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0E9@t f + V · @Z f = C(f ) + S4(S@G@! @H@I(7)The initial energetic
particle distribution function inehQnk (`7
0E9_bcvelocity space is shown in Fig. 1(a). The dashed curves
represent`;<3F
constant ", and particles evolve only along the+_[\c(IKdashed curves because " is an adiabatic invariant. In area@fj"¼const > 0, and the particles with positive @E
can#.,|o}`}qnkA, @E@f(D"@fdestabilize the EGAM. In area B, @E j"¼const < 0, and=> YZ 85w u!P/knparticles 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 theenergy transfer from particles to the EGAM, destabilizing(1)
f0 ¼ f0 ðE; "; P! ; #Þ;the mode. In contrast, the red color represents positiveenergy transfer that stabilizes the mode. The energy
P! ¼ Zh e c þ Rmvk b! ;(2)
transfer rate in the destabilizing region is higher than thatin the stabilizing region. Then, the EGAM is excited on thewhere E is the particle energy, " is the magnetic moment,
whole. Notice that the purple region in Fig. 1(b) is located
P! is the toroidal canonical momentum, # distinguishes
in area A in Fig. 1(a), and the red region in Fig. 1(b) isthe orbit types (with # ¼ 1 for copassing particles, # ¼ 0
located in area B in Fig. 1(a). These two figures are confor trapped particles, and # ¼ #1 for counterpassing parsistent with each other, clarifying the mode destabilizationticles). Zh e and m are the particle charge and mass, c is theU_[\c(IK`D"mechanism.
poloidal magnetic flux, vk is the parallel velocity,and b! isThe EGAM frequency chirping takes place in the nonthe toroidal component of the magnetic field unit vector.
linearphase, and the evolution of the frequency spectrum
Assuming the separation of variables, Eq. (1) is expand the poloidal velocity is shown in Fig. 2. The mode
ressed byLHD3sv⊥"x@f0JT-60v//yThe destabilization of the EGAM arises from the energy
derivative of f0 with the most important contribution fromthe second term of the equation below.

HI þ GI þ GH:¼3(IKD"GKV@E@E @!
@E@E [Watanabe,NF2006]@6S -:*v⊥"

zTe ¼ 4 keV, and bulk plasma beta value at the magnetic
axis equal to 7:2 " 10#4 . The neutral beam injection energy is ENBI ¼ 170 keV. Since the kinetic GAM frequency
at LHD is close to those in tokamaks [3], a tokamak typeequilibrium is examined with concentric magnetic surfaces, and with the safety factor profile and the aspectratio similar to the LHD plasma. The safety factor q profile
is a weak shear profile with q ¼ 2:0 at the magnetic axis
and q ¼ 0:83 at the plasma edge. The major radius of
the magnetic axis is R0 ¼ 3:9 m and the plasma minor
radius is a ¼ 0:65 m. Cylindrical coordinates (R, !, z) are
employed for the simulation with numbers of grid points(128, 16, 128), respectively, although the equilibrium andthe fluctuations do not depend on !. The number of thecomputational particles is 2 million.
The equilibrium energetic particle distribution function
f0 can be written using constants of motion asv//

3sα:T3(IKD"GT5D[Idomura,NF2009]

MHDD"MEGA[Todo,POP1998]

f ¼ f ðE; "; P α:T; #Þ ¼ GðEÞH ð!ÞIðE;"; P ; #Þ; (3)MHD/G`:(xe{ruE9_ehnk (`7 0E9_bcO]Ja(a)where ! ¼ "B =E is the pitch angle variable with the B!P' `FXR+` U magnetic
bcα:IK`Ffield strength at the magnetic axis. The energy0!

1!

060

00.8

Energy [keV]

0distribution GðEÞ#.,1Vfvi
is a slowing down distribution. The :`O]JaD"Area A
#.,|o}`>2H^N)8D"function H ð!Þ is introduced to model anisotropic distri30
Area
22butions in pitch angle H =>ð!Þ¼exp½#ð!#!
=> YZ 100w u!P/k nRD"
YZ 150wnB ITER|o}
peak Þ ="! (, u!P/keh;(`A=meonk j`D"2021/3/9 HPCIzg ~(4)Energy [keV]IðE; "; P! ; #Þ ¼ expð# c nrm =$2 Þ;

0fvi keV

where the !peak represents the pitch angle for the distribution peak and "! is a parameter to control the distribution
width. In the present simulation, !peak ¼0:3 and "!¼0:2.
The function I represents the radial profile which isMHD/G`5P%M
consistent with the energetic particle beta profile

60

0.6
0.4
0.2
0L5P`:
(b)

128
4
030

-4
P! # #R0 mv0c nrm ¼ 1 #;(5)
-8
Zh e c max-12pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ0
where v0 ¼ 2ðE # "Bmin Þ=m, c max is the maximum
00.2
0.4
0.6
value of c , and $ ¼ 0:5 in the present simulation.
ΛyrqC
The time derivative of %f ¼ f # f0 at each marker
particle is given byFIG. 1 (color).
Panel (a) shows the normalized initial energetic
Vfvi :TMHD/G`D"

d%f ¼

dðf # f0 Þ ¼ #dE @f0#dP! @f0

4:(6)particle distribution in (!, E) space, and panel (b) shows theenergy transfer rate from the EGAM to energetic particles.

[1] !.,}i~|z)IL{ {uz{: GKV, QST, NIFS

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W

ZF
ZF/5 in Hturb.
TEM through the collisional effects provides us with aWturb./5 in D
useful qualitative basis to investigate the isotope impacts
3on the turbulent transport. For the comparison, which will
week ending
H Y S I (labeledC A L RbyE V I E W L E T T E R S
21 APRIL 2017
PRLshown
118, 165002(2017)
bebelow, thenonlinear TEMP results
0NL-TEM) are also plotted in Fig. 1.
(a)(c)
H-plasma
theAs
ratio
electron-ion
collision
frequency
to the ion
0.2
for ofthethe
linearzonal-flow
response,
earlierp
theoretical
120 (c) H-plasma
ﬃﬃﬃﬃﬃ
D-plasma
1=2transit showfrequency,i.e., νisotope
ðmi =mi.e.,∝ zonal-flow
Ai , leads
D-plasmaei =ωti ∝e Þ theworks
the weakeffects;
to strongerkernel
collisional
stabilization
for heavier
ions.
response
indicates
no explicit
mass isotope
dependence
Notethealsofixedthat theeffect
on
ITG
modes
by
the0.160
fork⊥ ρstabilization[35],except
forthecaseswith
theti
ion-ioncollisions
isalmost
independentof
theionmass,
equilibrium radial electric field [13–15]. Therefore, thei.e., νii =ω
m0i . Then,
opposite ion
mass dependenceisotope
masson the nonlinear
zonal-flow
dynamics
ti ∝impacts
αofAwithα<0appears
fortheTEM
in a certain
0becomemore important.
i0(b) 2060
80
100120140160# ≥ 0.04 in the present case.
WZF in40
H
collisionality
regime,i.e.,νFollowing the above linear
analyses, we have pereiTime t [Rax /υtH]
WZF in D
6The reduction
in parallel
the mixing-length
diffusivity fortheformed
massively
nonlinear TEM-driven
turbuWturb./5 in H
TEM simulations
through thefor
collisional
effects provides
us plasma,with alencethe non-axisymmetric
LHD
LHD(</N(<}i)ILCWturb./5 inthe
D hydrogen isotope mass on (a) turbulent
FIG.
2.
Impacts
FIG. 3. Spatial ofstructuresof the potential fluctuations in theuseful qualitativebasis
to 69,120
investigate
the isotopecores
impacts
where∼200 hours
withcomputationareheat fluxes
normalized by the hydrogen gyro-Bohm unit3-)

ntie

WZF and Wturb./5ii
αii/q / Σ q L-1
ΣsTΣsJsq(ZF)
s s Tss s GB(H)ntiΣsq s/q GB(H)RYpvx|zkdty]a}i~week ending
PHYSICAL REVIEW LETTERS
21 APRIL 2017
PRL 118, 165002 (2017)|z){ {(a)H-plasmathe ratio of the electron-ion collision frequency to the ion120 ~|z){ {pﬃﬃﬃﬃﬃ
D-plasma=> |zQ)735A[Maeyama,PRL
2015]
transit frequency, i.e., ν =ω ∝ ðm =m Þ ∝ A , leads
PHYSICAL REVIEPRL 118, 165002 (2017)
to stronger collisional stabilization for heavier isotope ions.
Note also that thestabilization effect on ITG modes by theLHDN(<U2018-hT[cN(<iP^JmH60Dion-ion collisions is almost independent of the ion mass,
t* [Nakata, PRLi.e., ν2017]=ω ∝ m . Then, the opposite ion mass dependenceof A with α < 0 appears for the TEM in a certain
0(b) W in H
collisionality
regime,i.e.,ν≥
0.04
inthepresentcase.
=> `iLHDN(<Uhoq*Z#D\saW in D
6The reduction in the mixing-length diffusivity for theand Wturb./5nF
fow
li
reti
fl5n

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heatingVΦ ↓Electron heating
Pin,i=4MW Pin,e=4MW²·ª³k05101520Time(ms)6[3] .427&Zux=RaKlhs ~ryz: MEGA 'NIFS, QSTzz.427&=: .A#7&Zuxα=i|h@ 3g"VnZLhtswα=h 5:fRaKle !^"Bn|MHD1q I`, α=h)@ 3h ^7ao$p=> s ~zzgmoZux=RaKlDnnnZux=Xgmo|h:(q6 [Wang+, PRL 2018; NF2019]
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1Volume−(a)ALEintegratedALE
ALE
magnetic#2#1#3
fluct. amp.
0[a.u.]
60
80
100120140160[ms]

SIMULATION
MEGAcode

1Magnetic (b)fluct. amp
at wall[a.u.]
04280

Self−consist. sim. for short time scale (≤ 10 ms)
130−80(c) Sim. of ALE #2
kHz
Toroidal mode num.
signaln=1 n=2 n=30

EXPERIMENT
JT−60
shot
48424

Zux=gmo:(6H2021/3/9 HPCIv

120

122124(d) Representative ALE
Toroidal mode num.
n=1 n=2 n=34300

4320

4340

43604380

4Time[ms]

4338

4340

[ms]

30−80
kHz
signal4342

FIG.JT-60Ug]_o{:MHD6Hh},S{yD3: Comparison between ALEs in simulations (top) and experiments (bottom). In 7

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