Seminario Geometría
Dynamical properties of magnetic field lines for fusion reactors using shape differentiation
Ponente: Robin Roussel (Sorbonne Université)Fecha: miércoles 02 de octubre de 2024 - 11:30Lugar: Aula Naranja, ICMAT
Resumen:
In this talk, we consider a shape differentiation problem for Poincaré maps of harmonic fields. We begin by defining the notion of harmonic fields in toroidal domains of \(\mathbb{R}^3\) which we motivate through a small introduction to magnetic confinement in stellarators. We then briefly present some existing literature on harmonic fields and related topics. After defining the notion of Poincaré maps for harmonic fields we are interested in, we then introduce the shape differentiation problem. The idea is to study how perturbations of the toroidal domain leads to changes in the Poincaré maps of the harmonic fields at first order. Afterwards, we state a general shape differentiation result for the Poincaré maps of harmonic fields and give some elements of the proof. We then consider two specific cases for the study of the shape derivative; axisymmetric domains, and domains for which the harmonic field produces diophantine rotations on the boundary. We finally conclude by discussing a few open problems on this subject.
