A new multigrid solver for stellarator neoclassical transport

Solution of the drift kinetic equation [1] is a required step in analyzing and optimizing neoclassical transport in stellarators. We have developed a new neoclassical code that offers high fidelity solutions capturing as much of the physics as possible, while being significantly faster and more memory efficient than existing high fidelity codes. We do this by making use of novel stable finite difference discretizations combined with a multigrid method to solve the resulting linear system. Automatic differentiation is used to obtain derivatives for use in optimization. Applications are discussed including self consistent optimization of the bootstrap current and optimization of “electron root” plasmas [2].

References

[1] R. D. Hazeltine, “Recursive derivation of drift-kinetic equation,” Plasma Physics, 1973

[2] Neto, E. Lascas, et al. "Electron root optimisation for stellarator reactor designs." Journal of Plasma Physics, 2025