Abstract Details
Abstracts
Author: Sidney D.V. Williams
Requested Type: Consider for Invited
Submitted: 2026-03-10 18:45:33
Co-authors: Justin Burzachiello, Matthew Gudorf, Ben Zhu, Predrag Cvitanovic, Dmitri Orlov
Contact Info:
University of California San Diego
9500 Gilman Dr
La Jolla, California 92093
USA
Abstract Text:
Through chaos theory, plasma turbulence can be understood as motion organized by a deterministic backbone. Within this framework, turbulence is a “walk through a forest of exact solutions” [1] where these exact solutions are periodic trajectories which can be used to extract information about the flow. This is especially helpful in conjunction with modern theories of turbulence spreading [2], and resonant magnetic perturbation-induced separatrix splitting which have been utilized in diverter heat load control [3]. In these cases, our chaotic framework allows quantities such as turbulence spreading flux, and magnetic field line escape rate may be found in a fully deterministic manner.
We demonstrate the efficacy of this picture by relating electromagnetic turbulence simulated by BOUT++ to the Hénon map–a classical iterated equation from dynamical systems theory–through the concepts of horseshoes, and homoclinic tangles. Then, to better approximate the spatiotemporal complexity of turbulence, the Hénon map is elevated to a field theory and treated in spacetime. Applying this chaotic field-theoretic approach to a reduced model of plasma turbulence provides a framework for computing turbulence observables, including the average turbulence spreading.
To extend the applicability of this framework, computer vision techniques are used to determine the weights of the exact solutions in the forest of plasma turbulence. This is accomplished by building graph representations of full solutions, and rigorously comparing them to the periodic solution backbone of the aforementioned reduced model. The introduction of computer vision techniques circumvents key practical difficulties of this framework, enabling its extension to more realistic turbulence models.
[1] P. Cvitanović (2013).
[2] Xu Chu et al. (2022).
[3] M. Kobayashi et al. (2022).
Characterization: 4.0
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