# Astrophysical Plasmas

**DPhil Projects in Plasma Astrophysics with Alexander Schekochihin**

Candidates interested in any of these three projects or generally in plasma physics, plasma astrophysics, astrophysical turbulence and/or dynamo theory are welcome to contact A. Schekochihin for further information (a [dot] schekochihin1 [at] physics [dot] ox [dot] ac [dot] uk). 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 is negotiable).

*1. Magnetogenesis in the intergalactic plasma.*

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,” e-print arXiv:1407.4707

*2. Free energy flows in turbulent astrophysical plasmas.*

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 (I have done some preliminary work, so I 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)

*3. Turbulent cascade through the ion cyclotron resonance in space plasmas.*

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.

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)