Plasma and Fusion Research: Regular Articles

Volume 14, 3401112 (2019)

Simulation Study of Energetic Ion Driven Instabilities
near the Lower Hybrid Resonance Frequency
in a Plasma with Increasing Density∗)
Mieko TOIDA1) , Hiroe IGAMI1) , Kenji SAITO1) , Tsuyoshi AKIYAMA1,2) ,Shuji KAMIO1) and Ryosuke SEKI1,2)
1)2)

National Institute for Fusion Science, Toki, Gifu 509-5292, JapanSOKENDAI (The Graduate University for Advanced Studies), Department of Fusion Science, Toki,
Gifu 509-5292, Japan(Received 9 January 2019 / Accepted 26 April 2019)

Using a one-dimensional electromagnetic particle code which simulates self-consistently the full ion andelectron dynamics, we study instabilities driven by energetic ions injected continuously in a plasma where thedensity and the lower-hybrid resonance frequency ωLH increase with time. The simulation shows that the ion
cyclotron harmonic wave with ω  lΩi , where l is an integer and Ωi is the ion cyclotron frequency, is excitedwhen ωLH becomes close to lΩi . When ωLH is greater than lΩi , this wave couples with the ion Bernstein mode thathas the dispersion curve connecting to ωLH . It is also found that as a result of the instabilities and the wave-wave
coupling, the stair-like frequency chirping with the riser Ωi appears in the magnetic fluctuations in the frequency
range of ωLH . The frequency chirping has characteristics similar to the frequency chirping observed in the RFradiations at the plasma start-up phase of the LHD experiments.
c 2019 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: instabilities driven by energetic ions, PIC simulation, lower hybrid resonance frequency, ion cyclotron wave, ion Bernstein wave, Large Helical Device
DOI: 10.1585/pfr.14.3401112

1. Introduction
Waves with frequencies near the lower hybrid resonance frequency ωLH propagating perpendicular to themagnetic field can be excited by energetic ion beams
across the magnetic field when the beam speed is smaller
than the Alfvén speed [1–3]. Here, ωLH is defined as
ω2LH = Ωi Ωe (1 + Ω2i /ω2pi )/(1 + Ω2e /ω2pe )= (Ω2i + ω2pi )/(1 + ω2pe /Ω2e ),(1)where Ω j and ωp j are the cyclotron frequency and theplasma frequency, respectively, and j refers to ions ( j = i)and electrons ( j = e). The value of ωLH /Ωi increases withthe plasma density if the magnetic field strength is fixed.
In the Large Helical Device (LHD), radio frequency (RF)waves from the plasma are detected [4, 5], and RF waves
in the frequency range of ωLH were observed during theperiod of perpendicular neutral beam injection (NBI) [6].
Recently, stair-like frequency chirping is observed in the
RF radiation in the frequency range of ωLH when the
LHD plasma is initiated by almost simultaneous injectionsof the electron cyclotron wave and the tangential neutralbeam [7]. The energetic ions produced by tangential NBI
author’s e-mail: toida.mieko@nifs.ac.jp∗) This article is based on the presentation at the 27th International Toki
Conference (ITC27) & the 13th Asia Pacific Plasma Theory Conference(APPTC2018).

can have the finite speed across the magnetic field although
the angle between the magnetic field and the energetic ion
beam is small. The experimental results also show that theriser of the stair is Ωi and the RF wave with ω  lΩi , wherel is an integer, begins to grow when ωLH is close to lΩi .
We are studying the excitation mechanism of waves in
the frequency range of ωLH using a one-dimensional (onespatial coordinate and three velocity components), electromagnetic, particle-in-cell (PIC) code which simulates selfconsistently the full ion and electron dynamics. In ref. [8],we investigated the linear and nonlinear evolution of instabilities due to energetic ions produced by the perpendicular
NBI, assuming that the energetic ions have a ring-like distribution in the velocity space perpendicular to the magnetic field. It was shown that in addition to electromagnetic emissions near the ion cyclotron frequency and its
harmonics, the high-frequency magnetosonic waves withfrequencies slightly smaller than ωLH grow to large amplitudes. We also performed the simulations for various
plasma densities and demonstrated that the frequency ofthe large-amplitude magnetosonic wave increases with theelectron density when the density is relatively small. The
density dependence shown by the simulations qualitatively
agrees with the density dependence of RF waves of thelower hybrid wave frequency range observed in the LHD
experiments [6].

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In this paper, we consider a plasma in which the density and ωLH are gradually increasing with time, such asat the plasma start-up phase. The density and the value ofωLH /Ωi are much smaller than those considered in Ref. [8].
In order to study the mechanism of the stair-like frequency
chirping observed at the plasma start-up phase of the LHD
experiments [7], we perform a simulation of instabilities
driven by energetic ions injected continuously in a plasma
with the increasing density and the increasing ωLH . We
investigate how the time variation of ωLH influences thewave evolution.

2. Linear Theory
Before explaining simulations, we look at the linear
dispersion relations of energetic ion driven instabilities in
the frequency range of ωLH .
We assume that the velocity distribution function ofenergetic ions is given byf (v , v⊥ ) =1
δ(v − u )δ(v⊥ − u⊥ ),
2πu⊥

(2)

where the subscripts  and ⊥ indicate parallel and perpendicular to the external magnetic field, respectively, and uis the initial speed of the energetic ions. We assume thatu⊥ /u  1 and u/vA  1, where vA is the Alfvén speed,
because we consider the energetic ions produced by thetangential NBI in a low-density plasma where vA to bemuch greater than u.
We consider waves propagating perpendicular to theexternal magnetic field. These waves may play essential
roles in the stair-like frequency chirping in the RF radiations observed at the plasma start-up phase in the LHD
experiments. The radiations are detected by the antenna located in the direction nearly perpendicular to the magnetic
field from the point where the energetic ions are generated
by the tangential NBI [7]. Although the excited waves
will have both electromagnetic and electrostatic components, we use in this section the electrostatic approximation for simplicity, which may be valid because thesewaves will have short wavelengths such that kvA /Ωi  1since u⊥ /vA  1.
The dispersion relations of the perpendicular electrostatic waves in a plasma consisting of electrons, bulk ions,and the energetic ions can be written as [9]=(1 + ω2pe /Ω2e )(ω2 − Ω2i )(ω2 − ω2LHB ) + h = 0,(3)

where  is the plasma dielectric function, ω is the complex
frequency, ωLHB is the frequency of the Bernstein modedue to the bulk ions near ωLH , and h is the term due tothe energetic ions. Assuming that kvTi /Ωi  1, wherevTi is the bulk-ion thermal speed, and ωpi  Ωi , we canapproximate ωLHB as
ω2LHB = ω2LH −ω2pi

k2 v2Ti(1 + ω2pe /Ω2e )Ω2i,where electron kinetic eﬀects are neglected. In the limit of
k → 0, ωLHB goes to ωLH defined by eq. (1).
The energetic ion term h can be expressed as follows, depending on the magnitude of the wave growth rate
γ. When γ is much greater than Ωi , we can approximate
the energetic ions that can interact with the perpendicular
waves as the energetic ion beam across the magnetic field.
Because this situation is similar to the modified two-stream
instabilities [1, 2], the energetic ion term h can be writtenasω2phh = −,(5)(ω − k⊥ u⊥ )2where ωph is the plasma frequency of the energetic ions.
The equation (3) with this h indicates that the interaction
between the bulk-ion Bernstein mode connecting to ωLH
and the energetic-ion beam mode ω = k⊥ u⊥ can cause
strong instabilities [10].
When γ < Ωi , h is written as [11, 12](4)h = −

 ω2ph lg(λ)
lΩi (ω − lΩi ),g(λ) =

1 dJl2 (λ)
,
λ dλ

(6)

where l is an integer, λ = k⊥ u⊥ /Ωi , and Jl is the Bessel
function. We consider waves with frequencies near lΩi andwrite ω as ω = lΩi (1 + Δ). Then, the equation (3) leads to
2l2 Ω2i Δ2 + (l2 Ω2i − ω2LHB )Δ −

ω2ph (l2 − 1)g(1 + ω2pe /Ω2e )

= 0.
(7)

From this, we can obtain the unstable condition for thewave with ω  lΩi as(l2 Ω2i − ω2LHB )2 + 8

ω2ph Ω2i l2 (l2 − 1)g(1 + ω2pe /Ω2e )

< 0.

(8)

This can be satisfied when lΩi  ωLH and g < 0. Forl ≥ 2, g is negative in the range of λ1 < λ < λ2 , where λ1
and λ2 are the points at which Jl2 becomes maximum andminimum, respectively. Because λ1 is greater than 1, we
can expect that the wave with ω  lΩi and k⊥ u⊥ /Ωi > 1
may be destabilized when lΩi is close to ωLH . We callthis wave the lth harmonic ion cyclotron wave (ICW). The
ICWs are supported by the energetic ions. They are not theBernstein modes due to the bulk ions and can exist in thelimit of a cold plasma approximation, vTi → 0.

3. Simulation Model and Parameters
We study energetic ion driven instabilities in the frequency range of ωLH using a one-dimensional (one spatial
coordinate and three velocity components), electromagnetic, particle-in-cell (PIC) code which self-consistently
simulates full dynamics of electrons and ions. Although
the electrostatic approximation was used in Sec. 2, thesimulation code treats both the electrostatic and the electromagnetic fields by calculating the full Maxwell’s equation. We pay attention to magnetic fluctuations shown inthe simulation, as in the previous paper [8].

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The plasma consists of three components: minority energetic ions, electrons, and bulk ions. The ion-toelectron mass ratio is mi /me = 1000. The total charge ofelectrons is equal to that of ions. Initially, the electrons andbulk ions have Maxwell velocity distributions, whereas theenergetic ions have a velocity distribution function given
by eq. (2).
We set the speed of the energetic ions as u/vA0 = 0.1,
where vA0 is the initial Alfvén speed. This is equal to thevalue of u/vA for the H ions with the energy K = 178 keVin the H plasma with ne = 0.3 × 1019 m−3 and B = 2.6 T.
These values are close to the typical values in the plasmacore region at the start-up phase of the LHD plasma [7],where the waves can be excited by energetic ions generated by the tangential NBI. The ratios of vA0 to the electron
thermal speed vTe is vA0 /vTe = 2.6, which is the same orderas that for the electron temperature T e = 5 keV. Assumingthat the ion temperature T i is much smaller than T e , we set
vA0 /vTi = 300.
We choose the angle between the energetic ion beamand the magnetic field as α = arctan(u⊥ /u ) = 10◦ , according to Ref. [7]. Then, because u⊥ /vA0  0.1, we can
expect from the linear theory that the energetic ions would
excite short-wavelength waves such that kvA /Ωi  10.
These wavelengths are much smaller than 1cm, and thevariation of the LHD magnetic field and the density forthese lengths in the plasma core region would be small.
Therefore, we assume that the external magnetic field andthe plasma density are uniform.
The simulation system is periodic in the x direction
with the length L x = 2048Δg , where Δg is the grid spacing,
and the electron skin depth is c/ωpe = 10Δg . The waves
propagate in the x direction in the external magnetic fieldB0 = (B0 cos θ, 0, B0 sin θ), where θ is the propagation angle of the waves. Setting θ = 89.7◦ , we simulate the waves
propagating nearly perpendicularly to B0 .
The total number of the simulation particles is N =4 × 106 at t = 0. In order to simulate a situation where
the energetic ions are injected continuously in a plasma
with the increasing density and ωLH , we increase the numbers of electrons, bulk ions, and energetic ions as the timeproceeds. The increase rates of the three species of particles are equal. The positions and gyration phases of newly
added particles are given randomly. The newly added electrons and bulk ions obey the Maxwell velocity distributions, whereas the newly added energetic ions obey eq. (2).
Figure 1 shows time variations of the simulation parameters. The electron density ne normalized by the initial
density ne0 , the energetic-ion density nh normalized by thebulk ion density ni , where ne = ni + nh is satisfied, and thevalues of ωLH /Ωi and Ωe /ωpe are plotted. The increase of
ne /ne0 causes the decrease of Ωe /ωpe and the increase ofωLH /Ωi since Ωe and Ωi are constant. We study how theincrease of ωLH /Ωi influences wave evolution. The three
periods shown by the shaded regions in Fig. 1 will be focused on below.

Fig. 1 Time variations of simulation parameters.

4. Simulation Results
4.1 Wave evolution
We firstly present a result for a plasma without energetic ions. The left panel (a) of Fig. 2 shows the power
spectrum P(k, ω) of magnetic fluctuations obtained for theperiod from Ωi t = 0 to 100. During this period, the density and ωLH increase from ne /ne0 = 1 to 1.4 and from
ωLH /Ωi = 3.6 to 3.9, respectively, as shown by the left
shaded region in Fig. 1. The large-amplitude fluctuations
near the line ω = kvA0 in the long-wavelength region are
due to the magnetosonic mode. The fluctuations in the
short-wavelength region such that kvA0 /Ωi > 10 are due tothe bulk-ion Bernstein mode that has the dispersion curveconnecting to ωLH , which was expressed as ωLHB in Sec. 2.
The right panel (b) of Fig. 2 displays the power spectrum of the magnetic fluctuations in a plasma with the energetic ions for the same period as the left panel (a). Comparison between the two panels shows that the harmonics
of ICW with ω/Ωi = 2, 3, and 4 are excited by the energetic ions. Also, the large-amplitude fluctuations are excited near the point (kvA0 /Ωi , ω/Ωi ) = (280, 2.8). This
point corresponds to the intersection between the curve forthe bulk-ion Bernstein mode connecting to ωLH and theline ω = k⊥ u⊥ = k x u x for the energetic-ion beam mode
propagating in the positive x direction, where u x can be estimated as u x  0.01vA0 . Here, we neglected k , because
we performed the simulation for the exactly perpendicular case θ = 90◦ (k = 0), which is not shown here, andconfirmed that the point near which large-amplitude fluctuations are excited when θ = 90◦ is almost the same as thepoint shown in Fig. 2 (b). As predicted by eqs. (3) and (5),the strong instabilities occurred because of the interaction
between the bulk-ion Bernstein mode connecting to ωLH
and the energetic-ion beam mode.
As the time advances, ωLH rises and the power spec-

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Fig. 2 Power spectra of magnetic fluctuations for the period
from Ωi t = 0 to 100 in a plasma without energetic ions(a) and in a plasma with energetic ions (b).

Fig. 3 Power spectra of magnetic fluctuations in a plasma withenergetic ions for the periods 200 < Ωi t < 300 (a) and800 < Ωi t < 900 (b).

trum varies. Figure 3 displays the power spectra of magnetic fluctuations for the periods 200 < Ωi t < 300 (a)and 800 < Ωi t < 900 (b), which correspond the middle and right shaded regions in Fig. 1, respectively. In theleft panel (a), for which ne /ne0 and ωLH /Ωi vary from 1.7
to 2.0 and from 4.2 to 4.5, respectively, the 5th harmonic
ICW is newly excited slightly above ω = ωLH . In the rightpanel (b), for which ne /ne0 and ωLH /Ωi are in the rangeof 3.3 < ne /ne0 < 3.6 and 5.8 < ωLH /Ωi < 6.0, the 6th
harmonic ICW appears. The strong instabilities due to theinteraction between the bulk-ion Bernstein mode and theenergetic ion beam mode are not shown in the two panelsof Fig. 3, unlike in the right panel of Fig. 2. This is because
the velocity distribution function of the energetic ions isdrastically changed by the time Ωi t < 100, which will beshown below.
We now pay attention to how the dispersion curve nearωLH varies with time. In the left panel (a) of Fig. 3 whereωLH is slightly smaller than 5Ωi , the frequency of the 5th
harmonic ICW is almost constant, ω = 5Ωi , along the horizontal axis k in the wavenumber region kvA0 /Ωi > 100.

Fig. 4 Time variations of amplitudes of the waves with ω  5Ωi
and with ω  6Ωi . These were obtained by integrating
P(k, ω) over the wavenumber region kvA0 /Ωi > 100.

However, in the right panel (b) of Fig. 3 where ωLH is in
the range of 5.8 < ωLH /Ωi < 6.0, we cannot see thewave with the constant frequency ω = 5Ωi . This is because the 5th harmonic ICW excited by the energetic ionscouples with the bulk-ion Bernstein mode that has the dispersion curve connecting to ωLH . Its frequency gradually
decreases from ωLH to 5Ωi . The frequency of the 6th harmonic ICW slightly above ωLH is almost constant in thispanel. In the power spectrum P(k, ω) for the next time period, which is not shown here, this wave couples with thebulk-ion Bernstein mode connecting to ωLH . The 4th harmonic ICW shown in Fig. 2 (b) couples with the bulk-ion
Bernstein mode connecting to ωLH in Fig. 3 (a).
In order to show the time variations of amplitudes ofwaves excited by the energetic ions in more detail, we average the power spectra P(k, ω) over the wavenumber region
kvA0 /Ωi > 100. We focus on the waves excited by theenergetic ions near ω = ωLH and these waves are in thiswavenumber region as shown in Fig. 3. Figure 4 shows theamplitudes of waves with ω  5Ωi and 6Ωi , where the former is in the range of 4.9 < ω/Ωi < 5.1, and the latter isin the range of 5.9 < ω/Ωi < 6.1. Here, t5 and t6 are thetimes when ωLH becomes equal to 5Ωi and 6Ωi , respectively. This figure clearly shows that the amplitude of the
5th harmonic ICW begins to grow near t = t5 . The amplitude is saturated slightly after t = t5 and then gradually decreases, which is caused by the variation of the dispersion
curve shown in Fig. 3. The time variation of the wave with
ω  6Ωi is similar to that with ω  5Ωi , except that thetime t6 is important for the evolution of the 6th harmonic
ICW.
We then plot the amplitudes of all the waves in thefrequency range 0.5 < ω/Ωi < 8 in Fig. 5, where thecolor indicates the amplitudes of the magnetic fluctuations
and the yellow line represents the frequency ωLH . We findthat the stair-like frequency chirping appears in the region
ω/Ωi > 4. The riser of the stairs is Ωi and the wave withω  lΩi begin to grow when ωLH becomes close to lΩi ,where l = 5, 6, and 7. These characteristics are similar
to those of the frequency chirping observed in the RF ra-

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Fig. 5 Time variations of magnetic fluctuations in the frequency
range of 0.5 < ω/Ωi < 8. The stair-like frequency chirping appears near the line ω = ωLH .

diations at the plasma start-up phase of the LHD experiments [7].

4.2

Velocity distribution function and energy

Figure 6 displays the time evolution of the velocity
distribution functions of the energetic ions. The upper panels (a) and (b) show the perpendicular velocity distribution, and the lower panels (c) and (d) show the parallel
velocity distribution. In the panel (a), the perpendicularvelocity distribution function f (v⊥ ) is drastically changedby the time Ωi t = 84. This is caused by the strong instabilities due to the interaction between the bulk-ion Bernsteinmode connecting to ωLH and the energetic ion beam modeω = ku⊥ . Because of the change of f (v⊥ ), the strong instabilities do not occur after Ωi t = 100, as shown in Fig. 3.
In the panel (b), the steep positive slope, ∂ f (v⊥ )/∂v⊥ > 0,
is formed near v⊥ /u⊥ = 1 because the energetic ions withv⊥ /u⊥ = 1 are added continuously in the simulation system. This can excite ICWs with ω = lΩi near ωLH . In
the lower panels (c) and (d), the parallel velocity distribution function f (v ) maintains its shape, although the peakvalue increases with time. This indicates that eﬀects ofthe parallel velocity distribution on the wave evolution are
negligibly small, compared to those of the perpendicularvelocity distribution.
Figure 7 (a) shows the time variation of the kinetic energy of the energetic ions. Here ΔKh is defined as
ΔKh = Kh (t) − Kinj (t)= Kh (t) − N(t)mi (u2 + u2⊥ )/2,

Fig. 6 Time evolution of velocity distribution function of energetic ions. The upper panels (a) and (b) show the pependicular velocity distribution, and the lower panels (c) and(d) show the parallel velocity distribution.

N(t) is the total number of the energetic ions at t. The
values of ΔKh in Fig. 7 (a) are normalized by Kinj (0). The
negative ΔKh indicates that a part of the injected energy
is transferred to the waves. It is clearly shown that ΔKh
decreases rapidly during the period 0 < Ωi t < 100 anddecreases gradually after Ωi t  100. For comparison, weplot the time variations of the energies of magnetic fluctuations in the frequency ranges of 0 < ω/Ωi < 4.5 and4.5 < ω/Ωi < 7.5 in Figs. 7 (b) and (c), respectively. The
waves in the range of 0 < ω/Ωi < 4.5 were excited before
Ωi t  100, as shown in Fig. 2 (b). From Figs. 7 (b) and (c),we confirm that the waves in the range of 0 < ω/Ωi < 4.5
grow rapidly before Ωi t  100, whereas the waves in therange of 4.5 < ω/Ωi < 7.5 grow gradually after Ωi t  200.
In this paper, we assumed that the energetic ions continue to exist in the simulation system after they are injected there. That is, we did not consider the change off due to the loss of the energetic ions from the system although this may significantly influence the wave evolution.
The eﬀect of the energetic ion loss is an important future
problem.

4.3 Diﬀerent bulk-ion temperature(9)

where Kh (t) is the total energy of the energetic ions at thetime t, Kinj (t) is the total injected energy by the time t, andIn the previous subsections, we presented the results
for the case of vA0 /vTi = 300, where vA0 is the initial
Alfvén speed and vT i is the bulk-ion thermal speed, assuming that the bulk-ion temperature is much lower than the3401112-5

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Fig. 8 Power spectra of magnetic fluctuations for the period
200 < Ωi t < 300 for the cases of vA0 /vTi = 2.1 × 102(a) and 4.2 × 102 (b).

Fig. 7 Time variations of energies of energetic ions (a), magnetic fluctuations in the frequency ranges 0 < ω/Ωi < 4.5(b) and 4.5 < ω/Ωi < 7.5 (c). The fluctuation energies
are averaged over the wavenumber region kvA0 > 100, as
in Figs. 4 and 5, and are normalized by B20 L/(8π) with thesystem length L.

electron temperature. We also performed simulations fortwo cases of diﬀerent bulk-ion temperatures.
Figure 8 shows the power spectra of magnetic fluctuations for the cases of vA0 /vTi = 2.1 × 102 (a) and 4.2 × 102(b) obtained for the period from Ωi t = 200 to 300, whichis the same period as for Fig. 3 (a). Here, the values ofvA0 and the other parameters are the same as those forFig. 3 (a). We see almost the same spectra in Figs. 3 (a),7 (a) and 7 (b), although the values of vTi are diﬀerent. The
5th harmonic ICW is excited near ωLH , and the 4th harmonic ICW, which was excited before this period, couples
with the bulk-ion Bernstein mode connecting to ωLH .
Figure 9 shows time variations of amplitudes of the
waves with ω  5Ωi (a) and with ω  6Ωi (b) for thecases of (vTi /vA0 )/102 = 4.2, 3.0, and 2.1, where t5 andt6 are the same as those in Fig. 4. The waves with ω 
5Ωi and 6Ωi have the greatest amplitudes near t = t5 andt6 , respectively, for all the three cases, although there aresmall diﬀerences.
As a result of the wave evolution shown in Figs. 8 and
9, almost the same chirping in the frequency range of ωLH
appears in the cases of vA0 /vTi = 4.2 × 102 and 2.1 × 102 ,which is not shown here. We have not understood the reason for the small diﬀerences caused by the eﬀects of thebulk-ion temperature. We will study those eﬀects by performing more simulations in the future.

Fig. 9 Time variations of amplitudes of the waves with ω  5Ωi(a) and with ωi  6Ωi (b) for the cases of (vA0 /vTi )/102 =4.2, 3.0, and 2.1.

5. Summary
By means of a one-dimensional electromagnetic particle code, we have studied instabilities near the lowerhybrid resonance frequency ωLH caused by the energetic
ions continuously injected in a plasma with the increasing
density and ωLH . We have performed a simulation considering typical parameters for the plasma start-up phase of
the LHD experiments. We have analyzed how the increaseof ωLH influences wave evolution.
It has been shown that the lth harmonic ICW is excited by the energetic ions when ωLH becomes close to lΩi .
This wave couples with the bulk-ion Bernstein mode that

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Volume 14, 3401112 (2019)has the dispersion curve connecting to ωLH when ωLH becomes greater than lΩi . We have also found that as a resultof the instabilities driven by the energetic ions and the coupling between the ICWs and the bulk-ion Bernstein mode,the stair-like frequency chirping with the riser Ωi appears
in the frequency range of ωLH . The characteristics of thefrequency chirping are similar to those of the frequency
chirping observed in the RF radiations at the plasma startup phase of the LHD experiments.
In this paper, we did not discuss whether the waves
excited by the energetic ions can be detected by the antenna
located outside the plasma. This should be studied in the
future.

Acknowledgments
This work is performed with the support and under
the auspices of the NIFS Collaboration Research program(NIFS18KNSS103).

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