HL-2A

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Roles of Turbulence Induced Zonal Flow and Diamagnetic Flow in L-I-H Transitions

J.Q. Dong, J. Cheng, L.W. Yan, Z.X. He, K. Itoh, H. S. Xie, Y. Xiao, K. J. Zhao, W.Y. Hong, Z.H. Huang, L. Nie, S.-I. Itoh, W.L. Zhong, D.L. Yu , X.Q. Ji, Y. Huang, X.M. Song, Q.W. Yang, X.T. Ding, X.L. Zou, X. R. Duan, Yong Liu and HL-2A Team

Southwestern Institute of Physics, Chengdu, ChinaInstitute for Fusion Theory and Simulation, ZJU, Hangzhou, ChinaNational Institute for Fusion Science, Toki, Japan University of Science and Technology of China, Hefei, ChinaWCI Center for Fusion Theory, Daejeon, KoreaKyushu University, Kasuga, JapanCEA, IRFM, Cadarache, France

March 22-25, 2015The Third Theory and Simulation Workshop

Hefei, China

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Outline 1. Motivation

2. Experimental results

3. Summary and discussion

HL-2A1. Motivation

• Identification of the key plasma parameters, which control/determine the L-H transition and reveal its mechanism in tokamaks, has been a long term focus of investigation and a topic of interest.

• Limit cycle oscillations (LCO) were observed when heating power was close to L-H transition power threshold.

• Study on dynamics of LCO with expansion of time scale provides opportunity to investigate the subject quantitatively.

• The LCO has been studied theoretically with predator-prey and bifurcation models, respectively.

• In experiment, spontaneous LCOs were observed on JET, JFT-2M, AUG, DIII-D, EAST, H-1 and TJ-II stellarators, and NSTX.

• The roles of turbulence induced zonal flow and diamagnetic drift flow in LCO & L-I-H transitions are investigated in HL-2A experiment.

[Cheng, Dong & Itoh et al., PRL 110, 265002 (2013) ]

[Dong, Cheng & Yan et al., 25th IAEA FEC, oral talk(2014) ]

3

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• H-模物理研究：功率阈值

0

0.5

1

1.5

2

2.5

2 3 4 5 6 7 8 9

ECHH-NBI

ECHD-NBI

Pth

res

[MW

]

4He plasmas D plasmas

ne [1019 m-3]

0.98 0.74 0.73 0.5533 0.20.042

0.6083 0.3LH

MW for nP S B n

MW for n

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• Sampling rate = 1 MHz• Spatial resolution= 3 mm• Diameter of tips is 1.5 mm. • Height of tips is 3 mm.

3D Langmuir probe arrays

PP

TSLP

Parameters measured simultaneously:

etc. at a few radial and poloidal positions in two poloidal sections;

, , , , , , ' , ',e e f e r e r eT n n E P E P

The most complete data of edge turbulence in tokamak plasmas.

HL-2A

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The poloidal and toroidal symmetries, measured simultaneously, for LFZF and GAM.

AT

Coexistence of intensive LFZFs and GAMs

K. J. Zhao, J. Q. Dong, L. W. Yan, Plasma Phys. Control. Fusion 52, 124008 (2010).

(a) Radial wave vector-frequency and (b) wave vector spectra of LFZF and GAM potential fluctuations,

HL-2AModulation of turbulence by zonal flows

(a) Poloidal and toroidal coherency spectra of turbulence envelopes. (b) Corresponding phase shift spectra. (c ) Radial wave number-frequency spectra of turbulence envelopes, (d,e) The radial wave number spectra for the LFZF, GAM and envelopes of same frequencies.

1 100

0.2

0.4

0.6

0.8cohere

ncy

f(kHz)1 10

-1

-0.5

0

0.5

f (kHz)

phase (

rad/

)

kr (cm-1)

f (k

Hz)

-6 -4 -2 0 2 4 60

10

20

30

-8 -6 -4 -2 0 2 4 6 8 0

0.02

0.04

0.06

S (

a,u

)

-8 -6 -4 -2 0 2 4 6 8 0

0.02

0.04

0.06

kr(cm-1)

S(a

,u)

(a) (b)

Noiselevel

d=36mm

dt=2100mm

(c)(d)

S(kr,f)

(e)Envelope

GAM

EnvelopeLFZF

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2. Experimental results

Shot I with L-I-H transitionsBt=1.4 TIp=180 kA PNBI=1.0 MW Shot II with L-I-L transitionsBt=1.4 TIp=185 kA PNBI=1.0 MW

19 12.8 3.2 10en m

19 12.5 3.0 10en m

In the I-phases, all the fluctuations oscillate at same frequency of fLCO~ 2-3 kHz which is identified to be close to the local ion-ion collision frequency.

100

101

102

10-3

10-2

10-1

100

101

102

f(kHz)

Aut

o P

ower

Spe

ctru

m

L

I

H

0 0.5 1 1.5 2 2.5 3 3.5

x 104

0

0.5

1

1.5

D

Vf

(a)

(b)

HL-2A

0 0.2 0.4 0.6 0.8 1 1.2

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

|Er|orLpe-1 (a.u.)

Enve

lope

of n

e(a.u

.)

2

31

2 1

2

1

3

3

I-phase

H

LCO in L-I-H transitions

9

0.1 0.2 0.3 0.4 0.50.1

0.2

0.3

0.4

0.5

|Er|orLpe-1 (a.u.)

Env

elop

e of

ne(a

.u.)

1

2

3

0 0.5 1

0

0.1

0.2

0.3

0.4

0.5

|Er|(a.u.)

Env

elop

e of

ne(a

.u.)

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

|Er|(a.u.)

Env

elop

e of

ne(a

.u.)

1

2

3

1

3

2

0.6 0.8 1

0

0.1

0.2

0.3

0.4

0.5

|Er|(a.u.)

Env

elop

e of

n e(a.u

.)

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

|Er|(a.u.)

Env

elop

e of

n e(a.u

.)

1

2

3

1

2

3

0 0.2 0.4 0.6 0.8 1

0

0.1

0.2

0.3

0.4

0.5

|Er|(a.u.)

Envelo

pe o

f n e(a

.u.)

0.9 0.95 1 1.050

0.02

0.04

0.06

0.08

|Er| or Lpe-1 (a.u.)

Envelo

pe o

f ne(a

.u.)

1

2

3

3

1

2

Type-J

Type-Y

Type-Y

Type-J

Type-J

Type-J

Er(a.u.)Er(a.u.)

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LCO in L-I-L transitions

0.2 0.3 0.4 0.50

0.05

0.1

0.15

0.2

0.25

|Er|(a.u.)

Env

elop

e of

ne(a

.u.)

0.2 0.3 0.4 0.50

0.05

0.1

0.15

0.2

0.25

|Er|(a.u.)

Env

elop

e of

ne(a

.u.)

0.1 0.2 0.3 0.4 0.50

0.05

0.1

0.15

0.2

0.25

|Er|(a.u.)

n een(a

.u.)

2

3

11

2

3

shot=19274,range=[450 600]; index=8.0*1e4:10.0*1e4-1;Is

en=envelope

t(ep32,[495 530],[20 100]);

Isen

f=smooth(Is

en,100);

PA

T=Isen

f(indexx)

PLF=dp1

f(indexx)./2;

indexx=0.5*1e4:1.5*1e4-1;

3

1

20.2 0.3 0.4 0.50

0.05

0.1

0.15

0.2

0.25

|Er|(a.u.)

Envelo

pe o

f n e(a

.u.)

0.2 0.3 0.4 0.50

0.05

0.1

0.15

0.2

0.25

|Er|(a.u.)

Envelo

pe o

f n e(a

.u.)

0.1 0.2 0.3 0.40

0.05

0.1

0.15

0.2

0.25

|Er|(a.u.)

Envelo

pe o

f n e(a

.u.)

23

1

23

1 1

2

3

shot=19274,range=[450 600]; index=8.0*1e4:10.0*1e4-1;Is

en=envelope

t(ep32,[495 530],[20 100]);

Isen

f=smooth(Is

en,100);

PA

T=Isen

f(indexx)

PLF=dp1

f(indexx)./2;

indexx=0.5*1e4:1.5*1e4-1;

0.2 0.3 0.4 0.50

0.05

0.1

0.15

0.2

0.25

|Er|(a.u.)

Envelo

pe o

f n

e(a.u

.)

0.2 0.3 0.4 0.50

0.05

0.1

0.15

0.2

0.25

|Er|(a.u.)

Envelo

pe o

f n

e(a.u

.)

0.1 0.2 0.3 0.40

0.05

0.1

0.15

0.2

0.25

|Er|(a.u.)

Envelo

pe o

f n

e(a.u

.)2

3

1

23

1 1

2

3

shot=19274,range=[450 600]; index=8.0*1e4:10.0*1e4-1;Isen=envelopet(ep32,[495 530],[20 100]);

Isenf=smooth(Isen,100);

PA

T=Isen

f(indexx)

PLF=dp1f(indexx)./2;

indexx=0.5*1e4:1.5*1e4-1;0.2 0.3 0.4 0.50

0.05

0.1

0.15

0.2

0.25

|Er|(a.u.)

Envelo

pe o

f n

e(a.u

.)

0.2 0.3 0.4 0.50

0.05

0.1

0.15

0.2

0.25

|Er|(a.u.)

Envelo

pe o

f n

e(a.u

.)0.1 0.2 0.3 0.40

0.05

0.1

0.15

0.2

0.25

|Er|(a.u.)

Envelo

pe o

f n

e(a.u

.)

23

1

23

1 1

2

3

shot=19274,range=[450 600]; index=8.0*1e4:10.0*1e4-1;Is

en=envelope

t(ep32,[495 530],[20 100]);

Isen

f=smooth(Is

en,100);

PA

T=Isen

f(indexx)

PLF=dp1

f(indexx)./2;

indexx=0.5*1e4:1.5*1e4-1;

Type-Y

Type-Y

Type-Y

Type-Y

HL-2ALCO in L-I-H & L-I-L transitions

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t= 536-536.5 ms, t=538.5-539 ms, t=543-543.5 ms.

t=506-506.5 ms, t=510-510.5 ms, t=518-518.5 ms, t=525-525.5 ms.

495 500 505 510 515 520 525 530

1

2

1.5

t(ms)

D(a

.u.)

530 535 540 545 550

1

2

t(ms)

D(a

.u.)

19274/450-600msindex=8-10*1e4SOLep322-3 kHz10-20 kHz

[Cheng & Dong et al., PRL 110, 265002 (2013) ]

e e

HL-2A

[1] S.-I. Itoh, et al., Phys. Rev. Lett. 67, 2485 (1991). [2] H. Zohm, Phys. Rev. Lett. 72, 222 (1994). [3] S. J. Zweben et al., Phys. Plasmas 17, 102502 (2010). [4] G. D. Conway et al., Phys. Rev. Lett. 106, 065001 (2011). [5] G. S. Xu et al., Phys. Rev. Lett. 107, 125001 (2011). [6] L. Schmitz, et al., Phys. Rev. Lett. 108 155002 (2012). [7] G.R. Tynan et al., IAEA 2012, EX/10-3 [8] J. Cheng, et al., PRL. 110, 265002 (2013). [9] K. J. Zhao, et al.: IAEA 2012, EX/7–2Ra. [10] T. Kobayashi, et al.: PRL. 111, 035002 (2013). [11] T. Estrada, et al EPL 92 (3) (2010). [12] A. Fujisawa, et al. Phys. Rev. Lett. 81 (1998) 2256. [13] A. Fujisawa, et al.: Plasma Phys. Contr. Fus. 48 (2006) S205. [14] J. Cordey et al., Nucl. Fusion 35, 505 (1995).

Observations of LCO - Varieties

JET [14](95)

HL-2A

Predator-prey model for LCO

• Near H-mode power threshold ， LCO appears in turbulence and shear flow• Phase shift between turbulence and flow: ： turbulence precedes shear flow 90 degrees；

then phase shift becomes 180 degrees.

LCO Theory

+

0

<N>

<U2>

Er bifurcation model for LCO

flux

mean parameter

CCW

CW

[S-I. Itoh, et al., PRL 67, 2485 (1991).][Kim & Diamond et al., PRL 90, 185006, (2003).]

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• Oscillation of radial electric field (ZF) propagates inwards• Radial electric field(ZF) lags density fluctuation [ PRL 108, 155002 (2012) ]

DIII-D

Miki et al., PoP 19,092306 (2012)

Force balance equation of ions

/ 2

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蓝 -红背景对比

Bicoherence analysis

(a-c)Squared auto-bicoherence contour, (d) summed autobicoherence in the periods of time for the L-I-H

transition.

2 1 2 1 21 2 2 2

1 2 1 2

( ) ( ) ( )ˆ ( ) .[ | ( ) ( ) | | ( ) | ]

f f f f fb f f f

f f f f f

〉

1 2

2 21 2

ˆ ˆ ( ) / .N

ff f f

b b f f f N

HL-2ASpatio-temporal evolutions of fluctuations

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The fluctuations of floating potentials, radial electric fields andelectron density of frequency f~ 2-3 kHz.

HL-2ASpectrum of Mirnov coil signals ∂Bθ/∂t

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(a) The time evolution of the spectrum of Mirnov coil signals ∂Bθ/∂t , (b) the coherence γ and (c) phase shift spectra between ∂Bθ/∂t and fluctuations of the gradient of electron pressure ∂pe/∂r , respectively,in the frequency range of 2 − 3 kHz

HL-2APlausible loops for LCOs and I-H transition

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(a) ε, Vzf and N as functions of Q=0.01 t, (b) the Lissajous diagrams for ε versus Vzf (CW)(c) ε versus N (CCW)

Green for CW LCO, red for CCW LCO, yellow for I-H transitionyellow for I-H transition

HL-2A

• Limit Cycle discharge provideslaboratory to test L-H physics

– Turbulence induced flow insufficient to sustain H mode

– H-mode locked in by rise inion diamagnetic flow

– See ∇P term start to leaddrive to ExB rotation

• Measured L-mode seed flow shear consistent with upturn in L-H threshold

H Mode Access: Measurements Confirm Role of Ion Diamagnetic Flow in L-H Transition

Lmode H-modeLimit Cycle Oscillations

Rise in diamagnetic flow

Tim

e C

orr

elat

ion

m

s

0 4 8 12-4 16 20∇P leads : contributes to

∇P lags : not cause of ExB

t – tLCO (ms)

ExB

Schmitz

Ex

B di

a

0

3

6

Promising foundation for physics based L-H prediction

Before L-LCO transition

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3. Summary and discussion Two types of LCOs were observed in L-I-H and L-I-L transitions. Three plausible loops of zonal flow vs. turbulence and turbulence vs.

pressure gradient are proposed for the LCOs and I-H transition. The dominant roles (balancing Er, acceleration etc.) played by the

diamagnetic drift flow in I-phase and I-H transition are demonstrated The rates of energy transfer from the diamagnetic drift and turbulent

Reynolds stress E B flow in L-I-H transitions are compared. The triggering mechanism and conditions for L-I and I-H transitions

are discussed. Much more theoretical and experimental investigations are expected.

HL-2A

21

Thank you

for your attention!

HL-2ALCOs of plasma parameters in L-I-H transitions

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•The temporal evolutions of (a) Dα emission, (b) inverse of the electron pressure gradient scale length 1/Lpe, (c) the radial electric field Er, and (d) the Reynolds stress Rs.

• Negative peaks of Er| and Rs at L-I transition

• 1/Lpe and |Er| gradually increase; their oscillations are in phase• Rs is in /out of phase with |Er| in early/late LCO phase,

HL-2ATime averaged E B and diamagnetic flows

23

Force balance equation of ions

•( VE-Vdim)/VE > 50% in L-mode & early I-phase but <10% prior to I-H transition.

•Evolutions of ∂ Vdim/∂ t and VE and Vdim are strongly correlated.

•No evident correlations between ∂Rs/∂r and VE are observed in I-phase.

HL-2ARates of energy transfer

24

•The temporal evolutions of (a) the energy transfer rates from pressure gradient drive Pdim, (b) from Reynolds stress drive PRS, (c) the power of ambient turbulence PAT, (d) the ratio of PRS/ PAT,

•Pdim (PRS )fast increases prior to theI-H (L-I) transition.•PRS is positive, negative, then positive and keeps increasing with time,•PAT

increases and decreases, respectively, when PRS is negative and positive.

•The ratio of PRS /PAT has a peak prior to the I-H transition.

HL-2ATriggering condition for I-H transition

25

The time evolutions of soft X-ray

(a), inverses of the scale lengths of

electron temperature and density

(b), and pressure (c) , the ion-ion

collision frequency and the growth

rate of the diamagnetic drift flow

(d), the E B flow shearing rate

and the turbulence decorrelation

(e) for two shots.

(1) the I-phase has type-J LCOs, (2) the plasma pressure gradient scale length is less than a critical value (~ 1.7 cm)(3) the E B flow shearing rate is higher than a critical value (~10^6/ s) and the turbulence decorrelation rate (4x10^5 /s) , (4) the growth rate of the diamagnetic drift flow is equal to or slightly higher than the ion-ion collision frequency.

The conditions for I-H transition:

HL-2AFormation of density ETB

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•The evolutions of (a) ion saturation current Is~ne, (b) particle flux Γ, (c) the phase relations between the turbulent particle flux and the electron pressure gradient scale length in LCO.•The density increases/decreases at Δr = -6 mm/-3 mm•The turbulent particle flux is negative/positive at Δr=-6 mm/-3 mm•The density gradient scale length at Δr = -6 mm is in/out of phase with the particle flux Γ at Δr = -6 mm/ /-3 mm•The diffusion in this region is dominated by pressure gradient induced turbulence which leads to inward particle pinch in the process of particle ETB formation.