Joshua W. Burby, Los Alamos National Laboratory

"Slow manifold integrator for loop space dynamics"

Abstract: In a strong, weakly inhomogeneous magnetic field, charged particles rapidly gyrate around magnetic field lines on the cyclotron timescale. On longer timescales, the center of gyration suffers a slow drift. Computing this long-timescale drift is known as the guiding center problem. The established method for tackling the guiding center problem involves first moving into a perturbed coordinate system that decouples the gyration from the drift. Leveraging this decoupling, standard numerical integration schemes for non-stiff systems are then applied in the new coordinates. The major shortcoming of this approach is that the perturbed coordinates are only known as difficult-to-compute asymptotic series. High-order terms in the series are especially bothersome because they involve high-order derivatives of the magnetic field. In this talk I will describe an alternative solution of the guiding center problem that does not involve asymptotic coordinate transformations. The crux of the new approach is the observation that drift dynamics may be identified with a slow manifold in the phase space for loops entrained in the Lorentz force flow. I will demonstrate that loop dynamics on the slow manifold may be computed efficiently using a fully-implicit energy-conserving integrator for deformable loops coupled with a method for preparing initial conditions on the slow manifold. In particular, I will show that the slow manifold structure may be exploited to cast each implicit timestep as a well-conditioned fixed-point problem.