order of magnitude.