Structure-preserving Algorithms for Kinetic Simulations of Plasmas

Existing methods for kinetic simulations of plasmas are largely based on instantaneous error estimation and fail to achieve long-time-scale stability and accuracy. The purpose of this project is to design algorithms that circumvent the stability problems and reliably produce physically sound results. The project leverages on a mathematical, so-called metriplectic description of dissipative non-equilibrium dynamics and aims to develop discretization techniques that preserve invariants, such as the total energy and momentum, and guarantee the production of entropy in numerical implementations. The results of the project will facilitate stable first-principles simulations that extend to macroscopic time-scales in topics ranging from controlling thermonuclear fusion as an energy source, to understanding fast reconnection in magnetospheric storms driven by solar activity, to explaining astrophysical observations such as the structure of the far heliosphere.