Magneto-Fluid Dynamics Seminar

Integrability, Normal Forms, and Magnetic Axis Coordinates

Speaker: Nathan Duignan, University of Colorado, Boulder

Location: Warren Weaver Hall 905

Date: Wednesday, April 21, 2021, 3 p.m.

Synopsis:

Integrable or near-integrable magnetic fields are prominent in the design of plasma confinement devices. Such a field is characterized by the existence of a singular foliation consisting entirely of invariant submanifolds. A regular leaf of this foliation, commonly known as a flux surface, must be diffeomorphic to the two-torus. In a neighborhood of a flux surface, it is known that the magnetic field admits several exact, smooth normal forms in which the field lines are straight. These coordinates include Boozer and Hamada coordinates. They are crucial to understanding the dynamics of charged particles in the magnetic field. However, these normal forms break down near singular leaves including elliptic and hyperbolic magnetic axes.

In this talk we will establish smooth normal forms for integrable magnetic fields near elliptic and hyperbolic magnetic axes. Ultimately, these results establish previously conjectured smoothness properties for smooth solutions of the magnetohydro-dynamic equilibrium equations. The key arguments are a consequence of a geometric reframing of integrability and magnetic fields; that they are presymplectic systems.

This is joint work with Joshua Burby and James Meiss.

Notes:

Note the special time: 3:00PM