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Plasma Physics (Physics/ECE/NE 922) Seminar
Optical analogy for stellarators: Ridges as caustics and coils as singularities
Date: Monday, February 23rd
Time: 12:00 pm - 1:00 pm
Place: Engineering Hall - 1227
Speaker: Dr. Wrick Sengupta , Princeton Plasma Physics Laboratory
Abstract: Abstract: A common feature of most numerically optimized stellarator geometries is the presence of sharp ridges on flux surfaces, irrespective of the rotational transform. Despite their importance, an analytical theory for their existence has been lacking. In this work, we demonstrate that ridges are not artifacts but mathematical necessities. We develop such a theory for devices with quasi-axisymmetry (QA). We demonstrate that QA exhibits close connections with the theory of geometrical optics, following Parker's ``optical analogy" (E.N. Parker 1989). By mapping vacuum QA to the eikonal equation of geometrical optics, we derive the conditions for ridge formation, identified as caustics where magnetic field lines focus. Furthermore, we prove a rigorous geometric theorem for stellarator coil design: filamentary coils must lie on the zero-determinant manifold of the magnetic gradient tensor. This topological constraint unifies the description of plasma ridges and external coils, providing a precise criterion for identifying valid coil locations and explaining the efficacy of the magnetic gradient (LgradB) norm as a coil optimization parameter. We demonstrate that as the device becomes more compact, sharp ridges naturally form on the inboard side in QA. We support our analytical theory with extensive numerical evidence.

Bio: I am interested in the theoretical aspects of plasma physics, particularly kinetic theory and magnetic confinement. I develop analytically tractable reduced models to provide insight into nonlinear interactions and geometry in confined plasmas. I focus on magnetic fields with hidden quasisymmetry, which could benefit next-generation stellarators, and I also explore plasma turbulence using solvable models.
PhD (2016) in plasma physics from the University of Maryland. Advisor: Adil Hassam, co-advisors: Bill Dorland, Tom Antonsen.
Post doc (2016-2021): Courant Institute of Mathematical Sciences. PI: Harold Weitzner and Antoine Cerfon
Associate Research Scientist (2021 - present): Department of Astrophysical Sciences, Princeton University, PI: Amitava Bhattacharjee

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