OXFORD PLASMA THEORY GROUP

   

DPhil PROJECTS IN PLASMA PHYSICS

  starting in October 2017 (here are the 2018 projects)

 Application deadline: 20 January 2017

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.

Potential supervisors: Prof Michael Barnes (projects 1, 6), Prof Steven Cowley FRS (project 2), Prof Felix Parra Diaz (projects 3, 4), Prof Alexander Schekochihin (projects 5, 6, 8; also here), Prof Steven Balbus FRS (project 5), Prof Gianluca Gregori (project 7), Prof Subir Sarkar (project 7)

Size of intake: this depends on various hard-to-predict circumstances, in particular funding arragements; this year (2016), we accepted 4 fully funded students, sponsored by CCFE/EUROfusion, UK EPSRC, Berrow Foundation (Switzerland) and A*STAR Foundation (Singapore).

*** 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 all offered jointly with researchers at the U.K.A.E.A. Culham Centre for Fusion Energy (CCFE).

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. 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. Suppressing turbulence in magnetic confinement fusion plasmas
Supervisor: Prof Michael Barnes
CCFE co-supervisor: Dr Michele Romanelli

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. The aim of this project is to address a practical and fundamental open question regarding these multi-scale turbulent dynamics: What leads to the appearance of turbulence-free regions in some current experiments, and can we use these regions to optimise fusion energy production? The project will require a combination of analytical theory and cutting-edge numerical techniques and should benefit from comparisons with data from MAST and JET, two large fusion experiments housed nearby at the Culham Laboratory, as well as a strong collaboration with scientists working on the new JT-60SA experiment in Japan.   



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
CCFE 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 physics on the Edge: transition from electron- to ion-repelling wall in modern tokamaks
Supervisor: Prof Felix Parra Diaz
CCFE co-supervisor: Dr Fulvio Militello

In magnetised plasmas for fusion energy, the design of the region of the plasma in contact with the wall determines the heat and particle load to the chamber that contains the plasma. Simply scaling current machines to reactor size would give heat loads to the wall that are more than one hundred times the maximum load that any known material withstands. We need clever solutions to enable the wall to survive. A key aspect of this challenge to consider is the character of the wall-plasma interaction (the physics of the plasma "edge"). If the wall charges negatively, it will repel electrons and accelerate ions. The accelerated ions then hit the wall and sputter part of the material away. In contrast, positively charged walls repel ions and prevent sputtering, but they attract a large heat load from hot electrons. Due to the different dynamics of the two species and also different collective dynamics of the plasma along and across the magnetic field lines, the angle between the wall and the magnetic field determines whether the wall repels electrons or ions. Current machines are well into the electron-repelling regime, but designs of future fusion reactors are considering angles that are within approximately one degree of the transition between the electron-repelling and the ion-repelling cases (these designs are based on other optimisation considerations, which ignore this transition). This DPhil project focuses on a full theoretical characterisation of the transition between the electron- and ion-repelling regimes using novel analytical techniques (see [1] for an illustrative example). The idea is to determine whether angles of the order of one degree are indeed beneficial by considering that an ion-repelling wall would lead to a completely different balance between the ion and electron particle and energy losses to the wall, profoundly changing the plasma upstream (inside the device). 
   
SOL

Background Reading:
1. A. Geraldini, F. I. Parra, and F. Millitello, “Gyrokinetic treatment of a grazing angle magnetic field,” submitted to Plasma Phys. Control. Fusion (2016); preprint: arXiv:1608.02002

4. Explaining the High-Confinement Mode in JET
Supervisor: Prof Felix Parra Diaz
CCFE co-supervisor: Dr Jon Hillesheim

Perhaps the most puzzling and important observation in magnetic fusion experiments is the transition to a High-Confinement Mode (H-mode) when the input heating power is increased above a certain threshold. In H-mode, plasma turbulence is suppressed in a thin region near the edge. As the turbulent transport is thus reduced, the confinement of the plasma is significantly improved and the gradients of density and temperature are much larger than in the rest of the volume. In plain words, in H-modes density and temperature “jump” from one value to another on a surface that surrounds most of the volume of the magnetic-fusion plasma. This jump, known as the pedestal, makes it much easier to achieve the necessary conditions for fusion energy – in fact, it may be the only viable mode of operation for a reactor. Even though H-modes are routinely observed in all relevant fusion experiments, there is no quantitative theory that would explain the reduced turbulence level and that could predict the power threshold for triggering the H-mode. Recently, it has been possible to measure in detail [1] the structure of the plasma flow and turbulent fluctuations during formation of the pedestal of JET, the largest magnetic fusion experiment in the world, the machine that holds the world record for fusion-energy production. This measurement was possible thanks to a sophisticated technique (Doppler Backscattering, DBS). The student working on this DPhil project will use the new data obtained with DBS in JET and state-of-the-art kinetic turbulence simulations to determine the mechanisms that control the turbulence level near the plasma edge and allow the H-mode pedestal to form and be sustained.   
Er

Background Reading:
1. J. C. Hillesheim et al., “Stationary zonal flows during the formation of the edge transport barrier in the JET tokamak,” Phys. Rev. Lett. 116, 065002 (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).  

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, R. Sunyaev, W. Forman, and H. Boehringer, “Cooling flows as a calorimeter of active galactic nucleus mechanical power,” Mon. Not. R. Astron. Soc., 332, 729 (2002)
3. M. S. Rosin, A. A. Schekochihin, F. Rincon, and S. C. Cowley, “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, A. A. Schekochihin, S. C. Cowley, J. J. Binney, and J. S. Sanders, “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, A. A. Schekochihin, and M. W. Kunz, “Pressure-anisotropy-driven microturbulence and magnetic-field evolution in a shearing, collisionless plasma,” Mon. Not. R. Astron. Soc. 459, 2701 (2016)
7. J. Squire, E. Quataert, and A. A. Schekochihin, “A stringent limit of the amplitude of Alfvenic perturbations in high-beta low-collisionality plasmas,” arXiv:1605.02759
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)

7. Second-order Fermi acceleration by MHD 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)

8. 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)