1. Results from Helical Axis Stellarators Boyd Blackwell, H-1 National Facility Australian National University Thanks to: Enrique Ascasibar and TJ-II Group Prof. Obiki and Heliotron-J Group David Anderson and HSX Crew and the H-1 Team

2. Outline Acknowledgements: TJ-II, Heliotron-J, HSX and H-1 groups for their contributions and access to their data, in particular C. Alejaldre, E. Ascasibar, C. Hidalgo, T. Obiki, K. Nagasaki, D.T. Anderson, J.H.Harris, M.G. Shats, J. Howard, Nyima Gyaltsin, S. M. Collis and D.L. Rudakov. Brief history Comparative parameters magnetic surfaces plasma formation and heating diagnostic issues Transport Stability fluctuations

3. Spitzer 1951 Spitzer 1951 - figure-8 stellarator  “spatial axis” which produces rotational transform magnetic hill  unstable to interchange Koenig 1955 Koenig 1955 - helical winding/axis: = 1  one pair of helices Spitzer 1956 Johnson et al 1958 Spitzer 1956  possibility of shear stabilization for higher order windings = 2,3 demonstrated theoretically (resistivity  0) Johnson et al 1958 Furth, Killeen, Rosenbluth 1963 Furth, Killeen, Rosenbluth 1963 found resistive interchange instability possible even at low resistivity for small scale lengths 1964-5 several configurations proposed with magnetic well (average minimum B) found including heliac (straight). Exploitation of avg. min B  regions of bad curvature  possible ballooning instability Development of Helical Axis Stellarators -I +I = 1 

4. Nagao 1977 Nagao 1977 Asperator NP: toroidal helical axis stellarator (+extra helical windings) Yoshikawa... 1982-4 Yoshikawa... 1982-4 - toroidal heliac HX-1 proposal Blackwell, Hamberger... 1984 Harris.. 1985 Blackwell, Hamberger... 1984 - SHEILA prototype heliac (0.2M, 0.2T, 10 19 m 3 ) Harris.. 1985  flexible heliac: = 1 winding varies iota, well over large range 1985Ribe’s 1985 - Tohoku, H-1 and TJ-II and heliacs proposed - and Ribe’s linear heliac UW - Operation in 1987 (Tohoku, Sendai) 1992 (H-1) and 1996(TJ-II, Spain) 1988 Nuhrenberg and Zille - 1988 Nuhrenberg and Zille - quasi-helical symmetry - restore outstanding features of straight heliac. [transport, beta limit(Monticello et. al 1983)] 1996-9 1996-9 Heliotron-J - combine heliotron/torsatron with advances in transport (optimise bumpy cpt, quasi-isodynamic) 1999 H elically S ymmetric E X periment 1999 H elically S ymmetric E X periment first quasi-symmetric experiment exploit high iota, N-m  scaling Development of Helical Axis Stellarators II

5. Canberra, Australia external vacuum vessel CIEMAT, Madrid internal vessel, upgrade to NBI IAE Kyoto “ inverted heliac” bumpy field cpt TSL, Madisoncontrolled “spoiling” of symmetry. Device Type Aspect Iota H-1 Heliac H-1 Heliac 3 period heliac, toroidal > helical 5 .15 TJ-II Heliac TJ-II Heliac 4 period heliac, helical > toroidal 7  0.9-2.2 Heliotron J Heliotron J helical axis heliotron (TFC + =1) 7-110.2-0.8 HSX HSX modular coils, helical symmetry 81.05-1.2 Helical Axis Stellarators 2000 b n,m

6. Canberra, Australia external vacuum vessel CIEMAT, Madrid internal vessel, upgrade to NBI IAE Kyoto “ inverted heliac” bumpy field cpt TSL, Madisoncontrolled “spoiling” of symmetry. Device Type Aspect Iota H-1 Heliac H-1 Heliac 3 period heliac, toroidal > helical 5 .15 TJ-II Heliac TJ-II Heliac 4 period heliac, helical > toroidal 7  0.9-2.2 Heliotron J Heliotron J helical axis heliotron (TFC + =1) 7-110.2-0.8 HSX HSX modular coils, helical symmetry 81.05-1.2 Helical Axis Stellarators 2000 b n,m Brief history Comparative parameters magnetic surfaces Heliotron J and HSX plasma formation and heating diagnostic issues Transport Stability fluctuations

7. Device Parameters of Heliotron J Coil System L=1/M=4 helical coil 0.96MAT Toroidal coil A0.6MAT Toroidal coil B 0.218MAT Main vertical coil 0.84MAT Inner vertical coil0.48MAT Major radius 1.2m Minor radius of helical coil 0.28m Vacuum chamber2.1m 3 Aspect ratio7 Port65 Magnetic Field1.5T Pulse length 0.5sec Pitch modulation of helical coil Inner Vertical Coil Toroidal Coil A Outer Vertical Coil Toroidal Coil B Helical Coil Plasma Vacuum Chamber

8. The Heliotron J Device Main VFC TFC-A TFC-B Aux.VFC HFC

9. Magnetic Surface Mapping Fig.3 The magnetic surfaces at  = 67.5  in the standard configuration. (a) The experimental results (corrected) and (b) The calculated magnetic surfaces. (a) (b) STD config, 0.03 Tesla, corrected for earth’s field

10. Configuration “A” is designed to create a helical divertor region shown in red and yellow. The position of the plasma is shown relative to the helical conductor and the vacuum vessel Other configurations island divertor standard from T. Mizuuchi, M. Nakasuga et al. Stellararor Workshop 1999 Heliotron-J surfaces: cfg “A” - helical divertor

11. Helically Symmetric Experiment UW, Madison R = 1.2 a=0.15 B0=1.3T4 periods iota 1.05-1.12well ~1% essentially 1 term in B 0 spect 28GHz@200kW n e ~3e12 for 50kW@0.5T HSX Parameters

12. HSX Magnetic surfaces Good magnetic surfaces, iota ~ 1% accurate Drift surfaces coincide well with magnetic surfaces - low toroidal effects, high effective iota (  eff = N-m  )

13. HSX Magnetic surfaces Good magnetic surfaces, iota ~ 1% accurate Drift surfaces coincide well with magnetic surfaces - low toroidal effects, high effective iota (  eff = N-m  ) Measured drift surfaces mapped to Boozer coordinates Expected drift if fully toroidal

14. Canberra, Australia external vacuum vessel CIEMAT, Madrid internal vessel, upgrade to NBI IAE Kyoto “ inverted heliac” bumpy field cpt TSL, Madisoncontrolled “spoiling” of symmetry. Device Type Aspect Iota H-1 Heliac H-1 Heliac 3 period heliac, toroidal > helical 5 .15 TJ-II Heliac TJ-II Heliac 4 period heliac, helical > toroidal 7  0.9-2.2 Heliotron J Heliotron J helical axis heliotron (TFC + =1) 7-110.2-0.8 HSX HSX modular coils, helical symmetry 81.05-1.2 Helical Axis Stellarators 2000 b n,m Comparative parameters magnetic surfaces plasma formation and heating (H-1, HSX) diagnostic issues Transport

15. H-1 Heliac: Parameters 3 period heliac: 1992 Major radius1m Minor radius0.1-0.2m Vacuum chamber33m 2 excellent access Aspect ratio5+ toroidal Magnetic Field1 Tesla (0.2 DC) Heating Power0.2(0.4)MW GHz ECH 0.3MW 6-25MHz ICH Parameters: achieved / expected n3e18/1e19 T~100eV(T i )/0.5-1keV(T e )  0.1/0.5%

16. H-1 Heliac: Parameters 3 period heliac: 1992 Major radius1m Minor radius0.1-0.2m Vacuum chamber33m 2 Aspect ratio5+ Magnetic Field1 Tesla (0.2 DC) Heating Power0.2(0.4)MW GHz ECH 0.3MW 6-25MHz ICH Parameters: achieved / expected n3e18/1e19 T~100eV(T i )/0.5-1keV(T e )  0.1/0.5% Complex geometry requires minimum 2D diagnostic Cross-section of the magnet structure showing a 3x11 channel tomographic diagnostic

17. 2D electron density tomography coherent drift mode in argon, 0.08T H density profile evolution (0.5T rf) Helical axis  non-circular  need true 2D Raw chordal dataTomographically inverted data

18. HSX ECH Plasma Utilize 2 nd harmonic ECH at 28GHz to examine confinement of deeply-trapped electrons

19. Plasma production and heating: resonant and non- resonant RF 10 18 m -3 Non-resonant heating is flexible in B 0, works better at low fields. Resonant heating is much more successful at high fields. helicon/frame antenna  =  Ch on axis Magnetic Field (T)

20. radius Ion Temperature Camera Hollow Ti at low B 0 0102030 time (ms) Intensity temperature rotation

21. Canberra, Australia external vacuum vessel CIEMAT, Madrid internal vessel, upgrade to NBI IAE Kyoto “ inverted heliac” bumpy field cpt TSL, Madisoncontrolled “spoiling” of symmetry. Device Type Aspect Iota H-1 Heliac H-1 Heliac 3 period heliac, toroidal > helical 5 .15 TJ-II Heliac TJ-II Heliac 4 period heliac, helical > toroidal 7  0.9-2.2 Heliotron J Heliotron J helical axis heliotron (TFC + =1) 7-110.2-0.8 HSX HSX modular coils, helical symmetry 81.05-1.2 Helical Axis Stellarators 2000 b n,m diagnostic issues Transport confinement (Heliotron-J, TJ-II, H-1) Stability/Fluctuations

22. Heliotron-J: Confinement during ECH ECH 400kW 53GHZ 50ms ~ 0.2%, <20% radiated some Fe Ti C O impurities Plans: will upgrade to 70GHz, 500kW ultimately 4MW ~20kJ? impurity control explore bumpiness and hel. divertors Fig. 2 Dependence of the diamagnetic stored energy on the magnetic field strength. W-Diamagnetic vs B is peaked, 700J max Initial Plasma: 700J stored energy

23. TJ-II Heliac, CIEMAT, Spain R = 1.5 m, a < 0.22 m, 4 periods B 0 < 1.2 T P ECRH < 600 kW from 2 ECH systems P NBI < 3 MW under installation helium and hydrogen plasma T e ~ 2keV, low radiated powers (<20%) wall desorption rate limits operation in He at P< 600 kW Helical/central conductor

24. Helium plasmas with injected power of 300 kW Neoclassical Monte-Carlo agrees well  Inferred positive ambipolar E r, confinement time ~ 5ms ~ ISS95 yet no serious accumulation of impurities Thomson scattering

25. iota ~ 1.28 – 2.24, up to 1.2 x 10 19 m -3 and 2.0 keV Iota = 2 When corrected for volume changes, a positive dependence on iota is revealed in helium, (less in H) (tendency sim. to ISS95) Configuration Scan (iota)

26. Confinement transitions in H-1 “Pressure” (I s ) profile evolution during transition transition P RF (kW) B 0 (T) many features in common with large machines associated with edge shear in Er easily reproduced and investigated Parameter space map,  ~ 1.4

27. ExB and ion bulk rotation velocity in high confinement mode: magnetic structure causes viscous damping of rotation 0 0 V p, V t << V ExB ~ 1/(neB) dP i /dr Radial force balance Mass (ion) flow velocities much smaller than corresponding V ExB Bulk Rotation Damped in Heliac

28. diagnostic issues Transport Stability fluctuations Issues: Interchange and Ballooning Modes (DTEM low ) Tools:Configuration Flexibility e.g. transform and magnetic well (even hill!) First Impression: No unworkable instabilties or disruptions “ Drift-like” instability in H-1 at low field –Triple-Mach-Triple probe  –disappears as B increases Helical axis  high iota  short connection length All devices need  > 0.5-1% to test ballooning stability

29. TJ-II Turbulence/Fluctuation studies ExB sheared flows observed near edge rational surfaces (8/5, 4/2) Spectra mainly <200kHz, 10-40% (edge?), correlation time 10ms MHD (ELM-like) events (for W~1kJ) - magnetic activity - spike in the H  signal. Fluctuations increase with magnetic hill near edge resistive ballooning?

30. Summary - Future Confinement in heliacs ~ISS95 or better (2keV, ~5ms). Ion beam probe to elucidate role of E radial in improved confinement New configurations with improved neoclassical transport  initial results promising, await mature data, analysis HSX/H-J can compare similar configurations with vastly different neoclassical transport predictions. Confinement transitions possible at low power, many similarities with large devices/powers. Investigate effect of E-field imposed by localised ECH. No serious impurity accumulation problems yet.  Real test when the ions are strongly heated No fatal instabilities observed yet. Several devices should have the heating capacity to test ballooning limits, at least in degraded configurations (consequence of flexibility).