Precise quasisymmetry together with MHD stability at reactor pressure
In plain words
Quasisymmetry is a hidden symmetry of the field strength that makes particles in a 3D stellarator move as if in a symmetric machine, and it has been achieved almost exactly in vacuum fields. Whether it can be kept while the plasma pressure is high enough for a reactor and the plasma stays stable is unknown.
Precise statement
Quasisymmetry ($\left|B\right|$ depending on flux-surface angles only through one fixed linear combination) was achieved in vacuum with symmetry-breaking amplitude about 5e-5 of the field strength (about $0.5\,\mathrm{G}$ in a $1\mathrm{e}4\,\mathrm{G}$ field; Landreman and Paul, 2022). Determine whether equilibria exist with quasisymmetry error below 1e-3, volume-averaged $\beta$ of at least $5\,\mathrm{percent}$, ideal-MHD ballooning and kink stability, and nested flux surfaces, and map the trade-off frontier between these quantities. An answer is explicit configurations or a demonstrated frontier.
What would settle it
Published equilibria verified by independent equilibrium and stability codes, or a systematic frontier showing incompatibility.
Status in the literature
Finite-$\beta$ precisely quasisymmetric equilibria were reported after 2022; simultaneous stability at reactor $\beta$ is not established.