Stuart Hudson
Princeton Plasma Physics Lab

Title: Can Constructing “Chaotic coordinates” Help to Understand Transport in Non-Integrable Dynamical Systems?

Abstract: The structure of the toroidal magnetic fields has a profound impact on transport in fusion energy plasmas. Understanding the nature of tangled and chaotic magnetic fields is hence of immense importance. It is also a formidable mathematical challenge. Magnetic field lines are trajectories of Hamiltonian systems, and in toroidally-symmetric geometries, such as a tokamak, the field can be described as an integrable Hamiltonian dynamical system. In such systems action-angle coordinates can be constructed. Perturbations about toroidal symmetry (which occur either by design or instability) generally destroy integrability. Periodic orbits survive, as do cantori, as well as “KAM” surfaces that have sufficiently irrational frequency. There will also be irregular “chaotic” trajectories. By “fitting” the coordinates to the invariant structures, action-angle coordinates may be generalized to non-integrable dynamical systems. These coordinates, based on almost invariant "ghost-surfaces" capture the invariant dynamics and neatly partition the chaotic regions. In this talk I show isotherms of the anisotropic diffusion equation coincide with ghost surfaces. This surprising and unexpected result suggests a deep connection between transport and the optimal selection of ghost surfaces.

Bio: Dr. Stuart R. Hudson is a staff research physicist in the Theory Department. After completing a Ph.D. in Theoretical Physics in the Department of Theoretical Physics at the Australian National University he joined the Theory Department of the Japan Atomic Energy Research Institute as a post-doctoral Research Fellow, and then joined the Center for Plasma Theory and Computation in the Department of Engineering Physics at the University of Wisconsin--Madison. He joined PPPL in 2001, and is frequently a Visiting Professor at the National Institute for Fusion Sciences in Japan.

Dr. S.R. Hudson studies three-dimensional (3D), magnetohydrodynamic (MHD) equilibria, and their stability, with both integrable and non-integrable magnetic fields. He contributed to the design of National Compact Stellarator Design (NCSX), for which iterative techniques were developed to eliminate magnetic islands in high-pressure, ideally-stable stellarator designs, under both fixed- and free-boundary conditions. Dr. S.R. Hudson is the developer of the Stepped Pressure Equilibrium Code (SPEC), which accurately computes 3D MHD equilibria by allowing for discontinuous solutions. Dr. S.R. Hudson studies the fractal structure of chaotic dynamical systems, and showed that cantori and ghost-surfaces play an important role in anisotropic transport in nearly-integrable magnetic fields.