Type One Energy
Efficient computation of Taylor relaxed equilibria in stellarators
About Type One Energy
At Type One Energy Group, we are developing optimized stellarator designs to provide sustainable, affordable fusion power to the world. We apply proven advanced manufacturing methods, modern computational physics and high-field superconducting magnets to pursue the lowest-risk, shortest-schedule path to a fusion power plant over the coming decade.
The Problem
The purpose of the project is to expand the suite of numerical codes we rely on to design and analyze the performance of our fusion reactors. Specifically, we will explore a new framework for computing the magnetic steady states in our reactors.
An efficient and predictive approach to describing the magnetic field of stellarator steady states is to decompose the stellarator into subregions in which the magnetic field is in Taylor relaxed states, satisfying Beltrami’s equation. We will therefore investigate the possibility of using an automated framework for solving partial differential equations, such as Firedrake or FEniCS, to compute Beltrami’s equation in three-dimensional toroidal geometries, and replace our existing legacy codes for these applications.
For this project, we will provide the complete description of the partial differential equation to be solved and the toroidal geometry we will work with. We will also provide examples of solutions for the two-dimensional version of the problem with the FEniCS framework. The participants will develop a method for meshing the three-dimensional domain, for expressing the Beltrami partial-differential equation in the desired format for the automated PDE framework, and solve the problem in the three-dimensional toroidal geometry of interest.
Skillset
The project requires a good command of standard numpy tools and programming practices in Python. It also requires a good understanding of elementary partial differential equations (e.g. the first 4 chapters of Evans’ PDE textbook) and a good understanding of elementary numerical analysis / scientific computing. No prior knowledge of fusion or plasma physics is required. We will be happy to teach participants as much about fusion and plasma physics as they would like to learn!
To make this project tractable, we will rely on Python-based automated frameworks for solving partial differential equations, such as Firedrake or FEniCS.
