OXFORD PLASMA THEORY GROUP

   

DPhil PROJECTS IN PLASMA PHYSICS


 
starting in October 2018

Application deadline: 19 January 2018

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 Steven Cowley FRS (project 2), Prof Felix Parra Diaz (project 3), Prof Alexander Schekochihin (projects 4, 5, 6, 7, 9), Prof Steven Balbus FRS (project 5), Prof Gianluca Gregori (projects 7, 8), Prof Subir Sarkar (project 8)

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 and 3 in 2017.

*** MORE NEW PROJECTS MAY APPEAR ON THIS PAGE IN DUE COURSE. COME BACK AND CHECK! ***


Projects in Fusion Plasmas

MAST

 
Our 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 (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 Colin Roach

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. I. G. Abel et al., “Multiscale gyrokinetics for rotating tokamak plasmas: fluctuations, transport and energy flows,” Rep. Prog. Phys. 76, 116201 (2013)

2. Erupting plasmas: explosive instability and fusion
Supervisor: Prof Steven Cowley FRS
UKAEA co-supervisor: Dr Christopher Ham


The explosive release of energy from fusion plasmas is both dramatic and destructive. In such events a slowly evolving plasma suddenly erupts releasing a significant fraction of its stored magnetic or thermal energy in a few tens of dynamical times (which is typically the sound time). The stored energy is converted into some combination of heat, energetic particles, fast plasma flows and/or radiation. Tokamak disruptions and edge-localised modes are examples of such events and they severely limit current experiments and future fusion reactors.  Similar instabilities are seen in solar flares, accretion discs and the Earth's magnetosphere. While there are a number of theories of these phenomena (see, for example, Ham et al. [1]), many of the central questions are still without quantitative answers. For example: what triggers the instability? What sets the timescale? How much energy is released? How much energy is given to energetic particles? Are there universal mechanisms? Can explosive instabilties be prevented in fusion devices? The DPhil student would address these central questions using theoretical analysis and computational models.   
Cowley & Ham

Background Reading
:
1. C. J. Ham, S. C. Cowley, G. Brochard, and H. R. Wilson, “Nonlinear stability and saturation of ballooning modes in tokamaks,” Phys. Rev. Lett. 116, 235001 (2016)
2. S. C. Cowley, B. Cowley, S. A. Henneberg, H. R. Wilson,
“Explosive instability and erupting flux tubes in a magnetized plasma,” Proc. R. Soc. London A 471, 20140913 (2015)

3. Plasma turbulence response to topology changes in the tokamak edge

Supervisor: Prof Felix Parra Diaz
UKAEA co-supervisor: Dr Sarah Newton


The performance of nuclear fusion experiments depends sensitively on the ionized gas (=plasma) next to the wall of the device. This region, known as the plasma edge, is characterised by a change in the topology of the magnetic field lines. In the hot-plasma region where fusion reactions happen, magnetic-field lines cover surfaces ergodically and never come into contact with the wall, whereas in the region near the wall, magnetic-field lines encounter the wall after spanning a finite length. This change in the topology of the magnetic-field lines has important effects on the response of the plasma to perturbations and hence on the turbulence that transports energy away from the hot plasma region. In the course of this project, the student will develop an analytical model of the region of the plasma in which the change of topology takes place, comparing the results of the model with experimental observations.
  
SOL


4. Non-equilibrium plasma physics near criticality: phase-space cascades, wave-flow interactions, edge-of-chaos structures and turbulent transport
Supervisor: Prof Alexander Schekochihin
UKAEA co-supervisor: Dr Colin Roach

The rather mundane and "engineering" question of how large a temperature difference can be maintained between the core and the edge of the plasma in a fusion machine opens a window onto some of the most fundamental theoretical questions about the structure of nonlinear, non-equilibrium states in magnetised plasma (not just in a tokamak, but also in such natural evironments as Earth's magnetosphere, the heliosphere, the interstellar and intergalactic space). These questions revolve around the ways in which free energy extracted from macroscopic inhomogeneities of the system (in the case of a fusion plasma, from the background temperature gradient) in the form of electromagnetic fluctuations is distributed in phase space (particles' positions and momenta) so as to give rise to a chaotic, multiscale (=turbulent) state that accommodates a steady flow of energy from macro to micro scales and its return to its inevitable resting place in the form of the thermal motion of the particles. This distribution of energy is then what determines how the turbulent plasma transports heat and momentum. This project aims to follow up on a number of recent developments in our understanding of these phenomena and investigate: the implications of the nonlinear suppression of energy flows into phase space [1,2] for transport models; the delicate balance between a chaotic field of plasma excitations ("drift waves") and self-generated regular "zonal" flows [3] that maintains the nonlinear state of a plasma near the critical threshold separating the turbulent and quiescent phases; the emergence of persistent coherent structures at this so-called "edge of chaos" [4] --- and how all this fits together and conspires to set limits on the background gradients. The project can have analytical, numerical and even experimental [5] components, depending on the student's abilities and inclinations. This project is likely to involve a collaboration with Prof Bill Dorland at the University of Maryland.
  
turbulence

Background Reading:
1. A. A. Schekochihin et al., Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence,” J. Plasma Phys. 82, 905820212 (2016)
2. T. Adkins & A. A. Schekochihin,
A solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase space,” arXiv:1709.03203
3. G. J. Colyer et al.,
Collisionality scaling of the electron heat flux in ETG turbulence,” Plasma Phys. Control. Fusion 59, 055002 (2017)
4. F. van Wyk et al.,
Transition to subcritical turbulence in a tokamak plasma,” J. Plasma Phys. 82, 905820609 (2016)
5. M. F. J. Fox et al.,
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).  

5. Dynamics, thermodynamics and plasma physics of galaxy clusters: wave damping and turbulent heating
Supervisors: Prof Steven Balbus FRS and Prof Alexander Schekochihin

Galaxy clusters are the largest astrophysical objects: the basic units in which matter clumps together in the Universe. We observe them via X-ray emission of the hot, isonised gas (plasma) that makes up most of their visible mass (which is gravitationally confined within the potential well associated with the much more massive dark-matter component).
Clusters are believed to be self-regulated (thermo)dynamical systems: gas within them accretes onto the central black hole --- "Active Galactic Nucleus" --- whose ejecta then stir up and reheat the cluster gas [2]. How this heating occurs, i.e., how the ionised gas in clusters maintains its very high X-ray emission temperature has been a longstanding problem in theoretical astrophysics --- and, indeed, the heating problem extends to hot dilute gases in many other astrophysical environments as well. Before the loss of the X-ray satellite Hitomi, the instrument was able to carry out a study of the Perseus Cluster, directly measuring (via line widths) the turbulent velocities in a galaxy cluster for the first time. The values measured were precisely of the right order of magnitude for the turbulent heating to maintain the cluster gas against radiative losses from thermal Bremsstrahlung cooling [5]. This gives us some degree of confidence in ideas attributing the heating of the gas to the dissipation of internal waves [1] and mechanically stirred turbulence [2,4,5]. In this project, motivated by the notion that the heating of the cluster gas is dynamical, we will study how waves in cluster gas propagate and dissipate. The gas is extremely dilute in X-ray clusters, so dilute that ions and electrons spiralling around magnetic lines of force make very many such circuits before colliding with each other. How waves propagate under these conditions [1,7] and how macroscopic motions interact with rich microscopic zoo of fluctuations that feeds off them [3,6] is not fully understood, and is the topic of this proposed project. We will study the mathematical behaviour of waves in a dilute magnetised plasma both for its own sake and, because the waves are very likely thermalised by damping, as a possible solution to an outstanding problem in astrophysics. Depending upon the interest and abilities of the student, the approach may be primarily analytic (e.g., [1,3,7]), numerical (e.g., [6]), phenomenological (e.g., [2,4]) or a mixture of all three.

Background Reading:
1. S. A. Balbus and N. Soker,
Resonant excitation of internal gravity waves in cluster cooling flows,” Astrophys. J. 357, 353 (1990)
2. E. Churazov et al.,
Cooling flows as a calorimeter of active galactic nucleus mechanical power,” Mon. Not. R. Astron. Soc., 332, 729 (2002)
3. M. S. Rosin et al., A nonlinear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma,”  Mon. Not. R. Astron. Soc. 413, 7 (2011)
4. M. W. Kunz et al.,
A thermally stable heating mechanism for the intracluster medium: turbulence, magnetic fields and plasma instabilities,” Mon. Not. R. Astron. Soc. 410, 2446 (2011)
5. I. Zhuravleva et al., “Turbulent heating in galaxy clusters brightest in X-rays,” Nature 515, 85 (2014)
6. S. Melville et al.,
Pressure-anisotropy-driven microturbulence and magnetic-field evolution in a shearing, collisionless plasma,” Mon. Not. R. Astron. Soc. 459, 2701 (2016)
7. J. Squire et al., Amplitude limits and nonlinear damping of shear-Alfven waves in high-beta low-collisionality plasmas,” New J. Phys. 19, 055005 (2017)

6. Free-energy flows in turbulent astrophysical plasmas

Supervisors: Prof Michael Barnes and Prof Alexander Schekochihin

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 in velocity of the particle distribution functions. This gives rise to 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, fast heavy particles (e.g., alpha particles and heavy ions). 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). Our key objective will be to work out the energy partition between ions and electrons – this question has fascinated theoreticians for at least 15 years, but we now have the tools to sort it out. 

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. T. Tatsuno et al., “Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence,” Phys. Rev. Lett. 103, 015003 (2009)
3. M. W. Kunz et al, 
“Inertial-range kinetic turbulence in pressure-anisotropic astrophysical plasmas,” J. Plasma Phys. 81, 325810501 (2015)
4. A. A. Schekochihin et al., Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence,” J. Plasma Phys. 82, 905820212 (2016)
5. Y. Kawazura & M. Barnes,
A hybrid gyrokinetic ion and isothermal electron fluid code for astrophysical plasma,” arXiv:1708.07235
6. T. Adkins & A. A. Schekochihin, A solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase space,” arXiv:1709.03203

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)

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. 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,” arXiv:1702.03016
3. A. Bott et al.,
“Proton imaging of stochastic magnetic fields,” arXiv:1708.01738

8. Second-order Fermi acceleration by magnetohydrodynamic turbulence in young supernova remnants
Supervisors: Prof Subir Sarkar and Prof Gianluca Gregori
(for this project, you may also apply for a DPhil in Atomic and Laser Physics)

The origin of high-energy cosmic rays still remains a mystery, a century after their discovery. Although several different processes and astrophysical sites may be implicated, there is a consensus that diffusive shock acceleration in Galactic supernova remnants accelerates the bulk of hadronic cosmic rays, up to hundreds of TeV in energy. However, observations of radio synchrotron emission by high-energy electrons in young supernova remnants are better understood if the electrons are accelerated by turbulence behind a decelerating shock wave via the 2nd-order Fermi process. In this project, we propose to develop numerical simulations of such turbulence in order to determine its spectrum and thus calculate the time evolution of the relativistic-electron spectrum. The simulations will be validated against laboratory experiments in magnetohydrodynamic turbulence, using the largest laser systems in the world, and the predictions of the radio emission will be compared in detail with observations of Cassiopeia A as well as of other young supernova remnants such as SN1987A and G1.9+0.3.

Background Reading:
1.
V. Petrosian Stochastic acceleration by turbulence,” Space Sci. Rev. 173, 535 (2012)

9. Turbulent cascade through the ion cyclotron resonance in space plasmas
Supervisor: Prof Alexander Schekochihin


This project is related to the general theme of the project on free-energy flows, but focuses on a single problem that requires analytical handling in the fully kinetic 6D framework and a programme of numerical simulations of the full kinetic equation for a plasma. The computational challenges involved in 6D simulations are enormous. The problem proposed for this project is therefore carefully chosen to be both of fundamental importance and solvable in a definitive way with existing resources. In environments such as the solar wind (and, as far as we can fathom, more generally in cosmic plasmas from heliospheric to extragalactic), the turbulent cascade of electromagnetic fluctuations reaches ion Larmor spatial scales while frequencies remain smaller than the ion cyclotron frequency (these are the radius and frequency of the particle gyration in a magnetic field). Under these conditions, the “gyrokinetic” approximation (5D rather than 6D) holds. However, in many parameter regimes, the ion cyclotron frequency is reached at sub-Larmor scales. Linear theory tells us that in the narrow region of frequencies around the ion cyclotron, electromagnetic fluctuations fall into resonance with Larmor motion and thus can transfer their energy into the particle motion, leading to ion heating. The nonlinear question is how much (if any) of the turbulent free energy will be sucked into this resonance and how much will, via nonlinear coupling, simply leapfrog it and continue cascading until converted into electron heat at the electron Larmor scale? This question cannot be resolved via any low-frequency model (like gyrokinetics) and will therefore be answered via 6D fully kinetic simulations restricted to a narrow window of scales around the resonance. Theory is falsifiable in this area: one can (and does) measure ion distribution functions in the solar wind (although the physics results apply much more broadly). If the student is so inclined, we may get involved directly with analysis of such measurements. This project is likely to involve a collaboration with Prof Matthew Kunz at Princeton University.

Background Reading:
1. G. G. Howes et al., “A model of turbulence in magnetized plasmas: implications for the dissipation range in the solar wind,” J. Geophys. Res. 113, A05103 (2008)
2. A. A. Schekochihin et al., “Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas,” Astrophys. J. Suppl. 182, 310 (2009)