Type One Energy
Optimizing the geometry of magnetic fusion reactors
The purpose of this project is to identify, through numerical optimization, fusion reactor shapes which maximize the average pressure of the fusion fuel.
About Type One Energy
At Type One Energy Group, Inc., 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 goal of the project is to determine, via the application of local, global, and machine-learning based numerical optimization algorithms, the cross-sectional shapes of fusion reactors which maximize the average pressure of the fusion fuel. Since the average pressure is computed from the solution of a partial differential equation (PDE) describing force balance for the fusion fuel inside the reactor, this is a PDE constrained shape optimization problem.
The Type One Energy mentor will provide the complete description of the PDE to be solved and of the toroidal geometry we will work with. They will also provide Python examples of numerical solvers for the PDE of interest. The participants will therefore focus their efforts on the development of optimization algorithms for this shape optimization problem.
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!
If we make good progress on this project, it may become valuable to become familiar with Python-based automated frameworks for solving partial differential equations, such as Firedrake or FEniCS.
