starting in October 2019

Application deadline: 25 January 2019

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, 4), Prof Peter Norreys (project 3), Prof Felix Parra Diaz (project 2), Prof Alexander Schekochihin (projects 4, 5), Prof Gianluca Gregori (project 5)

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, and 3 in 2018.


Projects in Fusion Plasmas


Our magnetic-confinement-fusion theory projects (1 and 2) 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 (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. Plasma turbulence in 3D magnetic fields
Supervisor: Prof Michael Barnes
UKAEA co-supervisor:
Dr Sarah Newton

Turbulent transport limits the confinement of tokamak plasmas, i.e., plasmas immersed in axisymmetric—and thus 2D—magnetic fields. Consequently much effort has gone into understanding the properties of turbulence and transport in tokamaks. However, perfect axisymmetry of the confining magnetic field is marred by design constraints and by large-scale plasma instabilities. Furthermore, non-axisymmetric fields are potentially preferable for fusion reactors because they do not require a current through the plasma for confinement and thus allow for steady-state operation. There is thus considerable interest in stellarators, which use 3D magnetic fields to confine the plasma. Despite the importance of the problem, there has been little work done on turbulence in 3D magnetic fields. The aim of this project is to understand how breaking axisymmetry affects plasma turbulence. In particular, can 3D effects on turbulence explain some of the mysterious transport phenomena observed in tokamaks, and how much turbulent transport can we expect in optimised stellarators? The student would address these questions with a combination of analytical theory and high performance computing.   

Background Reading:
1. P. Helander,
“Theory of plasma confinement in non-axisymmetric magnetic fields,” Rep. Prog. Phys. 77, 087001 (2014)
I. Abel et al., “Multiscale gyrokinetics for rotating tokamak plasmas: fluctuations, transport and energy flows,” Rep. Prog. Phys. 76, 116201 (2013)

2. Turbulence suppression in the edge of tokamaks

Supervisor: Prof Felix Parra Diaz
UKAEA co-supervisor: Dr Samuli Saarelma

If sufficient power is injected into magnetically confined fusion plasmas, a region of reduced turbulence develops near the walls that contain the plasma. In this region, known as pedestal, the plasma gradients grow to be large because they are not reduced by the turbulent fluctuations that limit gradients elsewhere in the plasma. The pressure jump across the pedestal improves the performance of fusion plasmas significantly. Unfortunately, even though pedestals are robust experimental observations, there is no quantitative model that can explain their appearance and evolution. In this project, the student will develop an analytical kinetic model to determine what effect stabilises the plasma in the presence of large gradients that drive wild instabilities elsewhere in the fusion device. Examples of the effects to be considered are the interaction of the hot pedestal plasma with the much colder plasma near the wall or the fact that typical particles can sample a significant fraction of the pedestal width before they collide or are affected by turbulent fluctuations.

Background Reading:
1. J. W. Connor,
“A review of models for ELMs,” Plasma Phys. Control. Fusion 40, 191 (1998)

3. Maximising plasma turbulence in the hot spot of inertial fusion targets
Supervisor: Prof Peter Norreys
(for this project, you may also apply for a DPhil in Atomic and Laser Physics)

The student will investigate, using relativistic fluid theory and Vlasov-Maxwell simulations, the local heating of a dense plasma by two crossing electron beams generated during multi-PW laser-plasma interactions with a pre-compressed, inertial fusion target. Heating occurs as an instability of the electron beams that drives Langmuir waves, which couple non-linearly into damped ion-acoustic waves and into the background electrons. Initial simulations show a factor-of-2.8 increase in electron kinetic energy with a coupling efficiency of 18% [1]. By considering the collisionless energy deposition of these electron beams, we are able to demonstrate, via sophisticated radiation-hydrodynamic simulations, that this results in significantly increased energy yield from low convergence ratio implosions of deuterium-tritium filled “wetted foam" capsules, as recently demonstrated on the National Ignition Facility [2]. This approach promises to augment the heating of the central hot spot in these targets, and is attractive as a complementary approach that of fast ignition inertial fusion. The student will:
•   Simulate (Vlasov or possibly particle-in-cell) parameter scan of the energy cascade. The question is how dependent are we upon the electron energy, thermal spread, divergence, beam-to-background density ratio.
•    Simulate the energy cascade process in an inhomogeneous plasma.
•    Simulate energy cascade using finite beams. 
•    Help design experiments verifying the energy cascade process.
The student will also use machine learning to study the optimisation of the energy deposition process.

Background Reading:
N. Ratan et al., “Dense plasma heating by crossing relativistic electron beams,” Phys. Rev. E 95, 013211 (2017)
R. Olson et al., “First liquid layer inertial confinement fusion implosions at the National Ignition Facility,” Phys. Rev. Lett. 117, 245001 (2016)

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).  

4. 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,” arXiv:1807.07702
4. R. Meyrand, A. Kanekar, W. Dorland, and A. A. Schekochihin,Fluidization of collisionless plasma turbulence,” arXiv:1808.04284

5. 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)

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, diffusion and acceleration of particles by turbulence [3,4]. 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.

Background Reading:
1. G. Gregori et al., “The generation and amplification of intergalactic magnetic fields in analogue laboratory experiments with high power lasers,” Phys. Reports 601, 1 (2015)
2. P. Tzeferacos et al., “Laboratory evidence of dynamo amplification of magnetic fields in a turbulent plasma,” Nature Comm. 9, 591 (2018)
3. A. F. A. Bott et al.,
“Proton imaging of stochastic magnetic fields,” J. Plasma Phys. 83, 905830614 (2017)
4. L. E. Chen
et al., “Stochastic transport of high-energy particles through a turbulent plasma,” arXiv:1808.04430