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What makes radial diffusion tick? The symmetries driving radiation belt dynamics. (Advert ref: STFC23/EE/MPEE/BENTLEY)

   Faculty of Engineering and Environment

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  Dr Sarah Bentley  No more applications being accepted  Competition Funded PhD Project (Students Worldwide)

About the Project

Earth’s radiation belts are a collection of high energy electrons trapped by the magnetic field. Prediction of the particle populations here is an ongoing question due to the increasing number of satellites whose orbit coincides with the outer radiation belt. Space weather forecasting is needed to enable satellite operators to protect their spacecraft. At the same time, this plasma environment can be treated as natural laboratory for a plethora of waves and their interactions with the particles.

Radial diffusion is one of the large drivers of radiation belt physics, playing a significant role in the energisation and transport of radiation belt electrons. Due to decades of research and recent NASA missions collecting data in this environment, we are now poised to create new radiation belt models that explore exciting new aspects of the physical system, including uncertainty, complex phenomena, ensemble modelling and the incorporation of live data to models. We are looking for a PhD student to join and drive this effort.


Your project will focus on the theory behind radial diffusion. You would start by deriving the existing diffusion equation used to model this system from a conservation law perspective, using symmetry-based approaches and Noether theory. From this point, you would focus on clearly outlining where and when this model is valid, developing new approaches to capture radial diffusion when this existing theory breaks down (the “L* problem”) and identifying the new features and dynamics that emerge as a result.

This problem will include elements and techniques from Lagrangian and Hamiltonian mechanics, wave-particle interactions, conservation laws and symmetries, and bifurcation theory.

Supervisory team

Primary supervisor: Dr Sarah Bentley

Secondary supervisors: Prof. Jonathan Rae and Dr Daniel Ratliff

The Solar and Space Physics group in Maths and Physics is now one of the largest groups in the UK with expertise across near-Earth space. Dr Bentley and Prof. Rae use a variety of methods to represent and understand space physics processes and are exploring several techniques to approximate the radial diffusion problem. Dr Ratliff uses methods in applied mathematics to study wave phenomena, including symmetry-based methods, asymptotic analysis, and bifurcation theory.

Student Profile

Candidates should have:

  • A strong numerate background, such as a degree in applied maths, or physics with a strong theoretical component (essential);
  • motivation to explore challenging open questions (essential);
  • an ability to work alone or in a team (essential);
  • knowledge of electromagnetism, especially of plasma environments (highly desirable)
  • experience in scientific computation, e.g. numerical solution of PDEs (desirable)

Training opportunities

In addition to regular supervisor meetings, students are encouraged to participate in group activities, including our seminar series with national and international experts. Northumbria is part of the MAGIC consortium sharing live lectures in a wide range of PhD-level mathematics courses. We offer additional Masters-level modules to provide any necessary subject-specific knowledge or skills, and you are encouraged to attend national summer schools and apply to competitive international summer schools. We will help you choose conferences and workshops to discuss your results with the scientific community.

Eligibility Requirements:

  • Academic excellence of the proposed student i.e. 2:1 (or equivalent GPA from non-UK universities [preference for 1st class honours]); or a Masters (preference for Merit or above); or APEL evidence of substantial practitioner achievement.
  • Appropriate IELTS score, if required.
  • Applicants cannot apply for this funding if they are already a PhD holder or if currently engaged in Doctoral study at Northumbria or elsewhere.

Please note: to be classed as a Home student, candidates must meet the following criteria:

  • Be a UK National (meeting residency requirements), or
  • have settled status, or
  • have pre-settled status (meeting residency requirements), or
  • have indefinite leave to remain or enter.

If a candidate does not meet the criteria above, they would be classed as an International student. Applicants will need to be in the UK and fully enrolled before stipend payments can commence, and be aware of the following additional costs that may be incurred, as these are not covered by the studentship.

  • Immigration Health Surcharge
  • If you need to apply for a Student Visa to enter the UK, please refer to the information on It is important that you read this information very carefully as it is your responsibility to ensure that you hold the correct funds required for your visa application otherwise your visa may be refused.
  • Check what COVID-19 tests you need to take and the quarantine rules for travel to England
  • Costs associated with English Language requirements which may be required for students not having completed a first degree in English, will not be borne by the university. Please see individual adverts for further details of the English Language requirements for the university you are applying to.

You will join a strong and supportive research team. To help better understand the aims of the CDT and to meet the PhD supervisors, we are hosting a day-long event on campus on Monday 9th January 2023.

At that event, there will be an opportunity to discuss your research ideas, meet potential PhD supervisors, as well as hear from speakers from a variety of backgrounds (academia, industry, government, charity) discussing both STFC and data science as well as their personal paths and backgrounds. Click here for details.

How to Apply

For further details of how to apply, entry requirements and the application form, see

Please note:

You must include the relevant advert reference/studentship code (e.g. STFC23/…) in your application.

We offer all applicants full guidance on the application process and on details of the DTP. For informal enquiries, email Professor James McLaughlin (Northumbria: [Email Address Removed]). Please contact the Principal Supervisor of the project(s) [Email Address Removed] for project-specific enquiries.

Deadline for applications: 31st January 2023

Start Date: 1st October 2023

Funding Notes

The studentship supports a full stipend, paid for 3.5 years at UKRI rates (for 2022/23 full-time study this is £17,668 per year), full tuition fees and a Research Training and Support Grant (for conferences, travel, etc).


Reappraisal of Whitham's 1967 theory for wave–meanflow interaction in shallow water, Bridges, T., Ratliff, D. (2022), In: Wave Motion
Modeling the Varying Location of Field Line Resonances During Geomagnetic Storms, Elsden, T., Yeoman, T., Wharton, S., Rae, I., Sandhu, J., Walach, M., James, M., Wright, D. (2022) In: Journal of Geophysical Research: Space Physics
Genuine nonlinearity and its connection to the modified Korteweg–de Vries equation in phase dynamics, Ratliff, D. (2022), In: Nonlinearity
Pro-L* - A Probabilistic L* mapping tool for ground observations, Thompson, R., Morley, S., Watt, C., Bentley, S., Williams, P. (2021) In: Space Weather
Random Forest Model of Ultralow-Frequency Magnetospheric Wave Power, Bentley, S. N., Stout, J. R., Bloch, T. E., & Watt, C. E. J. (2020) In: Earth and Space Science
Capturing uncertainty in magnetospheric ultralow frequency wave models, Bentley, S. N., Watt, C. E. J., Rae, J., Owens, M. J., Murphy, K., Lockwood, M., & Sandhu, J. K. (2019) In: Space Weather
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