Characteristics of plasma parameters andturbulence in the isotope-mixing and thenon-mixing states in hydrogen–deuterium mixture
plasmas in the large helical device
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言語: English
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公開日: 2020-11-23
キーワード (Ja):
キーワード (En): isotope mixing, particle transport,
mixture plasma
作成者: IDA, Katsumi, YOSHINUMA, Mikiro, TANAKA,
Kenji, Nakata, Motoki, Kobayashi, Tatsuya, Fujiwara,
Yutaka, SAKAMOTO, Ryuichi, MASUZAKI, Suguru,
LHD, Experiment Group
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http://hdl.handle.net/10655/00012546
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International License.

Characteristics of plasma parameters and turbulence in the isotope-mixing and thenon-mixing states in hydrogen-deuterium mixture plasmas in the Large Helical Device
K.Ida,1, 2 M.Yoshinuma,1, 2 K.Tanaka,1 M.Nakata,1, 2 T.Kobayashi,1, 2 Y.Fujiwara,1
R.Sakamoto,1, 2 G.Motojima,1 S.Masuzaki,1, 2 and the LHD Experiment Group1
1

National Institute for Fusion Science, National Institutes of Natural Sciences, Toki, Gifu 509-5292, Japan
2
The Graduate University for Advanced Studies, SOKENDAI, Toki, Gifu 509-5292, Japan(Dated: October 16, 2020)
Characteristics of plasma parameters and turbulence in the isotope-mixing and the non-mixing
states in hydrogen-deuterium mixture plasmas in the Large Helical Device are discussed. The
isotope mixing state is characterized by the uniform isotope ratio profile regardless of the locationof the particle source of each species in the isotope mixture plasma. The isotope non-mixing state is
identified by the non-uniform isotope ratio profile measured with bulk charge exchange spectroscopy
when the beam fueling isotope species differs from the recycling isotope species. The effect ofcollisionality, Te /Ti ratio, sign of density gradient on transition between isotope mixing and nonmixing is discussed. The plasma parameters preferable for the non-mixing state are found to belower collisionality, higher Te /Ti , and negative or zero density gradient (peaked or flat density
profile). The time scale of transition from non-mixing to mixing is evaluated by the hydrogen anddeuterium pellet injection near the plasma edge and is found to be less than 5 ms, which is much
shorter than the particle confinement time. The strong correlation between isotope mixing andturbulence characteristics is observed. This strong correlation suggests the change in turbulence
is a strong candidate for the mechanism causing the transition between uniform and non-uniform
isotope density ratio profiles.
PACS numbers:

I.

INTRODUCTION

Isotope mixing is a new bifurcation phenomena [1]in the mixture plasma which can not be explained
solely by the conventional diffusive/non-diffusive transport in single-ion species plasma. In the conventional
diffusive/non-diffusive model, each isotope has its own
diffusion coefficient (D) and pinch velocity (V). These
coefficients between different isotope species (for example, hydrogen and deuterium) have been considered todepend on the local parameter such as electron density,
temperature, magnetic shear, and radial profile of eachisotope species is determined independently. However,recent simulation and experiment reveals that the radial
profile of each isotope species, for example, hydrogen (H)and deuterium (D), is determined by the complex transport processes with the strong coupling among the different particle species, rather than the individual diffusion
coefficients (DH and DD ) and pinch velocities (VH and
VD ) between two species.
In single-ion species plasma, the electron density ne isequal to ion density ni , and the electron and ion diffusion
coefficients are identical due to the quasi-neutral condition. However, in the isotope mixture plasma (hydrogenand deuterium mixture plasma) the ratio of ion diffusion
coefficient to electron diffusion coefficient Di /De (e.g.,
DH /De , DD /De ) has a strong impact on each isotope
density profile. Because the hydrogen and deuterium pellet injection experiment in LHD demonstrated that there

is no significant difference in particle transport betweenhydrogen and deuterium [2], the hydrogen diffusion coefficient is assumed to be equal to the deuterium diffusion
coefficient as DH = DD = Di . The transport simulation model (QuaLiKiz [3, 4]) using nonlinear gyrokinetic
simulation code (GKW [5]) predicts that the ratio Di /Destrongly depends on the mode of turbulence [6]. The electron diffusion coefficient is much larger than that of ions
(De /Di  1) when the trapped electron mode (TEM)[7, 8] is dominant. In this case, each isotope can have a
different profile because only the sum of the density of
isotope species is required to be balanced to the electron
density profile determined by a large electron diffusion
to satisfy the quasi-charge neutrality condition. The isotope density ratio profile varies significantly dependingon the location of the source of each isotope species forthe given electron density profile. For example, the hydrogen density profile can be significantly peaked by thehydrogen beam fueling in the hydrogen deuterium mixture plasma with the condition of deuterium dominant
recycling. In contrast, the ion diffusion coefficient becomes much larger than that of electron (Di /De  1)when the ion temperature gradient (ITG) mode [9, 10] is
dominant. In this case, the radial distribution of isotope
ratio (for example, the ratio of hydrogen density to deuterium density in the isotope mixture plasma) becomes
uniform regardless of the source location of each isotope
species because of the large ion diffusion. This is essential transport process in multiple-ion-species plasmas,
and leads to isotope mixing state or non-mixing state,
regardless of the almost identical shape of the electron
density profile.

2
Therefore, there are two states of isotope distribution
predicted in the isotope mixture plasma. One is isotope
mixing state which is characterized by the uniform isotope density ratio profile regardless of the source locationof each isotope species. The other is isotope non-mixing
state which is characterized by the non-uniform isotope
density ratio profile if the isotope species of core beamfueling differs from the isotope species of edge recycling.
The transition between the two states was reported in
the isotope mixture experiment in Large Helical Device(LHD) [11], where gyrokinetic simulation by GKV indicates the change of the dominant microinstability between TEM and ITG [12–16]. However, more experimental and theoretical study is necessary to understandthe physics mechanism for isotope mixing. The parameter dependence of the transition and the relation to theturbulence characteristics have not been investigated, although these studies are an important issue for testing
the hypothesis of isotope mixing/non-mixing profile formation by turbulence mode.
Although the turbulence characteristics in the ECH,
NBI, and ion-ITB plasma have been reported in LHD[17–20], the characteristics of turbulence in the isotope
non-mixing and mixing plasma has not been studied indetail due to the lack of measurements of radial profilesof isotope density. In this paper, parameter dependence
and the relation between turbulence characteristics andisotope mixing or non-mixing are discussed. The isotope
mixing and non-mixing states are evaluated by the radial profile of hydrogen to deuterium density ratio measured with bulk charge exchange spectroscopy [21–24],
while the turbulence characteristics are investigated by
the electron density fluctuation spectrum measured with
two-dimensional phase contrast imaging (2D-PCI).

II.

TURBULENCE CHARACTERISTICS IN
ISOTOPE MIXING AND NON-MIXINGPLASMAS

It should be noted that the isotope mixing/non-mixing
is determined by the ratio of anomalous ion diffusion
coefficient to anomalous electron diffusion coefficient(Di /De ) in turbulent transport. This is in contrast
to the ion/electron root in helical plasmas, where thesign of radial electric field (Er ) is determined by theratio of neoclassical ion diffusion coefficient to neoclassical electron diffusion coefficient (DiN C /DeN C ) for Er= 0. This is because electron and ion diffusion coefficients strongly depend on Er in neoclassical transport but they are independent of Er in turbulent transport. Therefore, Di /De > 1 corresponds to the mixing
state, while Di /De < 1 corresponds to the non-mixing
state in turbulent transport. In neoclassical transport,
DiN C /DeN C > 1 corresponds to ion root (Er < 0), while
DiN C /DeN C < 1 corresponds to electron root (Er > 0).
In the standard configuration in Large Helical Device(LHD), the anomalous diffusion coefficient is much larger

than the neoclassical diffusion coefficient (Di /DiN C  1
and De /DeN C  1) [25]. In the parameter regime ofthis experiment, TEM turbulence and ITG turbulence
are the most likely turbulence mode in the ion gyroradius scale. Because the density profile is flat or hollow,
the TEM turbulence is predicted to be destabilized near
the plasma edge where the density gradient is negative
and TEM or ITG turbulences are predicted to be more
pronouncedly destabilized in the core region where thedensity gradient is close to zero or positive. TEM indicates a higher wavenumber spectrum of the growth rate
than ITG mode and mode frequency around k⊥ ρti ∼ 1,
so that TEM and ITG turbulence are expected to coexist when the profile condition exceeds the criticality
for destabilizations in the plasma in LHD. Coexisteneceof multi modes (low k ITG, high k ITG, TEM, and ETG)
is commonly observed in tokamaks [26].
Since the TEM tends to be stabilized by the electronion collisions[27], the ITG turbulence becomes more dominant in higher collissionality plasma even for the same
R/LTi , R/LTe , and R/Lne , where R, LTi , LTe , and Lne
are major radius, scale length of ion temperature, electron temperature, and electron density. This is because
the growth rate of TEM turbulence sharply increases as
the collisionality decreases, while the growth rate of ITG
turbulence has weak dependence on collisionality [27].
In order to study the collisionality dependence of isotope mixing/non-mixing and turbulence characteristics,
simultaneous measurements for isotope density ratio profile and turbulence have been performed in LHD. In thisexperiment, the hydrogen neutral beam provides a significant particle source in the plasma core (reff /a99 < 0.4),
while the recycling from the wall and the divertor provides the particle source near the plasma edge. In order
to identify the non-mixing state from the isotope ratio
profile, ion species of the source near the plasma edge
should be different from the ion species of the source inthe plasma core. If the ion species of the core source isthe same as that of the edge source, a non-mixing state
can not be observed even when the plasma is in the nonmixing state. Therefore, the ratio of deuterium influx
to hydrogen influx was kept to be as high as possible bywall conditioning with deuterium gas before the experiment and between shots.
Figure 1 shows the radial profiles of electron density, electron temperature, ion temperature, hydrogenand deuterium density, and fraction of hydrogen density nH /(nH + nD ) measured with bulk charge exchange spectroscopy for lower collisionality plasma (n̄e
= 1.39×1019 m−3 ) and higher collisionality plasma (n̄e =3.85×1019 m−3 ), where n̄e is line averaged electron density. Although both electron temperature (Te ) and ion
temperature (Ti ) of lower collisionality plasma are higher
than those of higher collisionality plasma, the temperature ratio of electron to ion (Te /Ti ) is comparable forthese two discharges. The hydrogen density profile issimilar to the deuterium density profile in the isotope
mixing state. In the isotope non-mixing state, the hy-

mixing

non-mixing

mixingmixingnH(d)!n/ne (a.u.)nDnD (e)

non-mixingnH
H-beam

0.8
0.6
0.4
0.2
H-beam
0.0
0.2
0.4

10-70

fasym

non-mixing

0
3
2
1
0

mixingnon mixing
100
150
f (kHz)

50

3

(c)

(f)
mixing0.6
reff/a99

0.8

200

mixing1

non-mixing

00.4
non-mixing
0.2
0.0
mixing-0.2-0.4
10 ion-dia
non-mixing
50-5
mixing-10 electron-dia
10
5
0
-5
-10

0.6

(c)

(d)

dv"/dr < 0
non mixing(e)comixingctrdv"/dr > 0
0.5

250
(b)

2

0.4

non-mixing(a)

80 kHz10-6(b)

mixingH-beam

25 kHz10-5!n/n

non-mixing

10
5

10-4

(a)

vExB(km/s)

5
4
3
2
1
0
4
3
2
1
0
4
3
2
1
0

v" (km/s)

nH/(nH+nD)

nD nH (a.u.) nD nH (a.u.)Ti(keV)Te(keV)ne(1019m-3)

3

0.7 0.8
reff/a99

0.9

1.0

1.1

1.0

FIG. 1: Radial profiles of (a) electron density, (b) electron temperature, (c) ion temperature, and (d)(e) hydrogen and deuterium density, (f) fraction of hydrogen density
nH /(nH +nD ) in the isotope mixing (#142325 5.23s) and nonmixing (#142315 3.73s) states in the hydrogen and deuterium
mixture plasma with hydrogen beam fueling.

drogen density profile is peaked and deuterium density
profile becomes hollow. As seen in the radial profileof the fraction of hydrogen density nH /(nH + nD ), thepeaking of hydrogen fraction is clearly observed in the
low collisionality plasma. This peaking of hydrogen fraction is due to the combination of beam fueling of hydrogen (H) NBI and deuterium (D) dominated recycling(ΓD /ΓH =4), which indicates that the plasma is in the
non-mixing state. Here, ΓD and ΓH are the influx (inward radial flux of deuterium neutral and hydrogen neutral) evaluated from Hα and Dα intensity measured with
passive spectroscopy. This non-mixing state is an equilibrium steady-state with the balance between the source

FIG. 2: (a) Density fluctuation spectrum and radial profiles of(b) density fluctuation amplitude, (c) asymmetry factor fasymof density fluctuation, (d) E × B velocity, and (e) intrinsic
toroidal flow veloicty in the isotope mixing (#142325 5.23s)
and non-mixing (#142315 3.73s) states in the hydrogen anddeuterium mixture plasma with hydrogen beam fueling.

(hydrogen in the core and deuterium near the edge) andthe transport. In the mixing state, the hydrogen fraction profile becomes flat except for near the edge in thehigher collisionality plasma. The increase of hydrogen
fraction is attributable to the increase of hydrogen recycling (ΓD /ΓH =1.2) but the flattening of hydrogen fraction profile is due to the isotope mixing.
The clear difference in the turbulence spectrum between these two plasmas is also observed. Density
fluctuation spectrum, radial profile of fluctuation amplitude normalized by density and up-down asymmetry factor measured with 2D-PCI is plotted in Figure
2. Here, the up-down asymmetry factor is defined byfasym = (δndown − δnup )/(δndown + δnup ). The spectrum is from line integrated 2D-PCI signal, where spatially integrated at reff /a99 > 0.4, 5kHz < f < 500kHz,

4! (kHz)80k" = 0.2-0.4 mm-1(a) non-mixing

reff/a99=0.9

60
40

reff/a99=0.5

TEM

20

ITG

0
80
! (kHz)0.1mm−1 < k < 0.8mm−1 . 2D-PCI can resolve spatial
distribution of turbulence from the propagation direction of turbulence by assuming kk = 0 [28, 29]. However,frequency spectrum from spatially and wave number integrated turbulence shows clear difference in non mixing
and mixing state. Here, the background level of PCI
diagnostics evaluated from the fluctuation spectrum inthe period of no plasma is subtracted. Because the radial profile of E × B velocity is almost identical between
the isotope mixing and the non-mixing plasma, the E ×B
Doppler shift is considered to be almost identical between
the isotope mixing and the non-mixing plasma.
In the plasma with a non-mixing state, the density
fluctuation spectrum has a peak at a higher frequencyof 85 kHz. The characteristics of density fluctuation
with a higher frequency peak observed in LHD resemble the Quasi-coherent (QC) modes, known as a type ofthe trapped electron mode (TEM) turbulence, namely,
QC-TEM. This mode (QC-TEM) has been observed in
HL-2A and J-TEXT ohmic heating plasma [30] and in
KSTAR ECH plasmas [31]. The characteristic frequencies of a higher frequency peak in LHD are 40-100 kHz
with a peak of 80 kHz (see Figure 2(a)), which is thesame range of QC-TEM observed in HL-2A and J-TEXT(30-140 kHz). The parameter dependence of appearance/disappearance of the higher frequency peak of density fluctuation observed in LHD is also quite similar
to the parameter dependence of QC-TEM, where the
QC modes appear in the plasma with lower collisionality or higher Te /Ti ratio. The change of the mode
from QC-TEM to ITG associated with the transition
from the LOC regime to the SOC regime is also predicted from non-linear gyrokinetic simulation [32]. The
QC-TEM mode appears in the LOC regime (lower density regime) but it disappears in the SOC regime (higher
density regime), where the ITG mode becomes dominant.
In the plasma with the mixing state, this higher frequency peak disappears, and a lower frequency peak appears at 25 kHz. The frequency of the peak is consistent
with the frequency at the maximum growth rate for ITG
turbulence (f ≤∼20kHz) calculated by the GKV code
[11, 33]. The GKV code is a linear gyrokinetic numericalsimulation code for multi-ion species. Radial profiles ofhydrogen, deuterium, and carbon ions and the fractionof helium ion measured are taken into account in thissimulation. The amplitude of fluctuation normalized bydensity in the region of reff /a99 > 0.6 is larger in the
mixing state than the non-mixing state and the up-down
asymmetry factor fasym at reff /a99 = 0.7 is larger in theisotope non-mixing plasma than in the isotope mixing
plasma. The reason for the up-down asymmetry is thedifference of the projection of the two vectors (kr andkθ ) of turbulence propagation to PCI measurements [34].
Therefore, the difference in up-down asymmetry factor
implies the change in the type of turbulence in these twoplasmas.
As seen in Figure 2(e), the gradient of intrinsic toroidal
flow (dvφ /dr) has opposite sign between these two dis-(b)k" = 0.2-0.4 mm-1

mixing
reff/a99=0.9

60

reff/a99=0.5

40
20

ETG

0
-100

ITG
-50

f(kHz)

050

FIG. 3: Linear growth rate at reff /a99 = 0.5 and 0.9 for the
non-mixing (#142315) and isotope-mixing (#142325) states
calculated with GKV. The linear growth rates for the wave
number of kθ = 0.2 - 0.4 mm−1 are indicated with solid line
and the dashed lines correspond to the other wave number (kθ < 0.2 mm−1 and kθ > 0.4 mm−1 ).

charges, where there is no net toroidal torque driven bytangential neutral beams. It is well known that the residual stress produced the gradient of toroidal flow due tothe symmetry breaking ( kkco 6= kkctr ) ). Because of theboundary condition of Vφ = 0 at the plasma boundary,
this residual stress produced is a strong candidate for intrinsic toroidal flow [35, 36]. Therefore, the direction of
intrinsic toroidal flow depends on the turbulence mode.
In LHD, the intrinsic toroidal flow is in the co-directionin the low collisionality regime, while it is in the counterdirection in the higher colllisionality regime [37].
In Alcator C-mode, the TEM mode turbulence is observed when the direction of intrinsic toroidal flow is
co-direction and this TEM turbulence disappears associated with the flow reversal from co-direction to counterdirection, which demonstrates that the TEM mode turbulence drives the intrinsic toroidal flow in co-direction.
Therefore, the intrinsic toroidal flow in co-direction alsosuggests the existence of TEM mode turbulence [38]. The
characteristics of turbulent spectrum are quite different
between isotope mixing and non-mixing plasma. Theseobservations suggest that the change in isotope mixing/non-mixing is attributed to the change in turbulencemode.
Figure 3 shows the linear growth rate at core region(reff /a99 =0.5) and at the edge region (reff /a99 =0.9) for
the non-mixing and isotope-mixing states calculated with
GKV [12, 15]. PCI measurements show that the peak of
the wave number of density fluctuation is ∼ 0.3 m−1 .

5!n/n (a.u.)eEr(kV/m) n (1019m-3) Te(keV) Ti(keV)

frequency. This is because Te /Ti ratio is quite different
between ECH and NBI plasma. TEM turbulence is pre(b)dicted to be dominant in the low density ECH plasma beTe
Tecause of the large normalized electron temperature gradient in the plasma with high Te /Ti ratio. In contrast, the
ITG turbulence is predicted to be dominant in the NBI
Ti
plasma where the ion temperature gradient is steeper.
Figure 4 shows the radial profiles of electron and ion(d)temperature, electron density, and radial electric field.
The electron temperature is three times higher than the1
ion temperature in the ECH plasma, while the electron
temperature is almost identical to ion temperature in the0
NBI plasma. The electron density is low (1×1019 m−3 )10 (e)(f)and the electron density profile is almost flat. The linear0
gyrokinetic simulations GKV predicts that the TEM isdestabilized because the normalized ion temperature gra-10
dient is relatively small in the core (reff /a99 = 0.3) of the
0.4
0.6
0.8
1.0 0.4
0.6
0.8
1.0
reff/a99
ECH plasma, where the Te /Ti ratio is ∼ 3. It also prereff/a99-4
dicts that the ITG mode is destabilized in the core of the10(g)
80 kHz
NBI plasma, where the Te /Ti ratio is close to unity. Near
the plasma edge (reff /a99 = 0.9), the TEM is predicted
ECH plasma
to be destabilized due to the negative density gradients
Te > >Ti
10-5[39]. When both ITG mode and TEM are destabilized,
the growth rate of TEM often becomes larger than thatof ITG mode (γTEM > γITG ) at higher wave number
NBI plasma
10-6(and higher frequency).
Te ~ Ti
There are no large differences in the radial electric field
profile between these ECH and NBI plasmas. Therefore,
0
50
100
150
200
250
the Doppler shifts of density fluctuation due to the E ×B
f (kHz)drift are similar between these two plasma. However, thedensity fluctuation spectrum measured with PCI shows
the clear difference. The peak at 80 kHz is significant
in the ECH plasma, which is similar to the plasma withisotope non-mixing plotted in Figure 2. In the similar
FIG. 4: Radial profiles of (a)(b) electron and ion temperaECH plasma, TEM-like fluctuation characteristics areture, (c)(d) electron density, (e)(f) radial electric field, and(g) density fluctuation spectrum in the (a)(c)(e) ECH plasma
observed in the PCI measurements [39]. In the NBI(#139080) and (b)(d)(f) NBI deuterium plasma (#139727).
plasma, the peak at 80 kHz disappears completely, whichsuggests the reduction of TEM turbulence in the plasmacore. These observations imply the strong linkage between the transition from non-mixing to mixing and the
The linear growth rates for the wave number of kθ = 0.2−1change in turbulence characteristics.
- 0.4mm are plotted with a solid line in order to indicate the range for the density fluctuations measured with
PCI. In the isotope-mixing states, the TEM is destabiIII. IMPACT OF DENSITY GRADIENT TO
lized near the plasma edge where the density and elecISOTOPE MIXING AND NON-MIXING
tron temperature gradients are relatively sharp and ITG
mode is destabilized at the plasma core where the density gradient is positive (hollow density). In contrast, in
The density gradient is also an important parameterthe mixing state, the TEM is stabilized near the plasma
for the transition from TEM turbulence to ITG turbuedge and ITG is still destabilized at the plasma core. In
lence temperature gradient [39]. In order to investigate
the mixing state, the ETG mode is also destabilized near
the impact of the density gradient on the transition fromthe plasma edge. Because the wave number for the ETG
non-mixing to mixing, two discharges with similar line
mode is larger (k > 0.4mm−1 ) than the wave number for
averaged density and temperature are compared. FigTEM, this mode is not observed in the density fluctuaure 5 displays the time evolution of line averaged elections in PCI measurements.
tron density, density fluctuation spectrum, the ratio of
density fluctuation amplitude integrated in the range of
The comparison of the turbulence spectrum in the
40-90 kHz to that of 4-40 kHz, and the fraction of hydroECH plasma and the NBI plasma is important to ingen density nH /(nH + nD ) at reff /a99 = 0.68 and 0.96.
vestigate in the turbulence modes that contribute the
Schemes of heating are identical for the two discharges
turbulence peak at lower frequency and that at higher
5
(a)
4
3
2 T
i
1
0
2 (c)

f(kHz)non-mixing

100

non-mixing

dne/dr<0
non-mixing (t=4.5s)

0
1.5 (f)
1.0
0.5
0.0
3.0

nH
(c)

non-mixing

3
2
1
0

nD
nH
non-mixing

0.4

3.5

time (sec)4.0

mixing
4.5

FIG. 5: Time evolution of (a) line averaged electron density, (b)(c) the fraction of hydrogen density nH /(nH + nD ) at
reff /a99 = 0.68 and 0.96, respectively, (d)(e) density fluctuation spectrum, and (f) the ratio of density fluctuation amplitude integrated in the range of 40-90 kHz to that of 4-40 kHz,for mixing (#158390) and non-mixing discharge (#159396) inthe hydrogen and deuterium mixture plasma with hydrogen
beam fueling.

plotted. The plasma is initiated by ECH for t = 3.0 - 3.3
secs, followed by hydrogen neutral beam. The power ofhydrogen neutral beam increases from t = 3.8 sec. The
difference between these discharges is the amount of recycling. The density increases faster in the discharger withhigher recycling and the density increases slower in the
discharger with lower recycling. The isotope non-mixing
state is observed in the discharge with lower recycling,where the hydrogen fraction in the core (reff /a99 = 0.68)
increases rapidly after the increase of NBI power due tothe core beam fueling by hydrogen NBI. The increase

(d)

0.2
mixing(e)

non-mixing
mixing
0.6

0.7

10-5

non-mixing

(b)

nD

mixing

0.8
r /a
eff

50

mixing (a)(t=4.0s)

dne/dr>0

r

(e)

5
4
3
2
1
0
3
2
1
0

0
5
0
-5
-10
0.5

50
0

I40-90/I4-40

mixingE (kV/m) nH/(nH+nD) nH nD (a.u.) nH nD (a.u.) ne(1019m-3)

4
mixing3 (a)21
non-mixing
00.4 (b)
reff/a99=0.68
0.3
0.2
r /a =0.96
0.1 ECH eff 99
NBI(H)
0.0
0.4 (c)reff/a99=0.68
0.3
0.2
r /a99=0.96
0.1 ECH eff NBI(H)0.0(d)
mixing100!n/nf(kHz)

nH/(nH+nD) nH/(nH+nD) n (1019m-3)
e

6

0.9

1

1.1

99

(f)

60 kHznon-mixing
mixing

10-6
0

50

100
150
f (kHz)200

250

FIG. 6: Radial proles of (a) electron density, (b)(c) hydrogen and deuterium density, (d) fraction of hydrogen density
nH /(nH + nD ), (e) radial electric field, and (f) density fluctuation spectrum at t = 4.0s in the isotope mixing plasma(#158390) and at t=4.5s in the non-mixing plasma (#159396)
plotted in figure 3.

of the hydrogen fraction saturates in 0.2 sec, which is
the order of particle confinement time in the plasma coreregion. In contrast, isotope mixing (but not complete
mixing) state is observed in the discharge with higher
recycling. The increase of the hydrogen fraction in thecore (reff /a99 = 0.68) is smaller even for the same beamfueling. It is interesting that the hydrogen fraction near
the plasma edge (reff /a99 = 0.96) decreases for both discharges.
The density fluctuation spectrum shows a clear difference between these two discharges. The density fluctuation is peaked at the lower frequency (f < 40 kHz) regime
in the plasma with isotope mixing state. In contrast, thedensity fluctuation is peaked at the higher frequency (40kHz < f < 90 kHz) regime in the plasma with isotope

7

IV.

ISOTOPE MIXING TRIGGERED BYPELLET INJECTION

The shallow pellet injection [40] is a useful tool to trigger the transition from isotope non-mixing state to isotope mixing state, because the particles deposited near
the plasma periphery at reff /a99 ∼ 0.9 results in boththe increase of collisionality and hollow density profile,in which the electron density gradient is positive. The

fH

fH

ne(1019m-3)

4

fH(0.6)/fH(1.0)

non-mixing state. It should be noted that the higher frequency peak appears at the ECH phase both in thesetwo discharges. The ratio of density fluctuation amplitude integrated in the range of 40-90 kHz to that of 4-40
kHz decreases significantly after the switch from ECH to
NBI heating The ratio stays low in the discharge withisotope mixing state, but starts to increase to the level
in ECH phase in the discharge with isotope non-mixing
state. These results also show the strong correlation between isotope mixing and density turbulence spectrum.
The difference of recycling results in the differencein the density profile. The density profile becomes flat
for the discharge with lower recycling, while it becomes
hollow in the discharge with higher recycling. Figure
6 shows the radial proles of electron density, hydrogendensity, deuterium density, fraction of hydrogen density
nH /(nH + nD ), and radial electric field at the time forthe same line-averaged electron density. In the discharge
with non-mixing state, the electron density is flat anddensity gradient in the region of reff /a99 = 0.68-0.86 is
negative. In contrast, the electron density is flat and thedensity gradient in the region of reff /a99 = 0.68-0.86 is
positive in the discharge with mixing state. Because of
the beam fueling of hydrogen beam, the hydrogen density
in the isotope mixing state is lower than the hydrogendensity in the non-mixing state. In contrast, the deuterium density in the isotope mixing state is higher thanthe deuterium density in the non-mixing state due to thehigher influx of deuterium as the exchange of hydrogen
outflux to the wall. There are clear differences in thegradient of hydrogen fraction. The gradient of hydrogen
fraction of that region in the discharge with isotope nonmixing is much larger than that in the discharge withisotope mixing even for the same line-averaged density
and hydrogen beam fueling rate. The radial profiles ofradial electric field are almost identical between the discharges with isotope mixing and non-mixing. The density
fluctuation spectrum shows clear peak at 60 kHz in theisotope non-mixing plasma. This peak disappears in theisotope mixing plasma. This observation demonstrates
that the sign of the density gradient has a strong impact
on the isotope mixing turbulence characteristics. Linear gyrokinetic simulation predicts stronger decrease of
growth rate for TEM than that for ITG turbulence [39].
The transition from TEM turbulence to ITG turbulenceis expected by changing the sign of the density gradientfrom negative to positive [39].

(a)3H-pellet

2
1
0
(b)
0.8
0.6
0.4
0.2
0.0
1.0
(c)
0.8
0.6
0.4
0.2
0.0
(d)
2.5

D-pelletH-pelletfH = nH/(nH+nD)
reff/a99 = 0.6

reff/a99 = 1.0
D-pelletfH = nH/(nH+nD)
reff/a99 = 0.6

reff/a99 = 1.0
H peaked
D-pellet2.0
1.5

H-pellet

1.0

flat isotope density

0.5
0.0
3.7

H hollow
3.8

3.9
4.0
time (sec)

4.1

4.2

FIG. 7: Time evolution of (a) line averaged electron density,(b)(c) the fraction of hydrogen density fH = [nH /(nH +nD )] at
reff /a99 = 0.6 and 1.0, respectively, and (d) the ratio of hydrogen fraction at reff /a99 = 0.6 to that at reff /a99 = 1.0 in thehydrogen and deuterium mixture plasma with hydrogen beamfueling and with hydrogen (H) pellet injection (#142315) ordeuterium (D) pellet injection (#142314).

hydrogen and deuterium pellet injection experiments are
performed to study the time scale of isotope mixing.
Hydrogen and deuterium pellet is injected to the isotope mixture plasma with hydrogen beam fueling andwith deuterium recycling, where the hydrogen fraction
is peaked in non-mixing state. If the plasma remains in
the non-mixing state, the hydrogen pellet causes the flattening of hydrogen fraction, while the deuterium pellet
causes the peaking of hydrogen fraction. However, when
the transition from non-mixing state to mixing state occurs, the hydrogen fraction profile becomes flat regardlessof the species of the pellet.
Figure 7 shows line averaged electron density, the fraction of hydrogen density fH = [nH /(nH + nD )] at reff /a99

nH/(nH+nD)
vExB(km/s) vExB(km/s)

!n/n
!n/n

10-4 (e)
10-5
10-6
10-7
10-4 (f)
10-5
10-6
10-7
0

10
8
6
4
2
0
8
6
4
2
0

!ne (1019m-3)

1.0
5ms
0.8 (a)
25ms
0.6
145ms
0.4
"t= -15ms
0.2!ne (H-pellet)
0.0(b)"t= -15ms
0.5 145ms
0.4
25ms
0.3
0.2 5 ms
0.1
!ne (D-pellet)
0.0
H-pellet5 (c) "t= -15ms
0-5"t= 25ms-10
5 (d) "t= -15ms
D-pellet0-5"t= 25ms-10
0.4 0.5 0.6 0.7 0.8 0.9 1.0
reff/a99!ne (1019m-3)= 0.6 and 1.0, respectively, and the ratio of hydrogen
fraction at reff /a99 = 0.6 to that at reff /a99 = 1.0 in thehydrogen and deuterium mixture plasma with hydrogen
beam fueling and with hydrogen pellet injection or deuterium pellet injection. Associated with the pellet injection, the line averaged electron density sharply increaseby ∼ 50%. Here the decay of hydrogen fraction rather
than the decay of ion density in pellet is discussed. The
decay of the ion density indicates the transport characteristics which are related to the so-called diffusion coefficient. It was reported that the decay time of hydrogendensity after the hydrogen pellet is almost identical tothe decay time of deuterium after the deuterium pellet[2]. This result demonstrates that the diffusion coefficientof hydrogen is similar to that of deuterium (DH ∼ DD ).
The decay of the isotope fraction is determined by the
combination of decay of the species injected by pellet andrecycling. For example, when the deuterium wall recycling is dominant, the decay of hydrogen fraction at theplasma edge (reff /a99 = 1.0 ) after the hydrogen pellet isdetermined by the exchange of species with the outwardhydrogen flux and inward deuterium flux. In contrast, inthe discharge with deuterium pellet, the increase of hydrogen fraction due to the decrease of deuterium density
at the plasma edge is simply determined by the edge deuterium particle confinement time with the recycling ratioof unity where the outward deuterium flux is balancedwith the inward deuterium flux.
Hydrogen fraction fH both in the plasma core at
reff /a99 = 0.6 and plasma boundary at reff /a99 1.0 increase after the hydrogen pellet and gradually decreases
in 0.2 sec. In contrast, the hydrogen fraction fH at
reff /a99 = 0.6 and 1.0 decreases after the deuterium pellet
and recovers in 0.1 sec. The time evolution of the fraction
ratio at two radii, fH (reff /a99 =0.6)/fH (reff /a99 =1.0), isplotted as an indication of hydrogen peaking. This hydrogen peaking parameter decreases after the pellet injection of both hydrogen and deuterium, which indicatesthat the isotope mixing occurs by the pellet injection
regardless of pellet species. Hydrogen peaking parameter for deuterium pellet is larger than that for hydrogenpellet, because the flattening of hydrogen fraction of theisotope mixing is partially canceled by the increase of
deuterium ions near the plasma edge due to deuterium
pellet fueling. Hydrogen peaking parameter gradually
increases after the sharp drop and recovers to the level
before the pellet injection within 0.2 sec. This indicatesthat the isotope mixing state after the pellet injection istransient (short period) and the plasma returns to thenon-mixing state.
The radial profile of hydrogen fraction 15ms before thepellet injection (dashed lines) and 5ms, 25ms, and 145ms
after the hydrogen (H) and deuterium (D) pellet injection
are plotted in Figure 8. The increment of electron density by pellet injection is evaluated from the difference
in density profile before and after the pellet injection,
which indicates the source profile due to pellet injection.
The maximum increment of electron density is locatednH/(nH+nD)

8

1.1

H-pellet"t= 15ms

30 kHz80 kHz "t= -35ms
40 kHzD-pellet"t= 15ms

80 kHz50"t= -35ms
100
150
200
f (kHz)250

FIG. 8: Radial profiles of (a)(b) fraction of hydrogen density
nH /(nH + nD ), and (c)(d) E × B flow velocity, and (e)(f) density fluctuation spectrum before (∆t < 0) and after (∆t > 0)(a)(c)(e) the hydrogen (H) pellet injection (#142315) and(b)(d)(f) the deuterium (D) pellet injection (#142314). The
radial profiles of the increment of electron density δne by pellet injection are also plotted.

at reff/ a99 = 0.95 because of the shallow pellet penetration in this plasma. Before the pellet injection, thehydrogen fraction is peaked because of the beam fueling of hydrogen NBI in both cases. After the hydrogenpellet injection, the hydrogen fraction increases in thelevel of 0.8 with a flat profile. The flattening of hydrogen
fraction is due to the hydrogen fueling near the plasmaedge by hydrogen pellet and isotope mixing. At 25 ms
after the pellet injection, the hydrogen fraction profile
starts to be peaked due to the decay of hydrogen near
the plasma edge injection by pellet. Further hydrogenpeaking occurs due to the back transition from mixing
state to non-mixing state. Then the gradient of hydrogen
fraction at 145ms after the injection becomes comparable
to that before the pellet injection, although the absolutefH(0.6)/fH(1)!n (a.u.)!n (a.u.)

reff/a99 = 0.87
4 (a)dne/dr = 0
3
2
1
dne/dr > 0 reff/a99 = 0.68
0Te
reff/a99 = 0.87
1.5 (b)
1.0
0.5
Ti
0.0
(c) D-pellet
2.0
1.5
1.0

(d)

10

I(10-80kHz)

1
3.7
-3
10
(e)

3.8

3.9
time (sec)

4.0

4.1

"t= 50ms"t= 1ms"t= 26ms

10-4
10-5"t= 75ms"!n (a.u.)value of hydrogen fraction is still higher before the pellet
injection.
In the discharge for deuterium pellet injection, the hydrogen fraction decreases to 0.2 and the hydrogen fraction profile becomes flat. Because the deuterium fuelingby the pellet is mainly near the edge as seen in the radial
profile of the increment of electron density, this is clear
evidence for the isotope mixing. The hydrogen fraction
starts to increase 25ms after the pellet injection due tothe decay of deuterium and the hydrogen fraction profile
becomes almost identical to that before the pellet injection at 145ms after. These results demonstrate that theflattening of hydrogen fraction is observed immediately(at 5ms) after the pellet injection. This rapid flattening indicates that the large ion diffusion coefficient (i.e.,
Di /De  1) which is consistent with the prediction ofsimulation for ITG turbulence. On the other hand, therecovery of the peaked hydrogen fraction after the pellet
injection is relatively slow (∼100ms) and this slow recovery indicates the small ion diffusion (i.e., Di /De  1)which is consistent with the prediction of simulation for
TEM turbulence.
As seen in the radial profiles of E × B flow velocity,
the radial electric field is close to zero in the core and becomes more negative (in the electron diamagnetic direction) near the plasma edge (reff/ a99 < 1) and positive (inthe ion diamagnetic direction) outside the plasma boundary (reff/ a99 > 1). The E × B flow velocity increases
slightly in the electron diamagnetic direction in the core
after the pellet injection. The density fluctuation spectrum has a clear peak at 80 kHz before the pellet injection (∆t = -35ms). This is quite similar to the spectrum
in the plasma with higher collisionality (Fig.1), higher
Te /Ti ratio (Fig.3), and flat density profile (Fig.4). Afterthe pellet injection, the peak at 80 kHz disappears andincrease of density fluctuation at lower frequency (20-60
kHz) becomes more significant. The density fluctuation
spectrum after the pellet injection (∆t = 15ms) is quite
similar to that isotope mixing plasma in higher collisionality plotted in Figure 2.
The short period of mixing state is due to the quick recovery of Te /Ti ratio and density profile. Figure 9 showstime evolution of electron density, (b) electron and ion
temperature in reff /a99 = 0.87. After the pellet injection, the Te /Ti ratio drops to unity but the ratio recovers quickly (∼ 50 ms) to the level before the pellet injection. As seen in time evolution of electron density at
reff /a99 = 0.68 and 0.87 in Figure 9(a), the density gradient at reff /a99 = 0.68-0.87 is negative before the pellet
injection. After the pellet injection, the density gradientbecomes positive until t = 3.84 sec. Although the decayof the electron density is slow (∼ 0.3 sec) , the changeof the sign of density gradient at reff /a99 = 0.68-0.86 isrelatively short (∼ 0.1 sec). After the pellet injection,
the density fluctuation amplitude integrated in the rangeof 10-80 kHz increases sharply but its amplitude quickly
decays (∼ 50 ms) to the levels before the pellet injection. The frequency spectrum of the density fluctuation

Te,i(keV) ne(1019m-3)

9

10
8
6
4
2
0

"t= 1ms(f)"t= 26ms"t= 50ms
0

50

100
150
f (kHz)200

250

FIG. 9: Time evolution of (a) electron density at reff /a99 =0.68 and 0.87, (b) electron and ion temperature at reff /a99 =0.87, (c) the ratio of hydrogen fraction fH = [nH /(nH + nD )]at reff /a99 = 0.6 to that at reff /a99 = 1.0, and (d) density
fluctuation amplitude integrated in the range of 10-80 kHz,and frequency spectrum of (e) density fluctuation and (f) increment of density fluctuation after the pellet injection in thehydrogen and deuterium mixture plasma with hydrogen beamfueling and with deuterium (D) pellet injection (#142314).

and increment of density fluctuation after the pellet injection are also plotted. Here the increment of density
fluctuation by pellet injection is defined as ∆δn(∆t) =δn(∆t)−δn(∆t=-35ms). The increase of density fluctuation is mainly in the flow frequency range below the peakof density fluctuation (80 kHz) observed in non-mixing
state in Figure 8. The spectrum of density fluctuation
50 ms after the pellet injection is almost identical to that
before the pellet injection and the increment becomes
small, which indicates that the turbulence increases bypellet is transient. These characteristics of density turbulence are consistent with the short period of mixing

10state after the pellet injection. Time evolution of hydrogen peaking factor drops from 2.0 to 1.5 after the pellet
injection. Then the peaking factor remains at low level
for a short time (∼ 50 ms) then starts to increase fromt = 3.8 secs. The time evolution of density fluctuationand hydrogen peaking factor strongly suggests the linkage of turbulence and isotope mixing as predicted by the
gyrokinetic simulation.

V.

DISCUSSION AND SUMMARY

Typical characteristics of plasma with isotope nonmixing and mixing state plasmas are summarized in Table 1.
Table 1: Typical characteristics of plasma with isotope
non-mixing and mixing state plasmas.
parameters
non-mixing state mixing stateisotope density ratio
non-uniform
uniform
19 −3electron density< 2-3 x10 m> 2-3 x1019 m−3
density gradientdne /dr ≤ 0
dne /dr > 0
Te /Ti ratio
large (> 1-2)
small (< 1-2)
peak frequency
60-90 kHz
20-40 kHz
intrinsic toroidal flow
co-direction
counter-direction
The plasma parameters preferable for the non-mixing
state are 1) lower collisionality, 2) higher Te /Ti andhigher (R/LTe )/(R/LTi ), 3) negative or zero density gradient (peaked or flat density profile), where the TEM
is expected to be destabilized. In LHD, first and second preferable plasma parameters (low collisionality andhigher Te /Ti ) can be often obtained in the low density
plasma with ECH and with negative NBI where the beamenergy is high enough (160 - 180 keV) to heat electrons
rather than ions. The preferable plasma parameters for
mixing, that is higher collisionality and lower Te /Ti ∼ 1,
and positive density gradient (hollow profile), are produced by shallow pellet injection. The peaking of isotope
species of beam fueling is not always observed in the isotope mixture plasma with non-mixing state. In order toobserve the peaking of beam fueled isotope species, thenumber of particles of the species supplied by the beamfueling in the core should be large enough compared with
the number of particles supplied by recycling and gas
puff. For example, when the species of bean is hydrogen,the hydrogen recycling should be significantly reduced,that is ΓH /ΓD < 1. In the case of higher hydrogen recycling (ΓH /ΓD > 1), the peaking of hydrogen fraction can
not be achieved even in the isotope mixture plasma with
non-mixing state. The conditions for observing the peaking of beam fueled isotope species are 1) isotope mixture
plasma, 2) non-mixing state (Di /De  1), low recyclingof beam fueling (Γbeam−species /Γrecycling−species < 1).
The strong correlations between isotope mixing andturbulence characteristics are observed in LHD. The

peaking of beam fueled species is a direct indication of
non-mixing but can be observed only in the conditionof low recycling of beam species, which are not always
achieved. In contrast, the turbulence characteristics arefound to be relating to the isotope mixing and nonmixing. The density fluctuation peak at 80 kHz is observed in the plasma with non-mixing state, while thispeak disappears in the plasma with mixing state. Thisis a useful finding, because the turbulence characteristics
can be obtained even in the condition of higher recyclingof beam species. Furthermore, the reversal of intrinsic
toroidal flow also suggests the change in the turbulence
characteristics because the direction of intrinsic toroidal
flow driven by residual stress strongly depends on the turbulence mode (TEM or ITG), which has been observed
widely in tokamaks. It is difficult to identify the turbulence mode (for example, TEM or ITG) from the spectrum of density fluctuation. However, significant differences in density fluctuation spectrum observed between
isotope mixing and non-mixing states demonstrate thatthe change in turbulence observed is a strong candidate
for the mechanism causing the transition between isotope
mixing and non-mixing state.
Microinstability characteristics for the plasma with isotope non-mixing and mixing state are identified by thelinear gyrokinetic calculations, and are summarized in
the Table 2. In LHD, the TEM can be destabilized near
the plasma edge due to the large density gradient and
ITG mode or TEM mode can be destabilized in the coreregion. In this experiment, the ITG mode in the core region is destabilized for both non-mixing and mixing state.
The TEM is destabilized in the non-mixing state andstabilized in mixing state, which suggests that the TEM
contributes the non-mixing state, where the De  Di is
expected [11].
Table 2: Linear gyrokinetic simulation results for theplasma with isotope non-mixing and mixing state
non-mixing state
mixing stateedge reff /a99 = 0.9 TEM destabilized TEM stabilizedcore reff /a99 = 0.5 ITG destabilized ITG destabilized
The dependence of plasma parameters (collisionality,
Te /Ti ratio, density gradient) for the transition from nonmixing to mixing transition is consistent with plasma
parameter dependence where the gyrokinetic simulation
predicts the transition from TEM to ITG in the plasmacore. These experimental observations in LHD are incontrast to the observation of isotope mixing state in
JET where the large ion diffusion is observed in the isotope mixture (H and D) plasma. In JET experiment,
the electron density is higher (n̄e ∼ 3×1019 m−3 ) and the
Te /Ti is close to unity and ITG turbulence is expected
to be dominant [41]). The isotope mixture experimentin the low density and high Te /Ti plasma in tokamak
would be interesting. This is because the comparison ofcharacteristics of the plasma with non-mixing state be-11tween tokamak and helical plasma provides the deeper
understanding of isotope mixing mechanism, which is indispensable for the better control of D-T isotope mixture
plasma in future.

VI.

ACKNOWLEDGEMENTS

thors (KI) acknowledges Dr. M.Yoshida (National Institutes for Quantum and Radiological Science and Technology; QST) for providing us two spectrometers for thebulk charge exchange spectroscopy. This work is supported by the National Institute for Fusion Science grant
administrative budgets (NIFS10ULHH021) and JSPS
KAKENHI Grant Numbers JP15H02336, JP16H02442,
JP17H01368, and JP17K14899.

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