Dynamic method to study turbulence and turbulence transport S. - - PowerPoint PPT Presentation

Dynamic method to study turbulence and turbulence transport

• S. Inagaki, K. Ida1, S.-I. Itoh, K. Itoh1, T. Tokuzawa1, N. Tamura1, S. Kubo1,
• T. Shimozuma1, K. Tanaka1, H. Tsuchiya1, Y. Nagayama1, T. Kobayashi2, N. Kasuya,
• M. Sasaki, A. Fujisawa, Y. Kosuga3, K. Kamiya4, H. Yamada1, A. Komori1 and LHD

experiment group1 Research Institute for Applied Mechanics, Kyushu University

1National Institute for Fusion Science 2Interdisciplinary Graduate School of Engineering Sciences, Kyushu University 3Institute for Advanced Study, Kyushu University 4Japan Atomic Energy Agency

EX2-1

1

Conventional method has serious difficulty

Revisiting heat pulse propagation analysis

Lopes Cardozo PPCF 1995

e

T  

qe ne

cpb chp

Pulse Propagation

pb e e e e e e hp

c c         T n q T n q

Discovery of the New Transport Relation on LHD

Conventional Approach

Single-Valued Function Multiple-Valued Function (hysteresis)

Periodic power modulation

One time-scale Two time-scales

2

• S. Ingaki NF 2013

Contents

• Assessment of conventional method (What is chp?).
• A simplified new approach to understand the transport

with multiple-valued flux (hysteresis, barrier formation)

• Observation of coupling of micro-fluctuations at distant

locations

Method to study turbulence transport Method to observe multi-scale couplings of turbulence

3

• Target plasma (NBI+MECH)
• Modulations of Te, ∇Te and

fluctuation are observed simultaneously

• Exp. Set-up and Conditional Averaging

no ITB, no ETB no evidence of high-energy tail MECH 25Hz

Periodic temporal evolution of signals are precisely extracted.

Macro-mode Micro-fluctuations

4

• S. Ingaki NF 2013

Precise spatiotemporal structure of heat pulse

The conventional chp is flawed since it neglects two time scales in transient response.

two distinct time scales

• ne time scale

Diffusive Nature Experiment Simulation

5

Conditional averaging technique is very powerful tool

(Conditional Averaged)

Higher harmonics in the heat pulse propagation

The two-time scale feature should appear in the response

• f extremely-higher harmonics

6

More-than 10th harmonics are observed even far away from source

Observations far from diffusive nature Weaker decay in amplitude Faster propagation

Features of Higher harmonics

7

1 A ¶A ¶r ~ ¶ Q ¶r µ m

Diffusion 1st 3rd 5th

Higher harmonics in the heat pulse propagation

8

Fundamental mode can not catch the response around turn-on/off

• f ECH power where qe changes

discontinuously To describe a discontinuous function, higher harmonics is essential

Higher harmonics should be more routinely checked to clarify the transport with multiple-valued flux

Heat pulse propagation during ITB transition

• ECH modulation experiment near the ITB transition
• The ITB foot shifts back and forth during ECH modulation

Delayed rises and simultaneous drops are observed

foot

9 Similar to K. Ida NF 2009

• Three or four dynamics combined
• Fast propagation, Displacement of ITB front,

Global (non-local) response in Te

Mixed time-scale phenomena

ITB transition is involved with multi-mechanisms D

10

dTe d Te

D

d Te

D

/(d Te)max

D

Te drop

D

Global responses Fast Propagation

(Conditional Averaged)

Method to observe multi-scale couplings of turbulence

Non-locality of turbulence is one of the important keys to understand the multiple-valued flux (hysteresis and two time-scale response)

11

rA rB

F(f3, rA): Fluctuations at rA f(f1, rB), f(f2, rB): Fluctuations at rB

Cross Bi-Coherence of Fluctuations at Distant Locations

rB- rA >> correlation length of micro-modes

Non-Local Bi-Coherence

Micro-Turbulence Long-range modes

1 M 100 k 10 k 1 k 1 r/a

f (Hz)

b2

nl( f1, f2) =

F*( f3,rA)f( f1,rB)f( f2,rB)

2

F( f3,rA)

2

f( f1,rB)f( f2,rB)

2

12

Non-Local Micro-Global Coupling

• Summed bi-coherence shows a peak at 2.75 kHz

2.75kHz at

r = 0.63 17kHz (noise)

S b2 f3 (kHz) 17kHz

2.75kHz

S b2 1/n

150 kHz < f1 < 250 kHz at r = 0.88

Global fluctuation(2.75 kHz) at rA = 0.63 non-locally couples with micro-fluctuations (150-250 kHz) at rB = 0.88

• The summed bi-coherence converges to 0.2

(~1/10 of the local summed bi-coherence)

13

• S. Inagaki NF 2014

Tri-Coherence analysis is just started

4-Wave coupling between distant locations rA rB

f1 f2 f4 f3

Micro-Turbulence Long-range modes

1 M 100 k 10 k 1 k 1 r/a

f (Hz)

Tri-coherence at two distant locations is calculated

f1 + f2 = f3 + f4 gtri

2 > 0.1

14

Research

Summary

• Conditional averaging technique is very useful to

understand the transport with multiple-valued flux

• Non-local bi-/tri-spectrum analysis allows us to study the

non-local coupling between micro-fluctuations

This study established methods for analyzing (i) heat transport dynamics beyond Fick’s law and (ii) ’non-local’ coupling of micro- fluctuations. Hysteresis in transport = two-time scale response =Slow decay and fast propagation of the higher harmonics

These results are beneficial for understanding of the plasma dynamics in future fusion reactors.

15

Identification of three or four time-scale responses in the ITB plasma

Non-Local Micro-Micro Coupling

Tri-coherence suggests

• Micro-fluctuations (>50 kHz) at two

different locations are coupled

• Global-fluctuations (<10 kHz) are

involved

16

Like-scale couplings e.g 102kHz+101kHz 99kHz+103kHz < 10 kHz < 10 kHz