Transport Phenomena in the High Temperature Non-Equilibrium Plasma S. Inagaki Kyushu U., RIAM

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1 17aCN-7 ( ) 2015 Transport Phenomena in the High Temperature Non-Equilibrium Plasma S. Inagaki Kyushu U., RIAM

) A. Fukuyama (Kyoto U.) Y. Nagashima, T.

Fujisawa, H. Zushi, S.-I. Itoh (RIAM) P. H. Diamond (UCSD), R.

$Yagi (JAEA) Grant-in-Aid for Scien\fic$ $19360148) and by the collabora\on programs$

2 Acknowledgements K. Ida, N. Tamura, T. Tokuzawa, T. Kobayashi, S. Kubo, T. Shimozuma, Y. Nagayama, H. Tsuchiya, K. Itoh, A. Komori, Y. Takeiri, Experiment group & Technical group of LHD (NIFS) T. Kaneko (Tohoku U.) A. Fukuyama (Kyoto U.) Y. Nagashima, T. Yamada, N. Kasuya, M. Sasaki, A. Fujisawa, H. Zushi, S.-I. Itoh (RIAM) P. H. Diamond (UCSD), R. O. Dendy (Warwick U.) M. Yagi (JAEA) Grant-in-Aid for Scien\fic Research of JSPF, Japan ( , ) and by the collabora\on programs of NIFS (NIFS07KOAP017, NIFS10KOAP023) and of the RIAM of Kyushu University and Asada Science Founda\on.

3 Contents I. Background - Transport in non-equilibrium plasmas - Transient Transport Problem - Multi-scale plasma turbulence II. Confirmation of multi-scale plasma turbulence picture - Discovery of the long-range global mode - Coupling between the global mode and micro-turbulence - Possible Link with non-local transport III. Relationship between turbulence and transport - Mystery of impact of heating - Discovery of hysteresis in the flux-gradient relation - Immediate impact of heating on multi-scale turbulence IV. Summary

$Drive Compe\\on between structure$ $forma\on and transport is universal$

4 Background A variety of structures are formed in strongly heated non-equilibrium plasmas, which have large spatiotemporal inhomogeneity Limit Source Gradients Transport Sink Drive Compe\\on between structure forma\on and transport is universal Rela\on between structure forma\on and transport in magne\zed plasma

73 T e (kev) 600 ev 400 200 0.33 0.4 - o.49 0.55 ==~~ 0.66 ==--=-==- 0.72 ρ=0.83 -- --=---=- 0.84 52.30 Time (s) 52.

5 Transient transport problem: mystery of 30 years Fast propagation (faster than diffusive propagation) JET Long distance correlation TEXT ρ=0.47 Diffusive Model T e (kev) EXP ρ=0.61 ρ=0.73 T e (kev) 600 ev o ==~~ 0.66 ==--=-== ρ= =---= Time (s) J. G. Cordey PPCF 36 (1994) A t sec Time (s) K. W. Gentle PRL 74 (1995) 3620 Global response à Non-local transport

$Turbulence structure forma\on We have$ Gradient ( T) Turbulence can form

$spa\al inhomogeneity - Micro-turbulence$ $structure forma\on is a key issue to$

6 Turbulence structure forma\on We have believed T Transport (q) Micro-turbulence r Gradient ( T) Turbulence can form structures - Turbulence is excited by spa\al inhomogeneity - Micro-turbulence drives transport - Turbulence transport is diffusive L micro << L T Turbulence structure forma\on is a key issue to understand transport in magne\zed plasmas

$Hea\ng Micro Zonal$ Avalanche Drii modes

$Coexistence of mul\-$

7 Working hypothesis Meso Macro Global mode Transport Pressure gradient Hea\ng Micro Zonal flows Streamer Avalanche Drii modes D angelo mode Background turbulence Transport - Coexistence of mul\- scale fluctua\ng structures - Structure interferes each others

8 II. Confirmation of physical picture of multi-scale turbulence - Discovery of the long-range global mode - Coupling between the global mode and micro-turbulence - Possible link between the global mode and non-local transport

9 Target Plasma High temperature low collisionality regime Target Plasmas of LHD ECH+NBI plasma T e ~4keV, n e ~0.4x10 19 m -3 β~0.1%, ν *h ~0.03 no MHD activity no GAMs no transport barrier no power modulation R ax /a=3.5m/0.6m B ax =2.83T

$Correla\on Hun\ng (a) Single instrument Single HIBP Dual HIBP+ Cross-Correla\on Discovery of Zonal Flow HIBP#1 observation points φ E r out φ ctr φ in ExB flow$ $Fujisawa PRL 2004 r 1 =12cm Radial structure of zonal flow Heterogeneous Signal Correla\on ~ T e (r) T ~ e (t) ~ n e, A~ n ~ b(θ, φ) Poloidal/Toroidal Structure T ~$

10 Correla\on Hun\ng (a) Single instrument Single HIBP Dual HIBP+ Cross-Correla\on Discovery of Zonal Flow HIBP#1 observation points φ E r out φ ctr φ in ExB flow Poloidal Crosssection 1 90 HIBP#2 observation points φ out φ ctr φ in ExB flow Poloidal Cross section 2 (b) E r 2 C (r 1,r 2 ) r 2 (cm) (color online). A. Fujisawa PRL 2004 r 1 =12cm Radial structure of zonal flow Heterogeneous Signal Correla\on ~ T e (r) T ~ e (t) ~ n e, A~ n ~ b(θ, φ) Poloidal/Toroidal Structure T ~ e (r 1,t 1 ) ~ n e (t), A~ n (t): envelope ~ T e T ~ e (r 2,t 2 ) Radial Correla\on Nonlinear Coupling & Φ ~ 1-ch X-mode ~ b Multi-channel.. LHD Top View

$Dis\nguish signals from noise - Clear$ 5-6 khz - Noise is reduced in the

11 Dis\nguish signals from noise - Clear peak around khz - Noise is reduced in the cross-power spectrum ~ b/b ax <10-6 Noise f -1/2 S. Inagaki PRL 107 (2011) m/n=1/1 or 2/1 Existence of low frequency fluctuations is evident

$Discovery of long distance correla\on Two-point two-time correlation 1 1.5-3.$ "# 0 τ (msec) ~1 km/s Life Time ~0.3msec 0.5 &'(! $!"# ECE sight of view Image $%"! $%"! $!"#!!"# %"!

12 Discovery of long distance correla\on Two-point two-time correlation kHz Reconstructed image (m=1, rigid rotation) %"! *+, ρ Ref Ballistic!"# 0 τ (msec) ~1 km/s Life Time ~0.3msec 0.5 &'(! $!"# ECE sight of view Image $%"! $%"! $!"#!!"# %"! )'( - Long radial correlation length ~ a - Ballistic propagation from core to edge ~V D - Spiral structure connects core and edge

Coupling with micro-turbulence Microdensity turbulence ~ T e

cross-bi-coherence f 3 =2 khz f 2 (khz) f 1 +f 2 =f 3 ~2 khz f 1

13 Coupling with micro-turbulence Microdensity turbulence ~ T e couples non-linearly with high frequency n ~ e Cross-bi-Coherence n ( f 1 ) n ( f 2 ) T * e ( f 3 ) 2 n ( f 1 ) n ( f 2 ) 2 T e ( f 3 ) 2 Global T e fluctuations Total cross-bi-coherence f 3 =2 khz f 2 (khz) f 1 +f 2 =f 3 ~2 khz f 1 (khz) S. Inagaki JPSJ 81 (2012) Global long-range modes couple with micro-turbulence

Meaning of bi-coherence - Envelope of micro-turbulence is modulated - Parametric modulational instability is suggested - Potential fluctuation can be estimated

14 Meaning of bi-coherence - Envelope of micro-turbulence is modulated - Parametric modulational instability is suggested - Potential fluctuation can be estimated from the envelope Envelope modulator = Potential Structure Α~ n /<Α~ n > ~ (ω micro /ω) (k r L n ) (eδφ/t) Global modes modulate the amplitude of micro-turbulence

15 Possible link with non-local transport - Spontaneous increase in the global mode involves decrease in the mean T e - Change of the global mode precedes the change in the mean T e - Change propagates between core and edge in 100 µs times faster than diffusive time The long-range modes can play an important role in edge-core interaction of transport

What happens at the onset of transport event 2.84 2.85 t (s) 2.86 1.

854s) "#$ $#% ρ (7' $#% $#$ &'(()*+,-'.!$#% 0-0.4-0.2 0 0.2 0.4 τ (msec) $#$ -0.4-0.2 0 0.2 0.4 τ (msec)!/!

16 What happens at the onset of transport event t (s) (a) Before TESPEL Injection (2.839s) "#$ (b) After TESPEL Injection (2.854s) "#$ $#% ρ (7' $#% $#$ &'(()*+,-'.!$#% τ (msec) $#$ τ (msec)!/!0 $ 0 /,-4)516)&3 12"$!/ 3 Change of global modes during transient phase!"#$ S. Inagaki NF 52 (2012)

17 Discussion r/a~0 Micro-Turbulence Long-range modes r/a~1 Micro-turbulences at distant locations can correlate through the coupling with the global modes Multi-scale turbulence picture can explain the long distance correlation of transport Further Challenges How does the energy flow? Why does T e increase? Correla\on à Causal rela\on

18 III. New between flux, gradient and turbulence - Mystery of impact of heating - Discovery of hysteresis in the flux-gradient relation - Immediate impact of heating on multi-scale turbulence Revisit to experiments of ~20 years ago U. Stroth (W7AS) 1996 PPCF

$Precise measurement using MECH - Target plasma (NBI+MECH) MECH 25Hz - Modula\ons of T e, T e and fluctua\on are observed simultaneously LHD No$

19 Precise measurement using MECH - Target plasma (NBI+MECH) MECH 25Hz - Modula\ons of T e, T e and fluctua\on are observed simultaneously LHD No MHD, No ETB, No GAMs Macro-mode Micro-fluctuations no evidence of high-energy tail Periodic temporal evolution of signals are precisely extracted

20 Coexistence of short and long \me scales δq e = 1 S # % $ 3 2 n e δt e t δ p ECH & ( dv ' At location distant from heating Macro-mode Micro-fluctuations - Characteristic time of the change in mean variables (T e and T e ): ~ 40 ms - Time-scale of the rise and fall of heat flux and fluctuation amplitude: ~ 1 ms Two time-scales! S. Inagaki NF 2013

21 Flux-Gradient Rela\on Two \me-scales (short, transport) Hysteresis in Lissajous diagram Microfluctuations Macro-mode ~20% of total heat flux at ρ=0.66 The hysteresis appears also in the response of fluctuation intensity appears in the wide region of plasma

22 Characteriza\on of hysteresis - Barrier region - Cri\cal gradient/flux - Jump between stable branches - Wide region (Ubiquitous) - No cri\cal condi\on - States are determined by hea\ng (conceptual) On Off (- p) c1 Δ (- p) c2 Δ Hea\ng organized global hysteresis (New)

23 Roles of hea\ng on turbulence intensity The turbulence intensity (at r/a = 0.66) - jump between states of ECH-on/off - depends on hea\ng power The hea\ng power determines the state of turbulence at distant loca\ons from hea\ng I f n 2 e( f ) = I f (P ECH ; T e,t e,...)

$Immediate impact of hea\ng 1 M - Through phase-space - Couple with the global modes f (Hz) Direct Influence ϕ 1 ϕ 1 ~ 1 1 γ h χ 0 1 k 2 ϕ 1 ϕ 1 0 S.I. Itoh, K. Itoh Sci. Rep.$

24 Immediate impact of hea\ng 1 M - Through phase-space - Couple with the global modes f (Hz) Direct Influence ϕ 1 ϕ 1 ~ 1 1 γ h χ 0 1 k 2 ϕ 1 ϕ 1 0 S.I. Itoh, K. Itoh Sci. Rep. (2012) Micro-Turbulence 100 k 10 k Turbulence Spreading Meso-scale coupling Long-distance interaction 1 k Long-range modes r/a (Conjecture) The on/off of hea\ng power at center immediately influences the global modes which couple with micro-turbulence at far distance

25 Summary A variety of transport phenomena are observed in the non-equilibrium plasma 1. Transient transport problem is a mystery of 30 years Non-diffusive transport, long distance correlation 2. Multi-scale turbulence picture is strongly supported Discovery of the global modes, Coupling between disparate scale fluctuations, Discovery of new hysteresis 3. Leading phase space turbulence and cross scale physics 4. Precise measurement using new analysis method is one of the important key words Correlation Hunting, Conditional Averaging, Bi-Spectrum Analysis...

Non-Equilibrium and Extreme State of Plasmas

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