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Apr 04, 2023 446 likes •751 views

TH/1-1 Multi-Scale ITG/TEM/ETG Turbulence Simulations with Real Mass Ratio and Value S. Maeyama, Y. Idomura, M. Nakata, M. Yagi, N. Miyato Japan Atomic Energy Agency Collaborators T.-H. Watanabe (Nagoya Univ.), M. Nunami, A. Ishizawa

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SLIDE 1
  • 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

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SLIDE 2

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 Poloidal direction

“Streamers” in ETG turbulence

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SLIDE 3

Motivation & Outline

Linear instabilities from electron to ion scales

Poloidal wave number kyρti Linear growth rate γR/vti 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?

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SLIDE 4

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

Poloidal wave number kyρti Linear growth rate γR/vti 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

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SLIDE 5

5 2.5

  • 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, T

e=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

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SLIDE 6

Multi-scale turbulence simulation（β=2.0%）

Time evolution of the electrostatic potential fluctuations

(at mid-plane of the flux tube) 5

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SLIDE 7

Field energy Wk R2/(n0Tiρti

2)

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%）

Poloidal wave number kyρti Linear growth rate R/vti

10 1 0.1 0.1 1 10

ITG/ TEM ETG/ Strea mers Med.

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SLIDE 8

Field energy Wk R2/(n0Tiρti

2)

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

Poloidal wave number kyρti Linear growth rate R/vti

10 1 0.1 0.1 1 10

ITG/ TEM ETG/ Strea mers Med.

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SLIDE 9

Field energy Wk R2/(n0Tiρti

2)

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

Poloidal wave number kyρti Linear growth rate R/vti

10 1 0.1 0.1 1 10

ITG/ TEM ETG/ Strea mers Med.

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SLIDE 10

Field energy Wk R2/(n0Tiρti

2)

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

Poloidal wave number kyρti Linear growth rate R/vti

10 1 0.1 0.1 1 10

ITG/ TEM ETG/ Strea mers Med.

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SLIDE 11

Field energy Wk R2/(n0Tiρti

2)

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

Poloidal wave number kyρti Linear growth rate R/vti

10 1 0.1 0.1 1 10

ITG/ TEM ETG/ Strea mers Med.

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SLIDE 12

Field energy Wk R2/(n0Tiρti

2)

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

Poloidal wave number kyρti Linear growth rate R/vti

10 1 0.1 0.1 1 10

ITG/ TEM ETG/ Strea mers Med.

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SLIDE 13

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

Ion-scale sim.

e=1.2gB

Electron- scale sim.

e=5.4gB

Multi-scale

  • sim. e=4.5gB

Poloidal wave number kyρti 0.1 1 10 Finite β case (β=2.0%) 102 1 10-2 10-4 Electron thermal diffusion coefficient ek/gB

* Ion energy diffusion is similar (see proceedings). 0.0001 0.01 1 100

Ion-scale sim.

e=6.4gB

Electron- scale sim.

e=7.2gB

Multi-scale

  • sim. e=6.3gB

102 1 10-2 10-4 Electron thermal diffusion coefficient ek/gB Zero-β case (β=0.04%) Poloidal wave number kyρti 0.1 1 10

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SLIDE 14

Analysis of nonlinear interactions

Gyrokinetic triad transfer

  • Mode-to-mode nonlinear

transfer of perturbed entropy

𝐽𝑡𝒍 = 𝐾𝑡𝒍

𝒒,𝒓 𝒓 𝒒

𝐾𝑡𝒍

𝒒,𝒓 = 𝜀𝒍+𝒒+𝒓,𝟏

𝒄 ⋅ 𝒒 × 𝒓 2𝐶 × Re 𝑒𝑤3 𝜓 𝑡𝒒𝑕𝑡𝒓 − 𝜓 𝑡𝒓𝑕𝑡𝒒 𝑈

𝑡𝑕𝑡𝒍

𝐺𝑡𝑁

（Generalized potential 𝜓 𝑡𝒍 = 𝜚 𝒍 − 𝑤∥𝐵 ∥𝒍 、 Nonadiabatic distribution 𝑕𝑡𝒍 = 𝑔

𝑡𝒍 + 𝑓𝑡𝐺𝑡𝑁 𝑈

𝑡

𝜚 𝒍）

8 Radial wave number qxρti Poloidal wave number qyρti

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]

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SLIDE 15

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

9

Radial wave number qxρti Poloidal wave number qyρti 6 4 2

  • 2
  • 4
  • 6
  • 6 -4 -2 0 2 4 6

[a.u.] 2×10-5 1×10-5

  • 1×10-5
  • 2×10-5

k (Streamer)

Triad transfer 𝐾𝑡𝒍

𝒒,𝒓 𝑡

for a streamer (kxρti,kyρti)=(0,4.4) at t=20-30R/vti

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SLIDE 16

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

9

Radial wave number qxρti Poloidal wave number qyρti 6 4 2

  • 2
  • 4
  • 6
  • 6 -4 -2 0 2 4 6

[a.u.] 2×10-5 1×10-5

  • 1×10-5
  • 2×10-5

k (Streamer)

Triad transfer 𝐾𝑡𝒍

𝒒,𝒓 𝑡

for a streamer (kxρti,kyρti)=(0,4.4) at t=20-30R/vti

p (~1.6ρti

  • 1)

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

[Dominski12JPCS, Maeyama14PoP]

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SLIDE 17

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

9

Radial wave number qxρti Poloidal wave number qyρti 6 4 2

  • 2
  • 4
  • 6
  • 6 -4 -2 0 2 4 6

[a.u.] 2×10-5 1×10-5

  • 1×10-5
  • 2×10-5

k (Streamer)

Triad transfer 𝐾𝑡𝒍

𝒒,𝒓 𝑡

for a streamer (kxρti,kyρti)=(0,4.4) at t=20-30R/vti

p (~1.6ρti

  • 1)

At the reduction phase, these radial structures suppress streamers. Kinetic electrons create fine radial structures (kxρti>1).

[Dominski12JPCS, Maeyama14PoP]

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SLIDE 18

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

9

Radial wave number qxρti Poloidal wave number qyρti 6 4 2

  • 2
  • 4
  • 6
  • 6 -4 -2 0 2 4 6

[a.u.] 2×10-5 1×10-5

  • 1×10-5
  • 2×10-5

k (Streamer) q (Finer

mode) Triad transfer 𝐾𝑡𝒍

𝒒,𝒓 𝑡

for a streamer (kxρti,kyρti)=(0,4.4) at t=20-30R/vti

p (~1.6ρti

  • 1)

At the reduction phase, these radial structures suppress streamers. Kinetic electrons create fine radial structures (kxρti>1).

[Dominski12JPCS, Maeyama14PoP]

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SLIDE 19

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.

Triad transfer 𝐾𝑡𝒍

𝒒,𝒓 𝑡

for a streamer (kxρti,kyρti)=(0,4.4) at t=60-80R/vti

Radial wave number qxρti

  • 6 -4 -2 0 2 4 6

6 4 2

  • 2
  • 4
  • 6

[a.u] 2×10-6 1×10-6

  • 1×10-6
  • 2×10-6

Poloidal wave number qyρti k (Streamer)

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SLIDE 20

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.

Triad transfer 𝐾𝑡𝒍

𝒒,𝒓 𝑡

for a streamer (kxρti,kyρti)=(0,4.4) at t=60-80R/vti

Radial wave number qxρti

  • 6 -4 -2 0 2 4 6

6 4 2

  • 2
  • 4
  • 6

[a.u] 2×10-6 1×10-6

  • 1×10-6
  • 2×10-6

Poloidal wave number qyρti p (Ion

scales)

k (Streamer)

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SLIDE 21

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.

Triad transfer 𝐾𝑡𝒍

𝒒,𝒓 𝑡

for a streamer (kxρti,kyρti)=(0,4.4) at t=60-80R/vti

Radial wave number qxρti

  • 6 -4 -2 0 2 4 6

6 4 2

  • 2
  • 4
  • 6

[a.u] 2×10-6 1×10-6

  • 1×10-6
  • 2×10-6

Poloidal wave number qyρti p (Ion

scales)

k (Streamer) q (Finer

mode)

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SLIDE 22

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 WZonal/Wnon-zonal 0 20 40 60 80 Time t vti/R 0.4 0.3 0.2 0.1 Ion-scale simulation Multi-scale simulation Ion-scale simulation Multi-scale simulation Ik

Zonal/Driving term

Ratio of zonal to non- zonal field energy

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SLIDE 23

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 Multi-scale simulation

Poloidal wave number kyρti

0.1 1 10 102 1 10-2 10-4

Electron thermal diffusion coefficient 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

  • 0.001

Jk

Ωp,Ωq(ky=0)/Driving term

Radial wave number kxρti

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SLIDE 24

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.

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SLIDE 25

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 / Strea mers 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

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SLIDE 26

26

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SLIDE 27
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SLIDE 28
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SLIDE 29