Multi-Scale ITG/TEM/ETG Turbulence Simulations with … · Multi-Scale ITG/TEM/ETG Turbulence...

S. Maeyama, Y. Idomura, M. Nakata, M. Yagi, N. Miyato

Japan Atomic Energy Agency

Collaborators： T.-H. Watanabe (Nagoya Univ.), M. Nunami, A. Ishizawa (NIFS)

25th IAEA FEC, 15 Oct. 2014

This work is supported by HPCI Strategic Program Field No. 4 and MEXT KAKENHI Grant No. 26800283.

Multi-Scale ITG/TEM/ETG Turbulence Simulations with Real Mass Ratio and β Value

TH/1-1

Introduction

2

One of the critical issues in ITER is electron heat transport, which is inherently multi-scale physics. 2000 [Jenko00PoP]

A candidate is electron temperature gradient modes (ETG). 2007 [Candy07PPCF,Waltz08PoP,Görler08PRL]

ETGs give small transport if there are ion temperature gradient and trapped electron modes (ITG/TEM). However, these multi-scale simulations were limited:

• Reduced mass ratio (mi/me=400, 900) • Electrostatic approximation (β=0)

Radial direction

Polo

idal

dir

ection

“Streamers” in ETG turbulence

Motivation & Outline

Linear instabilities from electron to ion scales

Poloidal wave number kyρti

Lin

ear

gro

wth

rate

γR/v

ti

Scale separation with real mass ratio

10

1

0.1

0.1 1 10

Ion-scale stabilization with real β

β=0.04% β=2.0%

3

Following points are not yet clarified: (i) Are there multi-scale interactions even with the real mass ratio and β value?

(ii) If yes, how do the interactions occur?

Motivation & Outline Following points are not yet clarified: (i) Are there multi-scale interactions even with the real mass ratio and β value? Multi-scale simulation

demonstrates cross-scale interactions.

(ii) If yes, how do the interactions occur? Nonlinear interaction

analysis reveals their mechanisms.

Linear instabilities from electron to ion scales


Lin

ear

gro

wth

rate

γR/v

ti

Scale separation with real mass ratio

10

1

0.1

0.1 1 10

Ion-scale stabilization with real β

β=0.04% β=2.0%

3

5

2.5

0

-2.5

-5

The GKV code [Watanabe06NF,Maeyama13CPC]

• Solve gyrokinetic ions and electrons with electromagnetic fluctuations in a flux-tube geometry.

• Validation with experiments. [Posters:Nakata,Ishizawa,Nunami]

• High scalability allows ITG/TEM/ETG simulations with ~100k CPU cores in ~100 hours. [Maeyama13SC]

ITG/TEM

ETG

Plasma parameters are Cyclone base case parameters [Dimits00PoP]

• R/LTi=R/LTe=6.82, R/Ln=2.2, Te=Ti, r/R=0.18, q=1.4, s=0.786

• Real mass ratio: mi/me=1836

• Real β value: β=2.0% (below NZT [Pueschel13PRL])

4

Multi-scale turbulence simulation（β=2.0%）

Time evolution of the electrostatic potential fluctuations (at mid-plane of the flux tube)

5

Fie

ld e

ne

rgy W

k R

2/(

n0T

iρti2)

Time t vti/R

102

101

1

10-1

10-2

10-3

0 20 40 60 80

Zonal (kyρti=0)

ITG/TEM (kyρti<1)

Med. (1<kyρti<4)

ETG/Streamers

(4<kyρti)

ITG

Spectra

6

Energy spectrum

（β=2.0%）


Lin

ear

gro

wth

rate

R/v

ti

10

1

0.1

0.1 1 10

ITG/

TEM

ETG/

Strea

mers

Med.

Fie

ld e

ne

rgy W

k R

2/(

n0T

iρti2)

Time t vti/R

102

101

1

10-1

10-2

10-3

0 20 40 60 80

Zonal (kyρti=0)

ITG/TEM (kyρti<1)

Med. (1<kyρti<4)

ETG/Streamers

(4<kyρti)

ITG

Spectra

6

Energy spectrum

（β=2.0%）

Wk

ky

10

10-6

0.1 10


Lin

ear

gro

wth

rate

R/v

ti

10

1

0.1

0.1 1 10

ITG/

TEM

ETG/

Strea

mers

Med.

Fie

ld e

ne

rgy W

k R

2/(

n0T

iρti2)

Time t vti/R

102

101

1

10-1

10-2

10-3

0 20 40 60 80

Zonal (kyρti=0)

ITG/TEM (kyρti<1)

Med. (1<kyρti<4)

ETG/Streamers

(4<kyρti)

ITG

Spectra

6

Energy spectrum

（β=2.0%）

ky

Wk

10

10-6

0.1 10

Wk

ky

10

10-6

0.1 10


Lin

ear

gro

wth

rate

R/v

ti

10

1

0.1

0.1 1 10

ITG/

TEM

ETG/

Strea

mers

Med.

Fie

ld e

ne

rgy W

k R

2/(

n0T

iρti2)

Time t vti/R

102

101

1

10-1

10-2

10-3

0 20 40 60 80

Zonal (kyρti=0)

ITG/TEM (kyρti<1)

Med. (1<kyρti<4)

ETG/Streamers

(4<kyρti)

ITG

Spectra

6

Energy spectrum

（β=2.0%）

ky

Wk

10

10-6

0.1 10

Wk

ky

10

10-6

0.1 10

Wk

ky

10

10-6

0.1 10


Lin

ear

gro

wth

rate

R/v

ti

10

1

0.1

0.1 1 10

ITG/

TEM

ETG/

Strea

mers

Med.

Fie

ld e

ne

rgy W

k R

2/(

n0T

iρti2)

Time t vti/R

102

101

1

10-1

10-2

10-3

0 20 40 60 80

Zonal (kyρti=0)

ITG/TEM (kyρti<1)

Med. (1<kyρti<4)

ETG/Streamers

(4<kyρti)

ITG

Spectra

6

Energy spectrum

（β=2.0%）

ky

Wk

10

10-6

0.1 10

Wk

ky

10

10-6

0.1 10

Wk

ky

10

10-6

0.1 10

Wk

ky

10

10-6

0.1 10


Lin

ear

gro

wth

rate

R/v

ti

10

1

0.1

0.1 1 10

ITG/

TEM

ETG/

Strea

mers

Med.

Fie

ld e

ne

rgy W

k R

2/(

n0T

iρti2)

Time t vti/R

102

101

1

10-1

10-2

10-3

0 20 40 60 80

Zonal (kyρti=0)

ITG/TEM (kyρti<1)

Med. (1<kyρti<4)

ETG/Streamers

(4<kyρti)

ITG

Spectra

6

Energy spectrum

（β=2.0%）

ky

Wk

10

10-6

0.1 10

Wk

ky

10

10-6

0.1 10

Wk

ky

10

10-6

0.1 10

Wk

ky

10

10-6

0.1 10

Wk

ky

10

10-6

0.1 10


Lin

ear

gro

wth

rate

R/v

ti

10

1

0.1

0.1 1 10

ITG/

TEM

ETG/

Strea

mers

Med.

Electron energy diffusion spectrum in multi-scale turbulence is NOT a sum of single-scale ones.

7

In zero-β case, due to strong electron-scale suppression, ion-scale simulations give a good estimate.

In finite-β case, electron-scale suppression is weak. Ion-scale transport is enhanced in multi-scale analysis.

0.0001

0.01

1

100

0.1 1 10

(ce/c

gB

i)/(

Dk

yr

ti)

Poloidal wave number kyrti

Ion-scale sim. e=1.2gB

Electron-scale sim. e=5.4gB

Multi-scale sim. e=4.5gB


0.1 1 10

Finite β case (β=2.0%)

102

1

10-2

10-4

Ele

ctr

on

th

erm

al d

iffu

sio

n

coeffic

ient

ek/

gB

* Ion energy diffusion is similar (see proceedings).

0.0001

0.01

1

100

0.1 1 10

(ce/c

gB

i)/(

Dk

yr

ti)

Poloidal wave number kyrti

Ion-scale sim. e=6.4gB

Electron-scale sim. e=7.2gB

Multi-scale sim. e=6.3gB

102

1

10-2

10-4

Ele

ctr

on

th

erm

al d

iffu

sio

n

co

effic

ien

t

ek/

gB

Zero-β case (β=0.04%)


0.1 1 10

Analysis of nonlinear interactions Gyrokinetic triad transfer - Mode-to-mode nonlinear transfer of perturbed entropy

𝐼𝑠𝒌 = 𝐽𝑠𝒌𝒑,𝒒

𝒒𝒑

𝐽𝑠𝒌𝒑,𝒒= 𝛿𝒌+𝒑+𝒒,𝟎

𝒃 ⋅ 𝒑 × 𝒒

2𝐵

× Re 𝑑𝑣3 𝜒 𝑠𝒑𝑔𝑠𝒒 − 𝜒 𝑠𝒒𝑔𝑠𝒑𝑇𝑠𝑔𝑠𝒌𝐹𝑠𝑀

（Generalized potential 𝜒 𝑠𝒌 = 𝜙 𝒌 − 𝑣∥𝐴 ∥𝒌 、

Nonadiabatic distribution 𝑔𝑠𝒌 = 𝑓𝑠𝒌 +𝑒𝑠𝐹𝑠𝑀

𝑇𝑠𝜙 𝒌）

8

Radial wave number qxρti

Polo

idal w

ave n

um

ber

qyρ

ti

k

q

p

k+p+q=0

Electron-scale suppression mechanism: • Ion-scale ZF shearing? Or, Another structures? Ion-scale enhancement mechanism: • Inverse cascade to ion-scale turbulence? Or, Damping of ion-scale ZFs?

[Nakata12PoP]

Suppression of electron-scale streamers by high-kx ITG/TEM structures.

9


Polo

idal w

ave n

um

be

r q

yρ

ti

6

4

2

0

-2

-4

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

[a.u.]

2×10-5

1×10-5

0

-1×10-5

-2×10-5

k (Streamer)

Triad transfer 𝐽𝑠𝒌𝒑,𝒒𝑠 for a streamer

(kxρti,kyρti)=(0,4.4) at t=20-30R/vti


9


Polo

idal w

ave n

um

be

r q

yρ

ti

6

4

2

0

-2

-4

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

[a.u.]

2×10-5

1×10-5

0

-1×10-5

-2×10-5

k (Streamer)



p (~1.6ρti-1)

Kinetic electrons create fine radial structures (kxρti>1). [Dominski12JPCS,

Maeyama14PoP]


9


Polo

idal w

ave n

um

be

r q

yρ

ti

6

4

2

0

-2

-4

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

[a.u.]

2×10-5

1×10-5

0

-1×10-5

-2×10-5

k (Streamer)



p (~1.6ρti-1)

At the reduction phase, these radial structures suppress streamers.


Maeyama14PoP]


9


Polo

idal w

ave n

um

be

r q

yρ

ti

6

4

2

0

-2

-4

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

[a.u.]

2×10-5

1×10-5

0

-1×10-5

-2×10-5

k (Streamer)

q (Finer

mode)



p (~1.6ρti-1)

At the reduction phase, these radial structures suppress streamers.


Maeyama14PoP]

After suppression of ETG/streamers, normal cascade dominates electron scales.

10

At the steady state, normal cascade dominates via the direct coupling with ion-scale turbulent eddies.




-6 -4 -2 0 2 4 6

6

4

2

0

-2

-4

-6

[a.u]

2×10-6

1×10-6

0

-1×10-6

-2×10-6

Po

loid

al w

ave

nu

mb

er

qyρ

ti

k (Streamer)


10





-6 -4 -2 0 2 4 6

6

4

2

0

-2

-4

-6

[a.u]

2×10-6

1×10-6

0

-1×10-6

-2×10-6

Po

loid

al w

ave

nu

mb

er

qyρ

ti

p (Ion

scales)

k (Streamer)


10





-6 -4 -2 0 2 4 6

6

4

2

0

-2

-4

-6

[a.u]

2×10-6

1×10-6

0

-1×10-6

-2×10-6

Po

loid

al w

ave

nu

mb

er

qyρ

ti

p (Ion

scales)

k (Streamer)

q (Finer

mode)

Inefficient zonal mode generation in multi-scale turbulence.

11

Inverse cascade from electron to ion scales seems not to be responsible.

Comparing multi-scale simulation with single-scale one, Zonal part of field energy is relatively weak. Inefficient zonal mode generation is observed.

Nonlinear entropy

transfer for zonal modes

0 20 40 60 80

Time t vti/R

0.12

0.08

0.04

0

WZ

ona

l /Wn

on

-zona

l

0 20 40 60 80 Time t vti/R

0.4

0.3

0.2

0.1

0

Ion-scale simulation

Multi-scale simulation

Ion-scale simulation


I kZ

ona

l /Drivin

g t

erm

Ratio of zonal to non-

zonal field energy

Enhancement of ion-scale turbulence is caused by damping of zonal modes.

12

Splitting ion- and electron-scale contributions clarifies Electron-scale turbulence has damping effects on

zonal modes around kxρti~1. → The reduction of ZF shearing enhances transport.

Entropy transfer spectrum

for zonal modes

Drive by ion scales

Damping by electron scales

Total Ion-scale simulation



0.1 1 10

102

1

10-2

10-4

Ele

ctr

on

the

rmal diffu

sio

n

co

effic

ient

ek/

gB

Ion-scale sim. filtering ZFs (kxρti>0.8) Elec

tron-scale sim.

Test of reduced ZFs

0 0.5 1 1.5 2 2.5 3

0.003

0.002

0.001

0

-0.001

JkΩ

p,Ω

q(k

y=

0)/

Drivin

g t

erm

Radial wave number kxρti

Summary and discussion

13

We have first analyzed multi-scale ITG/TEM/ETG turbulence with real mass ratio and β value. We have demonstrated the existence of multi-

scale interactions even with real mass ratio. - ETG/Streamers are suppressed by ITG/TEM turbulence.

ITG stabilization by finite-β effects makes

electron-scale contributions non-negligible. - We newly found that electron-scale turbulence can enhance ion-scale turbulent transport.

Summary and discussion

14

In terms of transport level estimation Multi-scale spectrum is NOT a sum of single scales. When ITGs are highly unstable, ion-scale simulations

give a good estimate of transport levels. In high-β regimes, electron scales can be important.

• Effective damping of ion-scale ZFs

ZF damping by Electron-scale turb.

ITG / TEM

ETG / Streamers

Zonal Flows

ETG reduction by ITG/TEM

Normal cascade via coupling with ITG/TEM turbulent eddies dominates electron scales.

Electron-scale turbulence acts as effective damping of ZFs.

In terms of turbulence physics

Multi-Scale ITG/TEM/ETG Turbulence Simulations with … · Multi-Scale ITG/TEM/ETG Turbulence...

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