Transition between Isotope-Mixing andNonmixing States in Hydrogen-Deuterium
Mixture Plasmas
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言語: English
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公開日: 2021-07-05
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キーワード (En):作成者: IDA, Katsumi, Nakata, Motoki, TANAKA, Kenji,
YOSHINUMA, Mikiro, Fujiwara, Yutaka, SAKAMOTO,
Ryuichi, MOTOJIMA, Gen, MASUZAKI, Suguru,
Kobayashi, Tatsuya, Yamasaki, kotaro
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Transition between isotope-mixing and non-mixing states in hydrogen-deuterium
mixture plasmas
K.Ida,1, 2 M.Nakata,1, 2 K.Tanaka,1 M.Yoshinuma,1, 2 Y.Fujiwara,1
R.Sakamoto,1, 2 G.Motojima,1 S.Masuzaki,1, 2 T.Kobayashi,1, 2 and K.Yamasaki3
1

National Institute for Fusion Science, National Institutes of Natural Sciences, Toki, Gifu 509-5292, Japan
2
SOKENDAI (The Graduate University for Advanced Studies), Toki, Gifu 509-5292, Japan
3
Research Institute for Applied Mechanics Kyushu University, Kasuga, Fukuoka, Japan(Dated: December 14, 2019)
Transition between isotope-mixing and non-mixing states in hydrogen-deuterium mixture plasmas
is observed in the isotope (hydrogen and deuterium) mixture plasma in Large Helical Device. In
the non-mixing state, the isotope density ratio profile is non-uniform when the beam fueling isotope
species diﬀers from the recycling isotope species and the profile varies significantly depending on
the ratio of the recycling isotope species, although the electron density profile shape is unchanged.
The fast transition from non-mixing state to isotope-mixing state (nearly uniform profile of isotope
ion density ratio) is observed associated with the change of electron density profile from peaked tohollow profile by the pellet injection near the plasma periphery. The transition from non-mixing
to isotope-mixing state strongly correlates with the increase of turbulence measurements and thetransition of turbulence state from TEM to ITG is predicted by gyrokinetic simulation.
PACS numbers: 52.55.Fa, 52.35.Ra, 52.35.Py

Control of the isotope ratio in the plasma core is oneof the crucial issues regarding fusion plasma, because thefusion power decreases as the deuterium-tritium (D-T)
ratio in the core region deviates from 1:1. Although theisotope ratio of influx can be easily monitored by Dα
and Tα lines, the individual isotope density has not beenclarified whether the tritium density profiles are identical to the deuterium density profile. Although the isotope mixture plasma is necessary for this study, there are
only a few experiments using the isotope mixture plasma[1, 2]. Hydrogen-deuterium (H-D) mixture plasma experiment in JET demonstrates that the H-D ratio profiles
are insensitive to the isotope species of the recycling fromthe wall in the ITG dominant regime, where nearly uniform profile of the H-D ratio can be expressed as isotopemixing state. Knowledge of the isotope state is limited
due to a lack of precise measurements of isotope profiles.
In many cases, the ion density profile shape, including
the isotope-mixing state, is assumed to be identical tothe electron density profile due to the quasi-neutrality.
However, in the isotope mixture plasmas, the individually diﬀerent isotope ion profiles are possible as longas the ambipolar condition is maintained, but the nonmixing state has never been observed experimentally sofar. In recent work with gyrokinetic simulations, thenon-mixing state is predicted in the TEM regime, whileisotope-mixing state is predicted in the ITG regime [2].
There are also earlier works on the gyrokinetic simulations for the turbulent transport of the multiple isotope
ions [3–5].
In this letter, we show a novel observation of evidence of the formation non-mixing profile and its transition to the isotope-mixing state in the plasma associated with the increase of turbulence level propagating in
the ion diamagnetic direction. These results demonstratethat either of two isotope states (non-mixing or isotopemixing) can exist in the H-D mixture plasma depending on turbulence state as predicted by the gyrokinetic
simulations. Bulk charge exchange spectroscopy system[6–9] has been applied to measure the radial profiles ofnH /(nH + nD ) and nD /(nH + nD ) in the plasma fromHα and Dα lines emitted by the charge exchange reaction
between the bulk ions and the neutral beam injected inLarge Helical Device (LHD) [10–12]. In order to study
whether the ion particle transport is in the non-mixing
state or the isotope-mixing state, the hydrogen and deuterium density profiles are measured in the plasmas withcore hydrogen fueling by H-beam and edge deuterium
fueling by recycling (ΓD > ΓH ), where ΓD and ΓH are
influx of deuterium and hydrogen evaluated with passive
spectroscopy.
Figure 1 shows radial profiles of electron density normalized by the line-averaged electron density. The lineaveraged electron density increases from 2 to 4 ×1019 m−3
shot by shot due to increasing the hydrogen recycling,ΓH /ΓD , from 0.3 to 0.8. The electron density profile
shapes are almost identical for these three discharges
with diﬀerent line-averaged density and diﬀerent wall recycling isotope ratio. However, radial profile shapes ofhydrogen and deuterium density are quite diﬀerent depending on the ratio of hydrogen recycling. The amountof hydrogen density increases as the hydrogen recycling
is increased, although the amount of deuterium density
is similar for these three discharges. The increase of density is mainly due to the increase of hydrogen recyclingfrom the wall. When the isotope recycling ratio is close tounity, there is almost no diﬀerence in profiles between hydrogen and deuterium as seen in Fig.1(b). In contrast, asignificant diﬀerence in the profile shape (peaked or hollow) between hydrogen density and deuterium density
is observed in the lower density plasma where the hy-

2nD, nH (a.u.)

4
3
2
1
0

nD, nH (a.u.)

e

3

H

D

nH
nD

H-beam(d) n =1.9x1019m-3 (! /! =0.3)eHDxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
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0.2 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
H-beamxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
D
0.0 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
1.0 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxD(b)
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0.8
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0.6 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
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0.4
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0.2 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
D-beamxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
H
0.0
0.2
0.4
0.6
0.8
1.0
1.2
reff/a99

recycling fraction

0.4

recycling fractionnH/(nH+nD)

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

0.6 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

FIG. 2: Radial profiles of (a) hydrogen isotope fraction,nH /(nH + nD ) with H-beam fueling and (b) deuterium isotope fraction, nD /(nH + nD ) with D-beam fueling. The isotope fractions of recycling are indicated with arrows at theright y-axis.

nD

2

nH

1
0

nD/(nH+nD)

1.0 (a)0.8
ne=3.8x1019m-3
0.6
ne=3.1x1019m-3
0.4
0.2
ne=1.9x1019m-3
0.0(b) ne=3.8x1019m-3 (!H/!D=0.8)
8
6
nH
4
nD
2
H-beam019-35 (c) n =3.1x10 m (! /! =0.5)

nD, nH (a.u.)

ne/nexxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

1.0 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxH(a)xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
0.8

0.0

0.2

H-beam
0.4 0.6
reff/a990.8

1.0

FIG. 1: (a) Radial profiles of electron density and (b)(c)(d)radial profiles of H and D density in the plasma with H-beamfueling for the diﬀerent line-averaged density and wall recycling isotope ratio of (b) 3.8 ×1019 m−3 (ΓH /ΓD = 0.8), (c)3.1×1019 m−3 (ΓH /ΓD = 0.5), and (d) 1.9×1019 m−3 (ΓH /ΓD= 0.3).

drogen recycling is low enough (ΓH /ΓD = 0.3), as seenin Fig.1(d). These results clearly show the non-mixing
state, where the isotope density profiles strongly dependon the location of the isotope source.
As seen in figure 2, the isotope fraction of bulk species,nH /(nH + nD ) for H-beam and nD /(nH + nD ) for Dbeam, shows clear peaked profile when the isotope fraction of influx by wall recycling (indicated by arrows) islow. The isotope fraction at the LCFS (reﬀ /a99 =1) decreases as the isotope fraction of influx is decreased. The
hydrogen density is peaked in the plasma with hydrogen beam fueling and deuterium density is peaked in theplasma with deuterium beam fueling when the recyclingof the beam species is low enough. In contrast, when
the isotope fraction of beam species is close to 0.5 (thehydrogen influx is identical to the deuterium influx) the

isotope fraction profiles become flat. These results show
clearly that the peaking of the isotope density is due tothe fueling location rather than the transport diﬀerence
between deuterium and hydrogen. Non-mixing state canbe observed more clearly when the recycling of the beamfueling species is low enough (< 0.3).
The transition from non-mixing state to isotopemixing state is observed after H and D pellet injections.
The peak of the pellet deposition is reﬀ /a99 ∼ 0.9 inthese plasma conditions, which are evaluated experimentally from the increment of the electron density [15]. Because of the relatively shallow pellet deposition, pellet
injections make the electron density profile more hollow.
Figure 3 shows the change of radial profiles of H and
D density by H-pellet and D-pellet injection in the target plasma with H-beam fueling and with low hydrogen
recycling influx. After the H-pellet injection, the H density shows the significant increase, while the profile of D
density is almost unchanged except for near the plasma
periphery of reﬀ /a99 > 0.85. In contrast, the significant
increase of H density as well as of D density is observedin the case of D pellet injection. This result indicatesthe fast redistribution of H density profile due to theadditional fast transport process after the D pellet injection. Before the pellet injection the hydrogen density
profile is much more peaked than the deuterium density
profile due to the hydrogen beam fueling and deuterium
dominant recycling. After the pellet injection the hydrogen density profile becomes similar in shape to deuterium
density profile regardless of the species of pellet.
This change in the hydrogen and deuterium density

3xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

nH, nD (a.u.)nH/(nH+nD)!t = +14 ms(a) H-pelletHD

1.0 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx(a)isotope-mixing
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0.8
0.6
0.4
0.2

H-beamnH/(nH+nD)

nH, nD (a.u.)!t = +15 ms
D

H-beam
0.5 0.6!t = -5 ms H
0.7 0.8 0.9
reff/a99

1.0

FIG. 3: Radial profiles of hydrogen (H) and deuterium (D)density in the plasma with H-beam fueling before (∆t < 0)and after (∆t > 0) (a) hydrogen pellet (#142315) and (b)deuterium pellet (#142314). The peak of deposition of pellets
is located at reﬀ /a99 ∼ 0.9.

profile by the pellet injection demonstrates the changeof states from non-mixing to isotope-mixing as clearlyshown in the radial profile of isotope fraction in figure 4.
Before the pellet injection, the hydrogen fraction profile
is significantly peaked and the hydrogen fraction profile
becomes flat after the hydrogen pellet near the plasma
periphery. The flattening of hydrogen fraction profile isalso observed in the deuterium pellet, although the peaking of hydrogen fraction profile is expected by the deposition of deuterium pellet. Therefore, the flattening ofhydrogen fraction profile both for the hydrogen and thedeuterium pellet is a clear evidence for isotope-mixing. If
plasma is non-mixing state, the hydrogen fraction profile
should be more peaked after the deuterium pellet injection because of the edge pellet deposition. The transition
from non-mixing state to isotope-mixing state occurs in ashorter time (less than ∼ 15 ms), which implies the large
ion diﬀusion coeﬃcient in the isotope-mixing state.
Figure 5 shows how the turbulence changes before(t=3.73sec) and after (t=3.77sec) pellet injection, whichcorresponds to the non-mixing and isotope-mixing states,
respectively. Figure 5(a) shows the density fluctuation
spectrum integrated from edge to core along the laser
beam line of the central chord of phase contrast imaging(PCI) [16–18]. The wave number of the turbulence measured in this plasma is 0.2 - 0.4mm−1 . Both turbulence athigh frequency (high phase velocity) and low frequency

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H-pellet
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non-mixing
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0.0 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
1.0(b)
0.8 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx!t = -6 ms(b) D-pellet

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D-pellet
0.6 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
non-mixing
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0.4 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
0.2 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
isotope-mixing
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0.0 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
0.5
0.6 0.7
0.8
0.9 1.0
reff/a99

FIG. 4: Radial profiles of hydrogen isotope fraction,nH /(nH + nD ) before and after the (a) H-pellet (#142315)
and (b) D-pellet (#142314).

(low phase velocity) increase by an order of magnitude in
the isotope-mixing state. The radial profiles of poloidal
rotation velocity measured with charge exchange spectroscopy are also over plotted in Fig.5(b)(c). Turbulencemeasured with PCI has E × B drift, the propagation
direction with respect to the E × B drift is important
to determine the type of the turbulence. The contourof density fluctuation in the space of normalized minor
radius and phase velocity shows that there are two turbulence modes in the isotope-mixing state after the pellet
injection. One is the turbulence propagating with E × B
drift and the other is near edge turbulence propagatingin the ion diamagnetic direction. The increase of turbulence and appearance of ion diamagnetic propagating
turbulence is clearly observed associated with the transition from non-mixing and isotope-mixing states.
Figure 6(a)(b) shows the electron density, electron
temperature, and ion temperature profiles for non-mixing
and isotope-mixing states. Figure 6(c) shows the linear growth rates calculated with gyrokinetic simulation
code GKV [19] for TEM and ITG turbulence, basedon the radial profile of the density and the temperature measured. The non-mixing state is observed in the
low-density plasmas (ne ∼ 1.5 × 1019 m−3 ) with electron cyclotron heating (ECH) and neutral beam injection (NBI), where the beam fueling isotope species differ from the isotope species due to recycling. Power of
ECH is 2 MW and the power of NBI is 4.2 MW. The
nH /(nH + nD ) density profile is peaked for H beam fu-

44
ne (1019m-3)

isotope-mixing

10-5
10-6

non-mixing-7

vExB (km/s)

vExB (km/s)

10

0

6
4
2
0
-2
-4
-6
6
4
2
0
-2
-4
-6

100

f (kHz)(b) non-mixing

200

0

10

10-1

(c) isotope-mixing

100

10-1

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
reff/a99

FIG. 5: (a) Density fluctuation spectrum in the non-mixing
and isotope-mixing states in figure 4(a) and contour of density
fluctuation in the space of normalized minor radius and phasevelocity for (b) non-mixing state and (c) isotope-mixing state(#142315). Radial profiles of the projection of VE×B to PCI
observation plane are also plotted.

eling and D recycling wall conditions. After the pellet
injection, the isotope-mixing state is observed in higher
density plasmas (ne ∼ 2.5 × 1019 m−3 ). As seen in figure 6(b), electron temperature and its normalized gradient (Rax /LTe ) decreases significantly but ion temperature decreases slightly. The ratio of electron temperature
to ion temperature (Te /Ti ratio) also decreases. Here,Rax is a major radius of magnetic axis and LTe and LTi
are the inverse of logarithmic gradients, (∂lnTe /∂r)−1
and (∂lnTi /∂r)−1 , respectively. The Te /Ti ratio and thenormalized Te gradient (Rax /LTe ) at reﬀ /a99 = 0.8 decreases from 1.73 to 1.30 and from 19.3 to 11.6, respectively, while the normalized Ti gradient (Rax /LTi ) increases slightly from 11.1 to 13.8. The impact of thecollisionality in isotope plasmas and the sign of the density gradient on TEM and ITG mode is studied in LHD
using gyrokinetic simulation [20–22]. When the sign ofdensity gradient changes from negative (∂ne /∂r (0.8) <0 : peaked) to positive (∂ne /∂r (0.8) > 0 : hollow),
the growth rates of both TEM and ITG decrease. The
gyrokinetic simulation predicts that TEM propagatingin the electron diamagnetic direction is unstable for the
non-mixing state. However, the TEM is stabilized and
ITG mode propagating in the ion-diamagnetic direction(a)3

isotope-mixing

2
1
0
4

300
Te, Ti (keV)

(a)

10-4

! (kHz)amp (a.u.)

10-3

non-mixing(b)

non-mixing

3

isotope-mixing

2 Te
1 T

i

0
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
reff/a99
25
e-diamag(c)ion-diamag
20
non-mixing
isotope-mixing
15
10

TEM

ITG

5
0

-30 -20 -10 0 10
"r (kHz)

20

30

FIG. 6: Radial profile of (a) electron density and (b) electron
and ion temperature before pellet injection (non-mixing state)
and after pellet injection (isotope mixing state) and (c) the
linear growth rate at reﬀ /a99 = 0.8 for the non-mixing andisotope-mixing states calculated with GKV.

becomes unstable for the isotope-mixing state. The modetransition from TEM to ITG mode is due to the decreaseof Te /T i ratio, increase of collisionality (ne rise and Tedrop), and sign flip of the electron density gradient fromnegative (peaked profile) to positive (hollow profile).
Eﬀective diﬀusion coeﬃcient of particle transport,(GK)/(∂ns /∂r), for ion (s=i) and for electron
Ds = −Γs(s=e) are evaluated from the quasi-linear approximationin the gyrokinetic calculations. The ratio of ion diﬀusion to electron diﬀusion coeﬃcient, Di /De , is 0.4 forthe case of TEM dominant state before the pellet injection, while Di /De is 2.5 for the case of ITG-dominantstate after the pellet injection. When the electron particle diﬀusion is dominant De > Di , the radial profile ofeach isotope species can diﬀer depending on the source
location of each species (non-mixing state). In contrast,
when the ion particle diﬀusion is dominant Di > De ,the radial profile of each isotope species becomes identical due to the large diﬀusion (isotope-mixing state).
The electron and ion diﬀusion coeﬃcient evaluated fromthe quasi-linear gyrokinetic calculations well reproduces
the qualitative tendency of the non-mixing and isotopemixing states observed in the experiment. Although non-5linear gyrokinetic simulation for multiple ion species in
LHD plasmas is numerically challenging, the systematicinvestigations of correlations among the turbulent particle transport levels, its direction, and the driving microinstabilities are useful for more quantitative comparisonswith the above experimental results. Also, the gyrokinetic simulations for the transient phase, which will remain as future works, can clarify the threshold between
the isotope-mixing and the non-mixing states. The nonlinear turbulence simulations, which are important formaking quantitative comparisons, will be addressed infuture.
In conclusion, both the non-mixing and the isotopemixing states are observed in the hydrogen-deuterium
mixture plasma in LHD. The non-mixing state is observed in the slightly peaked density plasma with low
recycling beam fueled plasma and the isotope fraction
profiles depend on the location of the isotope source(core beam fueling or edge influx due to recycling). The
isotope-mixing state is observed in the hollow density
plasma after the pellet injection and the isotope fraction

profile becomes flat regardless of the location of the isotope source. This paper reports important findings on
non-mixing state between hydrogen and deuterium ionsin the H-D mixture plasma. This finding implies that
non-mixing state between deuterium and tritium ions
could be also achieved in the D-T mixture plasma in JET
and ITER depending on the turbulence state and gives
insight for controlling the isotope ratio profile in future
fusion devices.

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The authors wish to thank the LHD experiment groupfor the excellent support of this work. One of the authors (KI) acknowledges Dr. M. Yoshida (National Institutes for Quantum and Radiological Science and Technology; QST) for providing us with two spectrometers
for the bulk charge exchange spectroscopy. This work
is supported by the National Institute for Fusion Science grant administrative budgets (NIFS10ULHH021,
NIFS17KLPH030, NIFS18KNXN369) and JSPS KAKENHI Grant Numbers JP15H02336, JP16H02442,
JP17H01368, JP17K14899.