1. Blackwell, GEM XV Conference 2/2008 The Effects of Plasma Shape on Stability and Confinement in the H-1NF Heliac. B. D. Blackwell, D.G. Pretty, J. Howard, D.R. Oliver, S.T.A.Kumar, G. Potter, F. Detering, D. Byrne, C.A. Nuhrenberg*, M. McGann, R.L. Dewar, M.J. Hole, M. Hegland and **J.H. Harris Australian National University, *Max Planck IPP Greifswald, and **Oak Ridge National Laboratory

2. Outline H-1 Heliac Configurations, parameters, diagnostics MHD Data Data mining, SVD Interpretation Alfvénic Scaling H-1’s unique twist control as an additional fit parameter Scaling discrepancies Radial Structure Confinement Effects Summary

3. Blackwell, GEM XV Conference 2/2008 H-1NF: National Plasma Fusion Research Facility A Major National Research Facility established in 1997 by the Commonwealth of Australia and the Australian National University Mission: Detailed understanding of the basic physics of magnetically confined hot plasma in the HELIAC configuration Development of advanced plasma measurement systems Fundamental studies including turbulence and transport in plasma Contribute to global research effort, maintain Australian presence in the field of plasma fusion power The facility is available to Australian researchers through the AINSE 1 and internationally through collaboration with Plasma Research Laboratory, ANU. 1) Australian Institute of Nuclear Science and Engineering International collaboration played an important role in the success of H-1 in obtaining facility funding Contract extended until 2010: includes some operational funding and limited collaborative funding

4. Blackwell, GEM XV Conference 2/2008 H-1 CAD

5. Blackwell, GEM XV Conference 2/2008 H-1NF Photo

6. Blackwell, GEM XV Conference 2/2008 H-1 Heliac: Parameters 3 period heliac: 1992 Major radius1m Minor radius0.1-0.2m Vacuum chamber33m 2 excellent access Aspect ratio5+ toroidal Magnetic Field  1 Tesla (0.2 DC) Heating Power0.2MW 28 GHz ECH 0.3MW 6-25MHz ICH Parameters: achieved to date :: expected n3e18 :: 1e19 T<200eV(T e ) :: 500eV(T e )  0.1 :: 0.5%

7. Blackwell, GEM XV Conference 2/2008 H-1 configuration (shape) is very flexible “flexible heliac” : helical winding, with helicity matching the plasma,  2:1 range of twist/turn H-1NF can control 2 out of 3 of transform (  ) magnetic well and shear  ( spatial rate of change) Reversed Shear  Advanced Tokamak mode of operation Edge Centre low shear medium shear  = 4/3  = 5/4

8. Blackwell, GEM XV Conference 2/2008 Large Device Physics on H-1 Confinement Transitions, Turbulence (Shats, 1996--) –High Confinement mode (’96) –Zonal Flows 2001 –Spectral condensation of turbulence 2005 Magnetic Island Studies –H-1 has flexible, controlled and verified geometry –Create islands in desired locations (shear, transform) –Langmuir probes can map in detail Alfvén Eigenmodes –May be excited in reactors by fusion alphas, and destroy their confinement –(more) D3D tokamakH-1

9. Blackwell, GEM XV Conference 2/2008 Plasma Production by ICRF ICRF Heating: B=0.5Tesla,  =  CH (f~7Mhz) Large variation in n e with iota Backward Wave Oscillator Scanning Interferometer (Howard, Oliver) Axis time

10. Blackwell, GEM XV Conference 2/2008 Configuration scan: rich in detail ICRF plasma configuration scan Mode spectrum changes as resonances enter plasma No simple explanation for “gap” left side corresponds to zero shear at resonance A clear connection with rational twists per turn – but what is it? 5/45/4 4/34/3 7/57/5 5/45/4 4/34/3 7/57/5 gap D. Pretty, J. Harris Plasma density increasing twist 

11. Magnetic fluctuations approach “high temperature” conditions: H, He, D; B ~ 0.5T; n e ~ 1e18; T e > conn spectrum in excess of 5-100kHz Low mode numbers: m ~ 0 - 7, n ~ 0 - 9  b/B ~ 2e-4 both broad-band and coherent/harmonic nature abrupt changes in spectrum randomly or correlated with plasma events

12. Python open source datamining tools David Pretty: http://code.google.com/p/pyfusion

13. Blackwell, GEM XV Conference 2/2008 Magnetic Probe Array  Poloidal mode number measurements Two “bean-shaped” 20 coil Mirnov arrays Phase vs poloidal angle is not simple –Magnetic coordinates –External to plasma Propagation effects Large amplitude variation Significant interpretation problem in advanced confinement configurations Expected for m =2 phase magnitude coil number (azimuthal angle )

14. Blackwell, GEM XV Conference 2/2008 Identification with Alfvén Eigenmodes: n e Coherent mode near iota = 1.4, 26-60kHz, Alfvénic scaling with n e m number resolved by bean array of Mirnov coils to be 2 or 3. V Alfvén = B /  (  o  )  B /  n e Scaling in  n e in time (right) and over various discharges (below) phase 1/ne1/ne nene f  1 /  n e Critical issue in fusion reactors: V Alfvén ~ fusion alpha velocity  fusion driven instability!

15. Blackwell, GEM XV Conference 2/2008 Mode Decomposition by SVD and Clustering Initial decomposition by SVD  ~10-20 eigenvalues Remove low coherence and low amplitude Then group eigenvalues by spectral similarity into fluctuation structures Reconstruct structures to obtain phase difference at spectral maximum Cluster structures according to phase differences (m numbers)  reduces to 7-9 clusters for an iota scan Grouping by SVD+clustering potentially more powerful than by mode number –Recognises mixtures of mode numbers caused by toroidal effects etc –Does not depend critically on knowledge of the correct magnetic theta coordinate 4 Gigasamples of data –128 times –128 frequencies – 2 C 20 coil combinations –100 shots Data miningincreasing twist 

16. Mode numbers consistent with twist Mode analysis of the clusters found is complex, but is consistent with the rotational transform (twist/turn) dominant azimuthal m=3 dominant toroidal mode n=4 (aliased to n=1) Iota=4/3

17. Blackwell, GEM XV Conference 2/2008 Identification with Alfvén eigenmodes: k ||, twist Why is f so low? V Alfven ~ 5x10 6 m/s  res = k || V Alfvén = k || B /  (  o  ) k || varies as the angle between magnetic field lines and the wave vector for a periodic geometry the wave vector is determined by mode numbers n,m Component of k parallel to B is   - n/m k || = (m/R 0 )(  - n/m)  res = (m/R 0 )(  - n/m) B /  (  o  ) Low shear means relatively simple dispersion relations – advantage of H-1 Alfvén dispersion (0-5MHz) Near rationals, resonant freq. is low Alfvén dispersion (0-50kHz) Small near resonance

18. Blackwell, GEM XV Conference 2/2008 Identification with Alfvén eigenmodes k ||  0 as twist  n/m  res = k || V A = (m/R 0 )(  - n/m) B /  (  o  ) k || varies as the angle between magnetic field lines and the wave vector k ||   - n/m iota resonant means k ||,   0 Expect F res to scale with  iota David Pretty Resonant   ota   = 4/3 Twist 

19. Blackwell, GEM XV Conference 2/2008 Two modes coexisting at different radii Cross-power between n e and Mirnov coils shows two modes coexisting (0,180 o ) Probably at different radii as frequency is different, mode numbers the same

20. Blackwell, ISHW/Toki Conference 10/2007 CAS3D: 3D and finite beta effects Carolin Nuhrenberg Beta induced gap ~5-10kHz Coupling to “sound mode” Gap forms to allow helical Alfven eigenmode, and beta induced gap appears at low f

21. Helical Alfvén eigenmode Good scaling with n e, Correction is ~ 0.7 – typical of 3D effect David Pretty Helical gap mode likely at coalescence of 7/5 and 10/7 as n 1 -n 2 3 = m 1 -m 2 2 n=10, m=7 n=7, m=5

22. Blackwell, GEM XV Conference 2/2008 Radial Mode Structure Jesse Read 865 poster today Radius configuration phase Cross-power between light emission and Mirnov coils shows phase flips in radius and configuration

23. Blackwell, GEM XV Conference 2/2008 Scaling discrepancies  res = k || V Alfvén = k || B /  (  o  ) Numerical factor of ~ 1/3 required for quantitative agreement near resonance –Impurities (increased effective mass) may account for 15-20% –3D MHD effects ~ 10-30% (CAS3D), still a factor of 1/1.5-2x required Magnetic field scaling is unclear Unknown drive physics –V Alvfen ~5e6 m/s – in principle, H+ ions are accelerated by ICRH, but poor confinement of H+ at V A (~40keV) makes this unlikely. –Electron energies are a better match, but the coupling is weaker. –H+ bounce frequency of mirror trapped H+ is correct order?

24. Blackwell, GEM XV Conference 2/2008 Alfven Spectroscopy – potential as diagnostic Potential to be iota diagnostic (if shear low) Original iota calibration at reduced field Corrected iota agrees better with dispersion Santhosh Kumar Transform decreases by 0.5% at high field  iota  I 2 1.400 iota 1.408  discrepancy halved

25. Effect of Magnetic Islands Giant island  “flattish” density profile Central island – tends to peakPossibly connected to core electron root

26. Blackwell, GEM XV Conference 2/2008 Several Configurational effects demonstrated: –Confinement, magnetic fluctuations spectra Alfvénic modes observed Data mining – unsupervised reduction into significant clusters New Diagnostics (J. Howard Thurs PM) H-1 National Facility –Configurational flexibility –Large device physics accessible Confinement Transitions, Alfvén Eigenmodes, Magnetic Islands –Test Bed for Advanced Diagnostic Development, e.g. to develop reactor edge plasma diagnostics Alfvénic modes observed –H-1’s unique “twist” control is a valuable diagnostic parameter, especially at low shear –Increased dimensionality of data space is handled by datamining –Strong evidence for Alfvénic scaling between n e, k ||, f –Unclear B scaling (resonant plasma production), frequency is low by a factor of ~ 1.5 - 3. –Interferometer and PMT array  valuable mode structure information –Currently David Pretty is applying technique to data at Heliotron J (Kyoto), TJ-II (Madrid) and W7-AS (Max Planck IPP) –“Alfven Spectroscopy” an emerging field, information about rotational transform –Confinement inside magnetic islands is very interesting! Summary See also Posters today Jesse Read 865 Frank Detering 856 Jesse Read 865

27. Blackwell, GEM XV Conference 2/2008 Mode Structure: 2mm interferometry Mode simulated by rotating m=4 Fourier Bessel object in magnetic coordinates Howard, Byrne, Oliver m=4 simulation Measured projections near iota=5/4 (line integrated electron density) Average minor radius Height above magnetic axis (Note: this radial profile is as much indicative of the azimuthal structure as it is of the radial mode structure)

28. Blackwell, GEM XV Conference 2/2008  ota   = 4/3

29. Blackwell, GEM XV Conference 2/2008 Data Mining Classification by Clustering Full dataset See Frank Detering, D. Pretty, Wednesday 9:30

30. Blackwell, GEM XV Conference 2/2008 Closer inspection  radial location Better fit of frequency to iota, n e obtained if the location of resonance is assumed be either at the zero shear radius, or at an outer radius if the associated resonance is not present. David Pretty Assumed mode location  ~ 5/4

31. Blackwell, GEM XV Conference 2/2008 Helical Alfvén eigenmode Good scaling with n e, Correction is ~ 0.7 – typical of 3D effect David Pretty Helical gap mode likely at coalescence of 7/5 and 10/7 as n 1 -n 2 3 = m 1 -m 2 2 n=10, m=7 n=7, m=5

32. Blackwell, GEM XV Conference 2/2008 Beta-induced Alfvén eigenmodes? At low beta in H-1 (10 -4 ), the beta- induced gap is in the range 5-10kHz. This is within the range of the modes near resonance, when iota-n/m is small Beta induced gap scales with temperature rather than magnetic field  interactions between the beta induced gap and Alfvén continuum could help explain the ambiguous B dependence. Scaling of f ~n/m (not  - n/m ) does not explain frequency dependence on . Evidence of electrostatic modes, but not at resonance where GAM-like behaviour may be expected. 10kHz

33. Blackwell, GEM XV Conference 2/2008 Alfvén eigenmode frequency: radial variation  res = k || V A = (m/R 0 )(  - n/m) B /  (  o  ) Iota ~ 7/6 just below iota ~ 5/4 Global mode possible Gap mode possible HAE gap likely as n 1 -n 2 3 = m 1 -m 2 2 iota ~ 4/3