PhD opportunities

Study of magnetic presheath stability to parallel drifts

Supervisor Dr Robert Kingham
Type Computational & Theoretical

EPSRC CDT  (in Nuclear Energy Futures) or  Imperial President’s PhD Scholarship


The proposed project focusses on kinetic study of sheaths at the interface between plasma in the scrape-off layer (SOL) and wall structures, for oblique angle between the magnetic field and the surface.  The sheath is crucial as it sets the boundary condition for the plasma exhaust streaming to the diverter in tokamaks.  In order to manage the power flux to the diverter, modern tokamaks operate with the magnetic field impinging on the diverter at a very shallow angle, to spread the power over as large an area as possible and thereby mitigate material damage.  In this geometry, the sheath separates into three regions; the thin Debye sheath adjacent to the solid, followed the magnetic pre-sheath (thickness on the order ion Larmor radius) and then the collisional pre-sheath.

There are large ExB drifts in the magnetic presheath (MPS) due to the sheath E-field (normal to the wall, and strongly varying with distance) and the component of B-field parallel to the wall. These ExB flows will be sheared and potentially prone to Kelvin-Helmholtz-like instabilities. This has been observed in a limited number of collisionless, PIC simulations [Theilhaber and Birdsall (1989), which Parker et al (1992)], which were of limited applicability to divertor conditions in modern tokamaks and also poorly resolved. Yet such instabilities have the potential to change the sheath characteristics (e.g. transmitted particle and energy fluxes) and concentrate fluxes on small areas of the surface, which could be detrimental to the survivability of plasma facing components to exhaust in tokamaks. Understanding this instability, and how to mitigate it is therefore of importance.

The idea is to develop a kinetic code and use it to study sheared flows in the MPS for planar, electron-repelling sheaths, including warm ion effects (needed for Ti>Te found near the divertor) and ion collisions. The code will focus on solving the ion Vlasov-Fokker-Planck equation across the entire sheath, encompassing the collisional presheath (up to several collisional mfp thick), magnetic presheath and Debye sheath, together with adiabatic electrons.

This project is part of a collaboration with Culham Centre for Fusion Energy (CCFE).  The PhD student would be primarily based at Imperial, with regular visits to CCFE. There will be a CCFE co-supervisor.

Background reading

P. C. Stangeby, "The Plasma Boundary of Magnetic Fusion Devices”, IoP Press (2000)

R. Chodura,  Phys. Fluids 25, 1628 (1982);   [ ]

K. Theilhaber and C.K. Birdsall, Phys. Fluids B 1, 2244 (1989); [ ]

A. Geraldini, F.I. Parra, F. Militello, Plasma Phys. Control. Fusion 60, 125002 (2018);  [ ]

L-H Transition Studies on the ST40 Tokamak

Supervisor Dr Robert Kingham and Dr Yasmin Andrew
Type Experimental, Theoretical and Computational

EPSRC CDT  (in Nuclear Energy Futures)


The plasma transition from the low to high (L-H) confinement regime in tokamaks, one of the most remarkable discoveries in fusion history, refers to the sudden improvement of confinement when input power is increased above a critical value.  The L-H transition is accompanied by the formation of a pedestal at confined plasma edges, a relatively narrow edge plasma region with significantly enhanced pressure profile gradients and reduced transport. This in turn boosts the temperature of the core plasma thus improving the fusion performance compared to L-mode.  This phenomenon has been reliably reproduced in different fusion devices since its first discovery in 1980’s; the study of the L-H transition, the backwards H-L transition and the pedestal, has remained one of the most important research topics in Magnetically Confined Fusion ever since. 

For ITER, questions on how to enter and exit the H-mode with the available heating power remain a crucial part of the practical machine operation planning.   Recently, new tokamak concepts wandering further away from the conventional design of ITER, JET, etc., have been proposed, which require understanding of the access to H-mode in new regimes.  The topic of L-H transitions is thus rapidly evolving, with a growing number of experimental studies planned on existing machines. These studies involve upgraded suites of edge, core and divertor plasma diagnostics and utilise advanced analysis techniques.

This project will make a unique and important contribution to ongoing world-wide H-mode access studies through the analysis of experimental results on the new ST40 super-conducting spherical tokamak at Tokamak Energy Ltd.  To facilitate this, a novel interpretative model will be developed.  ST40 plasmas will occupy new domains of low and high confinement operation with this spherical tokamak’s exceptional combination of high magnetic field, low aspect ratio and augmented heating power.  The validity of traditional analysis methodology, using mean values or variance across the instantaneous transitions into and out of H-mode, has limitations due to large, time-dependent fluctuations. Thus, the particular emphasis of this project will be on the investigation of the time-evolution of the L-H/H-L transitions, the edge pedestal where available and the development of a novel probability distribution function (PDF) statistical method.

The experimental aspect of the project will be to map out the operational space for L-H (and H-L) transitions over a series of available parameter scans, such as density, magnetic field, Ip, torque or additional heating scheme.  These results are expected to make a significant contribution to ongoing cross-spherical tokamak H-mode access studies on MAST, MAST-U and NSTX.  On the theoretical and computational side, the project will employ an existing simulation code to solve the 3D Fokker-Planck equation and use it to develop and tune the lighter PDF statistical model. The code will need to be parallelised to speed up computations and upgraded to include a wider range of noise sources.

This project is part of a collaboration with Tokamak Energy and Coventry University.  The PhD student would be primarily based at Imperial, with regular visits to Tokamak Energy. Prof. Eun-jin Kim is the co-supervisor at Coventry University.

Background Reading

Wagner, F., et al. “Regime of Improved Confinement and High Beta in Neutral Beam Heated Divertor Discharges of the ASDEX Tokamak”, Phys. Rev. Lett. 49, 1408 (1982)   [DOI: 10.1103/PhysRevLett.49.1408 ]

Gryaznevich, M., Asunta, O. et al., “Overview and status of construction of ST40”, Fusion Engineering and Design 123, 177 (2017)  [DOI:  10.1016/j.fusengdes.2017.03.011 ] Andrew, Y, Bahner, J-P, Battle, R., Jirman, T., “H-mode Power Threshold Studies on MAST”, Plasma 2, 328 (2019)   [DOI:  10.3390/plasma2030024]

Hollerbach, R., Kim, E. & Schmitz, L.S., “Time-dependent probability density functions and information diagnostics in forward and backward processes in a stochastic prey-predator model of fusion plasmas”, Phys. Plasmas 27, 102301 (2020)  [DOI:  10.1063/5.0011473 ]