DPhil PROJECTS IN PLASMA PHYSICS

starting in October 2016

Application deadline: 22 January 2016

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, 4), Prof Gianluca Gregori (project 5; also here), Prof Felix Parra Diaz (project 2), Prof Subir Sarkar (project 5), Prof Alexander Schekochihin (projects 3, 4, 6, 7; also here)

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

- If you are interested in MCF (either theoretical or experimental), apply for a DPhil in
Theoretical Physics.

- If you are interested in plasma
astrophysics, apply for a DPhil in Astrophysics.

- For the plasma astrophysics projects, we recommend that you ALSO apply for a DPhil in Theoretical
Physics
(indicating plasma physics as your preferred area) as this will allow
us to consider you for all available
projects and funding opportunities (scholarships). Please also apply to
both degrees if you are generally interested in plasma physics and are
flexible between its different areas.

- Internal
Oxford scholarships: there are a number of scholarships in physics
available at Oxford, including Clarendon Scholarships, the James Buckee
Scholarship at Merton College, the Oxford-Berman Studentship at University College
and others. Note that in order to be considered for a scholarship
funded by a particular College, you do not need to select that College
as your College of first choice, but you must indicate on your
application form that you are willing to move to another College to
gain an offer of funding (this simply requires that you leave blank the
box in the funding section of the University’s online application form
that must be ticked if you do not wish to be considered by another
college than your stated preferred college).

- If you are considering applying for an external scholarship and require our endorsement, in the first instance please contact the supervisor that you are most interested in working with.
- You are welcome to address inquiries on science to any of the project supervisors listed below and on the logistical aspects of applying to Ms Michelle Bosher (but do please check first if your question is perhaps already answered here or here).
- All graduate students in plasma physics will have access to graduate-level courses taught with the Oxford Master Course in Mathematical and Theoretical Physics (to which you can also apply as a stand-alone MSc degree) and the Oxford-Warwick-Imperial Centre for Postgraduate Training in Plasma Physics and High Energy Density Science.

Projects in Fusion Plasmas

These three projects are all offered jointly with researchers at the U.K.A.E.A. Culham Centre for Fusion Energy (CCFE). They also form part of a Plasma Turbulence Collaboration between Oxford Plasma Theory Group, CCFE and York Plasma Institute (YPI) at the University of York. York also offers PhD projects within this Collaboration --- if you wish to be considered for those, please apply to York as well as to Oxford (the competitions for admission at the two Universities are separate and students will follow different training programmes, but all will be involved in the Collaboration).

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 made an offer of 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. Turbulence suppression in magnetic confinement fusion plasmas

Supervisor: Prof Michael Barnes

CCFE co-supervisor: Dr Michele Romanelli

[see also this project at York]

2. Interaction between turbulent plasma fluctuations and high-frequency plasma waves

Supervisor: Prof Felix Parra Diaz

CCFE co-supervisor: Dr Jon Hillesheim

York collaborator: Dr David Dickinson [see also this project at York]

3. Zonal flow-drift wave interactions in ion-scale turbulence in differentially rotating tokamak plasmas: BES measurements and gyrokinetic models

Supervisor: Prof Alexander Schekochihin

CCFE co-supervisor: Dr Anthony Field

York collaborator: Dr Istvan Czeigler [see also this project at York]

Background Reading:

1. M. Barnes, F. I. Parra and A. A. Schekochihin, “Critically balanced ion temperature gradient turbulence in fusion plasmas,” Phys. Rev. Lett. 107, 115003 (2011)

2. A. A. Schekochihin, E. G. Highcock, and S. C. Cowley, “Subcritical fluctuations and suppression of turbulence in differentially rotating gyrokinetic plasmas,” Plasma Phys. Control. Fusion 54, 055011 (2012)

3. Y.-c. Ghim, A. A. Schekochihin, A. R. Field, I. G. Abel, M. Barnes, G. Colyer, S. C. Cowley, F. I. Parra, D. Dunai, S. Zoletnik, and the MAST Team, “Experimental signatures of critically balanced turbulence in MAST,” Phys. Rev. Lett. 110, 145002 (2013)

4. Y.-c. Ghim, A. R. Field, A. A. Schekochihin, E. G. Highcock, C. Michael, and the MAST Team, “Local dependence of ion temperature gradient on magnetic configuration, rotational shear and turbulent heat flux in MAST,” Nucl. Fusion 54, 042003 (2014)

Supervisor: Prof Michael Barnes

CCFE co-supervisor: Dr Michele Romanelli

[see also this project at York]

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.

2. Interaction between turbulent plasma fluctuations and high-frequency plasma waves

Supervisor: Prof Felix Parra Diaz

CCFE co-supervisor: Dr Jon Hillesheim

York collaborator: Dr David Dickinson [see also this project at York]

The performance of magnetic
confinement devices is limited by electromagnetic fluctuations driven
by unavoidable plasma instabilities. These fluctuations, commonly known
as plasma turbulence, spoil the confinement provided by the strong
external magnetic fields, and reduce the fusion energy yield. In this
project, the student will study how these intrinsic turbulent
fluctuations (with characteristic frequencies of the order of 10kHz),
interact with high-frequency waves (of the order of 100 GHz) that are
launched into the plasma. The nonlinear scattering of the
high-frequency waves by the plasma fluctuations is a fundamental
problem in plasma physics that requires sophisticated semi-analytical
treatments to bridge the large time-scale separation. The study of the
interaction between low- and high-frequency fluctuations is crucial for
plasma turbulence diagnostics that use the high-frequency waves to
probe the fusion plasma, which is at temperatures hotter than the
centre of the sun and inaccessible to physical probes. The student will
apply the developed theory to the Doppler Back-Scattering (DBS) systems
in JET and MAST, the two experiments at the Culham Centre for Fusion
Energy. In addition to having access to the large database accumulated
in the past three years, the student will have the opportunity to work
with the newly developed DBS system for MAST-Upgrade. This research is
highly relevant to the future of fusion energy because DBS diagnostics
are planned for ITER, the international collaboration to demonstrate
the feasibility of fusion power currently under construction in France,
and similar diagnostics will be necessary in future fusion reactors to
monitor the plasma in real time.

3. Zonal flow-drift wave interactions in ion-scale turbulence in differentially rotating tokamak plasmas: BES measurements and gyrokinetic models

Supervisor: Prof Alexander Schekochihin

CCFE co-supervisor: Dr Anthony Field

York collaborator: Dr Istvan Czeigler [see also this project at York]

While
electromagnetic turbulence in fusion plasmas is widely accepted to be
the main culprit in undermining confinement (by vigorously transporting
energy from the core of the plasma to its edge), until relatively
recently most of our understanding of this turbulence or even just of
our knowledge of what it "looks like" had been based on indirect
measures of its effects (primarily heat transport) and on gyrokinetic
numerical simulations. The Beam-Emission-Spectroscopy (BES) diagnostics
have allowed us to probe turbulent fluctuations directly. In
particular, BES data from MAST has been successfully
used to
determine statistical properties of ion-Larmor-scale turbulence and
thereby test
theoretical predictions and gyrokinetic
simulations. In particular, it appears that if the plasma is
differentially rotated, i.e., if locally the turbulence is embedded in
a sheared plasma flow, the nature of the turbulence changes and the
heat trasport can be suppressed. We are far from complete understanding
of this process or indeed the basic structure of the turbulence.
Simulations show that the
experimentally relevant near-marginal turbulent state is crucially
regulated by
the interaction between the equilibrium velocity shear, zonal flows
(coherent shear flows generated by the turbulence itself) and wave-like
electromagnetic fluctuations that form the bulk of the turbulence
(called "drift waves").
This project will focus on this interaction by determining the scaling
of the turbulent and equilibrium parameters, in particular with flow
shear and collisionality (which is a control parameter for zonal
flows), and by comparison with results of gyrokinetic numerical
modeling. The project involves both theoretical and experimental work
(which may mean developing analysis techniques and/or interacting with
actual hardware, depending on your inclinations). In particular, analysis
techniques are to be developed and tested for the detection of
fluctuating 2D flows, with the aim of detecting localised,
self-generated zonal flows.
Both the MAST tokamak and its BES system are being upgraded (due to
come online in 2016/17) and so the student working on this project will
have a unique opportunity to extract new physics results, including
planning dedicated experiments.

Background Reading:

1. M. Barnes, F. I. Parra and A. A. Schekochihin, “Critically balanced ion temperature gradient turbulence in fusion plasmas,” Phys. Rev. Lett. 107, 115003 (2011)

2. A. A. Schekochihin, E. G. Highcock, and S. C. Cowley, “Subcritical fluctuations and suppression of turbulence in differentially rotating gyrokinetic plasmas,” Plasma Phys. Control. Fusion 54, 055011 (2012)

3. Y.-c. Ghim, A. A. Schekochihin, A. R. Field, I. G. Abel, M. Barnes, G. Colyer, S. C. Cowley, F. I. Parra, D. Dunai, S. Zoletnik, and the MAST Team, “Experimental signatures of critically balanced turbulence in MAST,” Phys. Rev. Lett. 110, 145002 (2013)

4. Y.-c. Ghim, A. R. Field, A. A. Schekochihin, E. G. Highcock, C. Michael, and the MAST Team, “Local dependence of ion temperature gradient on magnetic configuration, rotational shear and turbulent heat flux in MAST,” Nucl. Fusion 54, 042003 (2014)

Projects in Plasma Astrophysics

Candidates interested in any of these three 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

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; turbulent velocities will become observable as well when ASTRO-H launches in 2015); (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. G. G. Howes et al., “Gyrokinetic simulations of solar wind turbulence from ion to electron scales,” Phys. Rev. Lett. 107, 035004 (2011)

3. T. Tatsuno et al., “Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence,” Phys. Rev. Lett. 103, 015003 (2009)

4. G. G. Howes et al., “Kinetic simulations of magnetized turbulence in astrophysical plasmas,” Phys. Rev. Lett. 100, 065004 (2008)

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; turbulent velocities will become observable as well when ASTRO-H launches in 2015); (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. G. G. Howes et al., “Gyrokinetic simulations of solar wind turbulence from ion to electron scales,” Phys. Rev. Lett. 107, 035004 (2011)

3. T. Tatsuno et al., “Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence,” Phys. Rev. Lett. 103, 015003 (2009)

4. G. G. Howes et al., “Kinetic simulations of magnetized turbulence in astrophysical plasmas,” Phys. Rev. Lett. 100, 065004 (2008)

5. 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)

6. Magnetogenesis in the intergalactic plasma

Supervisor: Prof Alexander Schekochihin

In weakly collisional plasmas such as those found in galaxy clusters (and in many other places, from the heliosphere to accretion discs around black holes), pressure is a tensor rather than a scalar – and there are perpendicular and parallel pressures, with respect to the local direction of the magnetic field. As it turns out, every time such a plasma is moved around (as a fluid), the magnetic field that threads it will change (because the field moves with the plasma) and every time that happens, pressure anisotropy is created, i.e., perpendicular and parallel pressures become different. This situation turns out to be violently unstable, a sea of small-scale fluctuations emerges and the plasma thereby contrives to limit the pressure anisotropy at a certain level, which itself depends on the magnitude of the magnetic field. This means the magnetic field can only evolve in a fairly constrained way, very differently to how it behaves in conventional conducting fluids (e.g., liquid metals or very collisional plasmas) described by the equations of magnetohydrodynamics (MHD). The reason this is interesting is that (1) no one knows how exactly the field evolves (the “industry-standard” models of most astrophysical plasmas are by and large MHD, so not appropriate to the case with pressure anisotropies) – this means there is new physics to be discovered; (2) the physical regime in which this is all relevant is precisely the regime in which most plasmas in the Universe are – and so we can't understand the magnetic field structure we observe in the intergalactic medium, predict how this medium moves (more broadly, its large-scale dynamics and thermodynamics) or know where the field came from in the first place without a good model for the magnetic-field dynamics. In this project, we will aim to develop such a model.

Background Reading:

1. F. Mogavero and A. A. Schekochihin, “Models of magnetic-field evolution and effective viscosity in weakly collisional extragalactic plasmas,” Mon. Not. R. Astron. Soc. 440, 3226 (2014)

2. A. A. Schekochihin et al., “Magnetofluid dynamics of magnetized cosmic plasma: firehose and gyrothermal instabilities,” Mon. Not. R. Astron. Soc. 405, 291 (2010)

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, A. A. Schekochihin, and J. M. Stone, “Firehose and mirror instabilities in a collisionless shearing plasma,” Phys. Rev. Lett. 112, 205003 (2014)

5. F. Rincon, A. A. Schekochihin, and S. C. Cowley, “Nonlinear mirror instability,” Mon. Not. R. Astron. Soc. 447, L45 (2015)

7. Turbulent cascade through the ion cyclotron resonance in space plasmas.

Supervisor: Prof Alexander Schekochihin

This project is related to the general theme of Project 1, 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 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)

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)

6. Magnetogenesis in the intergalactic plasma

Supervisor: Prof Alexander Schekochihin

In weakly collisional plasmas such as those found in galaxy clusters (and in many other places, from the heliosphere to accretion discs around black holes), pressure is a tensor rather than a scalar – and there are perpendicular and parallel pressures, with respect to the local direction of the magnetic field. As it turns out, every time such a plasma is moved around (as a fluid), the magnetic field that threads it will change (because the field moves with the plasma) and every time that happens, pressure anisotropy is created, i.e., perpendicular and parallel pressures become different. This situation turns out to be violently unstable, a sea of small-scale fluctuations emerges and the plasma thereby contrives to limit the pressure anisotropy at a certain level, which itself depends on the magnitude of the magnetic field. This means the magnetic field can only evolve in a fairly constrained way, very differently to how it behaves in conventional conducting fluids (e.g., liquid metals or very collisional plasmas) described by the equations of magnetohydrodynamics (MHD). The reason this is interesting is that (1) no one knows how exactly the field evolves (the “industry-standard” models of most astrophysical plasmas are by and large MHD, so not appropriate to the case with pressure anisotropies) – this means there is new physics to be discovered; (2) the physical regime in which this is all relevant is precisely the regime in which most plasmas in the Universe are – and so we can't understand the magnetic field structure we observe in the intergalactic medium, predict how this medium moves (more broadly, its large-scale dynamics and thermodynamics) or know where the field came from in the first place without a good model for the magnetic-field dynamics. In this project, we will aim to develop such a model.

Background Reading:

1. F. Mogavero and A. A. Schekochihin, “Models of magnetic-field evolution and effective viscosity in weakly collisional extragalactic plasmas,” Mon. Not. R. Astron. Soc. 440, 3226 (2014)

2. A. A. Schekochihin et al., “Magnetofluid dynamics of magnetized cosmic plasma: firehose and gyrothermal instabilities,” Mon. Not. R. Astron. Soc. 405, 291 (2010)

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, A. A. Schekochihin, and J. M. Stone, “Firehose and mirror instabilities in a collisionless shearing plasma,” Phys. Rev. Lett. 112, 205003 (2014)

5. F. Rincon, A. A. Schekochihin, and S. C. Cowley, “Nonlinear mirror instability,” Mon. Not. R. Astron. Soc. 447, L45 (2015)

7. Turbulent cascade through the ion cyclotron resonance in space plasmas.

Supervisor: Prof Alexander Schekochihin

This project is related to the general theme of Project 1, 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 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)