Phases and phase-transitions in quasisymmetric configuration space

Topology-mediated approach to the design of quasisymmetric stellarators

“…To represent them all in the same phase space, the magnetic axis harmonics are rescaled as R4n = RnN (1 + n 2 N 2 )/(1 + 16n 2 ). 24 The typical designs lie close to the bands of good quasisymmetric quality. The black lines represent phase transition curves for Rn = Zn.…”

“…We demonstrate that this approach reproduces existing designs in a more economical and reduced parameter space and furthermore, elucidates the structure of a 'phase space' in which 'phase transitions' separate QA and QH designs. 24 In the process, we are able to identify potentially attractive, entirely unexplored regions of designs, discussed below.…”

“…We start from the zeroth-order in the model, which describes configurations by the shape of the magnetic axis. 24 Identifying configurations with spatially closed curves at the outset endows configuration space with a structure missing in the conventional approach. The space becomes separated into distinct topological regions identified with different forms of QS, which we call quasisymmetric phases.…”

“…The dimensionality of the space will depend on the number of harmonics considered. Most typical quasisymmetric designs belong to a space spanned by two dominant harmonics (with R n ≈ Z n ) 24 .…”

“…1 shows the structure in the form of narrow branches of excellent QS and quasisymmetric phases and includes some well-known existing quasisymmetric designs. The phases are separated by phase transitions 24 (see black lines), close to which quasisymmetric designs are generally not practical because they involve very elongated cross-sections. In the QA phase (the phase that includes the origin), there is a dominant branch that grows from the origin in the positive a direction.…”