EPSRC DLA studentship - Mathematical analysis of runaway electrons in Tokamak reactors

Fusion reactors are a promising route towards low carbon energy generation. The studentship project on mathematical kinetic theory will open mathematical research into the genesis of runaway electrons in fusion reactors. Runaway electrons are a major obstacle in the development of fusion reactors. The term describes the presence of a population of electrons which accelerate far beyond the thermal plasma velocity. They pose a threat to the integrity of the confining reactor and are a key concern in the operation of fusion reactors. The runaway process can be roughly subdivided into two stages: 

  1. A small number of electrons entering the runaway regime through Dreicer mechanism.

  2. The runaway avalanche, generated by head-on collisions with runaway electrons, leading to an exponential growth of the runaway population.

While the problem has been extensively studied in plasma physics, a mathematically rigorous (kinetic) description of both stages is currently lacking. 

With the student, we will develop a mathematically rigorous theory for runaway electrons using kinetic partial differential equations. We will tackle questions of well-posedness for these equations, as well as their asymptotic behaviour for large times. The aim is to find the mathematical mechanisms behind the (in-) stability of plasma, particularly under the influence of external fields.

The theory of Partial Differential Equation is of fundamental importance for this studentship. However, the research on kinetic Partial Differential Equations with external electric and magnetic fields is in an early stage and offers many open questions. Therefore, the project can be developed according to the student’s background and strengths, such as prior knowledge in probability theory and stochastic analysis, numerics, spectral theory or Functional Analysis. 

What we offer:

Cardiff's School of Mathematics provides an excellent postgraduate research environment including:

·    research facilities at Abacws (co-designed by our PGR community),

·    a vibrant research culture including a wide range of research events,

·    access to national course centres in mathematics, statistics and Operational Research,

·    comprehensive professional skills training offered by Cardiff’s Doctoral Academy.

·  collaborations with other disciplines and with a wide range of external partners (industry and society).

The PGR community is very active in running the SIAM-IMA Student Chapter, a valuable forum for exchange of ideas and public engagement.

This studentship will be undertaken within the Mathematical Analysis research group at the School of Mathematics. The group’s members have wide-ranging interests, and offer a dynamic environment for the student to engage with experts in mathematical analysis and many other fields in mathematics and other disciplines. The group hosts a weekly seminar inviting external speakers.

Completing a PhD in mathematics opens up a range of possible next steps, from continuing an academic career to working in mathematically technical roles in industry.

The 3.5 year studentship includes fees, stipend at the UKRI rate and a Research Training Support Grant to cover costs such as research consumables, training, conferences and travel.

The start date for this PhD studentship is 1 October 2025.

What you bring:

You should have a 1st or upper 2nd class UK Honours degree (or equivalent) and/or a Master’s degree in mathematics or a suitable related subject.

Applicants for whom English is not their first language must demonstrate their proficiency by obtaining an IELTS score of at least 6.5 overall, with a minimum of 5.5 in each skills component, or equivalent qualification.

Shortlisted candidates will be invited to attend an interview.

Cardiff University is committed to supporting and promoting equality and diversity and to creating an inclusive research environment. We particularly welcome applications from underrepresented groups.

How to apply:

Applicants should apply through the Cardiff University online PhD application portal, for a Doctor of Philosophy in Mathematics with an entry point of 1 October 2025.

In addition to the standard application form, applicants should also:

* Attach a CV. Guidance on CVs for a PhD position can be found on the FindAPhD website .

* Ensure your personal statement (as part of the university application form, or as a separate attachment, if you prefer) provides a clear explanation of your research interest, preparation undertaken, and an understanding of the project.

Your personal statement should be no more than 500 words, and address the following questions:

1. What are your scientific research interests and ambition?

2. How has your academic and/or professional journey prepared you for PhD study? (for instance, give examples of work you particularly enjoyed, of challenges you overcame, of connecting with others about your work or ideas, of showing inventiveness, of developing new skills and knowledge)

3. Why do you think this project is important?

For general information about EPSRC-funded studentships at Cardiff, please see EPSRC - Study - Cardiff University.

Note that the 'register interest' option will not submit an application. Please follow the instructions above and submit your application via our online portal. Incomplete applications will not be considered.