Computational Time-Dependent Ginzburg-Landau (TDGL) Theory for high fields superconductors in fusion tokamaks (Durham Computational PhD) – materials strand project

Supervisor: Prof. D. P Hampshire (Durham University)


The ITER (International Thermonuclear Experimental Reactor) Tokomak that is being built in Cadarache in France is one of the most exciting scientific projects at the beginning of the 21st century ( It will produce 500 MW fusion power. Superconductivity is the enabling technology for this project since without it, the magnets that hold the plasma would either melt or consume more energy than the tokamak produces.

After ITER, we expect new tokamaks to be built across the world that will help enable commercial fusion energy (eg DEMO – Demonstration Power Plant – and STEP – Spherical Tokamak for Electricity Production). It is a completely open question as to which high-field superconductors are the best choice to produce the high fields needed in commercial fusion. The PhD will inform the fusion community’s materials choice and future designs for commercial MCF tokamaks.

The timescale for first-plasma at ITER (we are nearly there) offers a wonderful opportunity for early career Physicists to help develop our understanding of high field superconducting materials for fusion applications.

Computational PhD Research Project and Supervision:

In this PhD research programme, the student will use and develop computational techniques and Time Dependent Ginzburg-Landau (TDGL) theory to model polycrystalline low temperature superconductors and high temperature superconductors with inclusions. Recent work has demonstrated that the next generation of fusion tokamaks may be most effective at > 16 Tesla – which opens the question of whether we can develop new composite superconducting materials that have higher performance and are cheaper at 16 Tesla than those currently available. In addition, the values of current density in high-field superconductors are pitifully small, typically less than 1 % of the theoretical limit in high fields. In this PhD, we will use computational techniques to model and identify the mechanism for flux pinning and the modes of flux flow in high field superconductors. The focus for the PhD will be to identify routes for increasing the high-field critical current values by a factor of 10 in superconductors used in fusion applications and hence achieve values closer to their theoretical limits.

The PhD supervisor is Prof. Damian Hampshire who is an experienced member of the high-field applied superconductivity and fusion energy community. The 4 year PhD will be funded through the CDT in fusion at Durham University. We expect the PhD student to be based in Durham and to make regular visits to CCFE. We also expect them to work in an International laboratory (usually the USA, Japan or EU) for at least one collaborative project in the 2nd or 3rd year.

This is a fabulous PhD project that is ideal for a student with a good degree in Physics and a broad interest in fusion, materials and applied Physics. They will be expected to develop networking skills for working  with fusion scientists throughout the world. The 4 year PhD is funded through the Fusion CDT partnership which gives an excellent exposure to many of the best Universities in the UK, an excellent taught course in fusion energy and exposure to the fusion community across Europe. The PhD is formally based at Durham but the training in the fusion CDT means you spend about 6-8 months during the first year of your PhD at CDT partner Universities. The Research Group is committed to developing an environment that produces world-class science and is inclusive, flexible and family-friendly.

Skills the student will learn during the PhD:

i) Transferable Skills:

Communication – Presentations at conferences and developing collaboration. Personnel: Networking skills – Working with expert senior research staff, junior staff and staff providing services. Writing – Reports, Conference and Journal publications. Knowledge – Understanding magnetically confined fusion and high field superconductors. Research and critical thought. Time management.

ii) Specialist Skills:

High field superconductors modelled using TDGL for fusion applications. Advanced computation using HPC and theoretical skills.

The project will be mainly based in Durham University, but will include regular visits to CCFE. It will involve overseas travel to: Japan or the US for a collaboratory for 6 – 8 weeks; the USA and/or Japan and/or Europe for conferences and collaborations.

This project is offered by Durham University. For further information please contact Prof. Damian Hampshire at:

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


CCFE is the fusion research arm of UKAEA.

Figure above: Charles W.W. Haddon, A.I. Blair, F. Schoofs, and D.P. Hampshire Computational Simulations using Time-Dependent Ginzburg–Landau Theory for Nb–Ti-like Microstructures (2021)

Associated movie: