Machine Learning Enhanced Dynamic Mode Decomposition for High Fidelity Tokamak Turbulent Transport Modelling – Plasma Strand Project
Supervisor/s: David Dickinson (University of York) and Alexandra Dudkovskaia (Tokamak Energy),
The tokamak plasma is confined by strong magnetic fields. Various drift wave instabilities which have short wavelengths across the magnetic field, and the associated turbulence, behave in a way that degrades the confinement. The latter poses a serious issue for present tokamaks and future fusion pilot plant designs.
One of the key parameters in fusion plasmas is called beta, β, namely the plasma thermal pressure that can be held for a given magnetic field. For the purposes of economic viability and efficiency of the fusion-powered electricity of fusion power plants (FPP), it is important to achieve higher values of beta. The latter, unfortunately, also makes such plasma particularly vulnerable to electromagnetic drift wave instabilities, predominantly represented by kinetic ballooning modes (KBMs), micro-tearing modes (MTMs) and their hybrids with electrostatic drift waves. These instabilities have been reported in MAST/-U [1], STEP-like plasmas [2] and also observed in Tokamak Energy FPP like plasmas [3].
To accurately model plasma turbulence and to quantify the associated turbulent transport, one requires a 5-dimensional gyrokinetic theory. The latter is provided by averaging the full 6-dimensional kinetic equation over the rapid gyro-motion of charged particles in the electromagnetic field of the tokamak plasma. However, the computational cost of gyrokinetic simulations is expensive (often prohibitively so). It typically varies from 10^4 CPU hours for conventional, local gyrokinetic simulations of electrostatic turbulence to 10^6-10^7 CPU hours for multi-scale global-local gyrokinetic simulations of electromagnetic turbulence [4], which makes such simulations impossible to employ in an integrated modelling routine to model the FPP plasma. In practice, comprehensive gyrokinetic simulations are often replaced with various lower fidelity, reduced transport/ kinetic-fluid approaches, which allows one to significantly decrease the computational cost but comes at a price of accuracy.
To avoid sacrificing accuracy of the turbulent transport predictions with the use of reduced models, while maintaining comprehensiveness of the gyrokinetic simulations, the PhD project will be focused on exploring the physics-informed Dynamic Mode Decomposition (DMD) technique in relevance to gyrokinetic simulations. DMD is a machine learning associated, data-driven technique that performs spectral analysis of time-series nonlinear data by constructing a lower-dimensional linear dynamical model. The high computational efficiency of DMD in the gyrokinetic eigenmode analysis has previously been demonstrated in [5]. In contrast to [5], the proposed PhD project will adopt and apply DMD to nonlinear gyrokinetic simulations, investigating and comparing various DMD algorithms to retain comprehensive physical effects of fusion plasmas and to perform DMD incrementally on the fly. The PhD project will help build an extensive database of nonlinear gyrokinetic results suitable for surrogate modelling for machine learning, to be further employed in the integrated modelling tools to predict the FPP plasma behaviour. Furthermore, employing DMD in nonlinear gyrokinetic analysis, the PhD project will allow one to look at physical aspects of plasma turbulence in more detail (compared to a typical nonlinear gyrokinetic simulation), capturing multiple branches of drift wave eigenmodes and thus allowing one to understand and categorise turbulence in ST40 plasmas and future FPP designs. It is anticipated that the student will employ the DMD powered gyrokinetic modelling to quantify turbulent transport in ST40 plasmas, compare and validate the associated predictions against the existing ST40 data and inform future pilot plant scenarios.
Over the duration of their PhD, the student will gain experience in analytic and computational plasma theory, high performance computing, machine learning 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
[2] D. Kennedy et al. Nucl. Fusion 63 (2023) 126061
[3] A.V. Dudkovskaia, Y. Ren et al. in preparation (2025)
[4] J. Candy, A.V. Dudkovskaia, E. Belli Phys. Rev. E. 111 (2025) L053201
[5] A.V. Dudkovskaia, D. Li, J. Candy et al. Plasma Phys. Control. Fusion 67 (2025) 065033.
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.
The student will spend the first year of their PhD at the University of York, while they undertake the Fusion CDT training courses. After completing the CDT training, the student is anticipated to be at the Tokamak Energy site for the remainder of their PhD programme.
The proposed PhD project will be mainly based at the University of York and Tokamak Energy. However, there will be multiple opportunities for travel to attend scientific conferences and workshops and to engage with collaborators.
This project is offered by University of York. For further information please contact: David Dickinson (d.dickinson@york.ac.uk) or Alexandra Dudkovskaia (alexandra.dudkovskaia@tokamakenergy.com).
This project may be compatible with part time study, please contact the project supervisors if you are interested in exploring this.
For details on how to apply, please visit: Apply