starting in October 2021

Application deadline: 22 January 2021

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 (projects 1-2, 5), Prof Felix Parra Diaz (projects 3, 4) Prof Alexander Schekochihin (projects 5, 6), Prof Gianluca Gregori (project 6)

Size of intake: this depends on various hard-to-predict circumstances, in particular funding arragements; we accepted 2 fully funded students in 2015, 4 in 2016, 3 in 2017, 3 in 2018, 1 in 2019, and 3 in 2020.


Projects in Fusion Plasmas


Our magnetic-confinement-fusion theory projects are offered jointly with researchers at the U.K.A.E.A. Culham Centre for Fusion Energy (Projects 2-4) and at Tokamak Energy (Project 1).

At the application stage, you are not required (although you may if you wish) to 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.
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.

1. & 2. Turbulence and transport in spherical tokamaks
Supervisor: Prof Michael Barnes
UKAEA co-supervisor (Project 2):
Dr Colin Roach

In magnetic confinement fusion, a strong magnetic field is used to confine a hydrogenic gas as it is heated to over a hundred million degrees. At these temperatures, the gas becomes ionised and the constituent ions have enough thermal energy to tunnel through the Coulomb barrier and convert mass into energy via fusion. This ionised gas, or plasma, generates and responds to electromagnetic fields and demonstrates collective behavior including unstable modes of oscillation that result in turbulent mixing. The unstable modes are driven by gradients in the equilibrium plasma density, temperature, and flow; in turn, the equilibrium is itself constrained by the resultant turbulent mixing. This nonlinear feedback loop ultimately controls the fusion energy output and exhibits a variety of rich and puzzling dynamical features that span a wide range of space-time scales. Understanding the multi-scale turbulent dynamics of tokamak plasmas is thus both an interesting fundamental physics problem and a critical component required for the success of the magnetic confinement fusion programme. The main aim of these projects is to characterise the plasma turbulence expected in a spherical tokamak operating in reactor-like conditions. Spherical tokamaks are distinguished from conventional tokamaks by their compactness: both are topologically tori, but a spherical tokamak resembles a cored apple rather than the donut shape of a conventional tokamak. This difference in the confining magnetic geometry leads to strong  gradients in the toroidal magnetic field and in the plasma dynamics that result in improved plasma stability and more efficient confinement. These changes are expected to lead to qualitative differences in the turbulence properties that are yet to be studied. The student would employ a mixture of cutting-edge computer simulations and analytical theory to study turbulence in this new regime.

There is the potential for two projects on this topic. Project 1 will be co-supervised by researchers at Tokamak Energy, a UK-based private fusion energy company who are developing a promising new approach to fusion power based on spherical tokamaks and high field magnets made from high temperature superconductors. As part of this project, the student would have the opportunity to collaborate with researchers at Tokamak Energy, and be directly involved in the design of the next step high field spherical tokamak, ST-F1. Project 2 will be co-supervised by Dr. Colin Roach at UKAEA and would provide the opportunity to collaborate with researchers directly involved with the design of the recently-launched
Spherical Tokamak for Energy Production (STEP) at UKAEA.

3. Finite orbit width effects on pedestal formation and stability

Supervisor: Prof Felix Parra Diaz
UKAEA co-supervisor: Dr Jon Hillesheim

The pedestal is a region of reduced plasma turbulence that naturally appears in the edge of tokamak plasmas when the input power is above a threshold that is currently determined experimentally. It is widely accepted that the electric field gradient observed in the pedestal is responsible for shearing turbulence and reducing energy losses in the pedestal. This electric field gradient is sustained by the pedestal pressure gradient, i.e., the plasma tries to expand and it is pushed inwards by a large electric field. In the usual picture of pedestal formation, if the plasma pressure gradient increases, the electric field and its gradient increase as well, and eventually, the turbulence reduction due the electric field gradient dominates over the increase in turbulence driven by the pressure gradient, leading to a sharp transition and the appearance of the pedestal. What determines the critical pressure gradient? One possible answer is that the critical gradient is reached once the characteristic scale length of the pressure is comparable to the width of the confined particle orbits in the edge. This picture is somewhat supported by the fact that the radial extent of particle orbits can be a large fraction of the pedestal width. We propose to study this possibility by searching for reduced turbulence states supported by finite-orbit-width effects. We will start by studying pedestals observed in current machines. It has been possible to construct neoclassical models that incorporate finite orbit width effects [1,2]. Based on the techniques developed in these previous works, we will investigate the effect on stability of finite drift orbit widths with analytical and semi-analytical approaches. We will consider both microinstabilities and MHD-like modes. The project will build on previous experience in local gyrokinetic stability in pedestals (see for example, [3]) and on work previously done to include the MHD kink drive in gyrokinetics [4]. We intend to use the model to study the formation and stability of JET and MAST-U pedestals, comparing experimental results, including DBS measurements, to theoretical predictions. To extend the work to MAST-U, in which the drift orbit width can be comparable to the ion gyroradius, we have developed techniques to include finite ion gyroradius effects self-consistently [5].

Background Reading:
1. G. Kagan & P. J. Catto, "Arbitrary poloidal gyroradius effects in tokamak pedestals and transport barriers," PPCF 50, 085010 (2008)
M. Landreman & D. R. Ernst, "Local and global Fokker–Planck neoclassical calculations showing flow and bootstrap current modification in a pedestal," PPCF 54, 115006 (2012)
3. D. Hatch et al., "A gyrokinetic perspective on the JET-ILW pedestal," PPCF 57, 036020 (2017)
4. I. Pusztai et al., "A current-driven electromagnetic mode in sheared and toroidal configurations," PPCF 56, 035011 (2014)
5. A. Geraldini, F. I. Parra, & F. Militello, "Gyrokinetic treatment of a grazing angle magnetic presheath,"  PPCF 59, 025015 (2017)

4. Plasma-wall interaction in magnetic confinement fusion plasmas

Supervisor: Prof Felix Parra Diaz
UKAEA co-supervisor: Dr Stefan Mijin

As we build more efficient fusion devices, the amount of power released by the fusion plasma onto the vacuum chamber walls increases rapidly. The walls of the next generation of fusion experiments are expected to suffer heat loads that existing materials can barely withstand. Thankfully, there are several proposals to reduce the heat load using concepts from magnetized plasma physics and atomic physics. Some of these ideas (such as the super-X divertor [1]) are going to be tested in machines such as MAST-Upgrade (situated at UKAEA, a few miles from Oxford). The student working on this DPhil project will focus on one very important aspect for the success of the several schemes mentioned above: the interaction between the plasma and the wall. This is a problem at the boundary between plasma physics and condensed matter physics, and, despite being of fundamental importance for laboratory plasmas, several key questions remain unanswered. The fact that thin layers of non-neutral plasma form around the wall means that the problem can be treated accurately with simplified theoretical 1D or 2D models. The student working on this project will build on theoretical and numerical tools developed by the Plasma Theory Group in Oxford and UKAEA [2, 3] to study the highly nonlinear physics of the thin layers described above. The focus of this project is on new physical regimes that we expect to find in future reactors, and on the transitions and bifurcations between these regimes. This project is a collaboration with UKAEA, and the student will have the opportunity to work with the team that will exploit the exciting new facility MAST-Upgrade.

Background Reading:
1. P.M. Valanju et al., "Super-X divertors and high power density fusion devices," Phys. Plasmas 16, 056110 (2009)
A. Geraldini, F.I. Parra and F. Militello, "Gyrokinetic treatment of a grazing angle magnetic presheath," PPCF 59, 025015 (2017)
3. A. Geraldini, F.I. Parra and F. Militello, "Solution to a collisionless shallow-angle magnetic presheath with kinetic ions," PPCF 60, 125002 (2018)
4. A. Geraldini, F.I. Parra and F. Militello, "Dependence on ion temperature of shallow-angle magnetic presheaths with adiabatic electrons," J. Plasma Phys. 85, 795850601 (2019)
5. S. Mijin et al., "Kinetic and fluid simulations of parallel electron transport during equilibria and transients in the scrape-off layer," PPCF 62, 095004 (2020)

Projects in Plasma Astrophysics

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. Free-energy flows in turbulent astrophysical plasmas
Supervisors: Prof Michael Barnes and Prof Alexander Schekochihin
for this project, you may also apply for a DPhil in Astrophysics)

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 are large spatial gradients of electric and magnetic fields and large gradients of the particle distribution functions with respect to velocities. This prompts two very intriguing 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. (these fluctuations are best observed in the solar wind, but these days we can also measure density and magnetic fluctuations in galaxy clusters, 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). 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 (we have done some preliminary work, so we know how to start off on this calculation, but obviously at some point we’ll be wading into unchartered waters). 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). 

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. Y. Kawazura, M. Barnes, and A. A. Schekochihin,
Thermal disequilibration of ions and electrons by collisionless plasma turbulence,” PNAS 116, 771 (2019)
4. R. Meyrand, A. Kanekar, W. Dorland, and A. A. Schekochihin,Fluidization of collisionless plasma turbulence,” PNAS 116, 1185 (2019)
5. A. A. Schekochihin, Y. Kawazura, and M. A. Barnes,
Constraints on ion vs. electron heating by plasma turbulence at low beta,” J. Plasma Phys. 85, 905850303 (2019)

6. Magnetised plasma turbulence: from laser lab to galaxy clusters
Supervisors: Prof Gianluca Gregori and Prof Alexander Schekochihin
(for this project, you may also apply for a DPhil in Atomic and Laser Physics or a DPhil in Astrophysics)

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 laser 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, preprint arXiv:2007.12837
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)
J. Meinecke et al., “Strong suppression of heat conduction in a laboratory analogue of galaxy-cluster turbulent plasma,” in preparation (2020)