Free-energy flows and universal equilibria in turbulent astrophysical plasmas

Supervisors: Michael Barnes and 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 is large spatial gradients of electric and magnetic fields and large gradients of the particle distribution functions with respect to velocities. This prompts two fundamental 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 we can measure density and magnetic fluctuations even in extragalactic plasmas, 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. 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). 

Finally, with a theory of plasma turbulence in hand, it is possible to attack what is probably the most fundamental question of the field: in the absence of collisions, are there universal equilibria, or classes of equilibria, independent of initial conditions, that a turbulent plasma will want to converge to? There is some recent progress indicating that the answer is yes and that one predict statistical-mechanically the emergence of universal power-law (in particle energy) distributions---this is exciting both on its own merits and because of the astrophysical challenge of explaining theoretically power-law distributions that are observed for, e.g., cosmic rays or solar-wind electrons. How to construct a theory of that for a magnetised, turbulent plasma is an open and exciting question. Attempting to do this will again involve kinetic theory and/or kinetic simulations.   

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 et al., "Thermal disequilibration of ions and electrons by collisionless plasma turbulence," PNAS 116, 771 (2019)
4. R. Meyrand et al., "Fluidization of collisionless plasma turbulence," PNAS 116, 1185 (2019)
5. J. Squire et al., "High-frequency heating of the solar wind triggered by low-frequency turbulence," Nature Astron. 6, 715 (2022)
6. R. J. Ewart et al., "Collisionless relaxation of a Lynden-Bell plasma,'' J. Plasma Phys. 88, 925880501 (2022)
7. R. J. Ewart et al., "Non-thermal particle acceleration and power-law tails via relaxation to universal Lynden-Bell equilibria," arXiv:2304.03715

Magnetic-field amplification by the fluctuation dynamo in astrophysical plasmas

Supervisors: Archie Bott and Alexander Shekochihin

Understanding cosmic magnetism is a long-standing problem in astrophysics. Astronomical observations of various astrophysical environments – for example, those of our own galaxy by the MeerKAT telescope [1] or of more distant galaxy clusters [2] – reveal the presence of finely structured magnetic fields of sufficient strength to affect the dynamics of such systems. A possible mechanism for explaining the presence and characteristics of these magnetic fields is the so-called fluctuation dynamo, whereby stochastic or turbulent motions of the plasma in which these magnetic fields are embedded amplify and maintain them [3]. The fluctuation dynamo has mostly been studied using simplified magnetohydrodynamic (MHD) plasma models whose key transport properties (viz., resistivity and viscosity) do not depend on macroscopic plasma properties such as density, temperature, and the magnetic field. However, the plasma often found in the astrophysical systems of interest is often weakly collisional, and current theories for the transport properties of such plasma typically do predict a dependence on macroscopic plasma properties. It is an outstanding question whether `anomalous’ transport properties can explain why certain predictions of the simplified theory of the fluctuation dynamo are at odds with astronomical observations (for example, that the energy-containing scale of the magnetic field is macroscopic). In this project, a student would explore how more realistic models of transport properties affect the fluctuation dynamo using both theory and numerical simulations, and then attempt to identify key differences with simplified dynamo theories that could be detected in astronomical observations.

Key reading:

  1. I. Heywood et al., Nature 573, 235 (2019).
  2. C. L. Carilli & G.B. Taylor, Annu. Rev. Astron. Astrophys. 40, 319 (2002).
  3. F. Rincon, J. Plasma Phys. 85, 205850401 (2019).  
  4. A. A. Schekochihin et al., Astrophys. J. 612, 276 (2004).
  5. A. K. Galishnikova, M.W. Kunz, A.A. Schekochihin, PRX 12, 041027 (2022)
  6. A. A. Schekochihin, S. C. Cowley, Phys. Plasmas 13, 056501 (2006).
  7. A. F. A. Bott et al., Proc. Nat. Acad Sci. 118, e2015729118 (2021).

Magnetised plasma turbulence: from laser lab to galaxy clusters

Supervisors: Gianluca Gregori, Archie Bott, and Alexander Schekochihin

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 [3], diffusion and acceleration of particles by turbulence [4,5], suppression of thermal conduction in galaxy-cluster-like plasmas [6]. 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. Depending on the student's inclinations, it is also possible to pursue a project focused on theory and/or numerical modelling of plasma phenomena in astrophysical and laboratory-astrophysical environments.


1. P. Tzeferacos et al., "Laboratory evidence of dynamo amplification of magnetic fields in a turbulent plasma," Nature Comm. 9, 591 (2018) (2019 APS Dawson Prize)

2. A. F. A. Bott et al., "Time-resolved fast turbulent dynamo in a laser plasma," PNAS 118, e2015729118 (2021) (2020 EPS PhD Award in Plasma Physics)

3. T. G. White et al.,"Supersonic plasma turbulence in the laboratory," Nature Comm. 10, 1758 (2019)

4. A. F. A. Bott et al., "Proton imaging of stochastic magnetic fields," J. Plasma Phys. 83, 905830614 (2017)

5. L. E. Chen et al., "Transport of high-energy charged particles through spatially intermittent turbulent magnetic fields," Astrophys. J. 892, 114 (2020)

6. J. Meinecke et al., "Strong suppression of heat conduction in a laboratory analogue of galaxy-cluster turbulent plasma," Science Adv. 8, eabj6799 (2022)

Microphysics of gamma-ray bursts

Supervisors: Gianluca Gregori, Archie Bott, Alexander Schekochihin, Subir Sarkar, Todd Huffman

Gamma-ray bursts (GRBs) are among the most energetic events in the Universe. They occur at cosmological distances and are the result of the collapse of massive stars or neutron stars mergers, with emission of relativistic “fireballs" of electron-positron pairs. From astrophysical observations, a wealth of information has been gleaned about the mechanism that leads to such strong emission of radiation, with leading models predicting that this is due to the disruption of the beam as it blasts through the surrounding plasma. This produces shocks and hydromagnetic turbulence that generate synchrotron emission, potentially accelerating to ultra-high energies the protons which are observed on Earth as cosmic rays. However, there is no direct evidence of the generation of either magnetic fields or cosmic rays by GRBs. Estimates are often based on crude energy equipartition arguments or idealized numerical simulations that struggle to capture the extreme plasma conditions. We propose to address this lacuna by conducting laboratory experiments at large laser and accelerator facilities to mimic the jet propagation through its surrounding plasma. Such experiments will enable in situ measurement of the plasma properties, with exquisite details that cannot be achieved elsewhere. The experiments also complement numerical simulations by providing long measurement times extending into the non-linear regime where numerical simulations are not possible today. The proposed experiments will study fundamental physics processes, unveil the microphysics of GRBs, and provide a new window in high energy astrophysics using novel Earth-based laboratory tools.

Background Reading:

1. C. D. Arrowsmith et al., "Generating untradense pair beams using 400 GeV/c protons," Phys. Rev. Res. 3, 023103 (2021)

Nonthermal particle acceleration in extreme plasmas around black holes

Supervisors Dmitri Uzdensky and Alexander Schekochihin

Accreting supermassive black holes (SMBHs) residing in active galactic nuclei (AGN) at the centres of many galaxies, including our own, are rightfully regarded as some of the most fascinating and enigmatic objects in the Universe. These black holes, and the powerful relativistic jets emanating from them, often exhibit spectacular, violent phenomena, such as bright high-energy flares with nonthermal X-ray and gamma-ray spectra. They are also viewed as the most likely generators of highly energetic non-electromagnetic observational "messengers": extremely relativistic cosmic rays and ultra-high-energy neutrinos, detected on Earth with dedicated ground-based observatories. All these observational signals indicate that BH environments are very efficient relativistic particle accelerators. Understanding how these cosmic accelerators work is an outstanding problem in modern high-energy astrophysics. Nonthermal particle acceleration is believed to be a natural product of collective kinetic nonlinear plasma processes, such as magnetic reconnection, shocks, and magnetised plasma turbulence taking place in weakly collisional plasmas. How these processes operate under the extreme physical conditions expected in the exotic relativistic plasma environments of accreting black holes is, however, not well understood. The situation is greatly complicated by special- and general-relativistic effects, by strong interaction of the energetic emitting plasma particles with radiation, and by quantum-electrodynamic effects such as pair creation. Elucidating the complex interplay of these effects with collective plasma processes and, consequently, their impact on particle acceleration is an active area of today's plasma astrophysics research, presenting a number of interesting, nontrivial theoretical challenges. This project will address these fundamental plasma-theoretical questions and their observational implications through a combination of analytical and computational methods, with the balance between theory and computation to be decided based on the student's preferences.

Interaction between tides and convection in stars and giant planets

Supervisor: Caroline Terquem

A large proportion of stars are found in binary systems.  When the distance between the two stars in such systems is small enough, oscillations are excited in each of the stars by the tidal potential of its companion.  These tidal waves are dissipated in the convective regions of the stars.  Such dissipation of energy leads to circularisation of the orbits.  Observations show that close orbits are circular whereas wider orbits have eccentricities.  The period at which the transition occurs for a type of stars is called the 'circularisation period'.  Until now,  theoretical studies, which have relied on mixing length theory to model convection, have predicted circularisation periods significantly smaller than the observed ones.   We have developed  a new description of the interaction between tides and convection that yields the observed values of the circularisation period.  This new formalism is also able to account for the rate of tidal energy dissipation which is needed in giant planets to explain the orbital evolution of their satellites, and which had been a puzzle for the last 50 years.  There is a large number of problems that should be revisited using this new description, and this is the aim of the project.  These studies can be applied to a variety of systems, including binary systems with two stars, or with one star and a giant planet, or with a giant planet and a satellite.   The project will use analytical and numerical tools.