starting in October 2020

Application deadline: 24 January 2020

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, 6), Prof Peter Norreys (project 3), Prof Felix Parra Diaz (project 2), Prof Alexander Schekochihin (projects 4, 5, 6, 7), Prof Gianluca Gregori (project 7)

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, and 1 in 2019; we would like to take at least 2 this year.


Projects in Fusion Plasmas and Fundamental Plasma Physics


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. Theory of transition to reduced transport states in the edge of fusion devices

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. Based on the techniques developed in previous works [1,2], we will investigate the effect on stability of finite drift orbit widths with analytical and semi-analytical approaches. The project would build on previous experience in local gyrokinetic stability in pedestals (e.g., [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 et al., "Radially global delta f computation of neoclassical phenomena in a tokamak pedestal," PPCF 56, 045005 (2014)
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)

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)

4. Universal equilibria, phase-space structure of collisionless plasma systems, and turbulence in non-Maxwellian plasmas
Supervisor: Prof Alexander Schekochihin
(for this project, you may also apply for a DPhil in Astrophysics)

We know from statistical physics and kinetic theory that an ideal gas or plasma will strive towards a Maxwellian equilibrium and achieve it on time scales associated with inter-particle collisions. However, in many natural plasma systems, these time scales are very long and relaxation to some form of collisionless equilibrium appears to occur. In the absence of collisions, are there universal equilibria, or classes of equilibria, independent of initial conditions, that a plasma will want to converge to? Do collisionless plasmas have an "effective collisionality", caused by collective interactions between particles and fields? These are old questions [1,2], but they have stayed open because of the difficulty of nonlinear theory and impossibility of kinetic numerical simulations capable of sufficient resolution. The latter impediment to progress is being lifted as both computers and numerical methods get more powerful, while the nonlinear theory of phase-space plasma turbulence, with which the problem of collisionless relaxation is intimately intertwined, has recently been advanced in a new direction [3,4]. It is, therefore, a good time to revisit the old theories of collisionless relaxation and attempt new ones. A related topic is the nature and structure of turbulence in plasmas that are not close to the Maxwellian equilibrium: a seemingly simple but conceptually fascinating question is what is the counterpart to the energy cascade in such systems (indeed, what is the cascaded invariant) [5]. Depending on the student's inclinations, s/he will be able to take a numerical or analytical route, or, more likely, a mixture of the two.

Background Reading:
B. B. Kadomtsev & O. P. Pogutse, “Collisionless relaxation in systems with Coulomb interactions,” Phys. Rev. Lett. 25, 1155 (1970)
T. H. Dupree, “Theory of phase space density granulation in plasma,” Phys. Fluids 14, 334 (1972)
3. A. A. Schekochihin et al., Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence,” J. Plasma Phys. 82, 905820212 (2016)
4. T. Adkins & A. A. Schekochihin, “A solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase space,” J. Plasma Phys. 84, 905840107 (2018)
5. M. W. Kunz, A. A. Schekochihin, C. H. K. Chen, I. G. Abel and S. C. Cowley
, “Inertial-range kinetic turbulence in pressure-anisotropic astrophysical plasmas,” J. Plasma Phys. 81, 325810501 (2015)

5. Coherent structures and fluctuating flows in near-critical ion-scale turbulence in tokamaks
Supervisor: Prof Alexander Schekochihin
UKAEA co-supervisor: Dr Anthony Field

Complex interactions between turbulence and flow lie at the heart of understanding turbulence, especially saturation mechanisms and complex behaviour such as transport bifurcations [1]. Flow shear plays a dual role: flows along the field lines can drive turbulence, but flows across them suppress it, e.g., by shearing radial structures. In our recent work [2,3], we have found that, close to the critical temperature gradients required to drive turbulence (i.e., to marginal stability), the transition to turbulence occurs via a low-transport state dominated by coherent, long-lived structures (now known as "ferdinons", after the name of the student who discovered them). The evidence for such a state and its properties is so far numerical, with only a glimmer of experimental confirmation [4]. This project is to analyse data from the newly upgraded BES diagnostic on the newly upgraded MAST-U tokamak at UKAEA to search for long-lived structures experimentally. Coherence analysis of 2D velocity time series data derived using velocimetry techniques (CCTD and dynamic programming) will be used to characterise (poloidal/radial) fluctuating flows. Measured characteristics are to be compared with those predicted by gyrokinetic simulations. A feasibility study could also be undertaken to extend the BES optical hardware (using existing APD cameras) to make fast, spectroscopic charge-exchange measurements of carbon-ion temperature and parallel velocity fluctuations.

Background Reading:
1. E. G. Highcock, M. Barnes, A. A. Schekochihin, F. I. Parra, C. M. Roach, and S. C. Cowley, "Transport bifurcation in a rotating tokamak plasma,''
Phys. Rev. Lett. 105, 215003 (2010)
2. Ferdinand van Wyk, E. G. Highcock, A. A. Schekochihin, C. M. Roach, A. R. Field, and W. Dorland,
Transition to subcritical turbulence in a tokamak plasma,” J. Plasma Phys. 82, 905820609 (2016)
3. Ferdinand van Wyk, E. G. Highcock, A. R. Field, C. M. Roach, F. I. Parra, W. Dorland, and A. A. Schekochihin, Ion-scale turbulence in MAST: anomalous transport, subcritical transions, and comparison to BES measurements,Plasma Phys. Control. Fusion 59, 114003 (2017)
4. M. F. J. Fox, F. van Wyk, A. R. Field, Y.-c. Ghim, F. I. Parra, A. A. Schekochihin, and the MAST Team, Symmetry breaking in MAST plasma turbulence due to toroidal flow shear,Plasma Phys. Control. Fusion 59, 034002 (2017)

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).  

6. 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)

7. 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, 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