Exploration of burning plasma confinement physics using the supercomputer Fugaku
Tomo-Hiko Watanabe
Department of Physics, Nagoya University
In collaboration with Yasuhiro Idomura, Yasushi Todo, Mitsuru Honda, and the BPP project
1 This work is supported by Program for Promoting Researches on the Supercomputer
Fugaku, “Exploration of burning plasma confinement physics” (JPMXP1020200103)
2021/11/22 @COMDATA2021
Outline
n Introduction
n Project of burning plasma physics
n “Ab initio” (kinetic) plasma codes
n GKV, GT5D, and MEGA
n Recent highlights
n Energetic particle transport using MEGA
n Multiscale turbulence simulation using GKV
n Challenge to plasma rotation using GT5D
n Data science to run ab initio simulations more efficiently
n Summary
2021/11/22 @COMDATA2021
2
Key physics issues for burning plasma and “Fugaku”
n Multiscale transport phenomena
n Fusion plasma involves multiple spatiotemporal scales (e.g., ion and electron orbit widths, global equilibrium scale, and scales of electromagnetic fluctuations…)
n A variety of instabilities and fluctuations co-exist and make interactions each other
n Multispecies of particles in fusion plasma
n Burning plasma consists of a number of particle species (e.g., e, D, T, He, W…) and energetic components
n Burning Plasma Physics project by use of the supercomputer Fugaku
n Fugaku: massively parallel supercomputer with pre-exa Flops (#1 of Top500)
n Ab initio fusion plasma simulation
n Three major fusion applications with data science approaches
2021/11/22 @COMDATA2021
3
Fugaku@Riken
Major applications in BPP project
4
5D first principles based simulations
! " # $ + ̇' ( ! ' # $ = * # $ + +
advection collision sources
x y z
v
//v
⊥"v
//v
⊥"Local flux-tube δf GK code GKV [Watanabe,NF2006]
Systematic analysis of steady turbulent transport via ion-electron multi-scale turbulence simulations
JT-60 LHD
Validation studies against JT-60 and LHD
Global full-f GK code GT5D [Idomura,NF2009]
Analysis of global confinement scaling, numerical experiments on transient plasma responses
Hea t f lu x
Time scale of transient plasma (eddy turnover time x 10,000 ~ 10
6steps) Propagati
on of heat
flux
Time (s)
Long time numerical experiments via global full-f model
co re ed ge
α-driven MHD code MEGA [Todo,POP1998]
Analysis of α-particles transport via fluid-particle hybrid simulations of α-particle driven MHD modes
NBI-driven MHD modes on LHD
Te¼ 4 keV, and bulk plasma beta value at the magnetic axis equal to 7:2" 10#4. The neutral beam injection en- ergy is ENBI¼ 170 keV. Since the kinetic GAM frequency at LHD is close to those in tokamaks [3], a tokamak type equilibrium is examined with concentric magnetic surf- aces, and with the safety factor profile and the aspect ratio similar to the LHD plasma. The safety factor q profile is a weak shear profile with q¼ 2:0 at the magnetic axis and q¼ 0:83 at the plasma edge. The major radius of the magnetic axis is R0¼ 3:9 m and the plasma minor radius is a¼ 0:65 m. Cylindrical coordinates (R, !, z) are employed for the simulation with numbers of grid points (128, 16, 128), respectively, although the equilibrium and the fluctuations do not depend on !. The number of the computational particles is 2 million.
The equilibrium energetic particle distribution function f0can be written using constants of motion as
f0¼ f0ðE; "; P!; #Þ; (1)
P!¼ Zhecþ Rmvkb!; (2)
where E is the particle energy, " is the magnetic moment, P!is the toroidal canonical momentum, # distinguishes the orbit types (with #¼ 1 for copassing particles, # ¼ 0 for trapped particles, and #¼ #1 for counterpassing par- ticles). Zhe and m are the particle charge and mass,c is the poloidal magnetic flux, vkis the parallel velocity, and b!is the toroidal component of the magnetic field unit vector.
Assuming the separation of variables, Eq. (1) is exp- ressed by
f0¼ f0ðE; "; P!; #Þ ¼ GðEÞH ð!ÞIðE; "; P!; #Þ; (3) where !¼ "B0=E is the pitch angle variable with the B0
magnetic field strength at the magnetic axis. The energy distribution GðEÞ is a slowing down distribution. The functionH ð!Þ is introduced to model anisotropic distri- butions in pitch angleH ð!Þ¼exp½#ð!#!peakÞ2="!2(, where the !peakrepresents the pitch angle for the distribu- tion peak and "! is a parameter to control the distribution width. In the present simulation, !peak¼0:3 and "!¼0:2.
The function I represents the radial profile which is consistent with the energetic particle beta profile
IðE; "; P!; #Þ ¼ expð#cnrm=$2Þ; (4) cnrm¼ 1 #P!# #R0mv0
Zhecmax
; (5)
where v0¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ðE # "BminÞ=m
p , cmax is the maximum
value ofc , and $¼ 0:5 in the present simulation.
The time derivative of %f¼ f # f0 at each marker particle is given by
d
dt%f¼d
dtðf # f0Þ ¼ #dE dt
@f0
@E#dP!
dt
@f0
@P!
: (6)
The destabilization of the EGAM arises from the energy derivative of f0with the most important contribution from the second term of the equation below.
@f0
@E¼@G
@EH I þ G@!
@E
@H
@!I þ GH@I
@E: (7)
The initial energetic particle distribution function in velocity space is shown in Fig.1(a). The dashed curves represent constant ", and particles evolve only along the dashed curves because " is an adiabatic invariant. In area
A,@f@Ej"¼const> 0, and the particles with positive@f@Ecan
destabilize the EGAM. In area B, @E@fj"¼const< 0, and particles in this area stabilize the EGAM. Figure 1(b) shows the energy transfer rate from the EGAM to energetic particles in (!, E) space in the linear phase. The purple color represents negative energy transfer, which means the energy transfer from particles to the EGAM, destabilizing the mode. In contrast, the red color represents positive energy transfer that stabilizes the mode. The energy transfer rate in the destabilizing region is higher than that in the stabilizing region. Then, the EGAM is excited on the whole. Notice that the purple region in Fig.1(b)is located in area A in Fig.1(a), and the red region in Fig.1(b)is located in area B in Fig.1(a). These two figures are con- sistent with each other, clarifying the mode destabilization mechanism.
The EGAM frequency chirping takes place in the non- linear phase, and the evolution of the frequency spectrum and the poloidal velocity is shown in Fig.2. The mode
0 30 60
Energy [keV]
0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6
Λ 0
30 60
Energy [keV]
-12 -8 -4 0 4 8 12
Area A Area B
(a)
(b)
FIG. 1 (color). Panel (a) shows the normalized initial energetic particle distribution in (!, E) space, and panel (b) shows the energy transfer rate from the EGAM to energetic particles.
Dashed curves represent constant ".
PRL 110, 155006 (2013) P H Y S I C A L R E V I E W L E T T E R S week ending
12 APRIL 2013
155006-2
Beam-driven MHD mode Velocity distribution
Pitch angle
En erg y (ke V)
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Overview of GKV
5
JT-60 LHD
2021/11/22 @COMDATA2021
n Gyrokinetic Vlasov simulation code [Watanabe and Sugama, NF06]
n Local toroidal flux tube geometry for tokamak (axisymmetric) and helical (non-axisymmetric) configurations covering the 5D phase space.
n Spectral method for turbulence convection; FD for field-aligned coordinates and velocity space
n IMEX, Implicit (C-N) and explicit (RK4) time integration [Maeyama+ CPC19]
n Highly parallelized code ~600,000 cores on K and on Fugaku [Maeyama+ Parallel Comput.15]
n Main physics applications
n A variety of topics related to drift wave turbulent transport and zonal flows in tokamak and
helical systems [Watanabe+ PRL11, Maeyama+ PRL15, Nakata+ PRL17, Maeyama+ PRL17, Ishizawa+ PRL19,
Nunami+ PoP20 …]
Overview of GT5D
n Confinement time scale simulations of full-f models for multi-species ions and hybrid kinetic electrons using non-dissipative finite difference on 5D grids
[Idomura,CPC08,JCP16,SC20]
n Mixed-precision communication-avoiding Krylov methods
[Idomura,SC20]
→ Drastic speed-up on exa-scale machines, Fugaku & Summit
n Accuracy improved Sugama collision op. [Matsuoka,POP2021]
n Multi-species ions transport implemented [Idomura,POP2021]
n Main physics applications
n Avalanche like non-local transport [Idomura,NF09]
n Confinement scaling w.r.t. plasma size, heating power, isotope mass, etc… [Jolliet,NF12, Nakata,NF13,
Idomura,POP14a,POP19]
n Momentum transport, intrinsic rotation, neoclassical
toroidal viscosity [Camenen,NF11, Idomura,CSD12,POP14b,POP17,
Matsuoka,POP17] 6
x z y
v
//v
^v
//v
^0 10 20 30 40 50 60 70
1440 1440 2880 5760 1440 2880 5760
Oakforest-
PACS (KNL) Fugaku (A64FX) Summit (V100)
time/step (sec)
Other Collision Field Nonlinear Krylov
ITER size case (~10
11DOFs, m
i/m
e=3,672, Δt=5Ω
i-1)
4.4x 7.7x 13x
2.0x
3.4x 5.1x
2021/11/22 @COMDATA2021
n Kinetic-magnetohydrodynamics (MHD) hybrid simulation code MEGA [Todo PoP98, ITC2017]
n MHD electromagnetic field + kinetic energetic particles (EP) + thermal ions
n Long time simulations with “multi-phase (classical + hybrid)”
method
n Kinetic extension for thermal ions in high temperature burning plasma is newly developed.
n Main physics applications
n Long time evolution of Alfvén eigenmodes and the critical EP distribution
[Todo NF14, NF16, NJP16, PoP 17, NF19, Bierwage NF17, Nature Comm. 18, Seki NF19, NF20]
n Nonlinear evolution of EP driven geodesic acoustic modes
[Wang PoP13, PRL13, PoP15, PRL18, NF19, NF20]
n Kinetic thermal ion effects on MHD instabilities [Sato NF19, JPP20]
Overview of MEGA
2021/11/22 @COMDATA2021
7
Results from MEGA
n MHD instabilities with energetic particles and kinetic ions in LHD
n Precession drift reversal and rapid transport of trapped energetic particles
n Kinetic stabilization of MHD modes
n Energetic particle transport by Alfvén eigenmodes
n Kinetic thermal ion effects on a particle transport in ITER
2021/11/22 @COMDATA2021
8
n MEGA simulation of an energetic-particle-driven MHD instability in LHD clarifies …
n Helically trapped energetic particles strongly interacting with the MHD mode reverse the direction of their
precession drift, and are rapidly transported in the outward.
n The precession drift reversal and the outward transport are caused by the interaction with the electric field of the MHD mode (the interchange type with m/n=2/1).
Precession drift reversal and rapid transport of trapped energetic particles due to an MHD instability in LHD
9
[M. Idouakass+, Phys. Plasmas 28 (2021) 080701, cover figure]
n Kinetic effects of trapped thermal ions on magnetohydrodynamic (MHD) instabilities in the Large Helical Device (LHD) are
successfully simulated with MEGA.
n Response of the trapped ions to the MHD instability is averaged out by the poloidal precession drift motion.
n It results in the suppression of the ion perpendicular pressure perturbation to the magnetic field leading to the reduction of the instability growth rate.
Kinetic stabilization of MHD modes found by MEGA
10 MHD instability and trapped ion orbit in LHD
Growth rate of instabilities with MHD model and kinetic MHD model [M. Sato and Y. Todo, Nucl. Fusion 59
(2019) 094003, 61 (2021) 116012]
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Energetic particle transport by Alfvén eigenmodes
n Energetic particle transport in a tokamak by Alfvén eigenmodes (AE) is investigated by using MEGA extended with kinetic thermal ions.
n Discovery of energy transfer channel from fast to thermal ions
n Resonance condition of AE is clearly identified with the distribution function
11 Fluctuations of fast ion
distribution function interacting with Alfven eigenmodes
[Y. Todo+, PPCF 2021]
Co-rotating fast ions with current
Counter- rotating fast ions with current Time
2021/11/22 @COMDATA2021
n Energetic-particle driven instabilities in an ITER steady state scenario are investigated with and without kinetic thermal ions.
n Saturation level of the Alfvén eigenmodes and energetic-particle transport are drastically reduced in case with kinetic thermal ions.
12
MHD
with kinetic thermal
ions [Y. Todo+, AAPPS-
DPP2021]
Kinetic thermal ion effects on a particle transport in ITER
2021/11/22 @COMDATA2021
Results from GKV
n Multiscale turbulence simulation of TEM/ETG instabilities
n Reduction of electron heat transport in the multiscale turbulence
n Optimum of temperature ratio for electron confinement
n Turbulent diffusion suppresses the TEM instability growth
n Downshift of the critical density gradient by ITG turbulence
2021/11/22 @COMDATA2021
13
Multiscale turbulence simulation of TEM/ETG instabilities
n Suppression of micro-scale turbulence by hyperfine-scale fluctuations is
revealed by GKV simulation.
n Burning plasma model with e, D, T, He species and high electron temperature
n Trapped electron mode (TEM) is
stabilized by the electron temperature gradient (ETG) turbulence.
n Mean electron transport is reduced in presence of micro-scale turbulence
n Entropy transfer analysis demonstrates contribution of the ETG turbulence on the TEM fluctuations.
14
[S. Maeyama+, AAPPS-DPP2021]
2021/11/22 @COMDATA2021
Optimum of temperature ratio for electron confinement
n Dependence of the electron heat transport on T e /T i is investigated for the multiscale TEM/ETG turbulence
n As T e /T i increases, the dominant instability changes from ETG to TEM
n Multiscale turbulence makes the largest impact on the transport reduction around T e /T i =3, extending the favorable range of T e /T i .
=> Optimum rage of T e /T i
T e /T i 15
Relative contributions of large and small scale fluctuations to transport
T e /T i
T
e/T
idependence of electron heat transport
[S. Maeyama+, ITC30, 2021]
2021/11/22 @COMDATA2021
Turbulent diffusion suppresses the TEM instability growth
n The TEM instability is suppressed by the ETG turbulence even in H-plasma, where the growth rate reduction is well fitted by an effective diffusion.
n Detailed analysis of the TEM instability growth shows ! "# = ! − & '(( ) * +
n Nonlinear gyrokinetic theory elucidates stabilization of TEM in terms of turbulent diffusion by ETG
16
0 0.2 0.4 0.6 0.8 1
0 0.1 0.2 0.3 0.4 0.5 0.6
δ
eff= 1.9
γ R
0/v
tHk
yρ
tHlinear TEM(H) TEM(H) with ETG
γ
lin- δ
effk
2Downshift of critical density gradient of W in turbulence
n The critical density gradient providing the zero flux of W transport in the trace particle limit is lower in the ITG turbulence than that given by linear modes.
n Downshift of # $ ⁄ % &' ( | for zero particle flux is identified, that is, # $ ⁄ % &' ( | = 1.6 in nonlinear ITG turbulence, while # $ ⁄ % &' ( | = 1.9 and 2.7 for 0 1 2 34 = 0.4 and 0.2, respectively
n The lower critical gradient is attributed to an outward flux driven by the linearly stable fluctuations in turbulence.
17
Results from GT5D
n Challenge to plasma rotation and LOC-SOC experiment
2021/11/22 @COMDATA2021
18
n Ohmic L-mode plasmas on Tore Supra are analyzed to understand LOC-SOC transition
n Development of boundary, heating, dissipation models for Tore Supra
n Linear analysis of micro-instabilities confirms mode transition from the trapped electron mode (TEM) to the ion temperature gradient (ITG) mode.
19
0 0.02 0.04 0.06 0.08 0.1 0.12
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 cs/a
k ts LOCSOC
-0.4 -0.2 0 0.2 0.4 0.6
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 cs/a
k ts LOCSOC
Growth rate Frequency
TEM ITG
Linear analysis of micro-instabilities using GT5D Intrinsic rotation
Stored energy W
th, Density n, Z
effOhmic L-mode plasmas on ToreSupra
[Bernard,PPCF2015]
[Citrin,PPCF2017]
LOC: Linear Ohmic Confinement
n
Low density
n
Linear increase of confinement time τ E w.r.t. n e
n
High Z eff due to carbon impurity
n
Counter-current rotation w.r.t. edge velocity
SOC: Saturated Ohmic Confinement
n
High density
n
Saturation of τ E
n
Low Z eff due to exhaust of carbon
n
Co-current rotation w.r.t. edge
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Results from data science approaches
n Data science to run ab initio simulations more efficiently
n CNN model with ENet as a predictor for efficient runs
2021/11/22 @COMDATA2021
20
Data science to run ab initio simulations more efficiently
n Convolutional Neural Network model, EfficientNet-B4 (ENet), is applied for regression (prediction) of simulation time of GKV from the images of !" # $ % , $ '
n Feed images and their corresponding time in the linearly and nonlinearly growing phases into ENet for training
1e-10 1e-08 1e-06 0.0001 0.01 1 100 10000 1e+06 1e+08
0 4 8 12 16 20 24 28 32 36 40
eng
t/(Raxi/vtp)
GKV/data/gkv-case032/gkvpf0.55ito2/run/gkv-case032woClbbetanlv3/hst
"<cat gkvp_f0.55.eng.0*" u 1:2
"<cat ../../gkv-case032_woC_lb_beta_box/hst/gkvp_f0.55.eng.0*" u 1:2
T ab le A. 2: E x p lan at ion s on G K V ou tp u t fi le s • F il e ty p e — As ci i • T im in g for ou tp u t — d tou t eng • M P I ran k for ou tp u t — ran k g = = 0 • T ot al fi le n u m b er s — (T ot al ru n n u m b er s) • I/O u n it n u m b er in G K V — ow es • S tor ed d at a — ti m e, W
E, W
Ekywhere, * ti m e: S im u lat ion ti m e t [L
ref/v
ref] (r eal ) * W
E: T ot al el ec tr os tat ic fi el d en er gy in cl u d in g p ol ar iz at ion [δ
2 refn
refT
ref] (r eal ). * W
Eky(0: gl ob al ny ): k
ysp ec tr u m of th e el ec tr os tat ic fi el d en er gy [δ
2 refn
refT
ref] (r eal ). hst/gkvp f0.48.wem.(inum in 3 d igi ts ) • F il e ty p e — As ci i • T im in g for ou tp u t — d tou t eng • M P I ran k for ou tp u t — ran k g = = 0 • T ot al fi le n u m b er s — (T ot al ru n n u m b er s) • I/O u n it n u m b er in G K V — ow em • S tor ed d at a — ti m e, W
M, W
Mkywhere, * ti m e: S im u lat ion ti m e t [L
ref/v
ref] (r eal ) * W
M: T ot al m agn et ic fi el d en er gy [δ
2 refn
refT
ref] (r eal ). * W
Mky(0: gl ob al ny ): k
ysp ec tr u m of th e m agn et ic fi el d en er gy [δ
2 refn
refT
ref] (r eal ). hst/gkvp f0.48.eng.(inum in 3 d igi ts ) • F il e ty p e — As ci i • T im in g for ou tp u t — d tou t eng • M P I ran k for ou tp u t — ran k g = = 0 • T ot al fi le n u m b er s — (T ot al ru n n u m b er s) • I/O u n it n u m b er in G K V — o en g • S tor ed d at a — ti m e, !
kx,ky⟨| ˜ φ
k|
2⟩, !
kx⟨| ˜ φ
k|
2⟩ where, * ti m e: S im u lat ion ti m e t [L
ref/v
ref] (r eal ) * !
kx,ky⟨| ˜ φ
k|
2⟩: S q u ar ed am p li tu d e of th e p er tu rb ed el ec tr os tat ic p ot en ti al [( δ
refT
ref/e
ref)
2] (r eal ). * !
kx⟨| ˜ φ
k|
2⟩( 0: gl ob al ny ): k
ysp ec tr u m of th e sq u ar ed am p li tu d e of th e p er tu rb ed el ec tr o- st at ic p ot en ti al [( δ
refT
ref/e
ref)
2] (r eal ). hst/gkvp f0.48.men.(inum in 3 d igi ts ) • F il e ty p e — As ci i • T im in g for ou tp u t — d tou t eng • M P I ran k for ou tp u t — ran k g = = 0 • T ot al fi le n u m b er s — (T ot al ru n n u m b er s) • I/O u n it n u m b er in G K V — om en • S tor ed d at a — ti m e, !
kx,ky⟨| ˜ A
∥k|
2⟩, !
kx⟨| ˜ A
∥k|
2⟩ where, * ti m e: S im u lat ion ti m e t [L
ref/v
ref] (r eal ) * !
kx,ky⟨| ˜ A
∥k|
2⟩: S q u ar ed am p li tu d e of th e p er tu rb ed el ec tr os tat ic p ot en ti al [( δ
refρ
refB
ref)
2] (r eal ). * !
kx⟨| ˜ A
∥k|
2⟩( 0: gl ob al ny ): k
ysp ec tr u m of th e sq u ar ed am p li tu d e of th e p er tu rb ed el ec tr o- st at ic p ot en ti al [( δ
refρ
refB
ref)
2] (r eal ). hst/gkvp f0.48.dtc.(inum in 3 d igi ts ) 29 1e-06
0.0001 0.01 1 100 10000 1e+06 1e+08
0 2 4 6 8 10
t/(R
axi/v
tp)
GKV/data/gkv-case032/gkvpf0.55ito2/run/gkv-case032woClbbetanlv3/hst
"<cat gkvp_f0.55.eng.0*" u 1:35
"<cat ../../gkv-case032_woC_lb_beta_box/hst/gkvp_f0.55.eng.0*" u 1:35
Nonlinear calc.
(
Linear calc.
lin- and nl-
growing phase saturation phase:
stochastic saturation time 5.005
5.100 10.734
11.000 2.755
3.100 Prediction
True
High
predictability!
)
*= 0.9949
Pr ed ic tio n
True
Extremely high ) * : 0.9949
è ) * : Determination coefficient
è Excellent prediction over the entire time period è Feasible to get ENet forecast of the saturation time
2021/11/22 @COMDATA2021
CNN model with ENet as a predictor for efficient runs
n Predictive capability makes it possible to choose the fastest case of all.
n Make use of ENet trained with “Base” case data (black line)
n Execute several GK runs with different initial amplitudes for a while and pick up the seemingly fastest case
n The saturation time can be roughly forecasted at an early stage.
n Save numerical resources by keeping the fastest case and eliminating the rest.
Saturation time:
wall-clock time:
6~10 hours
1e-10 1e-08 1e-06 0.0001 0.01 1 100 10000 1e+06 1e+08
0 5 10 15 20 25 30 35 40 45 50 55 60
eng
t/(Raxi/vtp)
GKV/data/gkv-case032/gkvpf0.55ito2/run/gkv-case032woClbbetanlv3/hst
"<cat gkvp_f0.55.eng.0*" u 1:2
TableA.2:ExplanationsonGKVoutputfiles •Filetype—Ascii •Timingforoutput—dtouteng •MPIrankforoutput—rankg==0 •Totalfilenumbers—(Totalrunnumbers) •I/OunitnumberinGKV—owes •Storeddata—time,WE,WEky where, *time:Simulationtimet[Lref/vref](real) *WE:Totalelectrostaticfieldenergyincludingpolarization[δ2 refnrefTref](real). *WEky(0:globalny):kyspectrumoftheelectrostaticfieldenergy[δ2 refnrefTref](real). hst/gkvpf0.48.wem.(inumin3digits) •Filetype—Ascii •Timingforoutput—dtouteng •MPIrankforoutput—rankg==0 •Totalfilenumbers—(Totalrunnumbers) •I/OunitnumberinGKV—owem •Storeddata—time,WM,WMky where, *time:Simulationtimet[Lref/vref](real) *WM:Totalmagneticfieldenergy[δ2 refnrefTref](real). *WMky(0:globalny):kyspectrumofthemagneticfieldenergy[δ2 refnrefTref](real). hst/gkvpf0.48.eng.(inumin3digits) •Filetype—Ascii •Timingforoutput—dtouteng •MPIrankforoutput—rankg==0 •Totalfilenumbers—(Totalrunnumbers) •I/OunitnumberinGKV—oeng •Storeddata—time,! kx,ky⟨|˜ φk|2⟩,! kx⟨|˜ φk|2⟩ where, *time:Simulationtimet[Lref/vref](real) *! kx,ky⟨|˜ φk|2⟩:Squaredamplitudeoftheperturbedelectrostaticpotential[(δrefTref/eref)2] (real). *! kx⟨|˜ φk|2⟩(0:globalny):kyspectrumofthesquaredamplitudeoftheperturbedelectro- staticpotential[(δrefTref/eref)2](real). hst/gkvpf0.48.men.(inumin3digits) •Filetype—Ascii •Timingforoutput—dtouteng •MPIrankforoutput—rankg==0 •Totalfilenumbers—(Totalrunnumbers) •I/OunitnumberinGKV—omen •Storeddata—time,! kx,ky⟨|˜ A∥k
|2⟩,! kx⟨|˜ A∥k
|2⟩ where, *time:Simulationtimet[Lref/vref](real) *! kx,ky⟨|˜ A∥k
|2⟩:Squaredamplitudeoftheperturbedelectrostaticpotential[(δrefρrefBref)2] (real). *! kx⟨|˜ A∥k
|2⟩(0:globalny):kyspectrumofthesquaredamplitudeoftheperturbedelectro- staticpotential[(δrefρrefBref)2](real). hst/gkvpf0.48.dtc.(inumin3digits) 29 1e-10
1e-08 1e-06 0.0001 0.01 1 100 10000 1e+06 1e+08
0 5 10 15 20 25 30 35 40 45 50 55 60
t/(Raxi/vtp)
GKV/data/gkv-case032/gkvpf0.55/run/gkv-case032woClbbetanlv6/hst
"<cat gkvp_f0.55.eng.0*" u 1:2
"<cat ../../gkv-case032_woC_lb_beta_nl_v7/hst/gkvp_f0.55.eng.0*" u 1:2
"<cat ../../gkv-case032_woC_lb_beta_nl_v10/hst/gkvp_f0.55.eng.0*" u 1:2
Base High (×10
$) Low (×10
%$)
&
16
8 25
Changes in the initial fluctuation amplitude
wall-clock time:
33~36 hours
Images at ̅& = 5
Base High Low
Estimated
saturation time ̅( = 6.726 ̅( = 17.437
It will be saturated soon The simulation is still in the midst of the growing phase.
2021/11/22 @COMDATA2021
Summary
n Burning fusion plasma involves unresolved physics issues
n Turbulent transport under the burning plasma condition, intrinsic plasma rotation, and the energetic-particle confinement …
n Ab initio simulations for burning plasma physics (BPP) have made a progress by use of the supercomputer Fugaku towards ITER
n Three major applications and data science methods have been developed
n
GKV simulations revealed cross-scale interactions of turbulence
n
GT5D code has been applied to intrinsic (spontaneous) plasma rotation in LOC/SOC
n
MEGA simulations clarified kinetic effects of thermal ions on the a particle driven Alfvén eigenmodes and transport
n
EfficientNet as a CNN model is utilized for predictions of simulation time
n Fugaku is fully utilized for the study of burning plasma physics
n Successful development of novel schemes and code optimizations bring us new insights into BPP!
2021/11/22 @COMDATA2021
