stellarators

Stellarators are a proposed device for the magnetic confinement of plasma. The idea is to wrap the magnetic field lines in the shape of a torus. There are two types of toroidal confinement devices. The first is the widely studied tokomak in which the magnetic field lines exhibit axisymmetry. The second is the stellarator, in which axisymmetry is deliberately destroyed in order to generate a poloidal twist to better confine the magnetic particles in the stellarator. My work in this area is in collaboration with the Simons collaboration on Hidden Symmetries and Fusion Energy. There are many conjectures and interesting applications of mathematical theory to be found within the world of stellarator physics.

My most recent work includes:

• Reframing force-balance criteria and quasi-symmetry in terms of presymplectic geometry. Through this lens, we were able to establish the existence of so called magnetic axis coordinates (Burby et al., 2021).
• Relating the existence of flux surfaces to the notion of a conformal symmetry (Perrella et al., 2023).
• Understanding when magnetic fields can be considered as non-autonomous Hamiltonian systems (Duignan et al., 2024)
• Describing the use of Birkhoff–Gustavson normal form theory for toroidal magnetic field configurations in the neighborhood of a magnetic axis. We exemplify the process through an application to Beltrami (or force-free) magnetic fields. (Duignan & Meiss, 2021).
• An investigation of a new property of magnetic fields, isoprominence, which limits type transitions for guiding centre motions. (Burby et al., 2023)
• Recasting the theory of quasi-symmetry into that of integrable systems, ultimately showing that quasi-symmetric fields form a super-integrable system.
• Investigations into the existence of quasi-symmetric and magneto-hydro-static magnetic fields (Cardona et al., 2024).
• Developing measures of integrability for confinement devices. See measuring integrability.