Towards Differentiable, Structure-Preserving Magnetic Relaxation
Dr. Tobias Blickhan
, New York University
Abstract:
The magnetohydrodynamic equilibrium condition in a plasma can be characterized as the first-order stationarity condition of an energy minimization problem under constraints. This fact has been used as a basis for numerical methods to compute equilibria in codes such as high-beta stellarators (BETA 1978), Spanish Initiative for Electronic Simulations with Thousands of Atoms (SIESTA, 2011), and more. A promising feature of these formulations is that they do not rely on the assumption of nested flux surfaces. This talk will discuss ongoing work on an equilibrium solver with the following emphasis:
- Central constraints of the problem (preservation of helicity and divergence of the magnetic field) hold discretely when using structure-preserving finite element methods.
- Tools from Isogeometric Analysis, in particular so-called polar splines, allow doing so also in non-trivial, toroidal geometry. The structure preservation is crucial to avoid numerical dissipation effects that lead to un-physical or trivial solutions.
- Implementation in the just another accelerated linear algebra (JAX) ecosystem yields differentiable, portable, graphics processing unit (GPU) accelerated code. Besides the obvious benefits in speed, this allows researchers to work towards embedding the relaxation solver in an outer optimization loop to design the shape of the equilibrium field.
Speaker’s Bio:
Dr. Tobias Blickhan is a Faculty Fellow at the Courant Institute, New York University. He completed his Ph.D. in mathematics at the Technical University of Munich and the Max-Planck Max Planck Institute for Plasma Physics, working with Eric Sonnendrücker. His research focuses on reduced order modeling for parametrized partial differential equations and structure-preserving numerics with applications in plasma physics.
