1. Kinetic Alfvén waves driven by rotating magnetic islands K. L. Wong, K. Tritz, D. R. Smith, Y. Ren, E. Mazzucato, R. Bell, S. Kaye, K. C. Lee NSTX Physics Meeting LSB318, PPPL Feb 1, 2010 NSTX Supported by College W&M Colorado Sch Mines Columbia U CompX General Atomics INEL Johns Hopkins U LANL LLNL Lodestar MIT Nova Photonics New York U Old Dominion U ORNL PPPL PSI Princeton U Purdue U SNL Think Tank, Inc. UC Davis UC Irvine UCLA UCSD U Colorado U Illinois U Maryland U Rochester U Washington U Wisconsin Culham Sci Ctr U St. Andrews York U Chubu U Fukui U Hiroshima U Hyogo U Kyoto U Kyushu U Kyushu Tokai U NIFS Niigata U U Tokyo JAEA Hebrew U Ioffe Inst RRC Kurchatov Inst TRINITI KBSI KAIST POSTECH ASIPP ENEA, Frascati CEA, Cadarache IPP, Jülich IPP, Garching ASCR, Czech Rep U Quebec

2. NSTX Meeting name – abbreviated presentation title (last name)Month day, 20** Low freq high-k scattering signals from NSTX #125272 with giant ELMs (K. Tritz - PoP2008) 2 Distinct freq. peaks associated with MHD:  f~MHD freq.

3. NSTX Meeting name – abbreviated presentation title (last name)Month day, 20** Identification of MHD poloidal mode number m - SVD analysis of USXR data SVD analysis: T. Dudok de Wit et al., PoP(1994) – IDL program by D. R. Smith Topo shows m=2 eigenfunction – node at r/a~0.5 - for the m=1 eigenfunction, the node is at the magnetic axis - see K.L. Wong et al., PRL 85(2000)996. Toroidal Mirnov coil array gives n=1  m/n=2/1 islands In addition, f mhd = F  at q=2 surface. 3

4. NSTX Meeting name – abbreviated presentation title (last name)Month day, 20** Many peaks (~40) in spectra when approaching locked mode #135416 – provided by Yang Ren (has Lithium, n e <4e13 cm -3 ) Asymmetric spectrum,  f ~ f mhd as rotation freq  decreases islands at R~122-137cm, scatt. vol. at R~123cm 4

5. NSTX Meeting name – abbreviated presentation title (last name)Month day, 20** Thermal quench due to locked mode 5

6. NSTX Meeting name – abbreviated presentation title (last name)Month day, 20** Low freq scattering signal in NSTX is unchartered water Avoided by large grad_T e   ETG ~1-3 MHz by HHFW heating and / or by Doppler shift due to plasma rotation (large V  during NBI + non-zero k  ) - see Mazzucato (PRL-2008), Smith (PRL-2009), Yuh (PoP-2008) 6

7. NSTX Meeting name – abbreviated presentation title (last name)Month day, 20** 7 Prevailing explanation: Interferometry effect from stray light (no beam dump) - can explain some low freq. lines, but NOT those in #135416 @ t>0.5s Assumptions: 1. Stray light intensity strong enough ***(cannot quantify) 2. Phase modulation z large enough (z=2    L/0.1cm) L= optical path length, n = index of refraction : n 2 = 1 –  pe 2 /  2 Stray light modulated by low freq. density oscillation gives a signal S = e i z sin(  t) =  n J n (z) e i n  t - Bessel identity (Stix, p.253) FFT[S] gives amplitude J n (z) at harmonic freq n . – Symmetric about  =0 Need z > 15 to get 20 freq. peaks within 30db on each side of  =0, for shot 135416, z~2 – get only 6 peaks – cannot explain our data Note: low density plasma with Lithium: n e <4e13 all the time. Moreover, our data have asymmetric spectrum Asymptotic forms: z >1, J n (z)  [2/(  z)] ½ cos[z-(½n+¼  ]

8. NSTX Meeting name – abbreviated presentation title (last name)Month day, 20** Raw signals modulated by f mhd – are these scattering signals ? Raw signals provided by E. Mazzucato: “ modulation of signal  interferometry effect, not scattering signal ” - I disagree : Interferometry effect gives modulated signals, but the converse is not necessarily true, i.e., Scattering signals can also be modulated Interferometry effect gives discrete lines in freq. spectrum, so can scattering signals 8

9. NSTX Meeting name – abbreviated presentation title (last name)Month day, 20** Discrete lines in spectrum from coherent wave scattering - Scattering signals come in many forms - Many ways to modulate scattering signals i.e., : modulate the RF amplitude, frequency, chop the l.o. beam, move the scatt. vol, etc… Wurden, Wong & Ono, Phys. Fluids(1985): CO2 laser scattering of LH Waves 9

10. NSTX Meeting name – abbreviated presentation title (last name)Month day, 20** X-ray scattering in solid state physics (Bragg 2 -1915 Nobel): Scattering pattern  Reciprocal lattice (lattice in k-space) 10

11. NSTX Meeting name – abbreviated presentation title (last name)Month day, 20** Properties of kinetic Alfvén waves (KAW) – Stix p.354-358 Shear Alfvén waves: no plasma kinetic effects (assume zero m e and  i ) - dispersion relation from ideal MHD eqns:  /k || = V A - long wavelength (low k) - many forms of toroidal eigenmodes: TAE, GAE, EAE, NAE, RSAE etc.... - f~1-300 kHz (NSTX), have long wavelengths not observable by high-k scattering KAW: include kinetic effects (non-zero m e and  i ); - dispersion relation: (  /k || V A ) 2 = i / [ 1 – I o ( i ) exp (- i ) + (T i / T e ) i ] i =(k  i ) 2, V A = Alfvén velocity, I o = modified Bessel function - Polarization: electrostatic wave, strong E ||  sensitive to ELD - Weak electron Landau damping requires  /k || V e <1/3 which implies k  i < 2 for normal modes (weakly damped –  damp  <<1) of KAW - Our exp’t looks at k  i ~ 5 – 10,   /k || V e ~ 0.5 – 1,  strongly damped quasi-modes (forced oscillations); can still be excited but cannot propagate far from where they are generated. 11

12. NSTX Meeting name – abbreviated presentation title (last name)Month day, 20** Quasi-modes not new - were observed long time ago Nonlinearly driven: LHW  LHW + QM :      , k o = k 1 + k 2 Ref: Wong & Ono, PRL 47, 842(1981) Ref: Skiff, Wong & Ono: Phys. Fluids 27, 2205 (1984) 12

13. NSTX Meeting name – abbreviated presentation title (last name)Month day, 20** KAW quasi-modes excitated by rotating magnetic islands - this mechanism should be more efficient than 3 wave coupling Perturbed B of pure m/n=2/1 island near q=2 surface: b( , ,  ) = b(  )exp[i(  - 2  )] Include other toroidal harmonics: b( , ,  ) =  n b n ( ,  ) exp(in  ) Neoclassical tearing mode propagates in the plasma along the  direction with freq.  ’  f   i where f < 1 The q=2 surface rotates with angular freq  in the laboratory frame, and the 2/1 mode freq. is:  ’+k. V=  ’+k  V  +k  V  =  because   i <<  at low mode numbers, and V  <<V . b n ( ,  ) has freq n  in the laboratory frame. The induced E rf =Vxb n, i.e., the rotating island acts like an RF antenna driven at various harmonic freq n  and KAWs at these frequencies are excited. Island location: R~122-137 cm, scattering volume at R~123 cm (at island edge) 13

14. NSTX Meeting name – abbreviated presentation title (last name)Month day, 20** KAW not new - was observed in TFTR 15 years ago, - the excitation mechanism is new & common in tokamaks Ref: Wong et al., Phys. Lett. A. 244, 99 (1996) – mode conversion from TAEs - fast ions from ICRF; scattering from 5 Watt 60GHz (5mm) probing beam, no beam dump. “ghost feature” near f~0 NSTX data is interesting because of their association with locked mode Many KAWs appear in plasmas with violent MHD activities shortly before locking Can we use this as a locked mode / disruption precursor ? 14

15. NSTX Meeting name – abbreviated presentation title (last name)Month day, 20** Conclusion: Spectrum with 40 peaks is scattering from KAWs driven by rotating 2/1 islands 15 Generalized Interferometry effect :  n  More peaks, but..... Transition from n=2 to n=1 at 0.48s: flat to peaked n e (r),f  (r)