Plasma and Fusion Research: Regular Articles

Volume 17, 1403083 (2022)

Gyrokinetic Turbulent Transport Simulations on Steady Burning
Condition in D-T-He Plasmas
Motoki NAKATA1,2,3) and Mitsuru HONDA4)
1) National Institute for Fusion Science, National Institutes of Natural Sciences, Toki 509-5292, Japan2) The Graduate University for Advanced Studies, Toki 509-5292, Japan
3) PRESTO, Japan Science and Technology Agency, 418 Honcho, Kawaguchishi, Saitama 332-0012, Japan
4) Graduate School of Engineering, Kyoto University, Nishikyo, Kyoto 615-8530, Japan(Received 26 April 2022 / Accepted 17 May 2022)
Ion temperature gradient (ITG) and trapped electron modes (TEM) driven turbulent transport in an ITER-like
plasma is investigated by means of multi-species gyrokinetic Vlasov simulations with D, T, He, and real-masskinetic electrons including their inter-species collisions. Beyond the conventional zero-dimensional power balance
analysis presuming the global energy and particle confinement times, gyrokinetic-simulation-based evaluationof a steady burning condition with He-ash exhaust and D-T fuel inward pinch is demonstrated. It is clarified
that a significant imbalance appears in the turbulent particle flux for the fuel ions of D and T, depending on the
D-T density ratio and the He-ash accumulation. Then several profile regimes to satisfy Reiter’s steady burning
condition are, for the first time, identified by the gyrokinetic simulation. Also, the impacts of zonal flows andnonthermal He-ash on the optimal profile regimes are examined.
© 2022 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords: burning plasma, turbulent transport, steady burning condition, multi-species gyrokinetic simulation
DOI: 10.1585/pfr.17.1403083

1. Introduction
Burning plasmas are intrinsically composed of multiion species such as fuel hydrogen isotopes (Deuterium andTritium), the high-energy α particles produced by the fusion reaction, the thermalized He-ash, and high-Z impurities resulting from the plasma-facing materials. Morecomplex turbulent transport processes are, thus, expectedin the burning plasmas, compared to those in the single orvery few ion-species plasmas, which are usually addressedin experiments. Since simultaneous measurements of the
kinetic profiles for all particle species including the interspecies energy exchange are diﬃcult, the first-principlebased gyrokinetic turbulent transport simulations for themulti-ion mixture plasmas are indispensable to predict theconfinement performance, and to optimize the D-T fuelingand the impurity exhausts in the burning plasma. There areseveral earlier works regarding the ITG driven turbulent
transport of fuel hydrogen-isotope ions [1–5] and the lightand heavy impurity transport [6, 7], but the fuel and impurity ion transport has often been examined separately. The
impacts of multi-ion species on the ion- and electron-scale
microinstabilities have also been studied [8], and the reduction of turbulent heat flux through multi-scale interactionsin the multi-ion species plasma has been revealed [9]. In
addition, several recent experiments in the mixture [10–12]
and/or the D-T burning plasmas [13] with dedicated controls of the ion density have revealed the significant isotopeauthor’s e-mail: nakata.motoki@nifs.ac.jp

Fig. 1 Ignition curves influenced by He-ash accumulation(nHe /ne ) and the steady burning curves for ρτ := τp /τE ,where τp ≃ τHe . See also Ref. 14 and 15.

and impurity-eﬀects on turbulent particle and energy transport, which are important for optimizing the fusion power
output.
Multi-ion species not only complicates the transport
processes in burning plasmas, but also strongly aﬀects theignition and steady burning conditions. Indeed the zerodimensional power balance analysis shows that the accumulation of the thermalized He-ash in the core region leads toa more severe self-ignition criteria on the Lawson diagram,as shown in Fig. 1. Here the ignition curves on a plane of

1403083-1© 2022 The Japan Society of Plasma
Science and Nuclear Fusion Research

Plasma and Fusion Research: Regular Articles
the fusion triple product n0 τ̂ET0 and the on-axis temperature T0 are calculated according to Ref. 14 and 15, wheren0 and τ̂E = (1 + Prad /Pabs )−1 τE denote the on-axis density
and the eﬀective global energy confinement time including
the radiation-loss power Prad . In addition to the ignition
curves, the steady burning condition is described by theclosed curves, where the ratio of the particle (He-ash) toenergy confinement time, i.e., ρτ := τp /τE , where τp ≃ τHe ,is the critical parameter, as will be discussed later. It should
be noted, however, that any transport processes of the fuelions and He-ash are not incorporated in the above argument.
The multi-species turbulent transport studies are, thus, required to examine the steady burning condition, beyond theconventional zero-dimensional power balance analysis.
In this study, the multi-species gyrokinetic Vlasov simulations have been carried out to clarify the profile conditions with optimal balance of turbulent energy and particle transport in the steady burning state. Here, Reiter’s
steady burning condition τHe < α∗ τE [14], which describes
a permissible ratio of the He-ash confinement to the energy confinement, is investigated, where α∗ ∼ 7 - 15 depending on the wall and divertor conditions. We consider
the ion temperature gradient (ITG) and trapped electronmode (TEM) driven turbulent transport in an ITER-like
plasma [16] with D, T, the thermalized He-ash, and realmass kinetic electrons including their inter-species collisions [17]. A good prediction capability of the gyrokinetic
simulation has been confirmed for the JT-60U tokamak Lmode experiment [18].
The rest of the paper is organized as follows. In Sec. 2,
the gyrokinetic simulation model and the numerical setup
are described. Then the linear and nonlinear ITG-TEM
turbulence simulation results are presented. In Sec. 3, we
discuss the impact of the D-T ratio and the He-ash accumulation on the energy and particle transport. The gyrokineticsimulation-based evaluation of the profile regimes to satisfy the Reiter’s steady burning condition are presented inSec. 4. Finally, the summary is given in Sec. 5.

2. Multi-species Gyrokinetic Turbulence Simulations
2.1 Gyrokinetic model
In this study, a multi-species electromagnetic gyrokinetic Vlasov solver GKV [19] is used. The simulation
model is briefly summarized in this section. The governing equation is an electromagnetic gyrokinetic equation forthe particle species “s”, which describes the time evolutionof the non-adiabatic part of the perturbed gyrocenter distribution function δgs in the five-dimensional phase-space(xg, v ∥ , µ). The Fourier representation with respect to theperpendicular wavenumber k⊥ is given by()µb ·∇B ∂∂+ v ∥ b ·∇ + iωDs −δgsk⊥∂t
ms ∂v ∥∑()
c−b · k⊥′ × k⊥′′ δψsk⊥′ δgsk⊥′′B ∆Volume 17, 1403083 (2022)()µb ·∇Bes FMs ∂+ iω∗T s + v ∥
δψsk⊥
=
Ts
∂t
Ts
(
)
+ Cs δgsk⊥ ,(1)(g)

where δgsk⊥ = δ fsk⊥ + FMs J0s es δϕk⊥ /Ts , and J0s =J0 (k⊥ v⊥ /Ωs ) is the zeroth-order Bessel function. The
gyrophase-averaged electrostatic and electromagnetic potential fluctuations are combined into δψsk⊥ = J0s δϕk⊥ −(v ∥ /c)J0s δ A ∥k⊥ . Since we focus on the finite but low-β
plasmas here, the parallel magnetic field fluctuation δB ∥k⊥is ignored. The equilibrium part of the distribution function is given by the local Maxwellian distribution, i.e.,
FMs = ns (ms /2πTs )3/2 exp[−(ms v 2∥ + 2µB)/2Ts ].
The gyrokinetic equation shown in Eq. (1) is solvedin the local fluxtube coordinates (x, y, z) defined as x =a(ρ − ρ0 ), y = aρ0 q(ρ0 )−1 [q(ρ)θ − ζ] , z = θ with thestraight-field-line flux coordinates (ρ, θ, ζ), where a andq(ρ0 ) denote the plasma minor radius and the safety factor
on the flux surface of interest ρ0 , respectively. In these coordinates, the magnetic and diamagnetic drift frequencies
for k⊥ = k x ∇x + k y ∇y are given by()
cTsk⊥ · b × µ∇B + ms v 2∥ b ·∇b
ωDs =
es B
c(ms v 2∥ + µB) ()=
Kg k x + Kn k y ,(2)
es Bax[()]
ms v 2∥ +2µB 3cTs
ω∗T s =
1 + ηs−k⊥ · bes B
2Ts
2× ∇ ln ns ,(3)

where ηs = Lns /LTs with Lns = −(d ln ns /dx)−1 andLTs = −(d ln Ts /dx)−1 . The geometric coeﬃcients representing the geodesic curvature component Kg and thenormal curvature component Kn are defined as follows:g xz g x y − g xx g yz ∂ ln B ∂ ln B
−
,
(4)
Kg =
2
∂z
∂y
B2 /Baxg xz g y y − g x y g yz ∂ ln B ∂ ln B
Kn =
+
,
(5)
2
∂z
∂x
B2 /Bax
where g i j , (i, j) = (x, y, z) denotes the contravariant components of the metric tensor. Note that the pressure gradienteﬀect in the curvature drift is ignored by the low-β approximation, and ∂ ln B/∂ y = 0 for the axisymmetric fields.
Collisional eﬀects are introduced in terms of a multispecies gyrokinetic collision operator Cs expressed as∑ ∮ dφ{Cs (δgsk⊥ ) =eik⊥ ·ρs CssT′ [e−ik⊥ ·ρs δgsk⊥ ]
2π
s′
}
F
+ Css′ [e−ik⊥ ·ρs′ δgs′ k⊥ ] ,(6)where the field-particle part CssF ′ holds the particle, momentum, and energy conservation, as well as Boltzmann’s
H-theorem [17, 20].
The electromagnetic fluctuations are determined by
the Poisson-Ampère equations:
(
)
∑ ∫
−2
k⊥2 + λDδϕk⊥ = 4π
es dv J0s δgsk⊥ ,(7)1403083-2sPlasma and Fusion Research: Regular Articles∫
4π ∑k⊥2 δ A ∥k⊥ =es dv v ∥ J0s δgsk⊥ ,c sVolume 17, 1403083 (2022)(8)∑
where λD = ( s 4πns es2 /Ts )−1/2 is the Debye length. The
charge neutrality in the background density ns is described∑
as s,e fCs = 1, where fCs ≡ Zs ns /ne means the chargedensity fraction for ions with the charge number Zs . The
contribution of each species to the source terms in theright hand side of Eqs. (7) and (8) is proportional to fCs . In
addition, the radial derivative of the above charge neutrality
condition leads to another constraint for the background∑density gradient, i.e., s,e fCs Ln−1s = Ln−1e .
The radial turbulent fluxes with respect to the energy
and particle are, respectively, defined by
Qs := ⟨Q s ·∇x⟩⟩⟨ ∫c
ms v 2(∇x · b×∇⊥ δϕ) δgs ,
=
dv
(9)
B
2
⟨ ∫
⟩
c
Γs := ⟨Γs ·∇x⟩ =dv (∇x · b×∇⊥ δϕ) δgs ,B(10)where the flux-surface average is denoted by ⟨· · · ⟩. By
using the above gyrokinetic Vlasov and Poisson-Ampère
equations, one can derive the entropy balance/transfer equation which describes the relation among the fluctuations of
the phase-space distribution function, the transport fluxes,
the entropy transfer via nonlinear interactions, and the collisional dissipation [20,21]. It also provides us with a goodmeasure for the accuracy of the kinetic turbulence simulation.

2.2 ITG-TEM driven turbulence simulations
in ITER-like D-T-He plasma
In this section, we present multi-species gyrokinetic
simulations for the ITG-TEM instability and the associated turbulent transport in an ITER-like shaped plasma [16],where 4-species of D(AD = 2, ZD = 1), T(AT = 3, ZT = 1),
He(AHe = 4, ZHe = 2), and real-mass kinetic electrons
are incorporated. As a likely profile condition, we assume the normalized temperature and density gradient
lengths at ρ = 0.5 to be Rax /LTi = 6 for all the ionspecies, Rax /LTe = 8, and Rax /Ln = 2 for all the particle species, respectively. Also, the equal temperature of
TD = TT = THe = Te = 5 keV, and the electron density of
ne = 1.4×1020 m−3 are considered, where the normalized∗ ∼ 0.02. As for theelectron-electron collisionality is νeenumerical resolution, (169, 49)-mode numbers in (k x , k y )and (64, 64, 24)-grid numbers in (z, v ∥ , v⊥ ) are used, where(k xmin ρtH, k miny ρtH ) = (0.049, 0.05) and the velocity-spacedomain is taken with (|v max|, v⊥max ) = (4.5vts, 4.5vts ) at∥
2 = 1×10−3
z = 0. A small but finite β value of β0 := neTi /Bax
is imposed to suppress the fast dispersive Alfv́en waves
so-called the ωH mode.
The linear growth rate and mode frequency in the D-THe plasma with 10% He-ash, i.e., nD /ne = nT /ne = 0.4 andFig. 2 Normalized linear growth rate and mode frequency of ITG(ωr < 0) and TEM (ωr > 0) instabilities in pure-D, pureT, D-T (nD = nT = 0.5ne ), and D-T-He (nD = nT = 0.4ne ,nHe = 0.1ne ) plasmas.

nHe /ne = 0.1, are shown in Fig. 2, where the cases with pureD, pure-T, and D-T are also plotted for comparisons. Notethat the eﬀective thermal speed vt(eﬀ) and ion gyroradiusρt(eﬀ) are defined by using the eﬀective ion mass and charge∑∑
numbers, i.e., Aeﬀ ≡ s,e fCs As and Zeﬀ ≡ s,e fCs Zs .
One can see a only slight change of the normalized growthrate and the mode frequency even in the case with He-ash
accumulation, where the dilution eﬀect is absorbed in thenormalization with the charge-density fraction fCs .
The time evolution of turbulent energy and particle fluxes, i.e., Qs and Zs Γs , in the D-T-He plasma with
nD = nT = 0.4ne and nHe = 0.1ne is shown in Figs. 3 (a)and 3 (b), where the gyro-Bohm unit for hydrogen is used
here. Depending on the particle species, diﬀerent saturation levels, e.g., QHe < QT ∼ QD ∼ 0.5Qe appear in thestatistically steady state, where a slight deviation from thegyro-Bohm scaling is found for the hydrogen isotopes of D
and T. It has been confirmed that the ambipolar conditionof ΓD + ΓT + 2ΓHe = Γe is accurately satisfied. Note also
that, in contrast to the quasilinear flux, the direction of the
T particle transport flips from inward to outward after the
nonlinear saturation of the linear growth(t ∼ 45Rax /vtH ).
The snapshot of the temperature fluctuations in the real
space is displayed in Fig. 3 (c), where the fluctuations ofD, T, and He are simultaneously visualized by the superposition of diﬀerently colored luminescence, and a single
fluxtube is copied several times in the toroidal direction toform the torus volume.
Figure 4 shows the distribution of the turbulent particle
fluxes along the magnetic field lines, where the origin ischosen as the most outboard side of the plasma. In order toemphasize the importance of multi-species treatments on
the turbulent particle transport, we compare the results forthe case with multi-ion species (D-T) and with the singleion approximation by Aeﬀ = 2.5. The ballooning-type
distributions appear in all the species of D, T, and Aeﬀ ,1403083-3

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Volume 17, 1403083 (2022)

Fig. 4 Distributions of the turbulent particle fluxes along the fieldlines in the D-T plasma and the single-ion approximatedplasma with the eﬀective ion mass Aeﬀ . The flux surfaceof ρ = 0.5 is displayed by the curve in green.

3. Impacts of D-T Ratio and He-Ash
Accumulation on Turbulent Fluxes

Fig. 3 Time evolution of (a) turbulent energy flux and (b) particle
flux in the ITG-TEM turbulence of D-T-He plasma. (c)Temperature fluctuations at t = 65.4Rax /vtH of D (blue),
T (yellow), and He (red). The fluctuations are simultaneously visualized by the superposition of diﬀerently
colored luminescence.

where the outward particle flux has the peak around z =0. It should be noted that the inward particle flux of D,i.e., ΓD(local) < 0, occurs around the inboard side of z ∼ π,
whereas the single-ion case indicating the globally outward
flux does not reproduce such a flip of the particle-transport
direction on the flux surface. These results highlight anessential diﬀerence between the single-ion approach withthe eﬀective ion mass and the multi-species simulations,particularly for the particle transport, which will also beseen in Sec. 3.

In order to further examine the particle-species dependence of turbulent energy and particle fluxes, the nonlinear
simulation scans with respect to the D-T density ratio andHe-ash accumulation have been carried out. Here, the accumulations of thermalized He-ash with nHe /ne = {0%,5%, 10%} are considered for comparison.
Figures 5 (a) and 5 (b) show the dependence of the D-T
ratio nT /(nT + nD ) on the mean turbulent energy and particle fluxes for D and T (QD,T and ΓD,T ) in the cases withand without He-ash, where the ion fluxes are normalized
by the electron ones (Qe and Γe ). Note that both the energy
and particle fluxes for electrons are almost constant for all
the cases, i.e., Qe /QgB(H) ≃ 110 and Γe /ΓgB(H) ≃ 10. In
the figure, the D-T ratio corresponding to the balanced D-T
flux, i.e., QD ≃ QT and ΓD ≃ ΓT , is shown by the verticalline. It is stressed that, for the case with He-ash, the additional transport channel of He-ash leads to the reduction in
the energy and particle fluxes of D-T ions. One also findsthat the overall tendency indicating the linear D-T ratio dependence of QD and QT is unchanged regardless of He-ash
accumulations, where the balanced energy flux commonly
appears at nearly 50%-50% D-T ratio of nT /(nT + nD ) = 0.5.
On the other hand, for the D-T particle fluxes, an imbalanced particle transport associated with the nonlinear
D-T ratio dependence is revealed, where ΓD , ΓT even at
50%-50% D-T ratio. Moreover, the finite He-ash accumulations give rise to not only the reduction in the turbulent
flux, but also a more significant imbalance of the D-T particle transport. As also shown by the triangle symbols in
the figures, one can see that the single-ion approximation
with Aeﬀ fails to reproduce the imbalanced transport nature,
particularly for the particle transport.
The diﬀerence between the multi-ion species treatments and the single-ion approximation is attributed to the1403083-4

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Volume 17, 1403083 (2022)

4. Gyrokinetic-Simulation-Based
Evaluation of Steady Burning
Condition
The present multi-ion species gyrokinetic turbulencesimulations with the thermalized He-ash can provide quantitative evaluations of the steady burning condition, which
can never be addressed by the single-ion-species approaches. The profile conditions with optimal balance of
turbulent energy and particle transport in the steady burningstate are discussed in this section.
For sustainable fusion reactions, the He-ash should be
exhausted from the core region, where the ratio of τHe /τE
is the critical parameter as shown in Fig. 1. Then, Reiter’s
steady burning condition [14] is represented by τHe < α∗ τE ,where α∗ = 7 - 15 is a constant depending on the wall anddivertor conditions. For simplicity, we ignore the recycling
and exhaust eﬀects. This relation describes the permissible particle confinement time of He-ash, compared to theenergy confinement time.
To evaluate Reiter’s condition in terms of the gyrokinetic turbulence simulations, the expression with turbulent fluxes is useful. Introducing the approximations of(eﬀ)
τHe ≃ a2 /DHe
= a2 /(ΓHe /nHe Ln−1 ) and τE ≃ a2 / χi(eﬀ) =2−1
a /(Qi /niTi LTi ), Reiter’s steady burning condition with
the He-ash exhaust and the fuel inward pinch is rewritten
asFig. 5 D-T ratio dependencies of the mean (a) energy and (b) particle fluxes of D and T for He-ash accumulations of nHe /ne= {0%(solid), 5%(dotted), and 10%(dashed)}, where theion fluxes are normalized by the electron ones. The D-T
ratio corresponding to the balanced flux is shown by thevertical line.

constraint by the ambipolar condition for the particle fluxes.
In the single-ion approximation, Γ Aeﬀ must always be balanced with Γe , so that (1/2)Γ Aeﬀ /Γe = 1/2 exactly holds. On
the other hand, in the multi-ion species case, ΓD + ΓT = Γepermits the individual values for the ion particle fluxes
which can cause the imbalanced particle transport. Since
there is no such constraint for the thermal flux, the diﬀerence between multi-ion and single-ion cases becomes lesssignificant.
The imbalanced particle transport essentially resulting
from multi-ion species eﬀects, which strongly depends on
the background D-T ratio and the He-ash accumulation,
may enable us to develop more eﬃcient D/T fueling and thedensity-profile controls in burning plasmas. Then the D-T
density ratio providing the balanced flux is regarded as ameasure for the strength of imbalance in the global D-T ratio
dependence, i.e., a larger deviation from nT /(nT + nD ) = 0.5
suggests a more significant imbalanced flux.

ηiTi (ni /nHe )ΓHe > Qi /α∗,(11)

ΓHe > 0,(12)

ΓD,T < 0,(13)

where Qi denotes the summation of the ion energy flux,and ηi = Ln /LTi . In the following, we consider α∗ = 7 as a
typical case.
In order to identify the optimal profile regimes, thedensity-gradient(Rax /Ln ) scans of the turbulent energy andparticle transport are performed, where the case for DT-He(nHe /ne = 0.1) plasma is examined. As shown in
Fig. 6 (a), the density gradient dependence of Ti ΓD and
Ti ΓT gives rise to a threshold of the inward D-T fluxes
with ΓD,T ⩽ 0 shown by the vertical dashed line. It is
expected that the inward pinch related to the oﬀ-diagonal
contributions from Rax /LTi,e prevails over the outward diffusion from Rax /Ln in the D-T particle fluxes of ΓD and ΓT .
Indeed, the wavenumber spectra of ηiTi ΓHe and Ti ΓT shownin Fig. 6 (b) indicate the nonuniform changes, where thespectra do not change globally (like a flip of spectrum), but
the components of the inward tritium flux in the relatively
higher wavenumber modes gradually increase as Rax /Lndecreases, in contrast to the weak Rax /Ln dependence of
ΓHe > 0. This can also be attributed to the change of the
turbulence drive by the ITG and TEM instabilities.
Then, the profile regime of Rax /Ln ≤ 1.2 [hatchedregion in Fig. 6 (a)] to satisfy the above steady burning
condition of Eqs. (11) - (13) with α∗ = 7 is clearly identified.

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Fig. 6 (a) Density gradient dependence of turbulent fluxes,
where ηiTi (ni /nHe )ΓHe is scaled by the factor of 1/8 forvisibility. The steady burning condition with α∗ = 7 issatisfied in Rax /Ln ≤ 1.27 (grey-hatched region). (b)Wavenumber spectra of the T (solid) and He (dashed)particle fluxes.

Note also that we see Γe ≃ 0 around Rax /Ln = 1, which isnecessary for the steady electron density profile.
To further explore the other possible profile regimes tosatisfy the steady burning condition, Rax /LTe and Rax /LTiscans are performed as shown in Figs. 7 (a) and 7 (b), respectively, where Rax /Ln = 1 is fixed, and the encircled
symbols in each figure correspond to the previous one
shown in the hatched region of Fig. 6 (a). It is found that thelarger Rax /LTe tends to produce the inward particle fluxes
for D, T, and electrons, while the opposite dependence
appears for Rax /LTi . Thus, another steady burning profile
regime with steeper temperature gradients, but still keepingΓe ≃ 0, is anticipated for larger Rax /LTe and Rax /LTi . Actually, it has been confirmed that the case with {Rax /Ln = 1,
Rax /LTe = 10, Rax /LTi = 8} also satisfies the steady burning condition with ηiTi (ni /nHe )ΓHe /Qi = 0.496 > 1/α∗ ,Ti ΓD = −0.291 < 0, and Ti ΓT = −2.65 < 0, as well as{Rax /Ln = 1, Rax /LTe = 8, Rax /LTi = 6} shown in
Fig. 6 (a).
Finally, the impacts of the zonal-flow generation andnonthermal He-ash on the optimal profile regime are dis-Fig. 7 Dependence of (a) electron and (b) ion temperature gradient on turbulent particle and ion energy fluxes, whereηiTi (ni /nHe )ΓHe is scaled by the factor of 1/8 for visibility. The results encircled in black correspond to the
profile regime that satisfies the steady burning conditionin Fig. 6 (a).

cussed. As shown in Fig. 8 (a), for the case with numericallysuppressed zonal flows, the inward D-T particle transport nolonger appears while the other two conditions of Eqs. (11)and (12) still hold. It is thus considered that the zonal flows
play an important role in determining the direction of theD-T particle transport.
Moreover, the results with the nonthermal He-ash are
shown in Fig. 8 (b), where THe /Ti = 2.5, and Ti = TD = TT .
Since the He-ash with various temperatures is expected dueto the continuous thermalization process for the energetic
α-particles, the impact of He-ash with THe /Ti , 1 [8] on the
turbulent fluxes is examined here. One clearly finds thatthe significant decrease of the He-ash particle flux leads
to the violation of Eq. (11) for Rax /Ln ⩽ 2. Note alsothat the inward He-ash transport appears for Rax /Ln ⩽ 1.5.
This suggests the importance of treating the thermal andnonthermal He-ash simultaneously in evaluations of thesteady burning condition in realistic situations.

1403083-6

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Volume 17, 1403083 (2022)
clearly highlight the importance of the multi-species approach, which the eﬀective single-ion calculations cannot
replace.
Then the new findings on the D-T ratio impact andon the profile dependence for the steady burning condition
including the zonal-flow and nonthermal He-ash eﬀects
contribute to deeper understanding of the multi-species
transport processes in burning plasmas. This work proposed a novel gyrokinetic-simulation-based analysis of thesteady burning condition, but more extended investigations
including the radial dependence and the high-energy α particles, which remain as future work, are useful for the integrated predictive simulations of kinetic profiles in ITER
and DEMO.

Acknowledgments
The Authors thank Dr. Masanori Nunami for fruitful discussions. This work is supported by the MEXT
Japan, Grant Nos. 17K14899, 17K07001, 22K03574,
in part by the NIFS collaborative Research Programs(NIFS22KIST017, NIFS22KIST018), and in part by JST,
PRESTO Grant Number JPMJPR21O7, and in part by
PLADyS, JSPS Core-to-Core Program, and in part by Program for Promoting Researches on the Supercomputer Fugaku (Exploration of burning plasma confinement physics,
JPMXP1020200103).
Numerical simulations were performed by Plasma
Simulator at NIFS, and JFRS-1 at IFERC-CSC.
Fig. 8 Density gradient dependence of turbulent particle and ion
energy fluxes in the cases (a) without the zonal flow and(b) with the nonthermal He-ash with THe /Ti = 2.5, whereηiTi (ni /nHe )ΓHe is scaled by the factor of 1/8 for visibility. For comparison, the results shown in Fig. 6 (a) aredisplayed by the dashed curves.

5. Summary
In this study, the ITG-TEM driven turbulent transportin ITER-like D-T-He plasma is investigated by meansof multi-species gyrokinetic Vlasov simulations. It isfound that the accumulation of the thermalized He-ash hassignificant impacts on the turbulent particle fluxes, whichlead to imbalanced D-T transport. Nonlinear scans with thevarious density and temperature gradient parameters reveal
the oﬀ-diagonal contributions to the deuterium and tritium
particle transport, and identify several profile regimes thatsatisfy the steady burning condition, where the relatively
flat density profile of Rax /Ln ∼ 1 is expected to be suitable
for the fuel inward pinch. The present numerical studies[1] C. Estrada-Mila et al., Phys. Plasmas 12, 022305 (2005).
[2] C. Estrada-Mila et al., Phys. Plasmas 13, 112303 (2006).
[3] M. Nakata et al., Phys. Rev. Lett. 118, 165002 (2017).
[4] E.A. Belli et al., Phys. Rev. Lett. 125, 015001 (2020).
[5] C. Bourdelle et al., Nucl. Fusion 58, 076028 (2018).
[6] C. Angioni et al., Nucl. Fusion 49, 055013 (2009).
[7] C. Angioni, Phys. Plasmas 22, 102501 (2015).
[8] M. Nakata et al., Plasma Fusion Res. 17, 1203078 (2022).
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