Plasma and Fusion Research: Rapid Communications

Volume 17, 1203078 (2022)

Microinstability and Zonal-Flow Response in Mixture Plasmas
with Medium-Z and Nonthermal Impurity
Motoki NAKATA1,2,3)
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(Received 19 April 2022 / Accepted 9 May 2022)
Ion- and electron-scale microinstabilities and the linear zonal-flow response in mixture plasmas with themedium-Z impurity and He-ash are investigated by means of a multi-species gyrokinetic model. In addition tothe charge and dilution eﬀects, stabilization/destabilization by nonthermal He-ash ions is clarified.
© 2022 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords: burning plasma, He-ash, impurity, microinstability, zonal flow, gyrokinetic simulation
DOI: 10.1585/pfr.17.1203078
In contrast to experimental plasmas to usually maximize the hydrogen/deuterium purity, burning plasmas areintrinsically mixture states with multiple ion species. In
several experiments, the suppression of confinement degradation has been observed in the impurity-seeded plasma[1, 2]. Moreover, the medium-Z impurity seeding in thecore and edge regions is considered to be necessary forachieving a suﬃcient radiation loss in DEMO reactors [3].
In such mixture plasmas, ion- and electron-scale microinstabilities, the associated turbulent transport, and zonalflow generation are influenced by right and/or heavy impurities, and by thermal and/or nonthermal He-ash ions, aswell as the fuel isotope ions [4]. The ion-scale instabilities
have mainly been addressed in earlier works [5–8].
In this study, the impacts of medium-Z impurity andHe-ash ions on both the ion-temperature-gradient (ITG)
and electron-temperature-gradient (ETG) instabilities areinvestigated by means of a multi-species gyrokinetic modeland the numerical simulations. Particular focus is put on
the dilution and the unequal temperature for the ion species.
The linear zonal-flow response is also examined.
Here, dispersion equations for the ITG and ETG modes
in mixture plasmas are derived. The linearized electrostatic
gyrokinetic equation for the species “s” and the Poisson
equation are given byes δϕk⊥ ( 2 2 )J0 k ⊥ ρts FMs, (1)Ts∫()∑−2(k⊥2 + λD)δϕk⊥ = 4π
es d3J0 k⊥2 ρ2ts δgsk⊥ ,Ls δgsk⊥ = (ω − ω∗T s )s(2)where the collisionless limit in the Fourier-Laplace form isconsidered, and L s := ω − k ∥ 3 ∥ − ωDs with the complex
frequency ω. The non-adiabatic distribution function andthe potential fluctuation are denoted by δgsk⊥ and δϕk⊥ ,respectively. The squared inverse of the Debye length is−2 := ∑ λ −2 with λ −2 = 4πn e2 /T . The thermalgiven by λDs s ss Ds
Dsgyroradius ρts is defined by ρts = ms 3ts /es Bax with the thermal speed of 3ts = (Ts /ms )1/2 . More details are presented
in e.g., Refs. [9] and [10].
In this paper we treat 3 or 4 ion species: s = {e, H(=i), He, Ar}. Then, the dispersion equation for the ITG
mode is derived by combining Eqs. (1) and (2) in the longwavelength approximation (k⊥−1 > ρHe ⩾ ρH > ρAr > ρe ),−2k⊥2 + λD∫()∑−2=λDs d3Ls−1 (ω − ω∗T s )J02 k⊥2 ρ2ts FMs,

(3)

s,e

where the electrons are assumed to be adiabatic, i.e.,δgek⊥ = 0. Further reductions in the fluid limit k ∥ 3 ∥ /ω ≪1, ωDs /ω ≪ 1, and ω∗T s /ω ≪ 1 yield( −1 −1 )∑L n +L−1−ω∗T i ωDi s,e fCs Zs (Ts /Ti )Γ0s L −1s +LT−1sniTi,
ω2 = 2 2∑−1k ⊥ λDie +(Ti /Te )+ s,e fCs Zs (Ts /Ti ) (1−Γ0s )(4)
2 := T /4πn e2 and Γ := I (k 2 ρ2 ) exp(−k 2 ρ2 )where λDieie0s0 ⊥ ts⊥ tswith the modified Bessel function I0 describe the finite Debye length and the finite gyroradius eﬀects, respectively.
The charge number and the charge density fraction are rep∑resented by Zs and fCs := ns Zs /ne , where s fCs = 1. The velocity dependence in ω∗T s and ωDs is ignored for simplicity,
by evaluating 3 2 ∼ 4Ts /ms . The impurity and nonthermal
ion eﬀects also appear in k⊥2 ρ2ts = k⊥2 ρ2i As (Ts /Ti )Zs−2
As for the ETG mode, one can derive the dispersion equation in the long-wavelength approximation(ρHe ⩾ρH > ρAr > k⊥−1 > ρe ),author’s e-mail: nakata.motoki@nifs.ac.jp

1203078-1© 2022 The Japan Society of Plasma
Science and Nuclear Fusion Research

Plasma and Fusion Research: Rapid Communications

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Fig. 1 Growth rate of (a) ITG and (b) ETG modes.

Fig. 2 THe /TH dependence of (a) ITG and (b) ETG growth rate.
The open symbols are the cases without He. The analyticevaluation is applied for the case of H+He(10%).

ω2 =−ω∗T e ωDe Γ0e,
∑22k⊥ λDe + 1 − Γ0e + (Te /Ti ) s,e fCs Zs (Ts /Ti )−1(5)where all ion species is adiabatic due to J0 (k⊥2 ρ2ts,e ) → 0.
For both Eqs. (4) and (5), the charge and dilution eﬀects areincorporated in the dispersion equation. Note also that theunequal temperature for ions is explicitly treated in orderto examine the impact of the nonthermal He-ash ions.
In the dispersion equations, one can see the qualitative
impacts of the impurity (Ar) and nonthermal He-ash ions.
The dilution eﬀect to the main hydrogen ions in the presenceof impurity leads to the stabilization of the ITG mode, as
seen in fCs Zs−1 of Eq. (4). One also finds that the ETG
mode growth rate is reduced by the eﬀective charge, which∑is represented by s,e fCs Zs = Zeﬀ in Eq. (5).
On the other hand, nonthermal He-ash ions cause theopposite impact. Although He-ash ions have the low-Z
charge and the similar gyroradius to the main hydrogenions in the thermalized state, the ITG and ETG modes areaﬀected by unthermalized hot He-ash ions with THe /Ti > 1.
The destabilization of the ETG mode is easily found from(Ts /Ti )−1 in Eq. (5), whereas the complicated dependence
appears in the ITG case of Eq. (4) with Γ0s .
In order to examine the above theoretical arguments,
the gyrokinetic Vlasov simulations with GKV [11] havebeen carried out for the mixture plasma of the Hydrogen,Helium, Argon ions, and the kinetic electrons. Here, boththe ITG and ETG modes are solved in a fluxtube of theaxisymmetric configuration, and R/Lns = 2, R/LTs = 8for all species. Inspired from the ITER and DEMO [3],nHe /ne ∼ 10% and nAr /ne ∼ 0.6% are considered.
Figures 1 (a) and 1 (b) show the poloidal wavenumber
spectra of the ITG and ETG mode growth rate, respectively.
As is theoretically expected, the dilution eﬀects by He andFig. 3 Linear zonal-flow response.

Ar ions lead to the stabilization for both. Particularly, a significant stabilization of the ETG mode appears for the casewith Ar impurity. One also finds that the nonthermal Heash ions with THe /TH = 10 reduces the ITG mode growthrate, while the ETG mode becomes more unstable. Thenthe ratio of the ETG growth rate to the ITG growth rate,i.e., rγ := γk⊥ (k y ρte = 0.35)/γk⊥ (k y ρtH = 0.45), is enlarged
by hot He-ash ions, where rγ in the case of H+He(10%)
with THe /TH = 10 is 1.65 times larger than that in the casewith THe /TH = 1.
The opposite impacts of THe /TH in the ITG and ETG
modes are demonstrated in Figs. 2 (a) and 2 (b). One finds
the nonlinear and/or nonmonotonic dependence for bothcases in 1 ⩽ THe /TH ⩽ 15. Note that the analytic evaluation by Eq. (5) for the case of H+He(10%) qualitatively
reproduces the numerical result.
Lastly the linear zonal-flow responses are comparedin Fig. 3. It is found that both the dilution and nonthermal
eﬀects by He-ash lead to less GAM damping with enhanced
residual zonal-flow level. The enhanced residuals can be1203078-2

Plasma and Fusion Research: Rapid Communications

Volume 17, 1203078 (2022)

attributed from the decrease of shielding eﬀect to the zonal
potential, depending on the radial drift excursion of trappedions with diﬀerent gyroradius and the density fraction.
Also, one can see that the residual level does not change
so largely, but gradually decreases in time for the case of
H+He(10%)+Ar(0.6%) with THe /TH = 10, compared to thecase without Ar. Such a weak impact of the Ar ions is
associated with relatively smaller radial drift of the minorityAr ions[∝ ρAr = ρH /(ZAr /2)1/2 = ρH /3] in comparison to
those of the bulk H ions. Then the shielding to the zonal
potential by the Ar drift motion becomes less eﬀective. On
the other hand, the increased collisionality by Ar enhances
the collisional zonal-flow damping. Nonlinear zonal-flow
dynamics and its impact on the turbulent transport will be
addressed in future work.
This work is supported by JST, PRESTO Grant
Number JPMJPR21O7, in part by the NIFS collaborative

Research Programs (NIFS22KIST017, NIFS22KIST018),
and in part by PLADyS, JSPS Core-to-Core Program. Numerical simulations were performed by JFRS-1 at IFERCCSC, and Plasma Simulator at NIFS.
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