Multiscale Modelling of Magnetised Plasma Turbulence

Lead Research Organisation: EURATOM/CCFE
Department Name: Culham Centre for Fusion Energy

Abstract

Heisenberg reputedly said on his death bed, When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first. Understanding turbulence remains a fundamental open question in physics that is nowadays accessible to high performance computing (HPC).Plasma (ionised gas) is the fourth state of matter that dominates our observable universe, and burns in stars through nuclear fusion reactions to produce energy and the elements. Laboratory experiments replicate these processes, aiming to harness terrestrial nuclear fusion for energy, and an advanced approach exploits toroidal magnetic fields to confine hot plasma at temperatures >100 million K. Fusion requires good confinement, and this is limited by collisions and plasma turbulence. Collisional processes cause an irreducible minimum plasma loss rate that is understood theoretically, but larger losses, due to turbulent processes, are observed in devices. Recent experiments find dramatically enhanced confinement regimes with higher core pressures, where losses are strongly reduced in localised regions of plasma, approximately to the level predicted by collisional theory. In the region of the internal transport barrier (ITB), turbulence is strongly suppressed. There is much scope for optimising fusion devices through controlling turbulence.Calculations of magnetised plasma turbulence parallelise efficiently, and recent advances in HPC permit high fidelity first principles based calculations. HPC is essential because of the high dimensionality of the problem (5-D in kinetic approaches) and the huge ranges of scales of the physics processes in space and time. This proposal is for scientists at UKAEA Culham, Edinburgh, Oxford, Warwick and York to exploit the EPSRC national supercomputer HECToR to perform magnetised plasma turbulence simulations using state-of-the-art kinetic and fluid models. Multiscale simulations, ideally suited to HECToR, will resolve fundamental plasma processes that span in space from the short length scale associated with particle gyration around the magnetic field (eg the ion Larmor radius rho_i ~O(5)mm) to the device minor radius a (~O(1)m), and in time from the lifetime of turbulent eddies (~O(10^-6)s) to the energy confinement time (~O(1s)). We will approach our objectives using complementary models: (i) coupling multiple local kinetic turbulence simulations self-consistently with a transport solver to track the slower evolution of macroscopic plasma properties, (ii) global kinetic simulations and (iii) applying the two-fluid-MHD plasma model to describe turbulence at scales between rho_i and a. The key scientific issues to be explored include: (1) probing the fundamental triggers for the suppression of turbulence and the onset of transport barriers(2) assessing the relative importance of turbulent fluctuations on different length scales, and probing the cascade of turbulent energy between these scales(3) comparing model predictions with experiments (including spherical tokamaks like the UK experiment MAST), and suggesting routes to optimise plasma performance in future devices (eg the next step burning plasma experiment ITER).This internationally leading project team is well placed to make unique contributions towards addressing these important and challenging scientific questions. Our proposed simulations will parallelise to exploit 1000s of computational cores efficiently, and indeed require access to a state of the art supercomputer like HECToR. The science tackled is relevant to fusion and astrophysics. Success in achieving these ambitious scientific objectives will address long standing grand challenges, and will have a high international impact.
 
Description The plasma simulations carried out under this grant were focussed on understanding and improving on the capabilities of magnetic confinement devices to harness nuclear fusion for terrestrial energy production. In this approach to fusion energy, magnetic fields are exploited to confine the hot high pressure plasmas that are required to attain fusion conditions. Magnetic confinement is imperfect, and heat and particles leak from the device at a rate determined by turbulent and collisional transport processes. Progress in the first principles understanding of plasma turbulence, which usually dominates the loss rates and is widely recognised as a scientific Grand Challenge in its own right, offers the promise of unlocking new approaches that will significantly improve the performance of magnetically confined fusion (MCF) devices.



This transformative grant has provided UK MCF scientists with substantial resources (150MAUs) on the EPSRC supercomputer HECToR over 4 years. This resource has been extremely fruitful, delivering:

(i) state-of-the-art simulations of plasma turbulence that so far have been widely disseminated in >50 publications (>20 refereed journal papers, 4 PRLs, and numerous Invited Talks);

(ii) growth in the UK research base in plasma turbulence, establishing firmer foundations in the field at CCFE and the Universities of Edinburgh, Oxford, Warwick and York.

(iii) Training: >16 PhD students accessed HECToR through this grant and were trained in HPC +plasma physics. 7 of the completed PhDs subsequently moved on to post-doctoral positions in fusion plasma physics: 2 prestigious European Fusion Fellowships, 1 Junior Research Fellowship at Magdalen College Oxford, and 2 Culham Fusion Research Fellowships were awarded on the basis of PhDs completed using this grant..

(iv) an enhanced international reputation for UK plasma turbulence research;

(v) HPC performance optimisations, achieved in part through additional funding, for the widely used gyrokinetic plasma turbulence code, GS2.



Key Scientific Findings:



(A) Influence of sheared equilibrium flows on tokamak plasma turbulence.

Simulations under this grant have emphatically exposed the opposing impacts on turbulence from radial shear in the components of equilibrium flow parallel to and perpendicular to the equilibrium magnetic field. These components of the sheared flow respectively enhance and suppress plasma turbulence, and the overall impact of sheared flow on turbulence is therefore largely determined by the equilibrium magnetic field geometry. In tokamaks strong flows are required to influence turbulence, and these are constrained by axisymmetry to be toroidal. This favours sheared flow suppression of turbulence in devices where the ratio of poloidal to toroidal magnetic field strength is large (e.g. in spherical tokamaks like the UK experiment MAST).



High impact simulations by Highcock et al revealed that a transport bifurcation to a suppressed turbulence state can be triggered by strong sheared flow. This is a candidate mechanism to explain the onset of "transport barriers" observed in tokamak experiments. At very high flow shear, or at low magnetic shear, it is also found that subcritical turbulence driven by the parallel velocity gradient plays an important role.

==> 3 PRLs, numerous Invited Talks, and EPS Plasma Physics Division PhD Thesis Prize awarded to Edmund Highcock (2014)



(B) Understanding the "H-Mode" Edge Transport Barrier.

High confinement is achieved in "H-mode" tokamak plasmas through the development of a steep gradient region at the edge of the plasma. The edge pedestal that results strongly influences confinement, and its properties will be important to the performance of the next step burning plasma experiment, ITER. The physics governing the pedestal is poorly understood, but electromagnetic microinstabilities (where magnetic perturbations are crucial) are believed to play an important role.



In a pioneering study under this grant, microinstability physics was analysed close to the edge in H-mode plasmas using high quality plasma equilibrium reconstructions from the UK experiment MAST. Highly cited gyrokinetic simulations by Dickinson et al reveal that kinetic ballooning modes are marginally unstable in the MAST pedestal, while the plateau region (just inside the pedestal) is dominated by microtearing modes that tear apart the confining equilibrium magnetic flux surfaces. Increasing the density gradient, as occurs naturally following an edge localised mode when the pedestal expands into the core as the plasma is refuelled, was found to stabilise the microtearing modes until kinetic ballooning modes are driven unstable at a higher critical pressure gradient. This could be a very important mechanism in the pedestal dynamics. Further recent analyses find microtearing modes also to be unstable in the plateau region of other tokamaks including JET. Kinetic ballooning modes were, however, stable in the JET pedestal due to the high bootstrap current taking the pedestal into the so-called 2nd stable region. These exciting simulation results are now motivating experimentalists from various machines to compare state-of-the-art measurements from advanced turbulence diagnostics with the predicted properties of microtearing modes. Furthermore, Dickinson et als' detailed study of edge microtearing mode properties is also motivating new analytic theory to try to explain the basic linear microtearing drive mechanism.

==> 2 highly cited papers including 1 PRL, Invited Talks



(C) Multiscale Simulations Coupling the Transport and Turbulent Timescales.

The TRINITY code computes a set of local gyrokinetic simulations over the rapid

plasma turbulence timescale across a range of flux surfaces, and couples these simulations with a global solver for the slow transport evolution of the equilibrium profiles. Plasma turbulence simulations dominate the computation requirement. First TRINITY simulations were carried out under this grant by Barnes et al, and good agreement was found between data from JET and ASDEX Upgrade and the TRINITY predictions for the evolved profiles.

==> highly cited paper, and Invited Talks



(D) Comparing Simulated Plasma Turbulence with Measured Density Fluctuations

Ion-scale density perturbations were measured on MAST using a 2D imaging beam emission spectroscopy diagnostic. For a low-density L-mode discharge with strong equilibrium flow shear and an internal transport barrier in the ion channel, the observed turbulence was compared with synthetic density turbulence data from global nonlinear gyrokinetic simulations using the NEMORB code. This ambitious analysis highlighted the need to include increasingly sophisticated physics in the simulations in order to reproduce most characteristics of the observed turbulence. The gyrokinetic simulations need to include a kinetic treatment of trapped electrons, equilibrium flow shear and collisions. The simulations successfully described many of the observed characteristics, but underestimated the turbulence amplitude and heat flux at the plasma periphery and overpredicted the correlation time.

==> journal paper and conference paper



(E) Other Plasma Turbulence Studies.

Plasma turbulence simulations carried out under this grant and published in refereed journals, have contributed important insights into other important aspects of tokamak plasmas:

-- First gyrokinetic simulations to include the centrifugal force in a strongly rotating plasma show that the associated change in equilibrium electrostatic potential enhances the trapped particle fraction. This destabilizes trapped electron modes. For nonlinear ITG dominated turbulence, the increased trapped electron drive increases the ion heat transport (at constant flow shear). An increased fraction of slow trapped electrons also enhances the convective particle pinch, leading to an increase in the steady state density gradient with strong rotation.

-- Gyrokinetic simulations have assisted our understanding of impurity transport in experimental plasmas from MAST and the Italian experiment FTU.

-- Recent novel study of the evolution of microinstabilites during pellet fuelling in MAST, of international interest, is likely to be relevant to the particle fuelling of ITER using pellets.

-- Novel studies demonstrate that the nonlinear interaction between magnetic islands and plasma turbulence makes neoclassical tearing modes (which seriously degrade the performance of tokamak plasmas) more stable than was previously understood.

-- Nonlinear simulations of filament propagation in the geometry of the MAST scrape-off-layer using the BOUT++ code, find two regimes of filament propagation. At high collisionality filaments propagate radially through the interchange mechanism, but at lower collisionality radial transport is reduced as the filaments acquire Boltzmann character. Such modelling of transport processes in the scrape-off-layer is needed to find new ways to mitigate power loads onto the divertor plates in experiments.



(F) Code Optimisations.

Significant HPC performance optimisations were also achieved for the widely used gyrokinetic plasma turbulence code, GS2, mainly in collaboration with Edinburgh Parallel Computer Centre. Some of this work was carried out using additional funding from HECToR Distributed Computational Science and Engineering Support:

-- GS2's Fast Fourier Transform package was upgraded from FFTW2 to FFTW3 (http://www.hector.ac.uk/cse/reports/GS2/).

-- Costly redistributes for the evaluation of FFTs in GS2 were accelerated, saving up to 17% of runtime for a typical representative calculation (http://www.hector.ac.uk/cse/reports/GS202/).

-- The most impressive HPC achievement was a performance enhancement exceeding a factor of four for a typical GS2 benchmark on 4096 processors. This results from a number of optimisations working together, improves the code's scalability, and make GS2 more suitable for the next generation of HPC platforms including ARCHER. (http://gyrokinetics.sourceforge.net/wikifiles/CMR/GS2DEVMEETING_21May2013/DDICKINSON.pdf)
Exploitation Route The ultimate goal of nuclear fusion research is entirely non-academic. It is to produce a new clean and abundant source of energy. Our simulations of plasma turbulence are helping (i) to suggest some of the physical mechanisms at play in the formation of transport barriers in tokamak plasmas, and (ii) how the turbulence impacts on particle fuelling. This knowledge will potentially suggest new approaches to optimising the performance of future plasma confinement devices towards their ultimate objective of harnessing nuclear fusion to produce energy. Controlling the plasma turbulence will be crucial to obtain the hot and high pressure plasmas that will be required.
Sectors Energy

 
Description Tokamaks exploit toroidal magnetic fields to confine extremely hot and high pressure plasmas at the conditions required to produce significant nuclear fusion reactions, and have the production of energy from controlled nuclear fusion as their ultimate goal. Magnetic confinement is, however, imperfect, and heat and particles leak from the device at a rate determined by turbulent and collisional transport processes. Nevertheless, experiments find that confinement is often substantially improved in localised regions of the plasma, generally associated with the local suppression of turbulence. These regions of excellent confinement are frequently referred to as "transport barriers", and can form at the edge and in the core of tokamak plasmas. "Transport barriers" are extremely attractive as they considerably enhance the fusion reactivity of the plasma. First principles calculations of plasma turbulence carried out under this grant, contribute significantly to our understanding of basic mechanisms that may be responsible for the formation of these regions of favourable confinement. Several of the world's leading tokamak experiments are currently testing predictions from these simulations, and some early observations appear to be consistent. A better understanding of transport barriers may ultimately be exploited to make substantial gains in the performance of magnetic confinement devices and thereby improve the prospects for fusion. First principles calculations of plasma turbulence carried out under this grant contribute to the understanding of basic mechanisms that can lead to the formation of regions of favourable confinement, "transport barriers" (A) in the core and (B) at the edge of the tokamak plasmas. (A) Influence of spatially varying ("sheared") equilibrium flows on tokamak plasma turbulence. Our simulations expose the opposing impacts on turbulence from radial shear in the components of equilibrium flow parallel and perpendicular to the equilibrium magnetic field, which enhance and suppress plasma turbulence respectively. The overall impact of sheared flow on turbulence is largely determined by the equilibrium magnetic field geometry. Strong flows are required to influence turbulence, and in tokamaks these flows are toroidal. Turbulence suppression is favoured at high ratios of poloidal to toroidal magnetic field (e.g. in spherical tokamaks like the UK experiment MAST). Simulations by Highcock et al reveal that a transport bifurcation to a suppressed turbulence state can be triggered by strong sheared flow, offering a candidate mechanism to explain the onset of "transport barriers". (B) Understanding the "H-Mode" Edge Transport Barrier. High confinement "H-mode" tokamak plasmas are associated with a steep gradient region at the edge of the plasma. The edge pedestal strongly influences the confinement in experiments, but the underlying physics is poorly understood. Electromagnetic microinstabilities are believed to play an important role, and this is confirmed by Dickinson et als' pioneering study of microinstability physics close to the edge in H-mode plasmas from MAST. This reveals that kinetic ballooning modes are marginally unstable in the MAST pedestal, while the plateau (just inside the pedestal) is dominated by microtearing modes that destroy the confining magnetic flux surfaces. Increasing the density gradient stabilises the microtearing modes until kinetic ballooning modes become unstable at a higher pressure gradient. This is a mechanism that will occur naturally during plasma refuelling, and it could be very important for pedestal dynamics. Microtearing modes have since been found unstable in the plateau region of other tokamaks including JET. Leading experiments are now comparing state-of-the-art edge turbulence measurements with the predicted properties of microtearing modes, and some recent observations appear to be consistent with these simulations. Beneficiaries: Fusion scientists working to improving magnetic confinement systems, junior fusion scientists as part of their career development, wider society standing to benefit from the development of fusion energy., other academics interested in plasma turbulence in magnetised systems, expanded exploitation of HPC for leading-edge research. Contribution Method: Results from simulations carried out under this grant (see for example [1,2]) have suggested two basic physical mechanisms that may be associated with the development of favourable "transport barriers" in magnetised plasmas. This work has excited the international fusion community and has stimulated follow-on research that will test whether the particular mechanisms proposed are relevant to optimising fusion plasmas in power plant relevant regimes. [1] Highcock et al, PRL 105, 215003 (2010) [2] Dickinson et al, PRL 108, 135002 (2012)
Sector Energy
Impact Types Societal,Economic

 
Description Improved Data Distribution Routines for Gyrokinetic Plasma Simulations
Amount £57,997 (GBP)
Organisation University of Edinburgh 
Department High-End Computing Terascale Resource (HECToR)
Sector Academic/University
Country United Kingdom
Start 03/2011 
End 01/2012
 
Description Optimised Field Solves in GS2
Amount £60,000 (GBP)
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Department ARCHER Service
Sector Academic/University
Country United Kingdom
Start 09/2012 
End 07/2014
 
Description Plasma Physics HEC Consortia
Amount £279,240 (GBP)
Funding ID EP/L000237/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 05/2013 
End 05/2018
 
Description The Plasma-CCP Network
Amount £125,995 (GBP)
Funding ID EP/M022463/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 07/2015 
End 06/2020