1. 8 Feb 99Quasi-symmetry - Boyd Blackwell1 Quasi Symmetric Stellarators Boyd 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

2. 8 Feb 99Quasi-symmetry - Boyd Blackwell2 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| 2 spectra in terms of  =  B.dl

3. 8 Feb 99Quasi-symmetry - Boyd Blackwell3 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  ~  indep t –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 

4. 8 Feb 99Quasi-symmetry - Boyd Blackwell4 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

5. 8 Feb 99Quasi-symmetry - Boyd Blackwell5 The (US)NCSX, a QAS machine Garabedian’s concept 3 Field period saddle coil for PBX

6. 8 Feb 99Quasi-symmetry - Boyd Blackwell6 Flexibility in transform –optimum path may be “along field lines” in Boozer spectrum

7. 8 Feb 99Quasi-symmetry - Boyd Blackwell7 QAS Design studies simple elements for flexibility

8. 8 Feb 99Quasi-symmetry - Boyd Blackwell8 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

9. 8 Feb 99Quasi-symmetry - Boyd Blackwell9 Comparison of helical flexibility windings

10. 8 Feb 99Quasi-symmetry - Boyd Blackwell10 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 Real Time 3D B Field and Surface Calculations

11. 8 Feb 99Quasi-symmetry - Boyd Blackwell11 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.