May 8-10

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Abstracts

Author: Evan H. Toler
Requested Type: Poster
Submitted: 2023-03-29 16:52:38

Co-authors: A.J.Cerfon, D.Malhotra

Contact Info:
New York University
251 Mercer St.
New York, New York   10012
United States

Abstract Text:
To design and control magnetic confinement fusion reactors, one must compute the geometry of the confined plasma at equilibrium. We present a new method for solving the free-boundary equilibrium problem in tokamaks through integral equations and PDE-constrained optimization. We detail a formulation of the equilibrium equations that couples the Grad-Shafranov equation for the interior magnetic field with an integral equation for the exterior vacuum field. The computational domain is only the plasma domain and its boundary, which is parsimonious and reduces memory requirements. We introduce high order numerical methods for solving the associated integral equation, including a novel application of the Kapur-Rokhlin quadrature rule for singular integrals in axisymmetric magnetic confinement systems. Finally, we frame the coupled equations in the larger PDE-constrained optimization framework and present some gradient descent methods for the optimization iteration.

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