Plasma physics is the study of large collections of charged particles and their interactions. One key application of plasma physics is in magnetically confined nuclear fusion, where nuclei, typically of Hydrogen, are confined by a magnetic field, so that they can reach the high temperatures necessary to fuse together as they collide. A large research effort is underway to develop fusion reactors that exploit the energy release from fusion to produce electricity.
In a tokamak, which is a specific kind of fusion reactor design, the vacuum chamber containing the fusion fuel can be conceptually separated into a 'closed field region' where particles cannot escape along magnetic field lines, and an 'open field region' where they can stream along the field lines and hit the wall.
The quite sharp boundary between the open and closed field region is particularly interesting and important, because a strong additional 'transport barrier', called a pedestal, can develop there. A large difference in temperature and density is sustained across the narrow pedestal, allowing the core plasma to reach higher pressure, and leading to a major increase in fusion power. How the pedestal is formed, and when it breaks down, are questions of vital importance to fusion reactor operation, but these issues are quite poorly understood at present.
This proposal seeks to answer basic questions about the pedestal, and similar structures that develop in other laboratory and space plasmas. This is an investigation of the fundamental properties of magnetised plasmas. How do such structures evolve, and how does this interact with the plasma turbulence? What plasma instabilities develop in these plasmas?
To answer these questions, we need models of how the particles individually and collectively respond to electromagnetic fields, and for the hot plasmas of interest we usually need to keep track of the motion of particles, rather that just look at the overall fluid motion. In magnetised plasmas, the basic motion of plasma particles is a circular orbit, or gyration, perpendicular to the magnetic field, as well as a parallel motion along the magnetic field line. This can be formalized mathematically using a framework known as 'gyrokinetics', which has become the dominant way to understand the transport of hot plasma in tokamaks.
A new gyrokinetic formalism has been developed by the proposer which is designed to be more accurate in regions with large amplitude structures like the tokamak pedestal. It is based on a rethinking of the assumptions usually made, so that both short wavelength fluctuations and more global physics may be handled in a unified way. We relax the requirement that perturbations be small amplitude but instead require that the 'vorticity', which measures how rapidly blobs of plasma rotate, is relatively limited.
This proposal will develop and exploit this mathematical framework to solve a range of fundamental physics problems in magnetised plasmas with large perturbations. A computer code to embody this plasma model will be further developed, and this will require the development of new algorithms. This code will then be deployed to understand both fundamental physics problems of magnetised plasmas, as well as the specific applications to structured regions of tokamaks.
As well as computational work, physical understanding of these plasmas requires us to develop a deeper understanding of the mathematical framework. We will use limiting cases to determine how the physics relates to simpler formalisms, and determine the underlying conservation laws to tie the turbulent dynamics to the large scale physics of momentum and energy transport.
