Computational Generalised Time-Dependent Ginzburg-Landau (gTDGL) Theory to Describe Critical Current in the HTS Superconductors in 20 T Fusion Tokamaks (a Computational PhD) – Materials Strand Project

Supervisor: Professor Damian Hampshire (Durham University).

Background:

The fusion tokamaks that are to be built in the next 5 – 20 years are some of the most exciting scientific projects in the first half of the 21st century, The STEP-UKAEA project and the Tokamak Energy STX project in the UK, the ITER (International Thermonuclear Experimental Reactor) Tokamak in France, the tokamak being built by Commonwealth Fusion Systems in Boston, USA, and EAST in China, are all racing to develop fusion energy as the world’s carbon-free energy source. High Temperature Superconductors (HTS) are the enabling technology for these machines since without them, the magnets that hold the plasma would either melt or consume more energy than the tokamak produces. It remains a completely open question as to which HTS materials are the best choice to produce the high fields needed in commercial fusion. We welcome Physics, Maths and Engineering final year undergraduates or graduates to apply for this Physics PhD that will inform the community’s materials choices and future designs. The imminent timescale for first-plasma in fusion devices world-wide offers a wonderful opportunity for an early career Physicist, Mathematician or Engineer to help develop our understanding of high field superconducting materials for fusion applications and help lead this field.

Computational PhD Research Project and Supervision:

In this PhD research programme, the student will use and develop computational techniques and generalised Time Dependent Ginzburg-Landau (gTDGL) theory to model polycrystalline low temperature superconductors and high and low temperature superconductors (HTS and LTS) 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 at ~ 20 Tesla than those currently available. In this context, the values of current density in high-field superconductors are pitifully small, typically less than 1 % of the theoretical limit in high fields which offers a huge opportunity for technological improvement.

In this PhD, the main focus will be to use computational techniques to model and identify the mechanism for flux pinning and the modes of flux flow in high field superconductors. We intend 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 which gives an excellent exposure to many of the best Universities in the UK, an excellent taught course in fusion energy, exposure to the fusion community across the world. and provides a non-means tested stipend (£20780 tax-free in 2025). We expect the PhD student to be based in 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. We also expect the student 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 degree in Physics, Mathematics or Engineering and a broad interest in fusion, materials and applied Physics. 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:

Transferable Skills.

Communication: Presentations at conferences and developing collaboration. Personal: Networking skills. Working with expert senior staff, junior staff and staff providing services. Writing: Reports, Conference and Journal publications. Critical thought. Computerised Data Acquisition and Analysis. Knowledge: Understanding magnetically confined fusion and high field superconductors. Time management.

Specialist Skills and Know-how.

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

Materials projects:

For this project, the student will be based in Durham – during the first six months of the PhD, the student will typically travel to attend taught modules at all six of the Fusion CDT partner universities.

The project will be based in Durham, but there is the opportunity to travel to conferences and collaborate with other groups. The students will complete their collaboratory for 6 – 8 weeks – typically with colleagues in Japan, the USA or the EU.

This project is offered by Durham University. For further information please contact: Damian Hampshire (d.p.hampshire@durham.ac.uk).

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

Images above: Top: Standard TDGL equations. Bottom: TDGL simulations of the fluxons in a superconductor at different magnetic fields in a typical pinning landscape for Nb-Ti.

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: https://www.youtube.com/watch?v=7KmiTSx_Rok A. I. Blair and D. P. Hampshire Critical current density of superconducting-normal-superconducting Josephson junctions and polycrystalline superconductors in high magnetic fields, Phys. Rev. Research 4, 023123, 16 May 2022