Self-Regulation of Turbulence by Flows in Tokamaks – Plasma Strand Project
Supervisors: Steve Tobias (University of Edinburgh, lead), Patrick Diamond (UC San Diego), Moritz Linkmann (University of Edinburgh) & Daniel Kennedy (UKAEA).
Electromagnetic microinstabilities are likely to limit performance in future advanced steady state tokamak plasmas and are expected to dominate transport in high β next generation spherical tokamaks such as STEP [1]. While gyrokinetic simulations have thus far proven to be a very accurate tool in modelling turbulent transport in predominantly electrostatic regimes, obtaining saturated nonlinear simulations in higher β plasmas with unstable kinetic ballooning modes (KBMs) and microtearing modes (MTMs) has proven computationally challenging (see e.g. [2] and references therein).
Nonlinearly, a complex picture is emerging whereby it is possible to observe well-defined transitions between a finite-amplitude saturated state dominated by strong zonal-flows, and a state where the mean pressure gradient relaxes to near marginally, due to KBMs and/or MTMs. Delineating the effective phase boundary for zonal flow collapse at high β is of prime importance. How turbulence is regulated in the near-marginal, KBM states is currently unclear. Results from gyrokinetic simulations suggest that multi-scale interactions between electron-temperature gradient (ETG) turbulence and ion-temperature-gradient (ITG) turbulence result in a nonlinear suppression of ITG turbulence without excitation of zonal flows [3]. Moreover, the ETG modes, which are electrostatic in nature, may also suppress electromagnetic ion-scale MTMs [4], while themselves being damped by ITG modes [3]. Other possibilities include turbulence saturation by zonal magnetic fields or profile corrugations. In general, the breakup of the low-transport regime appears to be linked to a competition between the two different drives of zonal E X B shear in the system; the Reynolds stress (which grows zonal flows) and the Maxwell stress (which tends to work against the Reynolds stress). Understanding these mean field dynamics and how they are affected by multi-scale effects are crucial to the design and optimisation of next-generation fusion devices.
In this project, we will devise coupled reduced fluid models to describe such multi-scale interactions, by leveraging physics-based analytical modelling approaches for Reynolds and Maxwell stresses [5] that incorporate the different possible effects on turbulent transport through explicit model terms. These model terms must be weighted against one another as not all physical processes, that are in principle present, have the same quantitative contribution to turbulent transport. Therefore, we will supplement the analytical modelling ansatz by data-driven methods to infer and tune the weights of the devised closed-form model terms for turbulent transport [6]. More precisely, we will use convolutional neural networks, trained either on data from gyrokinetic simulations or higher-resolution fluid models. As a complementary approach, we explore how statistical approaches such as Direct Statistical Simulation [7] can be applied in this context. Finally, we compare new gyrokinetic and reduced-model computations with fluctuation measurements on MAST-U.
[1] E. Tholerus et al. submitted to NF.
[2] D. Kennedy et al 2023 Nucl. Fusion 63 126061
[3] S. Maeyama et al. 2024 Nucl. Fusion 64 112007
[4] S. Maeyama et al. 2017 PRL 119, 195002
[5] D. Capocci et al. 2025 J. Plasma Physics 91 E11
[6] R. A. Heinonen and P. H. Diamond 2020 Plasma Phys. Control. Fusion 62 105017
[7] S. M. Tobias et al 2011 ApJ 727 127
The student would be affiliated with the School of Physics and Astronomy. For entry requirements, please see here.
Plasma strand students are based at University of York for the initial six months of the PhD, for the taught modules. During that first six months students will typically travel to undertake taught modules at all of the Fusion CDT partner universities.
After the taught programme, for the remainder of the PhD, this project will be based at Edinburgh, Scotland with research visits to UKAEA in Culham, Oxfordshire.
The project will require at least one research visit to the US lasting several weeks.
This project is being offered by University Of Edinburgh as part of the Fusion CDT Community Studentship scheme. For further information about the project and details of how to apply please contact: Steve Tobias (S.Tobias@ed.ac.uk), Patrick Diamond (diamondph@gmail.com), Daniel Kennedy (daniel.kennedy@ukaea.uk) or Moritz Linkmann (moritz.linkmann@ed.ac.uk).
Application deadline for this project: 10th January 2026.