Experimental Achievements on Plasma Confinement and Turbulence

Transcription

1 Experimental Achievements on Plasma Confinement and Turbulence Akihide Fujisawa National Institute for Fusion Science since ~9 Zonal-flow Helical Plasma ITER- Summer School 28 in Fukuoka Japan

2 Introduction For more than 5 years efforts, the construction of ITER has begun. Empirical scaling laws 195 s stellarator JT-6, JET, TFTR,Tore-supra LHD, etc ITER The understanding from the first principle should give us more confidence by providing more precise prediction of plasma performance for any given magnetic configurations

3 Anomalous Transport TFTR TRANSPORT = COLLISIONAL+TURBULENCE NEOCLASSICAL Anomalously large transport R. J. Hawryluk, Phys. Plasmas (1998 ) ANOMALOUS TRANSPORT can be ascribed to DRFIT WAVE TURBULENCE. To understand the plasma transport is to study the turbulence

4 Turbulence & Transport ( s) ATC Wave-scattering played an important role in the turbulence studies in early days TFR n /n n n " 1 k # L n E. Mazzucato, PRL (1976) 1/k " L n C. Surko, R. Slusher, Science (1983) TFR group, Nucl. Fusion (1986) EXISTENCE OF DRIFT WAVE TURBULENCE and TURBULENT TRANSPORT has been proven.

5 A Sketch of Turbulence Research local & linear & deterministic view - Drift wave turbulence (micro-scale fluctuations) 1976 turbulence spectra (waves-cattering) Diagnostics Developments A point measurement mixing length estimate - Discoveries of improved confinement modes 1982 H-mode in ASDEX Bifurcation physics Sheared flow (macroscopic flows ) 1D or profile measurements - Discovery of zonal flow concept 24 Identification of zonal flows A paradigm shift (zonal flows & drift waves) meso-scale structure " a# non-local & nonlinear & probablistic view Wider (2D-3D) multipoint measurements

6 Improved Confinement Mode I Stored Energy - Discrete change in energy A list of Improved Confinement modes - Existence of multiple states H-mode ASDEX 1982 ASDEX Supershot TFTR 1987 H-mode PEP-mode(ITB) JET 1992 H-mode (ETB) W7-AS&CHS 1993 High-β p (ITB) JT Bifurcation ERS (ITB) TFTR 1995 L-mode NCS (ITB) DIII-D 1995 Power threshold Heating Power F. Wagner et al., PRL (1982) RI-mode TEXTOR 1995 N-ITB(ITB) CHS 1999 HDH (ETB) W7-AS 22 SDC (ITB) LHD 26 The findings have made it begin to dig the confinement law out of the phenomena.

7 Improved Confinement Mode II Transport barriers (ETB & ITB) DIII-D L H L W7-AS H K. H. Burrell, Rev. Sci. Instrum (21) F. Wagner et al. PPCF 39 A23 (1997) Turbulence suppression is observed at the barriers Bifurcation property is demonstrated in transport barrier formations

8 Shear Flow Stabilization I - Simulation Sheared mean flows tear the turbulence eddies apart with flows without H. Bigrali et al., Phys. Fluids B 2 1(199) Theoretical Expressions Empirical form " < # E$B (~ dv E$B /dr) T. S. Hahm et al., Phys. Plasmas (1995) General form " = " L 1+ #(E r ' ) $ Z. Lin et al., Science (1998) K. C. Shaing et al., 12th IAEA Vol. 2 p13 (1988) K. Itoh et al., PPCF (1994) Theories and simulations have demonstrated that the turbulence should be suppressed by sheared poloidal flows. The world-wide experimental efforts have begun to confirm the hypothesis.

9 Shear Flow Stabilization II Bias Experiments & Observation CCT TEXTOR " = " L 1+ #(E r ' ) $ R. Weynants et al. PPCF (1998) R. J. Taylor et al. PRL (1989) External driven sheared flows reduce fluctuations to form transport barrier.

10 Shear Flow Stabilization III In ITB, spatio-temporal properties of shear-stabilization are observed ITB f (khz) 2 row CHS Turbulence is really suppressed at the E r -shear layer with ITB without ITB E r (kv/m) 4 8 Electron root de r /dr Ion root (V/cm 2 ) -4-2 flux (a.u.) flux (a.u.) col 8 1 φ Flux at ~7kHz Time(ms) test_txt_3_md time (ms) A. Fujisawa et al., PPCF 48 S25 (26)..3.2! (kv) A number of experiments have confirmed sheared flow mechanisms

11 Physics of Bifurcation I Bifurcation nature could be associated with properties of plasma flows #E " " r p #t Some terms on the right-hand-side show strong nonlinearity. This causes the bifurcation of plasma flows. " i lc E r L = $ anom e%i ( ) " e#i ( E r ) % $ lc i % $ bv i % $ v&v i % $ Neo i + $ Neo e % $ CX i +L anom ( ) E r Itoh & Itoh model " anom e#i lc ( ) + " i ( ) = E r Shaing model E r S-I. Itoh, K. Itoh, PRL (1988) H " i bv lc ( ) + " i ( ) = E r E r K. C. Shaing E.C. Crume Jr., PRL (1989) Transition should happen much faster that confinement time scale High temporal resolution is necessary for experimental confirmation It is complicated in H-mode where a number of radial currents components are expected

12 Physics of Bifurcation II A simple case: ITBs in stellarators neoclassical term is dominant " " p #E r #t = $% i Neo (E r ) + % e Neo (E r ) +L CHS " (kv) Potential (or Temperature).5 ITB in CHS no ITB ITB electron root ITB ion root! radius 1.5 1! Electric field transition happens in much faster time scale (~1us) than confinement timescale (~ a few ms). j r (A/m 2 ) Experiment ITB Break-down B D C A ITB Formation Neoclassical calculation j r (A/m 2 ) I (T =63 ev) e B ' C ' A ' D ' II (T =8 ev) e The electric field bifurcation is a key mechanism for transport bifurcation E E r (kv/m) r (V/cm) A. Fujisawa et al. PRL (1997)

13 Physics of Bifurcation III Turbulent Reynolds stress term " i v#v $% r v & v r " " p #E r #t = $ anom e%i % $ lc i % $ bv i % $ v&v i % $ Neo i + $ Neo e % $ CX i +L Turbulence can drive the flows! The generated flows should have shearing on turbulence 1 de 2 dt = " E #$ 1 E 2 #$ 2 UE 1 du = #µu + $ 3 UE 2 dt E: fluctuation U: flow L H L Steady state condition gives two stable solutions corresponding to L and H-mode!! P. H. Diamond et al., PRL (1994)

14 Physics of Bifurcation IV Does turbulent Reynolds stress really generate plasma flows? Multi-point measurements for evaluating Reynolds stress Showing a significant contribution of turbulent Reynolds stress. L H HT-6M ISTTOK C. Hidalgo et al., PRL (1999) Y. H. Xu et al. PRL (2) Turbulent Reynolds stress plays a role in H-mode transition Many simulations have shown an important role of TRS even in L-mode transport

15 Concept of Zonal Flows The concept of zonal flows is not so new Hasegawa-Mima equation (1977) Zonal flows in toroidal plasma - stationary zonal flows - geodesic acoustic modes Jovian zonal flows Zonal flow caused by Rossby wave turbulence Zonal flows are ubiquitous Poloidal ExB flows Crosssection Features & Tasks i) zonal structure symmetry (m=n=) a finite radial wavelength no transport ii) nonlinear coupling with turbulence iii) effects on transport A number of simulations show the importance of zonal flows on transport. Experimental identification was an urgent issue. P. H. Diamond et al. PPCF 47 R35 (25)

16 Identification of Zonal Flows I Do zonal flows really exist in toroidal plasmas? CHS P E (V 2 msec) Electric Field Spectrum (measured with HIBP) P E (V 2 sec) f (khz) P~f -1.2 Coherence.5 P E (a.u.) Simulation!/" i Z. F. GAM.1 noise level f (khz) A. Fujisawa et al., PRL 93 (24) 1652 T.S. Hahm et al. PPCF 42 A25 (2) Zonal flows have been identified in the measurements using twin HIBPs

17 Identification of Zonal Flows II CHS HIBP#1 observation point HIBP System 9 degree apart!e " (V) 1 Temporal E 1 in r 1 =r 2 =12cm HIBP#2 observation point -1 E 2 in t (ms) poloidal cross-section #1 1 r 1 =12cm E 1 in r 1 =12.5cm R=1m, a=.2m poloidal cross-section #2!E " (V) -1 E 2 in t (ms) Symmetric around the axis, with a finite radial wavelength. The phase difference is robust, and dependent on radial distance.

18 Identification of Zonal Flows III Using the cross-correlation functions between two electric fields at different radii, C crs (r 1,r 2,") = E 1 (r 1,t)E 2 (r 2,t + ") / E 1 2 (r 1,t) E 2 2 (r 2,t + ") CHS τ (ms): time lag! (ms) 2 1 Wavelength ~1.5 cm Life time ~1.5 ms Correlation coefficient τ = ms τ =2 ms τ =1 ms inward r (cm) Δr (cm) -2 2 Δr (cm) The observation confirms the zonal structure of the fluctuations of the low frequency.

19 Identification of Zonal Flows IV The study of GAM is the most flourishing part in zonal flow experiments

20 How do we prove nonlinear interaction? A number of techniques have been developed to clarify nonlinear coupling between turbulent elements. Amplitude Correlation Technique F. J. Crossley et al., PPCF (1992) PTF analysis H. Xia, M. G. Shats, Phys. Plasmas (24); probe in H1-heliac Power Transfer Function (PTF) Analysis C. P. Ritz et al., Phys. Fluids B (1989); probe in TEXT J. S. Kim et al., Phys.Plasmas (1996); BES in TFTR H. Xia, M. G. Shats,PRL (23); probe in H1-Heliac P. Manz et al., PPCF (28); probe in TJ-K Bicoherence Analysis f 1 +f 2 =f 3 For evaluation of strength of three wave couplings (f 1 +f 2 =f 3 ) TEXT Y. C. Kim, E. J. Powers, Trans. Plasma Sci PS-7 12 (1979) C. Hidalgo et al., PRL (1993); probe in ATF

21 How do we prove nonlinear interaction? GAM f 2 (khz) 1 JFT2M f 1 +f 2 =f 3 ~±1kHz f 2 (khz) SZF Wavelet bicoherence CHS strong coupling f 1 +f 2 =f 3 ~±.5kHz strong coupling -1 f 1 (khz) 12 Y. Nagashima et al. PRL (25) f 1 (khz) A. Fujisawa et al., PPCF (27) Coupling between zonal flows and background turbulence is confirmed using bicoherence analysis

22 How do we prove nonlinear interaction? bulk flow (ion diamag.) CHS f(khz) Z(t) (V) 2 2 ZF f (khz) electric field zonal flow and turbulence.5 1. V 2 /khz zonal flow max min time (ms) t (ms) 7 φ(v 2 /khz)! (V 2 /khz) (a.u.).4 min min max max noise level f (khz) f (khz) 1 A. Fujisawa et al., JPSJ (27). Turbulence power is modulated with zonal flow phase

23 New Paradigm for Plasma Transport I s PLASMA TURBULENCE Drift waves gradients shearing szf>gam Drift waves + Zonal flows Drift waves v"v Zonal flows no transport the paradigm shift transport trapping damping The plasma turbulence is regarded as a system of zonal flows and drift-waves Nonlinear interaction between zonal flows and turbulence controls transport. Energy partition between zonal flows and turbulence should be a key

24 New Paradigm for Plasma Transport II A mystery: why is the confinement improved inside the barrier? Potential (or Temperature) no ITB CHS confinement is improved without shear ITB ~ Power ( E/ T) 1-3 L mode No ITB ion root inside barrier Low damping rate is expected in ITB state ITB H mode radius 1 electron root P ZF (V 2 ) K. Itoh et al., Phys. Plasmas (27) A larger fraction of zonal flows contributes to improving the confinement inside. Energy partition between zonal flows and drift waves is really the key for confinement

25 New Paradigm for Plasma Transport III The flow spectra consists of ZF, turbulence & GAM CHS 1 DIII-D D. K. Gupta et al., PRL (26) HIBP Power (V 2 /khz) 1.1 ρ~.3 GAM BES ρ~ frequency (khz) Dependence of spectra on dimensionless parameters should be investigated Scaling in dimensionless form B. B. Kadomtsev Sov. J. Plasma Phys (1975) Such studies give fundamental understanding of plasma transport based on the new paradigm

26 Future Directions

27 A Mystery in Plasma Transport Non-local Transport - How does the core plasma know the change happening at the edge TEXT JET core turbulence edge Edge turbulence may link core turbulence through the interaction with long wavelength fluctuations K. Gentle et al., PRL (1995). J. G. Cordey et al., Nucl. Fusion (1995). Disparate scale interaction could be a key to solve the mystery.

28 For Future Research I Disparate scale interaction should be investigated to clarify not only the non-local transport, but also plasma turbulence and confinement Simultaneous measurements of 1. Micro-scale turbulence 2. Macroscopic structures 3. Mesoscopic fluctuations DIII-D/BES furthermore, in many physical quantities (electric field, density, temperature, magnetic field and so on) G. McKee et al., RSI (23) At least wider range observation (2D-3D) with fine scale measurements Computers become cheaper and faster, and can manage massive experimental data. 197s Now it is the time for us to really do turbulence studies!

29 For Future Research II High accessibility and flexibility for physical experiments can be realized in low temperature plasmas - Roles of such devices are strengthen. LMD-U TJ-K 2D probe array S(k, w) Multi-channel probe frequency CSDX Streamer identified U. Stroth et al., Phys. Plasmas (24) Wave-number T. Yamada et al., Nature Phys. In press Linear Device G. Tynan et al., Phys. Plasmas (24) The ultimate physical laws should be expressed in dimensionless form

30 Summary The world-wide efforts have found a number of improved confinement modes Bifurcation property of plasma flows can be a cause of barrier formation Interplay between flows and turbulence forms transport barriers Now a new paradigm of plasma transport is coming up Turbulence is regarded as a system of zonal flows and drift waves. It should be the time to solve the remaining mysteries in plasma transport Disparate scale interaction should be the key. It should be the role for young plasma physicists to elevate the obtained knowledge to the laws of plasma confinement Now we have good tools for observing the plasma turbulence cf. The studies of heat engine deduced the second law of thermodynamics The studies of fusion should provide something universal for science

31 Review Papers Reviews of transport barriers F. Wagner, Plasma Phys. Control. Fusion 49 B1 (27) F. Wagner, Plasma Phys. Control. Fusion 48 A217 (26) A. Fujisawa, Plasma Phys. Control. Fusion 45 R1 (23) K. Itoh, S. -I Itoh, Plasma Phys. Control. Fusion 48 1 (1998) Reviews of turbulence & zonal flows P. H. Diamond, K. Itoh, S-I. Itoh, T. S. Hahm, Plasma Phys. Control. Fusion 47 R35 (25) A. Fujisawa et al., Nucl. Fusion 47 S718 (27) Reviews of turbulence experiments P. C. Liewer, Nucl. Fusion (1985) A. Wootton et al., Phys. Fluids B (199). Reviews of tokamak and stellarator comparison U. Stroth, Plasma phys. Control. Fusion 4 9 (1998)