O-4 12 th IAEA TM on Energetic Particles in Magnetic Confinement Systems, 7-10 Sep, Austin, USA Characteristics of Energetic-Ion-Driven Geodesic Acoustic Modes in the Large Helical Device(LHD) K. Toi, K. Ogawa 1, M. Isobe, M. Osakabe, T. Ido, A. Shimizu, M. Nakamura 1, T. Tokuzawa, D.A. Spong 2, F. Watanabe 3 and LHD Experiment Group National Institute for Fusion Science, Toki, Japan 1 Nagoya University, Nagoya, Japan 2. Oak Ridge National Laboratory, Oak Ridge, USA 3. Kyoto University, Kyoto, Japan
Introduction Geodesic acoustic mode (GAM N. Winsor, PF(1968)) A kind of zonal flow(zf) called High frequency ZF with n=0 ZF or GAM generated by nonlinear mode coupling in drift-waves with large radial wave number Promising player to regulate micro-turbulence GAM is also excited as global mode by energetic ions. (global GAM) Understanding of GAM may lead to find a way controlling GAM & ZF favorably for background plasma. <Tokamaks> Experimental observations JET DIII-D
(Type I) GAM excited quasi-stationary in reversed shear plasmas by EPs Introduction (ctd.) <Helical/Stellarators> Experimental observations in LHD (Type II) This GAM is excited just after the switch-on of NBIs n=0 T. Ido et al., NF(2011) This is excited transiently (just after NBI switch on ) in very low density range K. Toi et al, PRL(2010) ( <n Nonlinear evolutions: pitchfork splitting, e > < 0.2x10 19 m -3 ). mostly up-ward frequency chirping This GAM may be controllable and sustainable.
Theories of GAM (1) Many theoretical works for Tokamaks: MHD theory : Winsor et al. (1968: MHD theory of GAM) dδφ/dr ~ (B t Rω) δρ/ρ Kinetic Theory: F. Zonca, L. Chen (1996, 2009); D. Zhou (2007) G.Y. Fu (2008); Ph. Lauber (2009); A, Smoryakov (2009): H.L. Berk (2010); Z. Qui ((2010).. (2) Some theoretical works for helicals/stellarators Kinetic theory: T. Watari (2005, 2006); H. Sugama et al.(2006); Y. Kolesnichenko (PPCF 2011) Real frequency: ω 2 C s2 [1+7Ti/(4Te) ]/R 2 Collisonless damping rate: γ exp(-q 2 ) q-dependence on real frequency: ω 2 (1+1/(2q 2 )) (N. Winsor 1968) ω 2 7Ti/(4Te) υ s2 [1+46/(49q 2 )] for ions (H. Sugama. 2006) Electromagnetic effects D. Zhou (2007); A. Smoryakov(2009) b υ TiE ~ q / r 2 υ A
(Type I) GAM Activities Observed in LHD RS-Plasmas This GAM is excited by EPs quasi-stationary in the latter phase of NBCD. Noticeable level of magnetic fluctuations n-contour of magnetic flucruations #1 #4 n=0 0 1 2 3 4 5 time (s) m=1, 2, 3, #1 #4 The poloidal mode number m is dominantly ~1, but composed with other components (m=0, m=2, m=3, )
Frequencies of the n=0 Modes(1) GAM??? Teo (kev), Tio (kev) 1.5 1 0.5 Tio No data radl_raw_sn94757 2 3 time (s) 4 CTR-NBI5 6 3 ECH 2.5 Teo 2 <n e >~0.4 x 10 19 m -3 0 4 4.5 5 5.5 6 time(s) The n-mode frequency stays almost constant in the quasi-stationary phase of counter NBCD, and increases clearly during ECH. Note: Tio increase by ECH in this plasma, as well as Teo.
Frequencies of the n=0 Modes(2)??? GAM Teo (kev), Tio (kev) CTR-NBI 8 ECH radl_raw_sn94759 6 Teo 4 <n e >~0.3 x 10 19 m -3 Tio 2 No data 0 2 3 4 5 6 time(s) ECH increases both Teo and Tio, and the frequency of the GAM rises doubly.
Frequencies of the n=0 Modes(3) 50.0 dat_freq of n=0 mode vs Teo & Tio f exp (khz) of n=0 modes 40.0 30.0 20.0 10.0 0.0 0.0 0.5 1.0 1.5 2.0 2.5 [T eo + 7T io /4)/(mass)] 1/2 The observed frequency of the n=0 modes is proportional to the square root of (Teo+7Tio/4)/(Mass). The frequencies agree well with the GAM frequency evaluated at the plasma center.
Magnetic Fluctuation Amplitude of GAM GAM/BAE at r=r s &RSAE 100 f(khz) 0 5 6 7 8 time (s) Magnetic fluctuation amplitude of GAM increases with the decrease in the rotational transform, and reaches ~0.5x10-5 T. By ECH and perp-nbi with low energy from t=7s, the amplitude is enhanced noticeably to ~2x10-5 T. In LHD, b θ /Bt~10-5 -10-4 for TAE, ~10-4 for EPM, ~ 10-4 -10-2 for RIC at edge
Density fluctuations of GAM (by Reflectometer) This type of energetic ion driven GAM in LHD accompanies appreciable density fluctuation, although it is excited in plasma central region. Higher harmonic of GAM and splitting of the spectra Multi harmonics of GAM Splitting of the GAM spectrum t=4.25s The GAM peak locates r/a 0.3. (by ECE measure.) K. Toi et al., PRL(2010) Reflection point at r/a~0.55 δne/ne~0.2% ( away from GAM peak)
Potential and density Fluctuations (by HIBP) Density fluctuations (ι/π) min = 1/2 1/3 (δn e ) rms /n e 0.2 0.15 0.1 0.05 #81433 10-30 khz Potential fluctuations (ι/π) min = 1/2 1/3 (δφ) rms (kv) 0 1 2 3 4 5 Time (sec) 1 #81433 10-30 khz 0.5 0 1 2 3 4 5 time (s) Amplitudes of potential and density fluctuations induced by GAM gradually increase with the decrease in the rotational transform. These fluctuation amplitudes are very large near the GAM center: (δn e ) rms /n e ~up to 15 %, (δφ) rms /Te ~ up to 70%
Radial Profile of GAM Potential fluctuations of GAM (ι/π) min =1/2 1/3 ECH 0.5 1 0.4 δφ rms RSAE 0.8 δφ rms (kv) 0.3 0.2 0.6 0.4 δφ rms /Te K. Toi et al., PRL(2010) 0.1 0.2 δφ /Te rms 0 0 0 0.1 0.2 0.3 0.4 0.5 r/a Very small Te fluctuations by the movement of magnetic surface due to GAM. The potential perturbations due to the radial displacement < 10V. The observed potential fluctuations come from real potential oscillations of GAM. Rough estimate: δer by GAM ~ 10kV/m, δer ~ 2x10 5 V/m 2, v θ ~1-2x10 5 s -1
Impacts on Energetic Ion Transport (1) Magnetic fluctuations The plasma potential is raised by ECH and sometimes has a train of large negative pulses. These negative pulses synchronize with the bursts of GAM and TAEs.
Impacts on Energetic Ion Transport (2) For almost identical two shots, one has negative pulses and the other not. (1) Radial transport of energetic ions (GAM may enhance the loss through pitch angle scattering by GAM bursts.) (2) Other effects : Potential pulsation observed during ECH in CHS (A. Fujisawa et al., PRL 1998) Future important and interesting issue!
Summary and Future Prospects Magnetic fluctuations with n=0 that grows gradually with the decrease in the rotational transform are observed in reversed shear plasmas of LHD, and exhibits pitchfork splitting or frequency chirping (mostly upward). The relative amplitude B θ /Bt is not small (~2x10-5 ). This mode couples with RSAE and often have higher harmonics. The mode frequency increases with Te rise, in particular more significantly in the case of simultaneous increase of Te and Ti. Very Large potential and density fluctuations of this mode have been detected by HIBP near the plasma core region. GAM driven by energetic ions Can we explain this GAM consistently with existing theories? f/f tr ~0.2= f ~ f GAM ; but no unstable mode in this range ( G.Y. Fu, PRL (2008)) At a certain condition, a train of large negative potential pulses synchronized with GAM & TAE bursts was observed. Indication of radial transport of energetic ions? Need more studies!