Minimal Poincare Boundary Condition for 3D Ideal MHD Equilibria in DESC

We present a minimal Poincare boundary condition for solving 3D MHD equilibria, which is implemented in the DESC stellarator optimization code[1-4]. The fixed-boundary problem is often solved by specifying a toroidal surface as the LCFS BC, however, one can also specify a 2D toroidal cross-section as the BC and view the problem as a BVP in the toroidal angle as opposed to the radial coordinate. This approach is implemented in DESC, and offers new insights on uniqueness, as well as aid in optimization by reducing the number of variables required to represent the boundary. Results with this approach will be shown and compared to the conventional LCFS boundary method. A new metric for nested surfaces is also shown, based on the idea of re-solving a fixed boundary equilibrium using inner flux surfaces as the LCFS and comparing the resulting solution to the original equilibrium.

[1] Dudt and Kolemen, PoP (2020)

[2] Panici et al, arXiv:2203.17173 [under review in Nuclear Fusion] (2022)

[3] Conlin et al, arXiv:2203.15927 [under review in Nuclear Fusion] (2022)

[4] Dudt et al, arXiv:2204.00078 [under review in Nuclear Fusion] (2022)