1. J.R. Wilson, R.E. Bell, S. Bernabei, T. Biewer, J. C. Hosea, B. LeBlanc, M. Ono, C. K. Phillips Princeton Plasma Physics Laboratory P. Ryan, D.W Swain Oak Ridge National Laboratory 45 th Annual Meeting of Division of Plasma Physics American Physical Society October 27 – 31, 2003 Albuquerque, New Mexico Investigation of the Possible Role of Parametric Decay during HHFW Heating on NSTX Supported by Columbia U Comp-X General Atomics INEL Johns Hopkins U LANL LLNL Lodestar MIT Nova Photonics NYU ORNL PPPL PSI SNL UC Davis UC Irvine UCLA UCSD U Maryland U New Mexico U Rochester U Washington U Wisconsin Culham Sci Ctr Hiroshima U HIST Kyushu Tokai U Niigata U Tsukuba U U Tokyo JAERI Ioffe Inst TRINITI KBSI KAIST ENEA, Frascati CEA, Cadarache IPP, Jülich IPP, Garching U Quebec

2. High Harmonic Fast Wave Heating has been successful on NSTX Efficient heating of electrons –Electron temperatures of 2-4 keV obtained Unidirectional currents have been driven –Up to 120 kA of Co current –Efficiencies comparable to those obtained on D- IIID seen(Ryan:LP1.019)

3. Unexpected Behavior has been Observed Attempts to measure power deposition profile by power modulation have proven unsuccessful (Swain:LP1.017) Current drive efficiencies have sometimes been low(Ryan:LP1.019) Edge rotation and impurity heating has been observed (Biewer:LP1.024)

4. E r from He II and C III (cold) Ohmic v. RF heated The E r at the edge most region of the plasma (R>146 cm) is more negative during RF heated plasmas than during Ohmic. For R<146 cm the E r is similar (for the region measured) Implies that RF leads to ion loss at the edge of the plasma.  E r ~-5 kV/m RF on Ohmic

5. More power leads to more heating From NSTX Shot 110133 to 110145 the applied RF power was increased. Empirically, T i increases as P RF 0.47. Negative poloidal velocity is upwards on the outboard midplane. Negative toroidal velocity is opposite to the direction of I p.

6. Various non RF Specific Effects may be Responsible Stiff transport profiles could explain lack of central Te modulation MHD has been observed to affect current drive efficiency Edge effects may be instrumental complications due to enhanced neutral densities

7. A Possible Specific RF Effect is Parametric Decay Observed in many rf heating experiments (CMOD, ASDEX, DIIID, JET) Not usually sufficiently strong to play a major role in energy balance: Exception: Lower Hybrid current drive where it is responsible for density limit

8. Characteristics of Parametric Decay Review of Parametric Decay for the edge plasma in the ICRF Regime has been given by Porkolab Eng. Fusion and Design 12 (1990) pg. 93 Three wave coupling process with selection rules:  0 =  1 +  2 k 0 = k 1 + k 2 These correspond to energy and momentum conservation Since the “pump” fast wave has a long perpendicular wavelength and the “daughter” waves are expected to have short wavelengths the latter condition can be taken as: k 1 = -k 2

9. Parametric Decay Theory Dispersion Relation: Where

10. The Parametric Coupling Constant is given by: The first term is due to the polarization drift, the second the parallel drift and the third the E x B drift We will now assume that we will have decay into an ion Bernstein wave and either another ion Bernstein wave, an ion quasi-mode or an electron quasi-mode For HHFW,    i and the polarization term will dominate. E 0 is in the poloidal direction and this allows the IBW wave to propagate poloidally and stay in resonance with the pump

11. Combining the expression for the dispersion relation and the coupling, keeping only the polarization term and assuming the side band is a resonant IBW yields the following expression: Where    is the normalized growth rate of the instability and  2 the normalized damping of the IBW. The electron coupling term has been dropped since  e << 1 We now look for values of the right hand side >1.

12.       1 2 3 13 Frequency (  i ) Wavenumber (k perp r ci ) 14 51015 11 22 Dispersion relation for IBW and quasi- mode Frequency matching condition selects k perp 200

13. To make the Growth rate large you could have  0 or  i (  1 ) large Ono Phys Fluids 23 (1980) p. 1675  = 0 corresponds to a resonant lower frequency wave e.g. another Bernstein wave. However, it is very difficult to get both frequency and wave-number matching simultaneously for two resonant waves  i (   ) will be large when  =  i This is the ion quasi-mode, quasi because  ≠ 0 The quasi-mode has no k perp dependence so simultaneous matching of frequency and wave number is easily achieved

14. For  i large we are left with only the electron susceptibilities For  1 =  i the electron susceptibility terms can be simplified to: The first term dominates and to have growth we only require that This is easily satisfied

15. Numerically calculating the normalized growth rate for   i yields Normalized growth rate  i 0 0.1 0.2 -0.1 0.7 0.80.91.0 1.1 T e, T i = 50 eV n e = 2 x 10 18 B = 2.3 kG Growth rate maximizes for k || =  i /0.7v te Growth rate is found to decrease with increasing edge temperature and increase with increasing edge density

16. Where does the coupled power go? Both the ion Bernstein wave and the ion quasi-mode should deposit their energy into the majority ions The quasi-mode does not propagate and deposits its energy locally but because of its low frequency it can not contain much energy The Bernstein wave will propagate until it reaches the next cyclotron harmonic - for NSTX this is within about 10 cm of the edge So all the parametrically coupled power should damp within 10 cm of the edge

17. Dispersion relation for daughter Bernstein wave r(m)

18. r(cm) Power absorption for edge launched fast wave and IBW Fast wave IBW wave Fraction of launched power absorbed

19. Parametric decay is expected to occur in NSTX HHFW experiments Decay into ion Bernstein wave and ion quasi-mode is preferred Decay takes place at the plasma edge Decay waves will heat ions in outer 10 cm of plasma Threshold power level increases with increasing edge temperature and decreases with increasing edge density May explain edge heating and electric field change seen on edge rotation diagnostic