Seminar

Synopsis:

Magnetic confinement of plasmas in toroidal devices offers a broad variety of challenging and interesting mathematical problems of great relevance to the nuclear fusion community. Although well understood in two dimensions, the fundamental question of obtaining an equilibrium of the underlying magnetohydrodynamics (MHD) model in a three-dimensional space remains an open problem. This poses considerable theoretical and computational challenges for fusion engineers and plasma physicists. Asymptotic analysis offers valuable tools and great physical insight in tackling some of these questions. After discussing the mathematical difficulties that arise from the basic system of partial differential equations governing three-dimensional MHD equilibrium, I will present a variety of asymptotic expansion methods to resolve these issues and obtain a self-consistent solution order by order. In particular, I shall demonstrate that the expansions can be carried to all orders and thereby provide direct evidence for the existence of large classes of three-dimensional MHD equilibria in a toroidal system. I will show that our analysis provides theoretical explanations for certain experimentally observed self-organized plasma states near certain magnetic surfaces where the magnetic field closes on itself after one toroidal turn. 

Synopsis:

Recent advances in applied mathematics (Gamba and Rjasanow, JCP 2018) make direct solution of the Boltzmann equation particularly accessible. A newly-developed implementation has been optimized, parallelized, and rigorously benchmarked. Features include general-cross-section large-angle, inelastic, and/or self-collisions. The fully conservative
discrete collision operators are pre-computed and stored on an online database, making time advancement remarkably efficient on local workstations. I will also discuss possible applications for this tool including discharges, reentry blackout, tokamak divertors, runaway electrons, carbon sequestration, and more.

Synopsis: