14 物理学会若手奨励賞 2020 磁場閉じ込めプラズマの乱流・ …磁場閉じ込めプラズマの乱流・輸送および同位体質量効果に関する研究

磁場閉じ込めプラズマの乱流・輸送および同位体質量効果に関する研究

仲田資季自然科学研究機構核融合科学研究所

総合研究大学院大学

第14回物理学会若手奨励賞 2020年3月

授賞対象論文 Motoki NAKATA, Tomo-Hiko WATANABE and Hideo SUGAMA, ”Nonlinear entropy transfer via zonal flows in gyrokinetic plasma turbulence”, Physics of Plasmas, vol. 19, 022303 (2012).Motoki NAKATA, Masanori NUNAMI, Hideo SUGAMA and Tomo-Hiko WATANABE, “Isotope effects on trapped-electron-mode driven turbulence and zonal flows in helical and tokamak plasmas”, Physical Review Letters, vol. 118, 165002 (2017).Motoki NAKATA, Mitsuru HONDA, Maiko YOSHIDA, Hajime URANO, Masanori NUNAMI, Shinya MAEYAMA, Tomo-Hiko WATANABE and Hideo SUGAMA, “Validation studies of gyrokinetic ITG and TEM turbulence simulations in a JT-60U tokamak using multiple flux matching”, Nuclear Fusion, vol. 56, 086010 (2016).

Acknowledgements Special thanks for collaborations and fruitful discussions goes to

M. Nunami (NIFS), H. Sugama (NIFS), T. -H. Watanabe (Nagoya Univ.),S. Maeyama (Nagoya Univ.), A. Ishizawa (Kyoto. Univ.), M. Honda (QST), E. Narita (QST), M. Yoshida (QST), H. Urano (QST), N. Aiba (QST), S. Matsuoka (NIFS), S. Satake (NIFS), K. Tanaka (NIFS), H. Takahashi (NIFS), K. Nagaoka (NIFS), M. Yokoyama (NIFS), and the LHD experiment group

J. H. E. Proll (Eindhoven Univ.), F. Warmer (IPP), G. G. Plunk (IPP), P. Xanthopoulos (IPP), A. Zocco (IPP), A. Mollen (IPP), A. Micshchenko (IPP), P. Helander (IPP)

C. Hidalgo (Ciemat), Ivan Calvo (Ciemat), M. J, Pueschel (Univ. Wisconsin)and all the CWGM participants.

This work is supported by the MEXT Japan, Grant No. 17K06941, and in part by the MEXT grant for the post-K priority-issue project (#6-D).

Prologue: Towards the burning plasma

LHD ITG-turbulence ITER ITG-TEM turbulence

Burning plasmas: Mixture of D-T and He-ash, and the other impurities ---> Multi-species ITG and/or TEM are dominant causes of turbulent transport.

. . .

. . .

(from NIFS web)

(from IPP web)

(from IO web)

(from Euro-Fus. web)

LHD/FFHR

W7X

ITER

JET

Simult. treatment of isotope and impurity ions in turbulent transport is crucial

calc. by GKV

5D-gyrokinetic simulation is a promising way to explore turbulence and transport in burning plasmas.

Isotope mass effects in experiments - Better confinement (more or less) in D-plasma:

ASDEX L-mode : τE ~ A0.5 Bessenrodt-Weberpals NF1993 JET H-mode : τE ~ A0.03±0.1 Cordey NF1999 W7-AS ECRH: τE ~ A0.2±0.15 Stroth Phys. Sc.1995 JT-60U H-mode: τE ~ A0.26 　 Urano NF2013

Mass dependence of transport is opposite to “gyro-Bohm” scaling (τE ~ A -0.5). How do we solve this discrepancy from the gyrokinetic simulation point of view?

Te

neW7-AS ECRH

D

H

ASDEX L-mode JT-60U H-mode

D

H

τE ~ A0.5τE ~ A0.26 τE ~ A0.2±0.15

- Various isotopic dep. of turbulence and zonal flows: e.g., TEXTOR, TJ-II, HSX, Heliotron-J

A long-standing issue: Isotope effects

Contents・Prologue

・Gyrokinetic simulations and entropy transfer analysis

・Validation studies

・Isotope effects on turbulence and zonal flows

・Summary

Overview of GKV

---> δf-model: fixed-background Fs0

---> Eulerian (Continuum) solver: spectral in 2D (kx,ky)-space, Finite-Difference in 3D (z, v||, µ)-space

---> Realistic geometries for Tokamak and Helical systems

---> Electro-static & Electro-magnetic fluctuations

---> Entropy balance/transfer diagnostics

tokamak ITG turb.

ETG

[e.g., Watanabe NF2006/PRL2008/NF2011, Nunami PFR2011/PoP2012/PoP2013/PFR2015, Nakata PoP2012/NF2013/PFR2014/CPC2015, Maeyama CPC2013/PoP2014/PFR2014/PRL2015, Ishizawa PoP2014/NF2015/JPP2015, etc.]

---> Multi-ion species with kinetic electrons incl. collisions

---> Good comput. performance on PETA-scale system

helical ITG turb.

Local fluxtube 5D gyrokinetic simulation code

@

@t+Lsk?

!� fsk? +

X

�

N p?,q?k? ��p?� fq? = Fsk? [Fs0, ��k? ] +

X

s0Css0 [� fsk? ]

linear advection nonlinear advection source from gradients collisions

local fluxtube full-torus

Extension for Multi-species Multi-species EM gyrokinetic equation incl. inter-species collisions

Collisional thermal relaxation in D-T-He-e plasma

Nakata CPC2015

---> Accurate multi-species collision operator preserving conservation properties and H-theorem.

Multi-species simulation model is applied to more realistic plasmas with isotope and impurity mixtures.

- Analytic model: Sugama PoP2009- Numerical implement. w/ FLR: Nunami PFR2015- Improved form for kinetic elec.: Nakata CPC2015

@

@t+ 3kb·r + i!Da �

µb·rBma

@

@3k

!�gak?�

cB

X

p?

X

q?

b · (p?⇥q?) � ap?�gaq?�k?+p?+q?, 0

=eaFMa

Ta

@� ak?

@t+ i!⇤Ta� ak?

!+

X

b

Id'2⇡

eik?·⇢anCTS

ab [e�ik?·⇢a�gak? ] +CFab[e�ik?·⇢b�gbk? ]

o

⇤⌃

⌃t+ �⌥b· � + i⌅Ds �

µ

msb· �B

⌃

⌃�⌥

⌅� f (g)

sk⌅ �cB

⇧

�

Mp⌅,q⌅�⇤⇤p⌅� f (g)⇤

sq⌅

= FMs�i⌅⇤T s � i⌅Ds � �⌥b · �

⇥ es�⇤k⌅Ts

� Cs⌃� f (g)

sk

⌥

⇤

⇤t��S sk�+Wsk�

⇥= ⇥sQsk�+ Tsk�+ Dsk�

GK eq.

Entropy variable heat flux Entropy transfer function

Collisional dissipationEntropy balance eq.

�

�tEk = Tk + Dk

Tk =�

p

�

q�k+p+q=02Re

⇥Mk⇤upuquk⌅

⇤

⇥

⇥tuk +

�

�

Mkupuq = Fk � �k2ukNavier-Stokes eq.

Energy balance eq.

Energy transfer func.

Viscous dissipation

k-space structure of the energy transfer function

S. Kida, JFM(1997)

Analogy with isotropic fluid-turbulence system

Gyrokinetic entropy balance Nakata PoP 2012

�⌅⌅⌅⌅⌅⌅⌅⌅⇤⌅⌅⌅⌅⌅⌅⌅⌅⇥

transport-driving mode

kx

ky

kzf

p

q

kzf : zonal flows p : non-zonal q : non-zonal

⇤

⇤t��S sk�+Wsk�

⇥= ⇥sQsk�+ Tsk�+ Dsk�

Tsk� =�

p�

�

q�

�k�+p�+q�=0J[k� | p�, q�]

J[k⇧ | p⇧, q⇧] ⌅�

cB

b·(p⇧⇤q⇧)⇤

d�1

2FMRe[�⇥p⇧hq⇧hk⇧ � �⇥q⇧hp⇧hk⇧ ]

⇥entropy transfer function

triad entropy transfer function

In the following, the triad interactions among

(transport driving mode)are discussed based on the Detailed Balance Relation

J[k� | p�, q�] +J[p� | q�, k�] +J[q� | k�, p�] = 0

Triad entropy transfer function Nakata PoP 2012

Based on the entropy balance/transfer equation, nonlinear interactions among non-zonal and zonal modes are investigated.

toroidal ITG-ae turb. toroidal ETG-ai turb.

xyz

z=0

z=π

Streamer dominated structure (High transport level)

Zonal-flow-dominated structure (Low transport level)

Toroidal ITG/ETG turbulence simulation

gain

loss

gain

loss

- In the steady phase, the entropy transfer from non-zonal to zonal modes becomes quite weak in ITGs, i.e. .

steady phase

Entropy transfer from non-zonal to zonal modes: J[kzf|p,q]/ηQ

5.4 Nonlinear entropy transfer via zonal modes 95

phases, and the related transport suppression.

Hereafter, we consider the entropy transfer processes associated with the nonlinear interac-tions among two non-zonal modes with p⇤ and q⇤ and a zonal mode with kzf = kzf⌥x, whichsatisfy the triad-interaction condition kzf+ p⇤+ q⇤= 0. (A schematic plot is shown in Fig. 5.9.)The non-zonal mode with p⇤ is chosen to be the “ transport-driving mode” with (kx⇥0, ky⇥0.2)which makes the most dominant contribution to the turbulent heat flux, as shown in Figs. 5.7(a)and 5.7(b).

The wavenumber spectrum of the triad entropy transfer function normalized by the mean heatflux, i.e., Js[kzf | p⇤, q⇤]/�sQs, in the saturation phase of ITG and ETG turbulence are shown inFigs. 5.10(a) and 5.10(b), respectively, where the time-average is taken over 30� t � 45. Here,the wavenumbers of the ITG- and ETG-driven zonal flows are, respectively, set to kzf=0.1410⇥�1

ti

and kzf = 0.0705⇥�1te , which make the largest contribution to the zonal flow [see Fig. 5.5(a) and

5.5(b)]. In the ITG turbulence [Fig. 5.10(a)], one clearly finds that the large positive values ofJi[kzf | p⇤, q⇤]/�iQi spread over the linearly unstable region with qy ⇥ 0.4 [cf. Fig. 5.1]. Thissuggests that the saturation process of ITG instability is closely associated with the strong zonalflow generation due to the e�cient entropy transfer from the linearly unstable non-zonal modesto zonal modes. On the other hand, the lower amplitude of Je[kzf | p⇤, q⇤]/�eQe is observed in

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 40 80 120 160 200 240 280 320

Ts(z

f)/η

sQs

Time t [Ln0/vts]

toroidal ITGtoroidal ETG

FIG. 5.8: Time evolution of the entropy transfer function normalized by the mean heat fluxT (zf)

s /�sQs for the toroidal ITG (s= i) and ETG (s=e) turbulence.

98 Chapter 5 Nonlinear entropy transfer via zonal flows in toroidal plasma turbulence

(b)

-0.6 -0.4 -0.2 0 0.2 0.4 0.6wavenumber qx [ρte

-1]

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

wav

enum

ber q

y [ρ

te-1]

-1x10-4

-5x10-5

0x100

5x10-5

1x10-4kzf=0.0705

(a)

-0.6 -0.4 -0.2 0 0.2 0.4 0.6wavenumber qx [ρti

-1]

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

wav

enum

ber q

y [ρ

ti-1]

-1x10-4

-5x10-5

0x100

5x10-5

1x10-4kzf=0.1410

FIG. 5.10: Wavenumber spectrum of the triad transfer function normalized by the mean heat flux,J s[kzf | p⊥, q⊥]/ηsQs, for the fixed-kzf in the steady state of toroidal (a)ITG (s = i) and (b)ETG(s=e) turbulence, where the time-average is taken over 220! t!320.

driving modes [cf. Fig. 5.7(b)], but are partly canceled by the large negative values. Note that,as discussed above, the generation of ETG-driven zonal flows is less effective due to the largezonal-flow inertia, even though the relatively large positive values of Je[kzf | p⊥, q⊥]/ηeQe areobserved in comparison to those in the ITG case.

Although the entropy transfer to zonal modes is quite weak in the steady state of the ITGturbulence, i.e., J i[kzf | p⊥, q⊥]≃0, the ITG-driven zonal flows still play a “catalytic role” in theentropy transfer from non-zonal transport-driving modes to other non-zonal modes with higherradial-wavenumbers which make less contribution to the turbulent heat flux [cf. Fig. 5.1 and

ITG

ETG

- Low-k mode interactions are dominant in ETGs. Ji[kzf | p?, q?]/⌘iQi⌧1

Entropy transfer to ZF in steady phase


(c)


-1]

-0.6

-0.4

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0

0.2

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0.6

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enum

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y [ρ

ti-1]

-1x10-4

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0x100

5x10-5

1x10-4px=0.2820py=0.2250

(b)


-1]

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0

0.2

0.4

0.6

wav

enum

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y [ρ

ti-1]

-1x10-4

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0x100

5x10-5

1x10-4px=0.1410py=0.2250

(a)


-1]

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0

0.2

0.4

0.6

wav

enum

ber q

y [ρ

ti-1]

-1x10-4

-5x10-5

0x100

5x10-5

1x10-4px=0.0000py=0.2250

FIG. 5.11: Wavenumber spectra of the triad transfer function normalized by the mean heat flux,J i[p⊥| q⊥, kzf]/ηiQi, for three different p⊥’s with py = 0.2250ρ−1

ti (fixed) in the steady state oftoroidal ITG turbulence, where the time-average is taken over 220! t!320.


(c)


-1]

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0

0.2

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y [ρ

ti-1]

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0x100

5x10-5

1x10-4px=0.2820py=0.2250

(b)


-1]

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y [ρ

ti-1]

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0x100

5x10-5

1x10-4px=0.1410py=0.2250

(a)


-1]

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0

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y [ρ

ti-1]

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0x100

5x10-5

1x10-4px=0.0000py=0.2250




(c)


-1]

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0

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wav

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y [ρ

ti-1]

-1x10-4

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0x100

5x10-5

1x10-4px=0.2820py=0.2250

(b)


-1]

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0

0.2

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0.6

wav

enum

ber q

y [ρ

ti-1]

-1x10-4

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0x100

5x10-5

1x10-4px=0.1410py=0.2250

(a)


-1]

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0

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wav

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1x10-4px=0.0000py=0.2250



- In the steady state of ITG turbulence, the entropy of the primary mode (transport-driving mode) is “successively” transferred to the higher-kx mode (with less contribution to heat transport) via the triad-interaction with zonal modes. ( ZF works as a “mediator”. )

(a) (b) (c)

Spectra of (entropy transfer among non-zonal modes via ZF)Ji[p� | q�, kzf]/�iQi

cf. Detailed balance relation: negligibly small

Ji[p? | q?, kzf] = �Ji[q? | kzf , p?] �Ji[kzf | q?, q?]

Ji[q? | kzf , p?] = F(qx, qy)

Detailed transfer in steady phase: ITG

cf. Detailed balance relation: Spectra of (entropy transfer among non-zonal modes via ZF)

- In the steady state of ETG turbulence, the successive entropy transfer to the higher-kx modes is no longer observed. Instead, the triad interactions among low-wavenumber non-zonal modes are dominant.

(c)

Je[p� | q�, kzf]/�eQe

Je[p⇥ | q⇥, kzf] +Je[q⇥ | kzf , p⇥] = �Je[kzf | q⇥, q⇥] , 0102 Chapter 5 Nonlinear entropy transfer via zonal flows in toroidal plasma turbulence

(c)


-1]

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0

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wav

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y [ρ

te-1]

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5x10-5

1x10-4px=0.1410py=0.2250

(b)


-1]

-0.6

-0.4

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0

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0.4

0.6

wav

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y [ρ

te-1]

-1x10-4

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0x100

5x10-5

1x10-4px=0.0705py=0.2250

(a)


-1]

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

wav

enum

ber q

y [ρ

te-1]

-1x10-4

-5x10-5

0x100

5x10-5

1x10-4px=0.0000py=0.2250

FIG. 5.13: Wavenumber spectra of Je[p⊥| q⊥, kzf]/ηeQe, for three different p⊥’s with py =

0.2250ρ−1te (fixed) in the steady state of toroidal ETG turbulence, where the time-average is taken

over 220! t!320.

(a)


(c)


-1]

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(b)


-1]

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(a)


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te-1]

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over 220! t!320.

(b)


(c)


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(b)


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te-1]

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(a)


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over 220! t!320.

(c) not negligible

Detailed transfer in steady phase: ETG

(b)

-0.6 -0.4 -0.2 0 0.2 0.4 0.6wavenumber px [�te

-1]

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x [�

te-1]

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5x10-5

1x10-4|kzf|=0.0705

(a)

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-1]

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x [�

ti-1]

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1x10-4|kzf|=0.1410

(b)

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-1]

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1x10-4|kzf|=0.0705

(a)

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-1]

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enum

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x [�

ti-1]

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0x100

5x10-5

1x10-4|kzf|=0.1410

py=�qy=0.2 py=�qy=0.2

Qik Qek

Ji[p? | q?, kzf]/⌘iQi ⌘ Gi(px, qx) Je[p? | q?, kzf]/⌘eQe ⌘ Ge(px, qx)- Ent. transfer structures are well correlated to spectral shape in ITGs and ETGs.

Spectral elongation and entropy transfer

- Also found in TEM driven ZF in ETG turbulence: Asahi PoP2014, and in Helical system.

Entropy transfer is a powerful method to identify nonlinear interactions directly related to transport.

Nakata PoP 2012

Contents・Prologue




・Summary

Validations of tokamak ITG/ITG-TEM/TEM driven turbulent transportNakata PFR2014, IAEA2014GKV simulations with realistic JT-60U tokamak equilibrium

ρ=0.25: ITG

ρ=0.50: ITG-TEM

ρ=0.75: TEM

GKV simulations successfully reproduce the comparable ion and electron heat transport levels within +/-30% profile variations.

JT60U Lmode #45072 ion heat flux electron heat flux

Sim. results using EXP. equilibrium parameter (nominal case)Sim. results using slight variation of parameter (Flux-matching case)

Validation based on experimental measurements Nakata NF 2016

0.0 0.2 0.4 0.6 0.8 1.00.0

2.0

4.0

6.0

χ i

(m2 /s

)

ρ

ExperimentAnomalousNonlin. Sim. Model

(χiNL)

(χimodel)

Validations of LHD ITG driven turbulent transportGKV simulations with realistic 3D-VMEC LHD equilibrium Nunami PFR2011

LHD High-Ti plasma #88343 ion heat flux w/ adiabatic elec. electron heat flux

Nunami PoP2012Nunami PoP2013 Ishizawa NF2015&NF2018

---> GK-simulation-based transport modeling

---> Evaluations of electron heat and particle transport

Exp

GKV

Validation based on experimental measurements

Contents・Prologue




・Summary

Isotope effects on ITG & TEM instabilities

---> Confinement will be degraded by , unless .

= �GB(H)

pAs

(cf. gyro-Bohm scaling)

Turbulent diffusivity can roughly be estimated as

�turb ⇠�(k)

k2

?=�

s(ks)

k2

?s

⇢2

ts3ts

Rax

!=�

s(ks)

k2

?s

pAs

Z2s

0BBBB@⇢2

tH3tH

Rax

1CCCCA

For hydrogen isotope with Zs = 1:

For non-isotopic ions (i.e., impurities) with As ~ 2Zs: ---> Confinement will be improved by , unless .

The normalized ITG and TEM growth rates in LHD plasma are examined for hydrogen isotope ions by means of GKV. (LHD config. is used here)

�s(k?s)

ITG-dominated regime: Te/Ti=1, R/Lti=10, R/Lte=12, R/Ln=2TEM-dominated regime: Te/Ti=2.5, R/Lti=1, R/Lte=12, R/Ln=2

p2Z�3/2

s( cf. confinement improvements in H-He Exp. in LHD )

�s(k?s) / A�↵s , ↵ > 1/2

�s(k?s) / Z�s , � > 3/2

where, mean the normalized linear growth rate and wavenumber.�s = �Rax/3ts , k?s = k?⇢ts

Mixing length estimation of turbulent diffusivity for isotope and impurity ions

ITG and TEM instabilities in LHD plasma Comparison of magnetic configuration in ITG and TEM instabilitiesStandard LHD configuration: Rax=3.75m Inward-shifted plasma case: Rax=3.60m

---> Inward-shifted configuration leads to more significant TEM destabilization

---> TEM-dominated regime appears in the lower-R/LTi regime. (similar to Tokamak)

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

γ Rax

/υtH

Rax/LTi

Rax/LTe = 14Rax/LTe = 12Rax/LTe = 10Rax/LTe = 8

(a)

kxρtH=0, kyρtH=0.5

Std: Rax=3.75m

TEM ITG

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

γ Rax

/υtH

Rax/LTi

Rax/LTe = 14Rax/LTe = 12Rax/LTe = 10Rax/LTe = 8

(b)

kxρtH=0, kyρtH=0.5

Iwd: Rax=3.60m

Rax/Ln=2Te/Ti=2

Rax/Ln=2Te/Ti=2

ν*ei~0.04 ν*ei~0.04

TEM ITGTEM ITG

Ion temp. grad. scaleIon temp. grad. scale

---> Peaked density profile destabilizes TEM in LHD (nearly minimum-J prof.) cf. Helander PPCF2012, Proll PRL2012

Nakata PPCF2016

real freq.(elec. diamag)

ν*ei = 0.04kys

---> Mode frequency is almost isotope-indep. ---> In TEM, strong isotope dependence on the normalized growth rate appears. ( isotope dep. through )

Normalized dispersion spectra for TEM

real freq.(ion diamag)

kys

---> Mode frequency is almost isotope-indep.

ν*ii = 0.04

Normalized dispersion spectra for ITG

growth rate growth rate

�s(ks)---> In ITG, the normalized growth rate is also almost isotope-indep., indicating gB-like dependence for .

�s(ks)

�/k2? /p

As

Comparison of isotope ion mass dep. in ITG and TEM instabilities

Isotope effects on ITG/TEM in LHD

⌧�1ei /!⇤Ti / (Ai/Ae)1/2

Nakata et al., PPCF2016

Collisionality dep. of isotope impact on the mixing length diffusivity

Linear local GK analysis expects the improved confinement for TEM-dominated plasma in a certain ν*-regime (ν*>0.04).

For ITG: almost no isotope-dep. in

Remember

�turb ⇠�

k2?=�s

k2?s

pAs �gB(H)

For TEM: strong isotope-dep. in �s

�s

/p

As

�/k

2 ?in

Hydrogen

unit

(fi

xed)

Isotope effects on ITG/TEM in LHD Nakata et al., PPCF2016

Isotope effects on turbulent transportTEM turbulence simulations in LHD H- and D-plasmas

Fluctuations in H-plasma

0 0.1 0.2 0.3 0.4

WZF

/ W

tota

l

H-plasmaD-plasma

(b) 0

60

120

Σsq

s/qG

B(H

)

H-plasmaD-plasma

(a)

0

0.1

0.2

0 20 40 60 80 100 120 140 160

ΣsT

sJs(Z

F) / Σ

sqsL

Ts-1

Time t [Rax/υtH]

H-plasmaD-plasma

(c)

Fluctuations in D-plasma

Turbulent heat flux

ZF energy partition

Entropy transfer to ZF

HD

Transport reduction resulting from the linear stabilization and enhanced zonal flows is identified in D-plasma.

Nakata et al., PRL2017

Isotope effects on turbulent transportEntropy transfer from low to high-kx fluctuations via ZF in LHD-H plasma

Entropy transfer extent of turbulent fluctuations via ZF is well correlated to elongated nature in turb. spectrum.

s

(b)

-0.9 -0.6 -0.3 0 0.3 0.6 0.9wavenumber pxρtH

-0.9

-0.6

-0.3

0

0.3

0.6

0.9

wav

enum

ber q

xρtH

-1x10-4

-5x10-5

0x100

5x10-5

1x10-4kzfρtH=0.298

XJs[p|q,kzf ]/

�L�1Ts

Qs/Ts

�

(b)

-0.9 -0.6 -0.3 0 0.3 0.6 0.9wavenumber kxρtH

0

0.3

0.6

0.9

wav

enum

ber

k yρ

tH

10-2

10-1

100

non-zonal modes

ZF ZF

Wkx,ky/max[Wkx,ky 6=0]

kx⇢tH(from)

k0 x⇢ t

H(to)

@

@t

X

s

Ts�S sk? =X

s

3X

j=1

J js X j

s +X

s

TsTsk?+X

s

TsDsk?

Tsk? =X

p?

X

q?

�k?+p?+q?=0Js[k? | p?, q?]

⌘*

cB

b·(p?⇥q?)Z

d31

2FMsRe[� sp?�gsq?�gsk? � � sq?�gsp?�gsk? ]

+Js[k? | p?, q?]

Js[k? | p?, q?] +Js[p? | q?, k?] +Js[q? | k?, p?] = 0

Entropy balance equation

entropy variable turbulent fluxes entropy transfer

col. dissipation

Entropy transfer function

Detailed balance for the triad interaction

Nakata et al., PoP(2012)


Isotope effects on turbulent transport

0

6

12

18

24

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

(γ /

k ⊥2 ) / χ

GB

(H)

& α

scal

e Σsq

s/qG

B(H

)

2

ν*ei for TEM , ν*ii for ITG

L-TEM(H)L-TEM(D)L-ITG(H)L-ITG(D)

NL-TEM(H)NL-TEM(D)NL-ITG(H)NL-ITG(D)

CBC-like tokamak plasma

H-plasma D-plasmaComparison of nu*-dep. of mixing length diffusivity(line) and turbulent one(symbol)

Qualitatively similar isotope dependence in CBC-like tokamak TEMs

H D

reduction in < reduction in �/k2? �nonlin


Isotope effects on turbulent transport

0

6

12

18

24

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

(γ /

k ⊥2 ) / χ

GB

(H)

& α

scal

e Σsq

s/qG

B(H

)

2

ν*ei for TEM , ν*ii for ITG

L-TEM(H)L-TEM(D)L-ITG(H)L-ITG(D)

NL-TEM(H)NL-TEM(D)NL-ITG(H)NL-ITG(D)

CBC-like tokamak plasma

H D

Comparison of nu*-dep. of mixing length diffusivity(line) and turbulent one(symbol)

Isotope stabilization of TEM leads to zonal flow enhancement in near marginal stability (nu*~0.035). (cf. Dimits-shift in ITG case. )

-2-1 0 1 2

-80 -60 -40 -20 0 20 40 60 80

υZF

(x) /

Wto

tal

1/2

(x

0.1)

x/ρtH

NL-TEM(H)NL-TEM(D)

ν*ei=0.035(b)

-2-1 0 1 2 NL-TEM(H)

NL-TEM(D)ν*ei=0.018(a)

Far from marginal (nu*~0.018)

Near marginal (nu*~0.035)

H

D

Radial profiles of ZF

Qualitatively similar isotope dependence in CBC-like tokamak TEMs Nakata et al., PRL2017

Experimental verification of theoretical predictionNakata et al., PPCF2019, Nagaoka et al., NF2019

Reproduction of transport reduction ratio (~0.3-0.4) from GKV. —> More dedicated validation studies are in progress !

0.0 0.2 0.4 0.6 0.8 1.00

1

2

3

4

5

6 H 132031t3.74 D 139727t4.37

reff/a99

T i [k

eV]

LHD-Exp.

x0.41

transport coefficient@ρ=0.5̶> x0.31

GK simulations for isotope plasmas in LHD

GKV-calc. (ITG)

Summary - Entropy transfer analysis reveals a key physical mechanism on the nonlinear interaction among turbulence and zonal flows, which are directly related to energy and particle transport.

Nowadays, fundamental understandings on the physical mechanisms of turbulence, zonal flows, and related transport reduction have been well accumulated.

—> Innovative creation research for the next generation confined plasmas with enhanced zonal flows and turbulence suppression! (my current ambition!)

- Extensive GK simulation development enables us to perform quantitative validation studies by utilizing realistic experimental data.

- Large-scale GK simulations and dedicated experiments are accelerated toward the full understandings of a long-standing issue: Isotope effects.

Documents

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