Matt Landreman, a physicist at the startup Type One Energy, has published two families of analytical solutions for magnetohydrodynamic equilibrium equations on arXiv. These findings challenge the 59-year-old hypothesis proposed by Harold Grad in 1967, which suggested that smooth three-dimensional equilibria with non-constant plasma pressure could not exist without additional symmetry.
Unlike tokamaks, stellarators rely entirely on external coils to confine plasma. The existence of nested magnetic surfaces in 3D geometry was previously questioned, but Landreman provided explicit formulas for field, current, pressure, and surface shapes. The solutions were derived using the GPT-6 Astra Pro language model and subsequently verified through manual calculation and the VMEC numerical code.
The first family of solutions describes a configuration where field lines close after two rotations, while the second includes surfaces with infinitely winding lines, mirroring practical reactor conditions. These results remove a major conceptual barrier in plasma physics, confirming that highly asymmetric equilibria with ideal flow surfaces are mathematically possible.
The research provides benchmark tests for numerical codes used in reactor design. Landreman has made the verification scripts publicly available. While questions regarding vortex-free fields and exact quasi-symmetry remain, this work overcomes one of the oldest mathematical obstacles in the field of fusion energy research.
