Simons Hour Talk

Finding Invariant Circles from a Single Trajectory
Jul 20, 2023, 10:00 am11:00 am



Event Description

Abstract: A problem in stellarator optimization is how to automatically analyze MHD equilibria when they do not consist of nested flux surfaces. Typically researchers look at Poincaré plots to classify trajectories as invariant circles (flux surfaces), islands, or chaos. Moreover, after trajectory classification, additional work is needed to determine the Fourier coefficients of the invariant structures. The weighted Birkhoff average [1] has been shown to classify trajectories, but finding invariant circles and rotation numbers is still missing. In this talk, we will show how a technique from sequence extrapolation, the reduced rank extrapolation method (RRE), can also be used to classify trajectories with a single linear least-squares solve. For the non-chaotic trajectories, a subsequent eigenvalue problem returns the number of islands, the rotation number, and the Fourier coefficients of the trajectory. This method will be demonstrated with a variety of examples.
[1] E. Sander and J. Meiss, Physica D: Nonlinear Phenomena, 411 (2020), p. 132569

Talk time in other timezones:
AEST 12:00 AM Fri 21 Jul,
JST  11:00 PM Thu 20 Jul,
CEST  4:00 PM Thu 20 Jul,
BST   3:00 PM Thu 20 Jul,
UTC  14:00    Thu 20 Jul,
EDT  10:00 AM Thu 20 Jul,
CDT   9:00 AM Thu 20 Jul,
MDT   8:00 AM Thu 20 Jul,
MST   7:00 AM Thu 20 Jul,
PDT   7:00 AM Thu 20 Jul
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