OXFORD THEORETICAL ASTROPHYSICS AND PLASMA PHYSICS GROUP

   

DPhil PROJECTS IN PLASMA PHYSICS

  starting in October 2026

 Application deadline: TBA January 2026

Oxford Plasma Theory Group welcomes applications for DPhil studies and research in plasma physics in the areas of magnetic confinement fusion (MCF) and plasma astrophysics (including "laboratory astrophysics")

Potential supervisors: Prof Michael Barnes, Dr Archie Bott, Prof Gianluca Gregori, Dr Plamen Ivanov, Dr Daniel Kennedy, Prof Alexander Schekochihin, Prof Dmitri Uzdensky

Note that the project descriptions given below are not set in stone and we are willing to discuss modifications and adjustments to them that might better reflect your interests and inclinations.

*** PROJECT DESCRIPTIONS MAY BE ADDED/EDITED AND NEW ONES APPEAR IN DUE COURSE. COME BACK AND CHECK! ***

 Size of intake: probably 2 to 3, but depends on application pool and availability of funding; we took 5 fully funded students in 2025.

Projects in Fusion Plasmas and in Fundamental Plasma Theory

MAST

  Our magnetic-confinement-fusion theory projects are offered jointly with researchers at the U.K.A.E.A. Culham Centre for Fusion Energy.

At the application stage, you are not required to (although you may if you wish) indicate which project you prefer --- we will consider all applicants purely on intellectual merit. If you are offered admission, we will strive to give you the opportunity to work on the project of your choice.
1. Stellarator theory: turbulent plasmas in twisted magnetic topologies
Supervisor: Prof Michael Barnes
UKAEA co-supervisor: Dr Daniel Kennedy
[for this project, apply to DPhil in Theoretical Physics]

Turbulent fluctuations often dominate losses of heat, particles, and momentum in magnetic-confinement fusion devices. Tokamaks, which rely on axisymmetric magnetic fields to confine the plasma, have been the focus of much of our effort to understand plasma turbulence. However, perfect axisymmetry is inevitably broken by design constraints and large-scale instabilities. Moreover, non-axisymmetric fields are increasingly attractive for fusion reactors, as they do not require a plasma current for confinement and thus allow for steady-state operation. There is therefore growing interest in more exotic geometries that use fully three-dimensional magnetic fields to confine the plasma. Stellarators take the tokamak's concept and twist it---literally---into a 3D configuration [1]. These devices remove the need for plasma current and offer a promising route to steady-state fusion. Yet, despite their potential, our understanding of turbulence in 3D magnetic fields remains limited. For example, one basic open question that this project might help to address is what sets the plasma beta (ratio of thermal pressure to magnetic pressure) that can be achieved in an optimised stellarator before the emergence of strong electromagnetic turbulence (which is usually lethal for confinement). This PhD project will explore how the loss of axisymmetry in stellarators affects plasma microstability, turbulence, and transport. There are several directions the project could take: (i) the development and application of adjoint-based optimisation techniques [2] to reduce microinstability growth rates by identifying magnetic geometries that are optimally stable to drift-wave turbulence; (ii) investigating the electromagnetic microstability of stellarator plasmas at finite beta; and (iii) assessing the influence of field-line coupling on zonal-flow dynamics and turbulence saturation in advanced stellarators. The student will tackle these questions using a combination of analytical theory and high-performance computing, helping to chart the frontier of turbulence in complex magnetic topologies. The project will primarily focus on analytical and numerical work, but there will also be opportunities to engage with various exciting experiments.
Background Reading:
1. P. Helander, "Theory of plasma confinement in non-axisymmetric magnetic fields," Rep. Prog. Phys. 77, 087001 (2014)
2. G. O. Acton, M. Barnes, S. Newton, and H. Thienpondt, "Optimisation of gyrokinetic microstability using adjoint methods," J. Plasma Phys. 90, 905900406 (2024)

2. Runaway electron transport: relativistic-particle dynamics in semi-stochastic magnetic fields
Supervisor: Prof Dmitri Uzdensky
UKAEA co-supervisor: Dr Plamen Ivanov
[for this project, apply to DPhil in Theoretical Physics]
Runaway electrons present a fascinating problem in plasma physics. Their origin lies in a subtle feature of Coulomb collisions, first identified more than a century ago [1]: beyond a certain critical velocity, the collisional drag force on the particles decreases, allowing high-energy electrons to accelerate indefinitely, i.e., to 'run away', if a strong enough electric field is present. This peculiarity of plasma kinetics underlies the spontaneous emergence of relativistic electron beams in a variety of contexts where strong fields and rapid energy release occur. One prominent such setting is the tokamak, where disruptions---abrupt, millisecond-scale losses of thermal energy---generate large inductive electric fields. These fields, combined with avalanche multiplication (fast electrons colliding with slower ones and promoting them into the runaway regime), enable the formation of relativistic electron populations. The resulting runaway beams carry enormous energy and pose a serious risk of damaging the device, unless they are effectively controlled or, ideally, suppressed altogether.

One promising theoretical avenue involves the role of magnetic topology. Non-axisymmetric perturbations can destroy magnetic surfaces and render the field lines stochastic, enhancing the radial transport of energetic particles [2,3]. But stochasticity is rarely complete: non-chaotic regions (e.g., magnetic islands) may persist and coexist with chaotic ones, creating a complex phase space where particle trajectories alternate between ordered motion and stochastic wandering. For relativistic electrons subject to strong electric fields, this 'partially mixed' phase space poses a fundamental theoretical question: how does the coexistence of order and chaos govern their acceleration, diffusion, and loss? This problem lies at the intersection of single-particle dynamics and collective plasma response and remains poorly understood. This project is to develop a theoretical framework for runaway-electron dynamics in partially stochastic magnetic fields. The work will draw on tools from relativistic kinetic theory, nonlinear Hamiltonian dynamics, and the theory of chaotic transport. Key directions may include: (i) characterising electron orbits in perturbed magnetic geometries; (ii) quantifying diffusion and transport in partially mixed phase space; (iii) understanding how these dynamics reshape avalanche multiplication and the formation of runaway beams. The project will involve a combination of analytical work and numerical studies. While motivated by questions arising in tokamaks, the problems to be addressed---relativistic particle dynamics in complex magnetic fields and phase-space transport in partially chaotic systems---are of broad and fundamental interest in plasma physics, nonlinear dynamics, as well as in astrophysical contexts. The project is flexible and can be shaped according to the student's background and inclinations.

Background Reading:
1. C. T. R. Wilson, Proc. Phys. Soc. London 37, 32D (1924)
2. A. H. Boozer, Plasma Phys. Control. Fusion 53, 084002 (2011)
3. H. M. Smith, A. H. Boozer, P. Helander, Phys. Plasmas 20, 072505 (2013)

3. Explaining suprathermal ion populations produced in ignited inertial-confinement-fusion plasmas
Supervisors: Dr Archie Bott & Prof Alexander Schekochihin
[for this project, we recommend applying to both DPhil in Atomic & Laser Physics and DPhil in Theoretical Physics]

Recent indirect-drive inertial-confinement-fusion (ICF) experiments at the National Ignition Facility (NIF) have, for the first time, demonstrated ignition in a controlled fusion experiment [1,2]. In such experiments, the plasmas achieved at the centre of the deuterium-tritium capsule (the "hot spot") during its maximum compression are sufficiently hot and dense for heating by fusion-produced alpha particles to overcome other cooling mechanisms, leading to the possibility of high energy gain [3]. A surprising observation from these experiments is a discrepancy between measured neutron spectra and what would be expected if the plasma's underlying ion distribution function obeyed the Maxwell-Boltzmann statistics. Instead, the data suggests that a robust population of suprathermal ions is produced [4]. In this project, a student would investigate various possible explanations for this phenomenon, and in particular, acceleration due to alpha-particle-driven kinetic plasma instabilities and dynamics. Understanding these effects could be vital for realising robust ICF implosions with target gain well beyond unity, and their accurate modelling.

Background Reading:
1. H. Abu-Shawareb et al., Phys. Rev. Lett. 129, 075001 (2022)
2. H. Abu-Shawareb et al., Phys. Rev. Lett. 132, 065102 (2024)
3. A. Zylstra et al., Nature 601, 542 (2022)
4. E.P. Hartouni et al., Nature Phys. 19, 72 (2023) 

4. Kinetic theory of collisionless relaxation and phase-space turbulence in magnetised plasmas
Supervisor: Prof Alexander Schekochihin
[for this project, apply to DPhil in Theoretical Physics]
In recent years, we have made some rapid progress in understanding how (nearly) collisionless plasmas relax to non-Maxwellian, but still, in a certain sense, universal equilibria [1] and what is the underlying structure of their turbulent state, a multi-scale chaos in 6D phase space [2,3]. It turns out that one can construct a statistical mechanics of a collisionless plasma, based on maximising (appropriately defined) entropy subject to Casimir invariants conserved in a collisionless system, and then work out (subject to some assumptions the nature and validity of which are still to be understood) how the plasma relaxes to the maximum-entropy states dynamically, a process controlled by its phase-space turbulence---it then turns out that a small amount of dissipation (collisions or, equivalently, finite-particle-number effects) helps push the system into classes of universal equilibria (a complete analytical theory of this last process is still an unsolved problem, which a student taking up this project might attempt to solve, unless we get it done before October 2026). Much of this understanding is, however, limited to electrostatic plasmas (no magnetic fluctuations) and, in what concerns numerical tests, to 1D models. The plan for this project is to break away from these limitations: thus, a numerically inclined student might attempt to conduct a series of advanced numerical experiments, in 2D and 3D (where electromagnetic effects cannot really be avoided); an analytically inclined one might work on a theory of collisionless relaxation in magnetised plasmas, described by the Vlasov-Maxwell equations, or, in a strong mean field, by gyrokinetic ones [4]. The plan is flexible and will depend on the student's interests and abilities, and also on the state of our understanding in a year's time. Applications range from fusion plasmas (either magnetically or inertially confined) to space physics, high-energy astrophysics, and curious bespoke ones created in a (laser) laboratory---in all of these areas, one encounters particle species whose distributions have non-Maxwellian high-energy tails, embedded in a highly turbulent environment (in some cases, these are the dominant species, in others it is an energetic intruder, e.g., cosmic rays).

Background Reading:
1. R. J. Ewart et al., "Collisionless relaxation of a Lynden-Bell plasma,'' J. Plasma Phys. 88, 925880501 (2022); "Non-thermal particle acceleration and power-law tails via relaxation to universal Lynden-Bell equilibria," J. Plasma Phys. 89, 905890516 (2023) ; "Relaxation to universal non-Maxwellian equilibria in a collisionless plasma," PNAS 122, e2417813122 (2025); see also A. Schekochihin's MMathPhys Lecture Notes, sec. 10-11.
2. A. A. Schekochihin et al., "Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence," J. Plasma Phys. 82, 905820212 (2016)
3. M. L. Nastac et al., "Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence," Phys. Rev. E 109, 065210 (2024); "Universal fluctuation spectrum of Vlasov-Poisson turbulence," arXiv:2503.17278; see also A. Schekochihin's MMathPhys Lecture Notes, sec. 12
4. M. W. Kunz et al., "Astrophysical gyrokinetics: turbulence in pressure-anisotropic plasmas at ion scales and beyond,'' J. Plasma Phys. 84, 715840201 (2018)


Projects in Plasma Astrophysics and Laser Plasmas



Candidates interested in any of these projects or generally in plasma astrophysics, astrophysical turbulence and/or dynamo theory are welcome to get in touch with prospective supervisors for further information. A more bespoke project can be designed to align with the inclinations and interests of the student (for example how much emphasis is placed on analytical vs. numerical methods or kinetic theory vs. fluid dynamics, etc., is negotiable).  

5. Magnetised plasma turbulence: from laser lab to galaxy clusters
Supervisors: Prof Gianluca Gregori, Dr Archie Bott, & Prof Alexander Schekochihin
[for this project, we recommend applying to both DPhil in Astrophysics and DPhil in Atomic & Laser Physics]
There are a number of possibilities within this project to design, take part in, and theorise about laboratory experiments employing laser-produced plasmas to model astrophysical phenomena and basic, fundamental physical processes in turbulent plasmas. Recent examples of our work in this field include turbulent generation of magnetic fields ("dynamo") [1,2], supersonic turbulence mimicking star-forming molecular clouds [3], diffusion and acceleration of particles by turbulence [4,5], suppression of thermal conduction in galaxy-cluster-like plasmas [6]. Our group has access to several facilities (including the National Ignition Facility, the largest laser system in the world). Students will also have access to a laser laboratory on campus, where initial experiments can be fielded. Depending on the student's inclinations, it is also possible to pursue a project focused on theory and/or numerical modelling of plasma phenomena in astrophysical and laboratory-astrophysical environments.
Background Reading:
1. P. Tzeferacos et al., "Laboratory evidence of dynamo amplification of magnetic fields in a turbulent plasma," Nature Comm. 9, 591 (2018)
2. A. F. A. Bott et al., "Time-resolved fast turbulent dynamo in a laser plasma," PNAS 118, e2015729118 (2021)
3. T. G. White et al.,"Supersonic plasma turbulence in the laboratory," Nature Comm. 10, 1758 (2019)
4. A. F. A. Bott et al., "Proton imaging of stochastic magnetic fields," J. Plasma Phys. 83, 905830614 (2017)
5. L. E. Chen et al., "Transport of high-energy charged particles through spatially intermittent turbulent magnetic fields," Astrophys. J. 892, 114 (2020)
6. J. Meinecke et al., "Strong suppression of heat conduction in a laboratory analogue of galaxy-cluster turbulent plasma," Science Adv. 8, eabj6799 (2022)

6. Microphysics of gamma-ray bursts
Supervisors: Prof Gianluca Gregori, Prof Subir Sarkar, & Prof Dmitri Uzdensky
[for this project, we recommend applying to both DPhil in Astrophysics and DPhil in Atomic & Laser Physics]
Gamma-ray bursts (GRBs) are among the most energetic events in the Universe. They occur at cosmological distances and are the result of the collapse of massive stars or neutron stars mergers, with emission of relativistic "fireballs" of electron-positron pairs. From astrophysical observations, a wealth of information has been gleaned about the mechanism that leads to such strong emission of radiation, with leading models predicting that this is due to the disruption of the beam as it blasts through the surrounding plasma. This produces shocks and hydromagnetic turbulence that generate synchrotron emission, potentially accelerating to ultra-high energies the protons which are observed on Earth as cosmic rays. However, there is no direct evidence of the generation of either magnetic fields or cosmic rays by GRBs. Estimates are often based on crude energy equipartition arguments or idealised numerical simulations that struggle to capture the extreme plasma conditions. We propose to address this lacuna by conducting laboratory experiments at accelerator facilities to mimic the jet propagation through its surrounding plasma. Our intial work [1] has demonstrated that we can create enormous beams of electron-positron plasmas that have properties very similar to GRB Fireballs. We are now planning new experiments at CERN as well as at Laboratori Nazionali Frascati (INFN, Italy) to characterise fully the interaction of these beams with a surrounding (ambient) plasma. Such experiments will enable in-situ measurement of the plasma properties, with exquisite details that cannot be achieved elsewhere. The experiments also complement numerical simulations by providing long measurement times extending into the non-linear regime where numerical simulations are not possible today. The proposed experiments will study fundamental physics processes, unveil the microphysics of GRBs, and provide a new window in high-energy astrophysics using novel Earth-based laboratory tools.

 Background Reading:
1. C. D. Arrowsmith et al., "Laboratory realisation of relativistic pair-plasma beams," Nature Comm. 15, 5029 (2024)

7. Free-energy flows and universal equilibria in turbulent astrophysical plasmas
Supervisors: Prof Alexander Schekochihin & Prof Michael Barnes
[for this project, we recommend applying to both DPhil in Astrophysics and DPhil in Theoretical Physics]

In magnetised astrophysical plasmas, there is a turbulent cascade of electromagnetic fluctuations carrying free energy from large to small scales. The energy is typically extracted from large-scale sources (e.g., in the solar wind, the violent activity in the Sun's corona; in accretion discs, the Keplerian shear flow; in galaxy clusters, outbursts from active galactic nuclei) and deposited into heat---the internal energy of ions and electrons. In order for this dissipation of energy to happen, the energy must reach small scales---in weakly collisional plasmas, these are small scales in the 6D kinetic phase space, i.e., what emerges is large spatial gradients of electric and magnetic fields and large gradients of the particle distribution functions with respect to velocities. This prompts two fundamental questions: (1) how does the energy flow through the 6D phase space and what therefore is the structure of the fluctuations in this space: their spectra, phase-space correlation functions etc. [1,2,3] (these fluctuations are best observed in the solar wind, but we can measure density and magnetic fluctuations even in extragalactic plasmas, via X-ray and radio observations); (2) when turbulent fluctuations are dissipated into particle heat, how is their energy partitioned between various species of particles that populate the plasma: electrons, bulk ions, minority ions, fast non-thermal particles (e.g., cosmic rays) [4,5]. The latter question is particularly important for extragalactic plasmas because all we can observe is radiation from the particles and knowing where the internal energy of each species came from is key to constructing and verifying theories both of turbulence and of macroscale dynamics and thermodynamics. This project has an analytical and a numerical dimension (which of these will dominate depends on the student's inclinations). Analytically, we will work out a theory of phase-space cascade at spatial scales between the ion and electron Larmor scales. Numerically, we will simulate this cascade using "gyrokinetic" equations---an approach in which we average over the Larmor motion and calculate the distribution function of "Larmor rings of charge" rather than particles (this reduces the dimension of phase space to 5D, making theory more tractable and numerics more affordable).

With a theory of plasma turbulence in hand, it is possible to attack what is probably the most fundamental question of the field: in the absence of collisions, are there universal equilibria, or classes of equilibria, independent of initial conditions, that a turbulent plasma will want to converge to? There is some recent progress indicating that the answer is yes and that one can predict statistical-mechanically the emergence of universal power-law (in particle energy) distributions [6]---this is exciting both on its own merits and because of the astrophysical challenge of explaining theoretically power-law distributions that are observed for, e.g., cosmic rays or solar-wind electrons. How to construct a theory of that for a magnetised, turbulent plasma is an open and exciting question. Attempting to do this will again involve kinetic theory and/or kinetic simulations.  

Background Reading:
1. A. A. Schekochihin et al., "Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas," Astrophys. J. Suppl. 182, 310 (2009)
2. A. A. Schekochihin et al., "Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence," J. Plasma Phys. 82, 905820212 (2016)
3. R. Meyrand et al., "Fluidization of collisionless plasma turbulence," PNAS 116, 1185 (2019)
4. Y. Kawazura et al., "Thermal disequilibration of ions and electrons by collisionless plasma turbulence," PNAS 116, 771 (2019)
5. J. Squire et al., "High-frequency heating of the solar wind triggered by low-frequency turbulence," Nature Astron. 6, 715 (2022)
6. R. J. Ewart et al., "Relaxation to universal non-Maxwellian equilibria in a collisionless plasma," PNAS 122, e2417813122 (2025); see also A. Schekochihin's MMathPhys Lecture Notes, sec. 10-11

8. Nonthermal particle acceleration in extreme plasmas around black holes
Supervisors: Prof Dmitri Uzdensky
[for this project, we recommend applying to both DPhil in Astrophysics and DPhil in Theoretical Physics]
Accreting supermassive black holes (SMBHs) residing in active galactic nuclei (AGN) at the centres of many galaxies, including the Milky Way, are arguably the most fascinating and enigmatic objects in the Universe. These black holes, and the powerful relativistic jets emanating from them, often exhibit spectacular, violent phenomena, such as bright high-energy flares with nonthermal X-ray and gamma-ray spectra. They are also the most likely generators of highly energetic non-electromagnetic observational "messengers": extremely relativistic cosmic rays and ultra-high-energy neutrinos. All these observational signals indicate that BH environments are very efficient relativistic-particle accelerators. Understanding how these cosmic accelerators work is an outstanding problem in high-energy astrophysics. Nonthermal particle acceleration is believed to be a natural product of collective kinetic nonlinear plasma processes, such as magnetic reconnection, shocks, and magnetised turbulence. How these processes operate under the extreme physical conditions in the exotic relativistic plasmas of accreting black holes is not well understood because the underlying physics is much richer than in more traditional plasmas (like ones in the solar system): special- and general-relativistic effects, strong interaction of the plasma with radiation, and quantum-electrodynamic effects such as pair creation all come into play in nontrivial ways. Elucidating the complex interplay of these effects with collective plasma processes and, consequently, their impact on particle acceleration and radiation presents an exciting theoretical challenge and is a vibrant frontier of modern plasma astrophysics research. This project will explore these fundamental plasma-theoretical questions and their observational implications through a combination of analytical and computational methods, with the balance between theory and computation to be decided based on the student's preferences.