Plasma and Fusion Research: Regular Articles

Volume 18, 1403002 (2023)

Study on Fast Deuteron Diagnostics Method Using Fast 3He Visible
Spectra in the Large Helical Device Deuterium Plasma
Kento KIMURA, Hideaki MATSUURA, Chujo ITOH, Yasuko KAWAMOTO1) , Tetsutaro OISHI1,2) ,Motoshi GOTO1,2) , Kunihiro OGAWA1,2) , Takeo NISHITANI3) , Mitsutaka ISOBE1,2)
and Masaki OSAKABE1,2)
Department of Applied Quantum Physics and Nuclear Engineering, Kyushu University,
744 Motooka, Fukuoka 819-0395, Japan
1)
National Institute for Fusion Science, National Institutes of Natural Sciences,322-6 Oroshi-cho, Toki 509-5292, Japan2)
Department of Fusion Science, The Graduate University for Advanced Studies, SOKENDAI,
322-6 Oroshi-cho, Toki 509-5292, Japan
3)
Graduate School of Engineering, Nagoya University,
Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan(Received 1 July 2022 / Accepted 1 December 2022)
Fast ion diagnostic is one of the most crucial plasma diagnostics for nuclear fusion investigation. A new
diagnostic method for fast ions has been proposed using visible spectra of 3 He produced by a deuteron-deuteronreaction. This diagnostic method has a better energy resolution than methods using neutron/γ-ray and is superior
to conventional spectroscopy in measuring high energy (MeV order) ions. This diagnostic method has been
predicted using numerical analysis for ITER, but no verification experiments have been performed yet. In thisstudy, we examined the measurability of this diagnostic method in the large helical device (LHD) deuterium
plasma. Although very dependent on the measurement geometry and the spectrometer performance, it may bepossible to measure the fast 3 He visible spectrum.
c 2023 The Japan Society of Plasma Science and Nuclear Fusion Research⃝

Keywords: large helical device, deuterium plasma, velocity distribution function, charge-exchange spectroscopy,
visible light spectra
DOI: 10.1585/pfr.18.1403002

1. Introduction
Fast ion diagnostics are crucial in plasma diagnostics.
This is because fast ions are primarily the cause of plasma
heating. Fast ion diagnostics are significant for understanding and forecasting fast ion behavior. Measurement of thevelocity distribution function is crucial in fast ion diagnostics. Macroscopic quantities, including temperature anddensity, are derived by integrating the velocity distributionfunction. Furthermore, the magnitude and shape of the velocity distribution function are closely related to magnetohydrodynamics instability and fusion power.
There are various types of fast ion diagnostics [1].
An example is a use of fast ion D alpha (FIDA) for fast
deuterons in fast ion diagnostics using spectroscopy [2].
In this method, fast deuterons are neutralized by a neutral beam, and the Balmer-α emitted from the neutralized deuterons is measured. The Doppler broadening andDoppler shift of the spectra oﬀer information on the fast
deuterons’ velocity distribution function. For example,
FIDA measurements have been conducted at a large helical device (LHD) [3]. It has been noted that FIDA becomes
more challenging to measure as the fast deuteron’s energy
author’s e-mail: k_kimura@nucl.kyushu-u.ac.jp

increases [4]. Diagnostic methods using neutron/γ-ray energy spectra are eﬃcient for such fast deuterons [5, 6].
However, radiation spectrometers have a lower energy resolution than visible light spectrometers. To solve thesechallenges, a new fast ion diagnostic method using the visible light spectrum of fast 3 He produced by the deuterondeuteron (DD) reaction has been proposed [7, 8]. Since ituses the DD reaction, it is more sensitive to fast ions withenergies on the order of MeV than spectroscopy-based diagnostics, including FIDA. This is because the DD reaction’s cross-section is large in the high energy region. The
proposed method has superior energy resolution compared
to one of neutron/γ-ray. The neutron spectrometer measurements’ energy resolution is several hundred keV [5].
The proposed method has several good features, but thereis bremsstrahlung as a competing process. Thus, this diagnostic becomes challenging under conditions where theelectron density is high or where there is not a lot of fast3
He. It is necessary to increase the density of externallyinjected neutral particles or to design an observing line ofsight.
Numerical analysis of this diagnostic method has been
performed for ITER, but no empirical tests have been con-1403002-1

c 2023 The Japan Society of Plasma⃝
Science and Nuclear Fusion Research

Plasma and Fusion Research: Regular Articles

Volume 18, 1403002 (2023)

ducted, to the best of our knowledge. To confirm the eﬃciency of this diagnostic method, it is crucial to performdemonstration experiments using current equipment anddevice. To observe fast 3 He using spectroscopy, a large
amount of fast 3 He must be produced by the DD reaction.
Because the negative ion source neutral beam (NNB) is installed in the LHD, which has an energy of 180 keV, it is
the best option. Even under these conditions, the emissivity of the visible spectrum of fast 3 He is not expected to
exceed that of device noise, considering that device noiseis 100 times larger than bremsstrahlung. This is because
a specific percentage of the fast 3 He produced by the DD
reaction is lost from the LHD plasma. Thus, it is necessary to verify beforehand whether the visible spectrum of
fast 3 He can be measured with suﬃcient precision at LHD.
There are three possible sources of instrument noise: readout noise, shot noise, and dark shot noise. Increasing thesignal level by using a spectrometer with higher opticalthroughput can eﬀectively reduce the noise.
This study aims to assess the measurability of the validation experiment of the fast ion diagnostics using thevisible light spectrum of fast 3 He at LHD pure deuterium
plasma. Furthermore, an investigation of desirable experimental parameters for the measurement will be conductedusing numerical analysis.

this study focuses on the spectrum’s peak values, the discussion is unaﬀected. The expected 3 He+ visible spectrum
is obtained as a line-integrated value over the measurement
line of sight. The count rate is the photons’ number emitted from 3 He+ (or bremsstrahlung) multiplied by the spectrometer’s detection eﬃciency η. η (mm2 sr s nm) is defined as εQT ∆λ. ε is etendue, Q is quantum eﬃciency, T
is optical transmission, ∆λ is wavelength resolution. The
value of η is 3.8 × 10−13 , which is determined from experimental studies on spectroscopy in LHD [13]. The wavelength resolution ∆λ is 0.5 nm.
In the actual measurement, the visible spectrum of fast3
He+ is measured as a noisy spectrum. The number ofcount rates’ limit of detection (LOD) required for the signal in the visible light spectrum of fast 3 He+ to fall within
3σ is represented by nLOD . In this case, nLOD can be written as follows,
√

( )2
(
)




3
3
1 1 
3

nLOD = 
+
+
4n
+
,
(1)

b


2
t
t tb t
where, t(b) represents the measurement time of 3 He+ (background). In this study, t = tb is assumed. nb is the background (device noise) count rate.

3. Result and Discussion
2. Analysis ModelIn this analysis, two types of neutral beam are assumed to be used: NNB (deuterium beam) for heating
and PNB (hydrogen beam) for diagnostics. The 2D velocity distribution function f (v, r/a) of fast ions (i.e., beam
deuteron and fast 3 He2+ ) was assessed by guiding-center
orbit computation code DELTA5D [9]. v is the velocity vector of fast ion, r/a is normalized minor radius ofplasma. The velocity distribution function was computedby dividing r/a into twenty parts every 0.05. The equilibrium magnetic field is computed by VMEC code [10].
Profiles of electron temperature T e (r/a), deuteron temperature T d (r/a) and electron and deuteron density ne(d) (r/a)
are assumed as T e (r/a) = T e0 × (1 − (r/a)2 ), T d (r/a) =T d0 × (1 − (r/a)2 ) and ne(d) (r/a) = ne(d)0 × (1 − (r/a)8 ). Zeﬀ
is assumed to be 3. The NB deposition and neutral particle density in NB profiles are computed with the FIT3D
code [11].
The fast 3 He2+ emission spectrum produced by the
DD reaction is assessed according to Ref. [12]. Using theemission spectra of 3 He2+ , the orbit computation is conducted again to compute the 3 He2+ velocity distributionfunction. The energy and visible spectra of the chargeexchanged 3 He+ are obtained based on Ref. [7]. The center
wavelength λ0 of the visible light spectrum of fast 3 He+ is
468 nm.
In this study, the velocity distribution function of
3
He2+ is assumed to be isotropic. This model is unable
to determine the precise spectral shape. However, since

To verify the validity of the computational model inthis study, a comparison was made with previous investigations on FIDA. In that previous study, experimental
results of FIDA measurements at the LHD were reported.
Figure 1 shows the FIDA spectra computed by the modelin this study and the experimental values of the FIDA
spectra of previous investigations [3]. The model in thisstudy assumes that the 3 He+ velocity distribution function
is isotropic, so the Doppler shift does not occur. However,the spectra’s peak values are roughly consistent. The difference of a factor of several is also due to the isotropic
assumption.
Figure 2 shows the beam deuteron velocity distribution function for each r/a. As computation conditions, we
assumed, T e0 = 8 keV, T d0 = 1 keV, ne0 = nd0 = 1019 m−3 ,D
ENNB= 180 keV, PD
NNB = 9 MW, and Zeﬀ = 3. In thisfigure, the bulk component is added to the fast component
obtained from the orbit computation. Since the NNB is atangential injection, the beam tail is largest at the plasma
center. As the beam power is lowered (i.e., the number of
NNBs injected is reduced), the beam tail’s size is reduced
proportionally. Thus, only the 9 MW case is denoted here.
The emission spectrum of fast 3 He2+ produced by
the DD reaction was computed from the velocity distribution function of deuterons obtained using orbital computations. Figure 3 shows the fast 3 He2+ emission spectra for each r/a. A certain amount of fast 3 He2+ with energies >0.8 MeV, the production energy in the quiescentstate, is produced. Near the plasma center (r/a < 0.2), fast3
He2+ with energy of 1.5 MeV is produced in large quan-

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Fig. 1 The FIDA spectra calculated by the model in this paper
and the experimental values of the FIDA spectra of previous studies.

Fig. 2 The beam deuteron velocity distribution function for eachr/a when T e0 = 8 keV, T d0 = 1 keV, ne0 = nd0 = 1019 m−3 ,D= 180 keV, PDNNB = 9 MW, Zeﬀ = 3.
ENNB

tities. The emission spectrum of 3 He2+ for each r/a wasused as the initial condition for the test particles in the orbit
computation, and the 3 He2+ ’s velocity distribution function
was computed. Figure 4 shows the velocity distributionfunction of fast 3 He2+ for each r/a. Fast 3 He2+ with energies above 0.8 MeV existed in the plasma at about 1/10 of
the peak value. Unlike tritons that have similar mass, theFig. 3 The emission spectrum of fast 3 He2+ produced by the DD
reaction for each r/a when T e0 = 8 keV, T d0 = 1 keV,D
ne0 = nd0 = 1019 m−3 , ENNB
= 180 keV, PDNNB = 9 MW,
Zeﬀ = 3.

Fig. 4 The fast 3 He2+ velocity distribution function for each r/awhen T e0 = 8 keV, T d0 = 1 keV, ne0 = nd0 = 1019 m−3 ,D= 180 keV, PDNNB = 9 MW, Zeﬀ = 3.
ENNB

charge is 2, so confinement is better than for tritons. Thus,
measuring the visible spectra of fast 3 He+ at LHD is morefeasible than at triton. The fact that 3 He2+ above 1 MeV is
produced in large quantities at the plasma center is also afactor in better confinement. Since there is a 10-fold difference in the density of fast 3 He2+ between the plasma
center and r/a = 0.6, it is crucial to prepare a more central
line of sight. Furthermore, it is crucial to verify the density

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Fig. 5 The fast 3 He2+ density profile when T e0 = 8 keV, T d0 =D
1 keV, ne0 = nd0 = 1019 m−3 , ENNB
= 180 keV, Zeﬀ = 3.

of fast 3 He2+ in the plasma in more detail. Figure 5 thus
shows the fast 3 He2+ ’s density distribution with deuterium
beam power as a parameter. For PD
NNB = 3 MW, the fast3
He2+ ’s density surpasses 1014 m−3 at r/a < 0.5. However,at r/a > 0.5, the density of fast 3 He2+ is 1012 - 1013 m−3 .
3
2+
If PD
surpasses
NNB is increased, the density of fast He
14 −3
10 m at r/a = 0.6.
The 3 He2+ is recombined by PNB to become 3 He+ .
Then, photons are emitted, which are measured as visible spectra. We assumed, T e0 = 8 keV, T d0 = 1 keV,DH
ne0 = nd0 = 1019 m−3 , ENNB
= 180 keV, EPNB
= 40 keV,H
PPNB = 9 MW, and Zeﬀ = 3. Figure 6 shows 3 He+ ’s visible
spectra plotted with the NNB power as a parameter. Theorange line is the central wavelength, and the green line isthe bremsstrahlung. Device noise is diﬃcult to estimate accurately due to a combination of factors. The values of thedevice noise were determined with reference to the experimental values presented in the FIDA experiment [3]. The
noise line in the observed FIDA spectrum that appears to
be noise is 100 times larger than the estimated value of thebremsstrahlung. Therefore, the device noise was estimatedto be about 100 times higher than the bremsstrahlung. The
magnitude of the spectrum of 3 He+ is not proportional tothe beam power. This is due to the presence of some contribution from beam–beam reactions. The reaction rate ofa beam–beam reaction is proportional to the beam power’s
square. The larger contribution from the beam–beam reaction appears to be near the plasma center, where the beam
tail’s size is larger. The energy resolution is estimated fromthe calculation results in Fig. 6. For a wavelength bin of
0.01 nm, the energy resolution of the visible light spectrometer around λ = 468 nm is approximately 0.1 meV.
The measurement time needed for the verification experiment is calculated from the peak value of the obtained

Fig. 6 Visible spectra (solid line) from 3 He+ for NNB power
dependences when T e0 = 8 keV, T d0 = 1 keV, ne0 =DH
nd0 = 1019 m−3 , ENNB
= 180 keV, EPNB
= 40 keV,
PHPNB = 9 MW, Zeﬀ = 3.

visible spectrum of 3 He+ . For this purpose, we clarified
the relationship between the ratio of the fast 3 He+ signal
ns and the minimum count rate nLOD needed for the verification experiment and the measurement time. Figure 7 (a)shows the results with the detection eﬃciency as a parameter, while (b) shows the results with the NNB power as−13
a parameter. Under PD
NNB = 9 MW and η = 3.8 × 10
3(∆λ = 0.5 nm) [13], the He visible spectrum measurement
accuracy is 3σ after about 10 s of measurement time. Additionally, if the wavelength resolution is reduced to 1/10
to measure the visible spectral shape in detail, a measurement time of >100 seconds is required. Because these required measurement times are minimum, it is preferable totake ns /nLOD of at least 3 for actual measurements. Thisis because this ratio is for the spectrum’s peak value, anda longer measurement time would be required to measure
the entire spectrum. At ∆λ = 0.5 nm, a measurement timeof approximately 100 s is required. The required measurement time increases as the power of the NNBs diminishes (i.e., the number of injected NBs is reduced). AtPD
NNB = 6 MW, ns /nLOD = 1 requires 40 s and ns /nLOD = 3
requires 300 s. At 3 MW, ns /nLOD = 1 requires 300 s, so atleast two NBs (6 MW) are needed.
These results indicate that the measurement time forthe verification experiment requires tens to hundreds of
seconds. This is impossible to execute in a single shot since
the LHD’s discharge time is only a few seconds. However,this measurement time can be attained by adding up the results of numerous discharges. Thus, the number of shots
required is in the tens or hundreds. For this reason, it isfeasible to perform verification experiments at LHD.

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4. Conclusion
This study assessed the measurability of the validation experiment of the fast deuteron diagnostic method using the visible spectrum of fast 3 He produced by the DD
reaction at LHD. Under typical experimental conditions−13(PD), the device noise
NNB = 9 MW and η = 3.8 × 10
was assumed 100 times that of bremsstrahlung [3]. The
3
He visible spectrum’s measurement accuracy is <3σ after about 10 seconds of measurement time. Under similar−14
conditions (PD), if the
NNB = 9 MW and η = 3.8 × 10
wavelength bin is increased by a factor of 10, the required
measurement time is 100 s. Next, we assess the measurability using the deuterium beam’s power as a parameter.
The measurement time is 30 s when two of the NBIs are−13
injected (PD), and 300 s
NNB = 6 MW and η = 3.8 × 10
D
when only one of the NBIs is injected (PNNB = 3 MW andη = 3.8 × 10−13 ), respectively. The LHD discharge time isa few seconds, but this measurement time can be achievedby adding up the results of numerous discharges. These
results vary substantially depending on the measurement
geometry and the spectrometer performance.
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Fig. 7 The ratio of the fast 3 He+ signal ns and the minimum
count rate nLOD required for the verification experimentand the measurement time: (a) detection eﬃciency dependences, (b) NNB power dependences.

1403002-5