Past Event: Oden Institute Seminar

The non-perturbative adiabatic invariant is all you need

Joshua Burby, Assistant Professor, Physics, UT Austin

Abstract

Developing reduced models for highly-oscillatory dynamical systems traditionally proceeds by applying asymptotic averaging methods. However, the quality of asymptotic averaging degrades as timescale separation decreases. In studying a classical application of asymptotic averaging methods, charged particles moving in a strong inhomogeneous magnetic field, we identified a regime of marginal timescale separation where asymptotic averaging fails quantitatively in spite of strong indications that a good averaged model ought to exist. We developed a non-perturbative, data-driven averaging method for the marginal regime and found the resulting non-perturbative averaged model significantly outperforms asymptotic averaging, even when accounting for corrections from higher-order averaging. I will explain the method in general and in the charged particle context. Then I will report on results from the method's application to $\alpha$-particle dynamics in a fusion reactor concept known as the stellarator.

Biography

Joshua Burby is a mathematical plasma physicist whose research centers on stellarator magnetic fusion. Stellarators confine hot plasma using geometrically- and topologically-complex three-dimensional magnetic fields. Burby uses intuition from symplectic geometry, dynamical systems theory and asymptotic analysis to answer foundational questions about stellarator fusion, such as “which magnetic fields confine individual charged particles?” or “what is the best way to compute stellarator equilibria?” Burby has undergraduate and doctoral degrees from Cornell University and Princeton University, respectively. He received postdoctoral fellowships from the US DOE, the Mathematical Sciences Research Institute, and the Los Alamos National Laboratory. Before coming to UT Austin, he was a staff scientist at Los Alamos in the Applied Mathematics and Plasma Physics group T-5.