April 15-17

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Abstracts

Author: Joshua W Burby
Requested Type: Poster
Submitted: 2019-02-21 18:34:04

Co-authors:

Contact Info:
Los Alamos National Laboratory
P. O. Box 1663
Los Alamos, New Mexico   87545
USA

Abstract Text:
The established approach for simulating guiding center dynamics involves moving into the (asymptotically-defined) guiding center coordinate system, dropping sufficiently high-order terms from the equations of motion, and then applying conventional numerical integration methods for advancing time. Drawbacks of this approach include a complicated appearance of physical boundaries in guiding center phase space, as well as a reliance on extremely heavy and error-prone calculations when attempting to incorporate high-order effects. Curiously, there is an alternative approach to guiding center simulations based around the dynamics of loops entrained in the phase space flow. While a generic loop will rapidly distort as time evolves, there is a slow invariant manifold in loop space whose loops are parameterized by finitely-many degrees of freedom. It is not difficult to show that dynamics of these slow loops happens to be equivalent to guiding center dynamics to all orders in perturbation theory. I will present results on the development and test application of an integrator for loop space dynamics. The new integrator, which is implicit and energy conserving, accurately steps over the cyclotron timescale while working in particle-space coordinates. Moreover, by exploiting the slow manifold structure, the usual preconditioning problem associated with large implicit timesteps in stiff systems is completely avoided. I will argue that loop space integrators should enable incorporation of high-order guiding center effects without the need for horrendous perturbation calculations.

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