Nonlinear generalised gyrokinetic modelling of electromagnetic turbulence in finite beta plasmas representative of MAST U and STEP – plasma strand project

Supervisor/s – Daniel Kennedy (UKAEA, lead), Alexandra Dudkovskaia (University of York), David Dickinson (University of York)

In a tokamak, the plasma (typically anticipated to include deuterium and tritium in a power plant) is confined in a toroidal magnetic field geometry. Plasma charged particles closely follow the magnetic field lines, which are located on toroidally symmetric, closed, nested magnetic flux surfaces, upon which pressure is constant. The plasma pressure increases towards the tokamak core, providing the good tokamak plasma confinement. The tokamak confinement, however, is generally degraded by turbulence. This plasma turbulence is a result of drift instabilities with short wavelengths across the magnetic field (typically comparable to or below the Larmor radius length scale). The spherical tokamak plasma, in particular, has more compact plasma shaping and achieves higher beta values (i.e. ratios of plasma pressure to magnetic field pressure), which makes it vulnerable to electromagnetic drift instabilities (and associated turbulence) represented primarily by kinetic ballooning modes, peeling modes and microtearing modes. These instabilities have been previously observed in MAST plasmas [1], and their presence is anticipated in MAST-U [2] and future spherical tokamak power plants, such as STEP [3], where achieving higher betas is important for commercial viability.

Turbulent microinstabilities are generally described by gyrokinetic theory. Conventional gyrokinetics, however, is currently at the limit of what can be accurately solved on computer and does not retain all the necessary contributions to quantify these electromagnetic modes when beta is high, which makes it insufficient to design and predict future high beta reactor-grade spherical tokamak plasma operational scenarios. The project will generalise existing gyrokinetic codes, such as stella or GENE that allow for both local and global modes of operation, to incorporate recently derived higher order corrections to conventional gyrokinetics [4], such as neoclassical corrections due to steep pressure gradients. These corrections are particularly important for a spherical tokamak plasma, where high fractions of the pressure gradient- driven bootstrap current are achieved. This will complement the higher order gyrokinetic microstability analysis based on the neoclassical extension of the local, flux tube gyrokinetic code GS2 (currently ongoing in York), as well as turbulent transport studies for MAST-U pedestals at UKAEA. It is anticipated that the student will be able to quantify turbulent transport in spherical tokamak (MAST-U) plasmas, which will then be validated against spherical tokamak (MAST-U) experiments and offer predictions for future reactor-grade spherical tokamaks (STEP).

The student will gain experience in high performance computing, analytic plasma theory and data analysis, as well as opportunities for training and professional development in scientific communication.


[1] D. Dickinson et al. Phys. Rev. Lett. 108 (2012) 135002



[4] A V Dudkovskaia et al. Plasma Phys. Control. Fusion 65 (2023) 045010

The student will be based in York Plasma Institute, University of York during the first year of the project and then in Culham Science Centre. The project might also include travel to support collaborations, as well as participation in plasma physics conferences and workshops.

This project is offered by University of York. For further information please contact: Dr Daniel Kennedy ( or Dr Alexandra Dudkovskaia (

This project may be compatible with part time study, please contact the project supervisors if you are interested in exploring this.