Regularity and Long Time Dynamics of Fluids and Plasmas

The project is aimed at the study of nonlinear phenomena in fluids and plasmas that are of mathematical interest and of physical importance, introducing new mathematical approaches to central problems of fusion research and of astrophysics. A novel mathematical study of the effect of radiation on plasma dynamics is a significant component of the project. Another significant component of the project addresses mathematical models for magnetic reconnection of plasma. This is an ubiquitous process in nature, and its study is important in solar physics where it is manifested in solar flares, and in fusion research where it is manifested in plasma turbulence. Additionally, the project includes computational models of plasma relaxation to magneto-hydrostatic equilibria in complex geometries, which are particularly relevant to stellarator design. The project will also involve training and mentoring of postdoctoral associates, graduate students, and undergraduates in this research domain. This project addresses analytical challenges in radiative kinetics, relaxation to magnetohydrostatic equilibria, and magnetic reconnection via electron inertia. The mathematical study of radiative kinetics developed in the project introduces a new perspective in this area of applied analysis. The speedup of relaxation to magneto-hydrostatic equilibria involves non-diffusive nonlocal approximation schemes which do not alter the equilibria. The study of magnetic reconnection due to electron inertia concerns two distinct avenues for topological change which is not due to magnetic resistivity, through singularity formation and through smooth two-fluids dynamics. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.