1)K. Miki and 1,2)P. H. Diamond 1) WCI Center for Fusion Theory, NFRI, Korea 2) CMTFO and CASS, UCSD, USA

1

Spatio-temporal evolution of L→I→H transition

The 17th NEXT Workshop, March 15,16, Tokyo, Japan

Acknowledgements: G.R. Tynan, L. Schmitz, P. Manz, G.S. Xu, T.S. Hahm

Contents:

2

�  Motivating experimental observation �  Model description �  Simulation Results: L-I-H transition �  Analysis and Comparison to Experimental results �  Neutral CX scan �  Back Transition

�  (Transport Noise effects)

�  Summary

Motivating experimental observation: -- L-H power threshold scaling deviates in low density region -- New region related to I-mode, I-phase, and GAM -- No theoretical model to quantitatively predict the threshold and to show spatio-temporal evolution

3

fluctuations in the radial electric field Er ’ !u?B appeardirectly in the Doppler shift, while the Doppler peakintensity SD is proportional to the turbulence level at theprobed k? [11]. The measurements reported here wereobtained with an X-mode 50–75 GHz tunable frequencyreflectometer with 20 MHz signal sampling, located belowthe tokamak outer midplane [14].

GAMs are most clearly observed at low plasma densitiesand high safety factors q [15] due to weaker collisional andLandau damping [1]. Figure 1(a) shows a GAM existencediagram in terms of net heating power Pnet versus centralline averaged plasma density !ne for Ohmic and L-modeheated plasmas. GAMs are not observed in the H mode.Overlaid are the predicted (dashed line) and experimen-tally measured (curve) L-H power threshold showing twobranches; see [16] for details. The GAM appears as acoherent peak in the fD ( ~Er) spectrum, cf. Fig. 5(a) in Lmode. Note the absence of coherent low frequency ZFactivity, either as a peak or broadening of the spectraaround zero frequency. The spectra continues to be flatdown to the lowest spectral resolution investigated (a fewtens of Hz).

From the low density L mode (edge !"edge # 1) raising

either the heating power or the density causes the turbu-lence to rise across the whole edge region and to beginpulsating at around 2–4 kHz (sometimes with a slowersubpulse activity of a few hundred Hz) with an on-offduty cycle of less than 50%. This intermediate state(labeled I phase) is not transitory but can be maintainedfor the entire discharge. Observations from many dis-charges confirm that the L to I phase is a sharp transitionwith a well-defined threshold, while the full H modeappears to evolve more softly from the I phase. Theturbulence pulsing extends across the plasma edge intothe open flux surface scrape-off layer (SOL). Figure 2shows an example close to the power or density thresholdwhere the discharge dithers between the L and I phases—illustrated by the divertor tile shunt current (/ SOL flow).

The transition from continuous L-mode turbulence to puls-ing is shown below in the Doppler reflectometer spectro-gram S$f; t% from just inside the Er minimum location at anormalized poloidal flux radius "pol # 0:988. Below arethe corresponding (smoothed) traces of the u? velocity andfluctuation level SD at the probed k? # 9:8 cm!1.The u? and SD pulsing are synchronized and display all

the features of a limit-cycle behavior with a fast switchingbetween an enhanced and a reduced fluctuation state in lessthan 1 #s, i.e., on the turbulence time scale. The GAM isalso still present, however, only during the enhanced tur-bulence state. This is more clearly seen in Fig. 3 whichshows an expanded time trace of (a) the instantaneous Er

(100 ns resolution) plus (b) smoothed Er and turbulencelevel SD traces over four pulses. The figure shows a se-quence of events: (1) The turbulence rises between thepulses, (2) reaches a critical threshold (marked by thedashed lines) and triggers an exceedingly large GAMoscillation (3) together with a turbulence driven meanflow—indicated by the offset in the oscillation. [Thepeak-to-peak GAM flow oscillation amplitude during thepulse can exceed 100% of the mean flow—stronger than inthe preceding L mode. While earlier observations alsopoint towards a rTe (drive) threshold for the GAM onset[15], it is possible that the GAM is also enhanced by the

shot

FIG. 1 (color online). (a) GAM existence plot in terms of Pnet

vs central line average density. (b) Edge radial electric field Er

profiles for L (PECH & 0:35 MW) and I phase (1.1 MW)shot 24 811, BT & !2:3 T, Ip & 0:8 MA, q95 # 4:5, !ne & 3'1019 m!3, Teo # 2:4 keV, and favorable lower X point.

shot

FIG. 2 (color online). (a) Time trace of divertor shunt current,(b) expanded reflectometer spectrogram S$f; t%—darker colorsfor higher intensity, with (c) corresponding u? velocity andfluctuation level SD, and (d) estimated mean and oscillatoryshearing rates and turbulence decorrelation rate $!1

c across theL to I phase. BT & !2:3 T, Ip & 1:0 MA, q95 # 4, !ne & 2:8'1019 m!3, Teo # 3 keV, PECH & 1:0 MW.

PRL 106, 065001 (2011) P HY S I CA L R EV I EW LE T T E R Sweek ending

11 FEBRUARY 2011

065001-2

[Conway ‘11 PRL]

I-phase as a transient phase with limit-cycle oscillation(LCO), i.e. L→H transition can be replaced with L→I→H transition

4

T. Estrada et al.

0

5

10

10 -6

10 -5

10 -4

168.5 169.0 169.5 170.0 170.5 171.0

|Er| (

kV/m

) S (a. u.)

time (ms)

Fig. 5: (Color online) Time evolution of Er and densityfluctuation level obtained from the spectrogram shown in fig. 4.

6

8

10

12

10 -7 10 -6 10 -5 10 -4

|Er| (

kV/m

)

S (a.u.)

1

2

3

#23473, t=170-170.4 ms

Fig. 6: (Color online) Relation between Er and density fluctu-ation level. Only two of the cycles shown in fig. 5 are displayed.The time interval between consecutive points is 12.8µs.

The time evolution of both, Er and density fluc-tuations, reveals a characteristic predator-prey rela-tionship: a periodic behaviour with Er (predator)following the density fluctuation level (prey) with90! phase di!erence can be clearly seen. Er is observedto grow and decay at di!erent time rates ((100–150)µsand (50–80)µs, respectively), while the turbulence growsand decays in comparable times ((50–70)µs). These timescales being much faster than the energy confinementtime. The relation between Er and the density fluctuationlevel showing a limit-cycle behavior is represented infig. 6. For the sake of clarity, only two cycles are displayed.The turbulence-induced sheared flow is generated causinga reduction in the turbulent fluctuations (1 in fig. 6), thesubsequent drop in the sheared flow (2 in fig. 6) and theposterior increase in the turbulence level (3 in fig. 6).As has been already discussed, the coupling between

fluctuations and flows, described as a predator-prey evolu-tion, is the basis for some bifurcation theory modelsof the L-H transition [10,11]. The experiments reportedin this letter strongly support these models. However,these results do not necessarily exclude other mechanisms

working together in triggering the transition. In helicaldevices, the negative radial electric field imposed by theNeoclassical ion root condition in the L-mode can act as abias for the transition [16,22], either because a substantialEr-shear already can exist before the transition or becauseof the amplification of zonal flows by Er [27]. On the otherhand, as already mentioned, the magnetic topology caninfluence the H-mode occurrence through mechanisms asflow damping by poloidal viscosity [24] or spin-up of flowsby rational surfaces [28–30]. All these mechanisms mayact together to reach the specific conditions at which theself-regulation between turbulence and flows becomes thedecisive mechanism.To our knowledge, this is the first time that such

an experimental evidence is reported supporting thepredator-prey relationship of turbulence and flows as thebasis for the L-H transition. During the so-called IM modefound in DIII-D power scan experiments [21], the relationbetween electron temperature fluctuations and shearedflows seems to follow a predator-prey behavior, however,as the authors explain, the sheared flow is not directlyobserved but inferred from beam emission spectroscopydata. Two ingredients have been essential in attaining theresults presented in this letter, the possibility of achievinggradual L-H transitions and the capability of measuringsimultaneously both magnitudes, density fluctuations andsheared flows, with good spatiotemporal resolution.

Conclusions. – The dynamics of turbulence andflows has been measured during L-H transitions in thestellarator TJ-II. When operating close to the L-Htransition power threshold, pronounced oscillations inboth, Er and density fluctuation level, are measuredat the transition. The oscillations are measured rightinside the E!B shear layer (located at !" 0.83). Thetime evolution of both, Er and density fluctuation level,shows a characteristic predator-prey behavior, with Er(predator) following the density fluctuation level (prey)with 90! phase delay. These experimental observationsare consistent with L-H transition models based onturbulence-induced sheared/zonal flows.

# # #

The authors acknowledge the entire TJ-II team fortheir support during the experiments. This work has beenpartially funded by the Spanish Ministry of Science andInnovation under contract No. ENE2007-65927.

REFERENCES

[1] Wagner F., Becker G., Behringer K., CampbellD., Eberhagen A., Engelhardt W., Fussmann G.,Gehre O., Gernhardt J., v. Gierke G., Haas G.,Huang M., Karger F., Keilhacker M., KluberO., Kornherr M., Lackner K., Lisitano G., ListerG. G., Mayer H. M., Meisel D., Muller E. R.,Murmann H., Niedermeyer H., Poschenrieder W.,Rapp H. and Rohr H., Phys. Rev. Lett., 49 (1982) 1408.

35001-p4

T. Estrada et al.

0

5

10

10 -6

10 -5

10 -4

168.5 169.0 169.5 170.0 170.5 171.0

|Er| (

kV/m

) S (a. u.)

time (ms)

Fig. 5: (Color online) Time evolution of Er and densityfluctuation level obtained from the spectrogram shown in fig. 4.

6

8

10

12

10 -7 10 -6 10 -5 10 -4

|Er| (

kV/m

)

S (a.u.)

1

2

3

#23473, t=170-170.4 ms

Fig. 6: (Color online) Relation between Er and density fluctu-ation level. Only two of the cycles shown in fig. 5 are displayed.The time interval between consecutive points is 12.8µs.

The time evolution of both, Er and density fluc-tuations, reveals a characteristic predator-prey rela-tionship: a periodic behaviour with Er (predator)following the density fluctuation level (prey) with90! phase di!erence can be clearly seen. Er is observedto grow and decay at di!erent time rates ((100–150)µsand (50–80)µs, respectively), while the turbulence growsand decays in comparable times ((50–70)µs). These timescales being much faster than the energy confinementtime. The relation between Er and the density fluctuationlevel showing a limit-cycle behavior is represented infig. 6. For the sake of clarity, only two cycles are displayed.The turbulence-induced sheared flow is generated causinga reduction in the turbulent fluctuations (1 in fig. 6), thesubsequent drop in the sheared flow (2 in fig. 6) and theposterior increase in the turbulence level (3 in fig. 6).As has been already discussed, the coupling between

fluctuations and flows, described as a predator-prey evolu-tion, is the basis for some bifurcation theory modelsof the L-H transition [10,11]. The experiments reportedin this letter strongly support these models. However,these results do not necessarily exclude other mechanisms

working together in triggering the transition. In helicaldevices, the negative radial electric field imposed by theNeoclassical ion root condition in the L-mode can act as abias for the transition [16,22], either because a substantialEr-shear already can exist before the transition or becauseof the amplification of zonal flows by Er [27]. On the otherhand, as already mentioned, the magnetic topology caninfluence the H-mode occurrence through mechanisms asflow damping by poloidal viscosity [24] or spin-up of flowsby rational surfaces [28–30]. All these mechanisms mayact together to reach the specific conditions at which theself-regulation between turbulence and flows becomes thedecisive mechanism.To our knowledge, this is the first time that such

an experimental evidence is reported supporting thepredator-prey relationship of turbulence and flows as thebasis for the L-H transition. During the so-called IM modefound in DIII-D power scan experiments [21], the relationbetween electron temperature fluctuations and shearedflows seems to follow a predator-prey behavior, however,as the authors explain, the sheared flow is not directlyobserved but inferred from beam emission spectroscopydata. Two ingredients have been essential in attaining theresults presented in this letter, the possibility of achievinggradual L-H transitions and the capability of measuringsimultaneously both magnitudes, density fluctuations andsheared flows, with good spatiotemporal resolution.

Conclusions. – The dynamics of turbulence andflows has been measured during L-H transitions in thestellarator TJ-II. When operating close to the L-Htransition power threshold, pronounced oscillations inboth, Er and density fluctuation level, are measuredat the transition. The oscillations are measured rightinside the E!B shear layer (located at !" 0.83). Thetime evolution of both, Er and density fluctuation level,shows a characteristic predator-prey behavior, with Er(predator) following the density fluctuation level (prey)with 90! phase delay. These experimental observationsare consistent with L-H transition models based onturbulence-induced sheared/zonal flows.

# # #

The authors acknowledge the entire TJ-II team fortheir support during the experiments. This work has beenpartially funded by the Spanish Ministry of Science andInnovation under contract No. ENE2007-65927.

REFERENCES

[1] Wagner F., Becker G., Behringer K., CampbellD., Eberhagen A., Engelhardt W., Fussmann G.,Gehre O., Gernhardt J., v. Gierke G., Haas G.,Huang M., Karger F., Keilhacker M., KluberO., Kornherr M., Lackner K., Lisitano G., ListerG. G., Mayer H. M., Meisel D., Muller E. R.,Murmann H., Niedermeyer H., Poschenrieder W.,Rapp H. and Rohr H., Phys. Rev. Lett., 49 (1982) 1408.

35001-p4

TJ-II [Estrada ‘10 EPL] NSTX[Zweben, PoP 2010]

Can a simple model explain these? [E. Kim, PRL 2003]

Radial structure of I-phase is identified in DIII-D and TJ-II

5

113-11/LS/rs

L. Schmitz/APS/November 2011

Predator-Prey Oscillations and Zonal Flow-Induced Turbulence Suppression Preceding the L-H Transition

by

L. Schmitz1

withL. Zeng1, T.L. Rhodes1, J.C. Hillesheim1, W.A. Peebles1, R. Groebner2, G.R. McKee3,P.H. Diamond4,5, M. Kazuhiro5, E.J. Doyle1, K.H. Burrell2, G.R. Tynan4, G. Wang1, Z. Yan3

1University of California, Los Angeles2General Atomics, San Diego3University of Wisconsin, Madison4University of California, San Diego5NFRI, Korea

Presented at the

53rd Annual Meeting ofthe APS Division of Plasma PhysicsSalt Lake City, Utah

November 14-18, 2011

vExB

ñ

measured at ! ! 0:75 (see blue, open symbols, profile inFig. 2).

The amplitude of the Er oscillations is shown in Fig. 3together with the amplitude of the oscillations in the den-sity fluctuation level, i.e., rms"~ne#. While the Er oscillationamplitude decreases towards the Er shear position(! ! 0:82), the rms"~ne# oscillation amplitude is maximumright inside the Er shear position and tends to decreasetowards inner radial positions.

As already stated, the TJ-II Doppler reflectometer allowsmeasuring simultaneously at two radial positions whichcan be independently selected [19]. Therefore, it is pos-sible to obtain information on the radial propagation char-acteristics of the cyclic spatiotemporal pattern, extendingprevious temporal (0D) characterization to a spatiotempo-ral (1D) one. An example is shown in Fig. 4. It displays the

time evolution of both density fluctuation level [Fig. 4(a)]and Er [Fig. 4(b)] measured simultaneously at ! $ 0:8 and! $ 0:75. In addition, the time evolution of Er shearcalculated from the data shown in Fig. 4(b) is shown inFig. 4(c). The relation between Er shear and density fluc-tuation level showing a limit-cycle behavior is shown inFig. 4(d). Pronounced changes in Er shear appear linked tothe oscillations in rms"~ne#. Furthermore, a delay betweenthe two channels can be seen indicating a radial propaga-tion from the inner to the outer channel. This outwardpropagation is found in all the oscillation patternsmeasured at line densities between "2–2:5# % 1019 m&3.At densities above 3% 1019 m&3, in some particular casesthe propagation direction eventually reverses after a shorttime period without oscillations.The analysis of the delays yields propagation velocities

within the range ! 50–200 m=s with a radial trend asshown in Fig. 5. In this figure the vertical bars representthe error in the estimation of the propagation velocityand the horizontal ones represent the radial separationbetween the two channels in each discharge. The radialpropagation velocity decreases as the oscillation patternapproaches the Er shear position (at ! ! 0:82). The inwardpropagation velocities are also included in Fig. 5. Similarvalues are obtained although no clear radial dependencecan be inferred. Similarly, as can be seen in Fig. 2, theextreme values of the Er oscillations are comparable inboth cases, for inward and outward propagating oscillationpatterns. However, the time evolution shows differenceswhen comparing both cases. As the oscillation patternpropagates outwards, the increase in the turbulence levelproduces an increase in the shearing rate at the inner shearlayer. This can be seen in Fig. 4: at each oscillation cycle,the increase in the fluctuation level is follow by a decreaseof jErj that results in an increase in the negative Er shear.Oscillation patterns propagating inwards show differentdynamics. An example is shown in Fig. 6: the increase in

0

1

2

3

4

1

2

3

4

0.7 0.75 0.8 0.85

| Er| rms(ñ

e)

max / rms(ñ

e)

min

|E r| (

kV/m

)

rms(ñ

e )max / rm

s(ñe )m

in

FIG. 3 (color online). Amplitude of the Er and rms"~ne# oscil-lations vs plasma radius, measured during time intervals withline-densities between "2–2:5# % 1019 m&3. The striped areaindicates the radial location of the Er shear.

-30

-20

-10

ch1ch2

S (d

B)

#27137 a)

-12

-9

-6

-3

E r (kV/

m)

b)

-400

0

400

-30 -25 -20

174.5 - 175.5 ms

dEr/d

r (kV

/m2 )

S (dB)

d)

-500

-250

0

250

500

172 174 176 178

dEr/d

r (kV

/m2 )

time (ms)

c)

FIG. 4 (color online). The time evolution of (a) density fluc-tuation level and (b) Er, measured simultaneously at ! $ 0:8(channel 1: blue, broken line) and ! $ 0:75 (channel 2: red,solid line). (c) the time evolution of Er shear and (d) relationbetween Er shear and density fluctuation level (only two cyclesare displayed).

-100

0

100

200

0.65 0.7 0.75 0.8 0.85

prop

agat

ion

velo

city

(m/s

)

outwards

inwards

FIG. 5 (color online). Radial propagation velocity vs plasmaradius. The outward propagation velocity decreases as the Er

shear location (at ! ! 0:82) is approached. Inward propagationvelocities are represented using small symbols (in blue). Thestriped area indicates the radial location of the Er shear.

PRL 107, 245004 (2011) P HY S I CA L R EV I EW LE T T E R Sweek ending

9 DECEMBER 2011

245004-3

DIII-D [Schmitz, submitted to PRL] TJ-II [Estrada, PRL ’11]

→One-dimensional model to reproduce I-phase is necessary in that I-phase radial propagation and pedestal formation should be compared.

To address these issues, we have developed a 1D model.

6

� Spatio-temporal evolutions of 5-field (density, pressure, turbulence intensity, ZF, poloidal flow) equations

� Zonal flow / Mean flow competition , a’ la 0D Kim-Diamond � ZF/MF as different players [E. Kim, PRL ’03]

� NO MHD activities; NO ELMs

� No ‘first principle’ simulations have ever reproduced or elucidated the L-H transition!

Predator-prey model

∂t I = (γL −ΔωI −α0Eo −αVEV )I + χN∂x (I∂xI )

∂tE0 = AE0α0 (I / (1+ζ0EV )− I*)

ΕV = (∂xVE×B )2

Driving term Local dissipation

ZF shearing MF shearing Turbulence spreading

Reynolds stress drive MF/ZF competition

ZF collisional damping

critTT

sLL L

RLR

Rc

⎟⎟⎠

⎞⎜⎜⎝

⎛−0~ γγ

Short time scale normalization ω*(~cs/a)t →t Long time scale τii (=1/νii)~ 600(a/cs)

Small spatial scale ρi~0.01a Long spatial scale normalization r/a → r

I* = γdamp /α0

γdamp ~ (ν ii +νCX ) / R

)1( ~~ ac00 <<τρ

τααs

iacV c

a

acsi

NGBNN

2

00 ~~ ρχχχχ

Screening factor

by radial force balance

from p,n profile Turbulence intensity:

Zonal flow energy: E0=VZF2

Mean flow shearing:

1D transport model

VnnDDp

xoneon

xoneop

−∂+−=Γ

∂+−=Γ

)(

)( χχ

∂t p(x)+∂xΓ p = H∂tn(x)+∂xΓn = S

Neoclassical transport term

Banana regime χneo ~ χTi ~ εT

−3/2q2ρi2ν ii

Dneo ~ (me /mi )1/2 χTi

→Predator-prey model

D0 ~ χ0 ~τ ccs

2I(1+αt !VE

2 )

Turbulent transport term

pressure

density

)0 ,(

)( ,0,0

<∝⎟⎟⎠

⎞⎜⎜⎝

⎛−≅

+=

TT

TETEP

LILD

RD

vvV

TEP pinch Thermoelectric pinch

Inward pinch

→density peaking

)exp(~ rDVn −

Pinch term

x: radial direction

a la’ [Hinton ’90 PFB], [Z.H. Wang, P.D, ‘11 NF]

Poloidal momentum spin-up �  Full-f gyrokinetic simulation predicts that poloidal flow driven by

turbulence can be another mediator through L-H transition especially in low ρ* plasmas.[Dif-Pradalier ’08, PRL]

�  Coupling radial and parallel momentum force balance equations, we obtain

−∂uθ∂t

=1nm

∇⋅ (eyΠturb ) +µii

(neo) (uθ −uθ(neo) )

~α5γLω*

cs2∂xI + (ν ii +νCX )q2R2µ00 (uθ +1.17cs

ρiLT

)

Turbulence drive obtained from stress tensor [McDevitt, PoP ‘10] Neoclassical

effects Eq. of poloidal rotation

Radial force balance equation:

θ

θ

ρ uLLLc

uuqRrp

npn

neBV

dxdpnpsi

BE

ʹ′−+−=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛ʹ′−

ʹ′⎥⎦

⎤⎢⎣

⎡+⎥⎦

⎤⎢⎣

⎡ ʹ′ʹ′+ʹ′ʹ′−=ʹ′

−−−

×

)(

111

111

||2

Pressure curvature

Density gradient

Diamagnetic drift term Toroidal flow (not considered here)

Poloidal flow driven by neoclassical and turbulent drives

from global profiles

•  Pressure curvature (ignored by Hinton et. al., noted by Helander et al., Malkov, P.D. ) produces fine scale <VE>’ structure

•  Poloidal rotation from neoclassical, Reynolds drive •  Totally, time-evolving 5-fields (n, p, I, E0, and uθ) are solved

numerically.

Numerical simulation results: Slow Power Ramp Indicates L→I→H Evolution.

11

c.f. DIII-D, [Schmitz et al.], 1D Model

turbulence

ZF

MF

time

r/a

Cycle is propagating nonlinear wave in edge layer

Period of cycle increases approaching transition.

•  Turbulence intensity peaks just prior to transition.

•  Mean shear (i.e. profiles) also oscillates in I-phase.

ZF

Turbulence intensity

Mean flow shear

Mean shear location comparisons indicate inward propagation, and observed in experiments.

•  Inward propagation ~80 [m/s] •  Similar to exp.

[Estrada],[Schmitz]

Turbulence ZF shearing MF shearing

r/a=0.975

r/a=0.950

r/a=0.925

measured at ! ! 0:75 (see blue, open symbols, profile inFig. 2).

The amplitude of the Er oscillations is shown in Fig. 3together with the amplitude of the oscillations in the den-sity fluctuation level, i.e., rms"~ne#. While the Er oscillationamplitude decreases towards the Er shear position(! ! 0:82), the rms"~ne# oscillation amplitude is maximumright inside the Er shear position and tends to decreasetowards inner radial positions.

As already stated, the TJ-II Doppler reflectometer allowsmeasuring simultaneously at two radial positions whichcan be independently selected [19]. Therefore, it is pos-sible to obtain information on the radial propagation char-acteristics of the cyclic spatiotemporal pattern, extendingprevious temporal (0D) characterization to a spatiotempo-ral (1D) one. An example is shown in Fig. 4. It displays the

time evolution of both density fluctuation level [Fig. 4(a)]and Er [Fig. 4(b)] measured simultaneously at ! $ 0:8 and! $ 0:75. In addition, the time evolution of Er shearcalculated from the data shown in Fig. 4(b) is shown inFig. 4(c). The relation between Er shear and density fluc-tuation level showing a limit-cycle behavior is shown inFig. 4(d). Pronounced changes in Er shear appear linked tothe oscillations in rms"~ne#. Furthermore, a delay betweenthe two channels can be seen indicating a radial propaga-tion from the inner to the outer channel. This outwardpropagation is found in all the oscillation patternsmeasured at line densities between "2–2:5# % 1019 m&3.At densities above 3% 1019 m&3, in some particular casesthe propagation direction eventually reverses after a shorttime period without oscillations.The analysis of the delays yields propagation velocities

within the range ! 50–200 m=s with a radial trend asshown in Fig. 5. In this figure the vertical bars representthe error in the estimation of the propagation velocityand the horizontal ones represent the radial separationbetween the two channels in each discharge. The radialpropagation velocity decreases as the oscillation patternapproaches the Er shear position (at ! ! 0:82). The inwardpropagation velocities are also included in Fig. 5. Similarvalues are obtained although no clear radial dependencecan be inferred. Similarly, as can be seen in Fig. 2, theextreme values of the Er oscillations are comparable inboth cases, for inward and outward propagating oscillationpatterns. However, the time evolution shows differenceswhen comparing both cases. As the oscillation patternpropagates outwards, the increase in the turbulence levelproduces an increase in the shearing rate at the inner shearlayer. This can be seen in Fig. 4: at each oscillation cycle,the increase in the fluctuation level is follow by a decreaseof jErj that results in an increase in the negative Er shear.Oscillation patterns propagating inwards show differentdynamics. An example is shown in Fig. 6: the increase in

0

1

2

3

4

1

2

3

4

0.7 0.75 0.8 0.85

| Er| rms(ñ

e)

max / rms(ñ

e)

min

|E

r| (kV

/m)

rms(ñ

e )m

ax / rm

s(ñe )

min

FIG. 3 (color online). Amplitude of the Er and rms"~ne# oscil-lations vs plasma radius, measured during time intervals withline-densities between "2–2:5# % 1019 m&3. The striped areaindicates the radial location of the Er shear.

-30

-20

-10

ch1ch2

S (

dB

)

#27137 a)

-12

-9

-6

-3

Er (

kV/m

)

b)

-400

0

400

-30 -25 -20

174.5 - 175.5 ms

dE

r/dr

(kV

/m2)

S (dB)

d)

-500

-250

0

250

500

172 174 176 178

dE

r/dr

(kV

/m2)

time (ms)

c)

FIG. 4 (color online). The time evolution of (a) density fluc-tuation level and (b) Er, measured simultaneously at ! $ 0:8(channel 1: blue, broken line) and ! $ 0:75 (channel 2: red,solid line). (c) the time evolution of Er shear and (d) relationbetween Er shear and density fluctuation level (only two cyclesare displayed).

-100

0

100

200

0.65 0.7 0.75 0.8 0.85p

rop

ag

atio

n v

elo

city

(m

/s)

outwards

inwards

FIG. 5 (color online). Radial propagation velocity vs plasmaradius. The outward propagation velocity decreases as the Er

shear location (at ! ! 0:82) is approached. Inward propagationvelocities are represented using small symbols (in blue). Thestriped area indicates the radial location of the Er shear.

PRL 107, 245004 (2011) P HY S I CA L R EV I EW LE T T E R Sweek ending

9 DECEMBER 2011

245004-3

[Estrada ’11 PRL]

Phase delay between turbulence and zonal flow increases from π/2 to π during I-phase

14

1D model DIII-D [Schmitz, ‘11 APS] ~π/2 phase delay

~π phase delay

The phase lag relation is shown in DIII-D experiments!

Time evolution of diamagnetic shearing.

15

Diamagnetic shearing ωE×B,dia =∂∂r

1eBn#

$%

&

'(∂p∂r

c.f. DIII-D [Schmitz]

→Diamagnetic shear oscillates with growing amplitude in I-phase, then increases abruptly at L-H transition.

1D model:

Energy channel → Rate of coupling to ZF comparable to drive at the transition threshold.

16

•  Peak of ZF shearing contribution increasing •  Consistent with EAST results[Manz, Xu et al., submitted]

•  ZF triggers MF; ZF can be a heat ‘reservoir’ w/o increasing turbulence. •  Thus, ZF shearing dominant in prior to L→H transition.

1D Model:

Profile comparison in L, I, H �  Pressure and temperature profile

T(r ) pressure Density temperature

è Pedestal formation clearly recovered.

Fast ramp up indicates no LCO, but L→H transition occurs.

a) turbulence

b) ZF

c) log(MF)

Implications for Steady State Experiments (KSTAR, EAST, JT-60 SA, ITER)

19

�  neutral CX can damp zonal flows (c.f. Y. Xu, et al., in preparation) 　- high edge nneutral unfavorable to transition 　→ long established experimental lore concerning Qthresh , 　　‘dirty machines,’ re-cycling,...

�  But: - in SST, with long pulse H-mode, can expect: → eventual wall saturation

→ subsequent increase in re-cycling → increase in CX damping of ZF

If/When discharge drops out of H-mode, will recovery be possible???

γZF ~ νii+νCX

Increase γZF and µneo increases L→H power threshold. → neutral CX increases power threshold!

20

Back transitions --- More than hysteresis!

21

�  Back transitions now both an interesting and a pragmatically critical topic for ITER

�  Back transition issues: → hysteresis → rate of βp decay (D. McDonald, ’12) → observation of so-called ‘small,Type III ELMs’ during βp decay at back transition → beneficial, as allows ‘soft landing’ i.e. vs

→ hypothesize that ‘small Type III ELMs’ are really L.C.O. in back transition → Key Question: Does back-transition occur via H→I→L?

YES! See [Schmitz ’11 APS]

Case with slow power ramp up and down

Slow power ramp up Slow power ramp down

L.C.O. nucleates at pedestal shoulder.

Case with slow ramp up and fast ramp down Slow power ramp up Fast power ramp down

Little sign of I-phase

Hysteresis is here! Scan of χneo indicate relation to ‘strength of the hysteresis’

24

Area of hysteresis loop

Ahyst~Nuα

α∼1

Heat power ramp

Core pressure ~ <grad p>

Nu ~ χ turb,L→H

χneo[S.S. Kim and H. Jhang]

Summary of this study

25

�  One dimensional extension of the Kim-Diamond model is introduced, including Pressure/Density profile, 0D K-D model components (turbulence, ZF, MF) , Radial force balance, i.e. mean flow equilibrium. Poloidal rotation spin-up

�  L-I-H-transitions with power ramp up are shown. Observed properties are consistent with those observed in DIII-D, TJ-II, and EAST.

�  Damping of ZF increases the L→H power threshold �  ZF shearing contribution decreases the L→H power threshold. �  Neutral CX hinders plasmas from H-mode transition, by shrinking ZF shearing

contribution and increasing power threshold. �  I-phase on back transition possible but not certain.

�  Hysteresis: Ahyst ~ Nuα

There are REAL clues, both from experiments and the model study, to indicate the connection between L→H transition and ZF.

To-go message: