Quasi Symmetric Stellarators Boyd Blackwell, ANU

1. Quasi Symmetric StellaratorsBoyd Blackwell, ANU • History of Stellarator Optimisation • sigma optimisation, j|| minimisation • Quasi-Symmetry • QHS, QAS, QOS, QBS • The (US)NCSX, a QAS machine • Flexibility • in transform and spectrum • Real Time Surface Calculations • QAS Design studies Quasi-symmetry - Boyd Blackwell

2. Introduction • Stellarator: magnetic surfaces generated entirely by currents external to plasma • Nested magnetic surfaces • magnetic field cover nested surfaces before closing on themselves • Rotational transform: twist per turn (=1/q), generated by: • axially rotating multipole fields (torsatron/stell.) • axially rotating magnetic axis (heliac/helias) • Magnetic Coordinates: curvilinear coord. system in which field lines are straight • Boozer - Jacobian = 1/|B|2spectra in terms of =B.dl Quasi-symmetry - Boyd Blackwell

3. Optimisation: brief history • first device - figure 8 stellarator • finding/maximizing surfaces - ‘60s-‘70s • transform improves Eq. and Stab. • low order fields/symmetries reduce islands • transport optimisation • 1980-2: sigma optimisation reduces 1/ transport (helical pitch modulation) (single periodicity) • modular windings • j|| minimisation  ~ indept • W-7AS, 1983 • separation of physics and coil design(Merkel, 1987)W7-X, 1991 • quasi helical symmetry • Nuhrenberg and Zille, 1988 • quasi axisymmetry • Garabedian 1996( quasi isodynamicity/omnigeneity/bumpy...)  collisionality Quasi-symmetry - Boyd Blackwell

4. Quasi-Symmetry • QHS, QAS, QOS, QBS • W7X- beta indep • QO - alpha indep • need helical -> iota • single periodicity -> transport • QAS for low aspect ratio • Fourier c.f. Spatial Optimisation -Boozer paper 1997 Quasi-symmetry - Boyd Blackwell

5. The (US)NCSX, a QAS machine Garabedian’s concept 3 Field period saddle coil for PBX Quasi-symmetry - Boyd Blackwell

6. Flexibility • in transform • optimum path may be “along field lines” • in Boozer spectrum Quasi-symmetry - Boyd Blackwell

7. QAS Design studies • simple elements for flexibility Quasi-symmetry - Boyd Blackwell

8. Conforming Stellarator Flexibility Winding • L=2, M=1 stellarator winding shown in relation to the plasma to which it conforms.The main saddle coils are omitted for clarity Quasi-symmetry - Boyd Blackwell

9. Comparison of helical flexibility windings Quasi-symmetry - Boyd Blackwell

10. Real Time 3D B Field and Surface Calculations • Application: heliac configuration studies and QAS flexibility winding studies • 3D spline calculation of B from large arrays (~100MB) • linear combination of arrays for TFC, Ring provide instant adjustment of current ratios and configurations • variable geometry conductors not allowed, but simplified model can be evaluated on top of accurate model of the rest of the geometry. • Traces at ~20K steps/second  surfaces in secs. • BLINE code by Antony Searle • Demonstration at Remote Data Access Poster Quasi-symmetry - Boyd Blackwell

11. Conclusions • Quasi helical symmetry consistent with high transform and good orbits. • Quasi axi-symmetry consistent with low aspect ratio, but requires internal currents to generate enough transform - at high pressure, these currents are approximated by the bootstrap current • QO is a weaker condition than QA, QH • QO optimization of QAS? Best of both? • Flexibility is possible with Qsym, but often other parameters degrade (esp. symmetry) • H-1NF has comparable helical and toroidal components (mixed helicity), but is optimised for flexibility. Quasi-symmetry - Boyd Blackwell