The pedestal is a region of reduced plasma turbulence that naturally appears in the edge of tokamak plasmas when the input power is above a threshold that is currently determined experimentally. It is widely accepted that the electric field gradient observed in the pedestal is responsible for shearing turbulence and reducing energy losses in the pedestal. This electric field gradient is sustained by the pedestal pressure gradient, i.e., the plasma tries to expand and it is pushed inwards by a large electric field. In the usual picture of pedestal formation, if the plasma pressure gradient increases, the electric field and its gradient increase as well, and eventually, the turbulence reduction due the electric field gradient dominates over the increase in turbulence driven by the pressure gradient, leading to a sharp transition and the appearance of the pedestal. What determines the critical pressure gradient? One possible answer is that the critical gradient is reached once the characteristic scale length of the pressure is comparable to the width of the confined particle orbits in the edge. This picture is somewhat supported by the fact that the radial extent of particle orbits can be a large fraction of the pedestal width. We propose to study this possibility by searching for reduced turbulence states supported by finite-orbit-width effects. We will start by studying pedestals observed in current machines. It has been possible to construct neoclassical models that incorporate finite orbit width effects [1,2]. Based on the techniques developed in these previous works, we will investigate the effect on stability of finite drift orbit widths with analytical and semi-analytical approaches. We will consider both microinstabilities and MHD-like modes. The project will build on previous experience in local gyrokinetic stability in pedestals (see for example, [3]) and on work previously done to include the MHD kink drive in gyrokinetics [4]. We intend to use the model to study the formation and stability of JET and MAST-U pedestals, comparing experimental results, including DBS measurements, to theoretical predictions. To extend the work to MAST-U, in which the drift orbit width can be comparable to the ion gyroradius, we have developed techniques to include finite ion gyroradius effects self-consistently [5].

Background Reading:
1. G. Kagan & P. J. Catto, "Arbitrary poloidal gyroradius effects in tokamak pedestals and transport barriers," PPCF 50, 085010 (2008)
2. M. Landreman & D. R. Ernst, "Local and global Fokker–Planck neoclassical calculations showing flow and bootstrap current modification in a pedestal," PPCF 54, 115006 (2012)
3. D. Hatch et al., "A gyrokinetic perspective on the JET-ILW pedestal," PPCF 57, 036020 (2017)
4. I. Pusztai et al., "A current-driven electromagnetic mode in sheared and toroidal configurations," PPCF 56, 035011 (2014)
5. A. Geraldini, F. I. Parra, & F. Militello, "Gyrokinetic treatment of a grazing angle magnetic presheath,"  PPCF 59, 025015 (2017)

4. Plasma-wall interaction in magnetic confinement fusion plasmas
Supervisor: Prof Felix Parra Diaz
UKAEA co-supervisor: Dr Stefan Mijin

As we build more efficient fusion devices, the amount of power released by the fusion plasma onto the vacuum chamber walls increases rapidly. The walls of the next generation of fusion experiments are expected to suffer heat loads that existing materials can barely withstand. Thankfully, there are several proposals to reduce the heat load using concepts from magnetized plasma physics and atomic physics. Some of these ideas (such as the super-X divertor [1]) are going to be tested in machines such as MAST-Upgrade (situated at UKAEA, a few miles from Oxford). The student working on this DPhil project will focus on one very important aspect for the success of the several schemes mentioned above: the interaction between the plasma and the wall. This is a problem at the boundary between plasma physics and condensed matter physics, and, despite being of fundamental importance for laboratory plasmas, several key questions remain unanswered. The fact that thin layers of non-neutral plasma form around the wall means that the problem can be treated accurately with simplified theoretical 1D or 2D models. The student working on this project will build on theoretical and numerical tools developed by the Plasma Theory Group in Oxford and UKAEA [2, 3] to study the highly nonlinear physics of the thin layers described above. The focus of this project is on new physical regimes that we expect to find in future reactors, and on the transitions and bifurcations between these regimes. This project is a collaboration with UKAEA, and the student will have the opportunity to work with the team that will exploit the exciting new facility MAST-Upgrade.

Background Reading:
1. P.M. Valanju et al., "Super-X divertors and high power density fusion devices," Phys. Plasmas 16, 056110 (2009)
2. A. Geraldini, F.I. Parra and F. Militello, "Gyrokinetic treatment of a grazing angle magnetic presheath," PPCF 59, 025015 (2017)
3. A. Geraldini, F.I. Parra and F. Militello, "Solution to a collisionless shallow-angle magnetic presheath with kinetic ions," PPCF 60, 125002 (2018)
4. A. Geraldini, F.I. Parra and F. Militello, "Dependence on ion temperature of shallow-angle magnetic presheaths with adiabatic electrons," J. Plasma Phys. 85, 795850601 (2019)
5. S. Mijin et al., "Kinetic and fluid simulations of parallel electron transport during equilibria and transients in the scrape-off layer," PPCF 62, 095004 (2020)

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.