The th meeting of study on Plasma Science for Young Scientists, Mar. 7-9 28, JAEA, Naka, Ibaraki, Japan Coexistence of the drift wave spectrum and low-frequency zonal flow potential in cylindrical laboratory plasmas Y. Nagashima, S.-I. Itoh, S. Shinohara, M. Fukao 2, A. Fujisawa 3, K. Terasaka, T. Nishizima, M. Kawaguchi, N. Kasuya 3, Y. Kawai, G.R. Tynan 4, P.H. Diamond 4, M. Yagi, S. Inagaki, T. Yamada 5, T. Maruta, K. Kamataki, and K. Itoh 3 Kyushu University, 2 Uji (Kyoto), 3 NIFS, 4 UCSD, 5 Univ. Tokyo
Content. Observation of the drift-wave and the residual zonal flow 2. Linear dispersion relation i) Comparison of normalized fluctuation levels ii) Wave numbers of fluctuations iii) Poloidal velocity fluctuations derived from TDE method 3. Modulational instability 4. Bispectral analysis
Aim of the Specially-Promoted Research Quantitative study of Structural formation and selection rule in turbulent plasma Quoted from P.H. Diamond, et al., Plasma Phys. Control. Fusion 47 R35 (25) Plasma production: i) exitation of turbulence ii) excitation of zonal flow iii) Saturation of turbulence with zonal flows FreeEnergy Source, grad T,grad n Conventional picture of drift-wave turbulence DriftWave Turbulence Classic paradigm of drift wave turbulence Dissipation (i.e., Ion Ion Landau Damping, etc.) Picture of the drift wave-zonal flow system Observation: i) Spatio-temporal structure of the drift wave-zonal flow system ii) Comparison of intensity between the zonal flow and turbulent Reynolds stress iii) Nonlinear energy transfer Red: Completed now! Orange: Progress Free Energy Source, grad T, grad n Drift Waves Zonal Flows New paradi m of drift wave-zonal flow turbulence Figure. Newparadigm fortheplasmaturbulence. Wave Dissipation FlowEnergy Dissipation (i.e., Collisional Friction)
!! Experimental devices The Large Mirror device (LMD []) [] Y. Saitou, et al., Phys. Plasmas 4 (27) 723 coils pumping gas feeding quartz tube baffle plate Helicon source (2kW, 7MHz) Ar gas ion gauge double loop antenna -4 Magnetic field unit: mm 6 7 The Reynolds stress probe side view 65 2 5 5 5 4 3 2 5 3 top view 4 2 Magnetic field E E r = " 2 # " + " = (# $ # ) 3 d " (k θ ) (k r ) Reynolds stress per mass density { ( " ) 3 2} d r v r v " = E " E r B 2
Drift wave and residual zonal flow Time evolution of the potential spectrum during a single discharge Filling pressure scan (B=.2 T) -4-9 -5 Marginal transition to strong turbulence at 3.5 mtorr the drift-wave (DW)...2.3 time [sec] Measured at r=3.5 cm (a=~5 cm) DW (7-8 khz) and residual ZF (~4 Hz) are observed..4 the residual zonal flow (ZF)
-3-6 -9-2. Normalized fluctuation spectra Normalized power spectra (at.3 sec) (a) normalized power ZF ZF potential density -2-2. DW measured at r=6 cm measured at r=3.5 cm DW frequency [khz, log] frequency [khz, log] 5 5 Radial profiles (b) fluctuation level (4- khz).25 potential density n e. (c) fluctuation level (.3-.5 khz).6 potential density the ZF DW edge oscillation. radius [cm] Edge 7 DW (density ~ potential) is located at r=3.5-4cm. Residual ZF exists at r<~4.5cm (n > φ edge oscillations r>~4.5cm). φ>n ZF φ>n oscillation.6
Poloidal measured at r=4 cm Poloidal and axial wave numbers. Residual ZF coherence phase coherence m=. phase[rad/(2π)] DW m=4. -.2 8. 36 8 36. Poloidal angle (degree).2 Poloidal angle (degree) Axial coherence phase n=. -.2 3 6 9 Axial length [cm] n=2. -.2 3 6 9 Axial length [cm] DW has m=3-5 and n=2-3, while residual ZF potential has m,n~.
k r [cm - ] k r [cm - ] Radial wave numbers (radial profile) 4-2.5. DW Residual ZF coherence coherence Time averaged Reynolds stress per mass density RS [ 5 m 2 s -2 ] -4 2 4 6 Radius [cm] -. Stationary shear flow layer? 2 4 6 Radius [cm] Residual ZF has finite radial wave numbers, and propagates inward and outward. 6 coherence
Linear dispersion relation 6 Growth rate and frequency from Numerical Linear Device code [2]. 5 Frequency calculation based on Hasegawa-Mima equation " de,th = " *,e +k 2 #$ 2 s (ExB velocity is not considered.) -3 3 m=4 6 azimuthal mode number 9 ω de,th = 6.22-8.26 khz at minimum RS gradient ω de,exp = 7-8 khz NLD calculation shows that m=4 mode is most unstable. DW frequency base on HM eq. is consistent with observation. -5 2 [2] N. Kasuya, et al., J. Phys. Soc. Jpn. 76 (27) 445
Poloidal velocity fluctuation measured at r=2.5 cm where k r of the ZF is finite. Residual ZF (V θ and potential) Residual ZF is associated with the poloidal velocity fluctuation derived from the Time Delay Estimation [3]. [3] C. Holland, et al., Phys. Rev. Lett. 96 (26) 952
4 Modulational interaction Residual ZF Original potential [a.u.] DW Coherence between Original and envelope Measured at r=3.25 cm 2 Envelope of potential [a.u., 6.5-7.5 khz]. frequency [khz, log scale]. frequency [khz, log scale] Amplitude of the DW is significantly modulated by the ZF.
Bispectral analysis Squared cross-bicoherence of (f 3 =366 Hz, ZF frequency). E " ( f ) E r ( f # f 3 ) $ Z * ( ) f 3 Peak at DW frequency Noise level ~.25 Measured at r=3.25 cm 5 Frequency [khz, linear scale] Nonlinear energy transfer between the DW and the ZF is significant.
Summary. In this presentation, we have shown the drift wave zonal flow turbulence in a cylindrical laboratory plasma. 2. Linear dispersion relations of observed fluctuations are consistent with the zonal flow (potential and poloidal velocity fluctuation) or the drift-wave. 3. Modulation of the drift wave amplitude by the zonal flow was confirmed. 4. The bispectral analysis of <E θ E r Φ f > shows significant nonlinear energy transfers between the zonal flow and the drift wave spectrum.