The Department of Applied Mathematics weekly seminar is given by scholars and researchers working in applied mathematics, broadly interpreted.
Title: An implicit, asymptotic-preserving time integration scheme for charged particle motion in arbitrary electromagnetic fields
Abstract: In magnetic confinement fusion reactors, the strong background magnetic field used for confinement also induces a fast oscillation time-scale that can be on the order of nanoseconds. Meanwhile, global reactor codes must simulate scales on the order of seconds. While asymptotic limits that average over the fast oscillatory motion are known, these approximations break down in some critical physical regimes. Thus, one is motivated to seek asymptotic preserving schemes that can take large time-steps when physically permissible, but still recover accurate particle trajectories when the asymptotics break down. I will present such a scheme, along with a sketch of its derivation. Particular attention will be paid to energy conservation, as it will be shown that this has enormous consequences on the long-term accuracy of particle trajectories. I will also report on recent progress on adaptive time-stepping, efficient solution of the nonlinear system of equations the scheme requires, and capturing of so-called finite Larmor radius effects when electric fields feature small length scales.