RESEARCH ARTICLE | JUNE 06 2023

Optimization of a fast deuterium diagnostic method basedon visible energetic 3He spectroscopy for high electron
density plasmas 
K. Kimura ; H. Matsuura ; C. Itoh
T. Nishitani ; M. Isobe ; M. Osakabe; Y. Kawamoto; T. Oishi; M. Goto

; K. Ogawa;

Rev Sci Instrum 94, 063502 (2023)
https://doi.org/10.1063/5.0110088

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Review of
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scitation.org/journal/rsi

Optimization of a fast deuterium diagnostic
method based on visible energetic 3He
spectroscopy for high electron density plasmas
Cite as: Rev. Sci. Instrum. 94, 063502 (2023); doi: 10.1063/5.0110088
Submitted: 15 July 2022 • Accepted: 22 May 2023 •Published Online: 6 June 2023
H. Matsuura,1
C. Itoh,1
Y. Kawamoto,22,4M. Isobe,
and M. Osakabe2 , 4

T. Oishi,3 M. Goto,2 , 4

K. Ogawa,2 , 4

AFFILIATIONS
1

Department of Applied Quantum Physics and Nuclear Engineering, Kyushu University, 744 Motooka,
Fukuoka 819-0395, Japan
2
National Institute for Fusion Science, National Institutes of Natural Sciences, 322-6 Oroshi-cho, Toki 509-5292, Japan3
Department of Quantum Science and Energy Engineering, Tohoku University, 6-6-01-2 Aobayama, Sendai 980-8579, Japan
4
Department of Fusion Science, The Graduate University for Advanced Studies, SOKENDAI, 322-6 Oroshi-cho,
Toki 509-5292, Japan
5
Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japana)

Author to whom correspondence should be addressed: k_kimura@nucl.kyushu-u.ac.jp

ABSTRACTFast ions play a crucial role in plasma heating, and their behavior in the plasma must be accurately understood. A diagnostics method basedon charge exchange emission from the n = 4 − 3 transition (λ0 = 468.6 nm) of energetic 3 He produced by the deuteron–deuteron reaction has been proposed as a for fast deuterons with energies in the order of MeV. The proposed method has the following advantages:
No beam emission interferes with the spectra, the direction of the measuring line of sight, and the injection angle of the diagnostic beam
can be freely determined. In previous studies, due to competing bremsstrahlung, it was expected that the proposed method will not bepractical in the case of high electron density operation. This paper makes the proposed method available for measurement even at highelectron densities by optimizing the measurement line of sight direction and the diagnostic beam incidence angle. This allows an electron density five times larger than the range of applications shown in previous studies. This result will contribute to measure of DT alphain ITER.
Published under an exclusive license by AIP Publishing. https://doi.org/10.1063/5.0110088

I. INTRODUCTION
In high-temperature plasmas, fast ions are primarily responsible for plasma heating. Two factors determine the effectivenessof plasma heating: how long fast ions are confined in the plasmaand how much energy can be deposited into bulk ions. Several
experimental devices have been used to investigate the behavior offast ions in plasmas to date.1–4 Primarily, investigations have been
carried out to experimentally characterize the slowing down anddiffusion of fast ions in fusion plasma due to Coulomb collisions.5
Additionally, the interaction of fast ions with MHD instabilities
such as Alfven modes is an ongoing and active area of fast ion
research.6,7 In current fusion devices, the dominant populations ofRev. Sci. Instrum. 94, 063502 (2023); doi: 10.1063/5.0110088
Published under an exclusive license by AIP Publishing

fast ions result from external sources such as neutral beam injection(NBI) and ion cyclotron resonance frequency heating (ICRF) andare therefore the focus of experimental investigations. Furthermore,some large devices have also been used to studied the behavior of fastions (e.g., tritons, α-particles) produced by fusion reactions.8,9Many fast ion diagnostic methods have been proposed anddeveloped in parallel with the studies.10 The velocity distributionfunction must be measured to diagnose fast ions. Suppose the velocity distribution function of the ion does not follow the Maxwell
distribution. In that case, the macroscopic physical quantities likeion temperature and density are insufficient to predict ion behavior accurately. In measuring the velocity distribution function,acquiring information in two-dimensional (2D) velocity space is

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K. Kimura,1,a)T. Nishitani,5Review of
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Rev. Sci. Instrum. 94, 063502 (2023); doi: 10.1063/5.0110088
Published under an exclusive license by AIP Publishingscitation.org/journal/rsi

measurement. The measurement geometry is composed of the lineof sight (LOS) and the injection angle of the diagnostic beam. The
injection angle of the diagnostic beam was fixed to be completely
tangential in previous studies.27 Therefore, the effect of simultaneously varying the angle of the line of sight and the injection angleof the diagnostic beam on the emissivity of the visible spectra andits uncertainty is unclear. The uncertainty of 3 He visible spectra
may be reduced by changing the measurement geometry, and the
proposed method may be applicable under high electron density
operation.
The purpose of this paper is to make the proposed method
available for measurement even at high electron densities, where it
is currently unavailable. It is necessary to lower the visible spectra
uncertainty of fast 3 He2+ under high electron density operation. The
uncertainty reduction requires an increase in the emissivity of thevisible spectra of fast 3 He2+ . The following three points will be discussed in detail to apply the proposed method under high electron
density operation: (1) the relationship between the weight function28of the charge exchange recombination reaction for fast 3 He2+ andthe velocity distribution function of fast 3 He2+ ; (2) the spatial density
distribution of fast 3 He2+ in the plasma; (3) the spatial neutral particle density distribution in the neutral beam. These are closely related
to the measurement geometry and the direct factors that determine
the magnitude of emissivity.
II. ANALYSIS MODEL
The analysis model used in this study is adopted by the treatment of Ref. 27. Figure 1 shows the geometry of the NBI beamline
and line of sight. Two types of NBI are assumed to be used: adeuterium beam for heating and a hydrogen beam for diagnostics,
which is responsible for charge exchange reactions. In Fig. 1, only
the diagnostic (hydrogen) beam is plotted. We assumed that the NBI
path in plasma is the same as the width of 0.36 m. The angle thediagnostic beam makes with the vertical line of sight (#0) is φNBI .
For the hydrogen beam, φNBI is rotated counterclockwise from 90○
to 60○ in 10○ steps. φNBI is fixed at 90○ for the deuterium beam.
The lines of sight are assumed to spread radially with the first wallas the origin at 10○ intervals each. The definition of ζ is shown in
Fig. 2. ζ is the diagnostic beam with the tangent to flux surface at

FIG. 1. A schematic diagram of the beamline of diagnostic beam and line of sight.

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preferable, such as the velocity of fast ions and the pitch angle
relative to magnetic field lines. This is because the velocity distribution function of fast ions produced by external heating, such as
NBI or ICRF, is anisotropic in velocity space.11,12 Furthermore, if
the velocity distribution function of the fuel ions is anisotropic,
then the fusion products are also produced anisotropically.13 Diagnostic methods of confined fast ions can be classified into direct
and indirect measurements. Among the direct measurements, fast
ion D alpha (FIDA) has helped perform excellent measurements so
far.14,15 The main target of measurement is fast ions with energies of∼100 keV injected by the positive ion source NBI. However, devices
such as large helical device (LHD), JT-60SA, and ITER make use ofnegative ion source NBIs, which have beam energies on the order of
MeV.16–18 The beam energy of the negative ion source NBI reaches
the order of MeV. The feasibility study of FIDA measurement for
beam deuterons of negative ion source NBI in JT60-SA reported
a decrease in sensitivity and the measurable wavelength range due
to beam emission interference.19 One of the measurement methods that can focus on such fast ions is indirect measurement using
neutrons/γ-rays.20,21 If a nuclear reaction with a large cross sectionin the high-energy region is chosen, the sensitivity to fast ions in the
MeV region can be large. These methods are useful for measurementin the case of small tails.22,23 However, compared to spectroscopic
measurements, such as FIDA, its energy resolution is low due to theuse of radiation measuring instruments.
To solve this problem, we have proposed a fast deuteron
diagnostics method using charge exchange emission from then = 4 − 3 transition (λ0 = 468.6 nm) of fast 3 He produced bydeuteron–deuteron (DD) reaction in deuterium plasmas.24 Thismethod is based on information about the velocity distribution function of fast deuterons (size, shape, anisotropy, etc.) appearing in
the double-differential (per unit energy and unit solid angle) emission spectra of 3 He2+ . Although it would be ideal to obtain thevelocity distribution function of fast 3 He2+ directly, measuring theconfined fast ions directly in magnetized high-temperature plasma ischallenging. Therefore, the proposed method uses charge exchange
spectroscopy with a diagnostic beam like FIDA.25 In the MeV region,
the charge exchange cross section between hydrogen isotope atoms(mainly hydrogen and deuterium) and 3 He2+ is about four orders
larger than that between hydrogen isotope atoms and deuteron.26
Therefore, it is expected that the sensitivity to fast deuterons will
not be lower than FIDA. In previous experiments9 on α-particles
produced in the DT reaction, only the slowed-down component
down to 1 MeV or lower could be measured because the productionenergy of α-particles is too high. In the measurement proposed inthis paper, 3 He has an energy of about 2 MeV at most, so the possibility of measuring the full spectrum is higher than that of α-particles.
The feasibility of this method has been evaluated for ITER-like deuterium plasmas.24 Typical results of the analysis are shown below:
Under low electron density conditions, the change in shape of thevisible spectra of 3 He+ due to beam tail formation is sufficiently
large compared to the resolution of spectrometer; the ratio of theemissivity to the bremsstrahlung does not affect the uncertainty
much. In the previous study, the proposed method was only used
for low-density measurement due to bremsstrahlung competition.24
Although the previous study was not carried out and comparedwith experimental values, the intensity of bremsstrahlung is generally larger at high electron density operation, which hinders the

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l is the distance from the last closed flux surface. SNBI = PNBI /ENBI ,PNBI is the NBI power, ENBI is the NBI energy, ANBI is the crosssection of the beamline, vNBI is the velocity of the beam deuterium,and ne(d) is the electron (deuteron) density. σ e(d)i is the cross sectionof ionization by background electrons (deuterons) and σ CXDH is the
charge exchange cross section of the deuteron and hydrogen. Thesecross sections are adopted from the results of a previous study.32 The
signal-to-noise ratio (SNR) is calculated as follows:η ∫ SdλS=√,Nη(∫ Sdλ + ∫ Cdλ)the measurement point (charge exchange occurs). The steady-state
2D velocity distribution function f (v, r/a) of fast ions is evaluatedusing guiding-center orbit calculation code DELTA5D.29 Using theorbit calculation code, Sugiyama’s method is used to calculate thevelocity distribution function of the fast ion.30 The velocity distribution function is calculated by dividing r/a into 20 parts every 0.05.
The equilibrium magnetic field is calculated by VMEC code.31 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 follows:
T e (r/a) = T e0 × (1 − (r/a)2 )0.5 , T d (r/a) = T d0 × (1 − (r/a)2 )0.8 , andne(d) (r/a) = ne(d)0 × (1 − (r/a)2 )0.1 .
The weight function W(v) of the charge exchange reaction invelocity space is defined as follows:28
W(v) =(1)with vr = ∣v3He2+ − vH0 ∣. H0 denotes the neutral hydrogen, 3 He2+
denotes the full ionized helium-3, and σ CX_H_He is the charge
exchange reaction cross section of H0 and 3 He2+ . The neutral hydrogen distribution f H0 has mono-energy distribution. LOS geometry is
not taken into account in the calculation of the weight function. LOS
geometry is taken into account in the calculation of the visible light
spectrum. The weight function determines how susceptible a certain
region in velocity space is to charge exchange reactions. The spatial
distribution of the density of fast 3 He2+ in the plasma is calculated byintegrating the 2D velocity distribution function obtained for each
flux surface over the entire velocity and pitch. The spatial distribution of neutral hydrogen density in neutral beam nH0 (l) is calculated
as follows:
SNBI
exp (−ne σion l),
ANBI vNBI(2)⟨σei v⟩ nd ⟨σdi v⟩ + ⟨σCXDH v⟩
+
.
vNBI
ne
vNBI

(3)

nH0 (l) =where
σion =

Rev. Sci. Instrum. 94, 063502 (2023); doi: 10.1063/5.0110088
Published under an exclusive license by AIP Publishing

1.89 × 10−36 ne nd Zeff g ff
hc
dNbrem(λ, r/a) =exp (−
),
1/2
2
dλ
Te λ
Te λ Ebrem(5)with Ebrem = hc/λ. Zeff is the effective charge, g ff is the temperatureaveraged Gaunt factor, and h is the Planck constant. In this analysis,
we assumed that Zeff = 1.6 and g ff = 1.35T e 0.15 .36
III. RESULTS AND DISCUSSION1
f 0 (v 0 )σCX_H_He (vr )vr
nH0 ∬ H H× δ(v − v3 He2+ )dv3 He2+ dvH0 ,where S is the fast 3 He+ signal and C is the bremsstrahlung signal.
The effective optical throughput of the spectrometer η is defined asεt exp QT. ε is the etendue, t exp is the exposure time, Q is the quantum
efficiency, and T is the optical transmission. We assumed thatε = 1 mm2 sr, t exp = 0.1 s, Q = 90%, T = 5%, and wavelength range is
0.1 nm. We used this as a reference because a previous study of CXS
of DT reaction produced α-particles in ITER33 used a wavelength
bin of about 0.1 nm. The paper assumes a visible light spectroscopy
system for ITER, the details of which are given in Ref. 34. The
camera-lens spectrometer used in the LHD visible light spectrometersystem will increase the SNR because it increases the throughput of
the spectrometer.35 The spectrum of bremsstrahlung is evaluated as

When a deuterium beam is injected into a deuterium plasma,
the energy distribution function of the fast 3 He2+ producedby the DD reaction is determined. Figure 3 shows the steadystate 2D energy distribution functions of (a) beam deuteron at
r/a = 0, (b) beam deuteron at r/a = 0.2, (c) 3 He2+ at r/a = 0,
and (d) 3 He2+ at r/a = 0.2 As calculation conditions, we assumed
T e0 = 25 keV, T d0 = 20 keV, ne(d)0 = 2.0 × 1019 m−3 , ENBI = 1.0 MeV,PNBI = 33 MW (deuterium beam), PNBI = 16.5 MW (hydrogenbeam). In all magnetic flux surfaces, there is a large amount of 3 He2+
above 0.8 MeV in the direction of cos θtor = 1.0. θtor is the pitch
angle of the velocity vector to the magnetic axis. This is because theanisotropy of the 2D energy distribution function of beam deuteronis taken over by the 2D velocity distribution function of the 3 He2+
produced in the DD reaction. In this study, the deuterium beam
is injected tangentially into the plasma, forming a beam tail in the
direction of cos θtor = 1.0.
Using the above results, we calculated the visible spectra of3
He+ that would be measured. An example of the calculation
results is shown below. Figure 4(a) shows the visible spectrum ofenergetic 3 He+ and bremsstrahlung that would be measured inlines of sight #0 and #6 when the injection angle of the diagnostic beam φNBI is 90○ . As calculation conditions, we assumed
T e0 = 25 keV, T d0 = 20 keV, ne(d)0 = 2.0 × 1019 m−3 , ENBI = 1.0 MeV,PNBI = 33 MW (deuterium beam), PNBI = 16.5 MW (hydrogen

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FIG. 2. The definition of ζ.

(4)

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scitation.org/journal/rsibeam). The solid line indicates the injection of deuterium beam forheating and the broken line indicates non-injection. The expected
intensity of bremsstrahlung emission is represented by a dashedline. Figure 4(b) shows the normalized visible spectra of energetic
3
He, normalized by the respective peak values. In #0, the emissivity of the visible spectra of the energetic 3 He+ is 1500 times higher
when the deuterium beam is injected than when no deuterium beam
is injected. Not only that, but the full width at half the maximumof the visible spectra also increases. At the vertical line of sight(#0), the spectra are symmetrically spread around the central wavelength (λ0 = 468 nm). In contrast, the tangential line of sight (#6)
shows a large blueshift. These features are attributed to the beam tailbeing formed anisotropically on the deuteron velocity distributionfunction and the 3 He2+ emission spectra following an anisotropic
and non-Gaussian distribution. As shown in Fig. 4(a), the expected
intensity from visible 3 He emission is slightly higher than that of thebremsstrahlung intensity within the wavelength range 465–475 nm
on LOS#0. LOS#6 is difficult to measure unless the emissivity is
increased in some way. It can be inferred that the measurement
accuracy of the 3 He+ visible spectra becomes significantly smaller as
the electron density increases because the bremsstrahlung is higher.
No modulation of the diagnostic beam is assumed in this paper. In
the previous CXS of DT reaction produced α-particles in TFTR,9
the bremsstrahlung level was measured during the DD shot, andthe bremsstrahlung level during the DT shot was estimated. If thebremsstrahlung level is known, the 3 He spectrum can be extracted

Rev. Sci. Instrum. 94, 063502 (2023); doi: 10.1063/5.0110088
Published under an exclusive license by AIP Publishingby subtracting it from the measured spectrum. It may also be possible to measure the bremsstrahlung level by preparing a line of sightthat does not pass the diagnostic beam. In this paper, one of the ITER
heating beams is used as a diagnostic beam. Assuming that the diagnostic beam is injected only during the measurement (0.1 s in thispaper), proton dilution of 1.25 × 1016 m−3 occurs in the entire DD
plasma. This is 0.1% of the deuteron density and does not affect themeasurement. The above could be achieved with the ITER heating
beam without modulation. The visible spectrum emitted from thermalized 3 He+ with the ion temperature (20 keV) has a full widthat half maximum (FWHM) of about 3 nm. The FWHM of the visible spectrum from cold 3 He+ (20 eV), which will exist in large
quantities at the plasma edge, is ∼90 pm. In the case of fast 3 He+ ,the FWHM is about 15 nm at a vertical line of sight, which does
not significantly affect the measurement. In the case of a tangential line of sight, a large Doppler shift occurs, which can be further
avoided.
We will now discuss the three elements necessary to improvethe measurement accuracy of the visible spectra of 3 He+ underhigh electron density operation. First, we consider the relationship between the charge exchange recombination reaction weightfunction for fast 3 He2+ and the velocity distribution function of
fast 3 He2+ . This is important because it is related to the amountof 3 He+ produced by charge exchange. Figure 5 shows the weightfunction as 3 He2+ energy function for angle ζ of the diagnostic
beam with the tangent to flux surface at the point where charge

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FIG. 3. Steady-state 2D energy distribution functions of (a) beam deuteron at
r/a = 0, (b) beam deuteron at r/a = 0.2,(c) 3 He2+ at r/a = 0, and (d) 3 He2+ at
r/a = 0.2, when T e0 = 25 keV, T d0
= 20 keV, ne(d)0 = 2.0 × 1019 m−3 , E NBI= 1.0 MeV, PNBI = 33 MW (deuteriumbeam), PNBI = 16.5 MW (hydrogenbeam).

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exchange occurs. When ζ is small, the peak of the weight function appears with a small width in the direction of cos θtor = 1.
In this case, the direction of the H0 and 3 He2+ velocities coincide
around cos θtor = 1, and the relative energy is small. The peak of
the charge exchange reaction’s cross section exists where the relative energy is 100 keV, so the weight function becomes large.
Conversely, for cos θtor = −1, the weight function becomes significantly smaller due to the larger relative energy. When the ζ is 90○ ,a wide peak appears near cos θtor = 0. When ζ is small, the velocity
in the direction perpendicular to the magnetic field is small, and thedeviation between the direction of beam injection and the directionof the 3 He2+ velocity vector is small. Conversely, when ζ is large,
the velocity in the direction perpendicular to the magnetic field islarge. Hence, the direction of the beam injection rarely matches the
direction of the 3 He2+ velocity vector. The same reason applies tothe difference in the thickness of the peak widths. When the peakof the energy distribution of 3 He2+ coincides with the peak of theweight function in velocity space, many charge exchange reactions
occur. Comparing Figs. 3 and 5, the situation is closer to this when
ζ is small.

Rev. Sci. Instrum. 94, 063502 (2023); doi: 10.1063/5.0110088
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Furthermore, we investigated how ζ changes for each lineof sight with a change in injection angle of the diagnostic beam.
Figure 6 shows the relationship between the injection angle φNBI of
the diagnostic beam and ζ for each line of sight. For #0, ζ is equal
to φNBI . The vertical line of sight (#1, #2) has a smaller ζ if φNBI isgreater than 80○ . When φNBI is smaller than 80○ , ζ is negatively proportional to φNBI . If φNBI is greater than 80○ , the oblique line of sight(#3, #4) has a larger ζ than the vertical line of sight. However, if φNBI
is less than 80○ , ζ will be smaller than the vertical line of sight. Particularly, ζ of #4 has a minimum value around φNBI = 65○ and is suitable
for small injection angles. The tangential line of sight (#5, #6) has alarger ζ at any φNBI than the vertical or oblique line of sight. For #5,
since ζ dramatically increases when φNBI exceeds 70○ , it is preferable to use φNBI from 70○ to 80○ where the minimum value exists.
The minimum value of ζ of #6 exists when φNBI = 90○ , so it becomeslarger as φNBI decreases. If φNBI is less than 75○ , the diagnostic beamline does not intersect with the line of sight, making measurement
impossible.
Next, the spatial distribution of the density of fast 3 He2+ in theplasma is discussed. Figure 7 shows the spatial distribution of thedensity of fast 3 He2+ with the electron density as a parameter. As
calculation conditions, we assumed T e0 = 25 keV, T d0 = 20 keV,
ENBI = 1.0 MeV, PNBI = 33 MW (deuterium beam). The fast 3 He2+
is unevenly distributed in the plasma center, and the density in theplasma center is one to two orders of magnitude larger than the density around r/a = 0.5. This is because the deuterium beam is injectedin the tangential direction and passes through the plasma center
for a long time. The density of 3 He2+ decreases at the plasma center as the electron density increases. This is because the ionizationof beam deuterium is accelerated as the electron density increases.
Conversely, for density around r/a = 0.5, it is evident that it increases
with increasing electron density. Here, we consider the intersectionof the diagnostic beam and the line of sight. Figure 8 shows the position of the plasma at the intersection of the diagnostic beam and theline of sight as a function of the injection angle φNBI of the diagnostic beam. In the vertical line of sight (#1, #2), if φNBI is greaterthan 80○ , r/a is smaller than 0.1. Moreover, the emission intensity
can be increased above 80○ . As φNBI decreases to 60○ , r/a = 0.1 for#1 and r/a = 0.2 for #2. In this case, if ne(d)0 is 2.0 × 1019 m−3 , thefast 3 He2+ density decreases to 1/10 and 1/50 of the fast 3 He2+ density at the plasma center, respectively. In the oblique line of sight(#3, #4), if φNBI is 80○ , r/a becomes 0, and the emissivity can beincreased. If φNBI is 60○ and ne(d)0 is 2.0 × 1019 m−3 , r/a becomes
0.4, and the fast 3 He2+ density decreases to 1/140 compared to thedensity at the plasma center. In the tangential line of sight (#5), theline of sight passes near the center of the plasma at φNBI of 70○ . If
φNBI is 60○ and ne(d)0 is 2.0 × 1019 m−3 , r/a becomes 0.9, and the fast3
He2+ density becomes 1/3600 compared to the plasma center. In
the case of #6, the line of sight is only expected to be greater thanr/a = 0.4.
Finally, we discuss the density distribution of neutral hydrogen in the diagnostic beam. Figure 9 shows the density distributionof neutral hydrogen in the diagnostic hydrogen beam for (a) ne(d)0= 2.0 × 1019 m−3 , (b) ne(d)0 = 10 × 1019 m−3 . As calculation conditions, we assumed T e0 = 25 keV, T d0 = 20 keV, ENBI = 1.0 MeV,PNBI = 16.5 MW (hydrogen beam). To increase the emissivity,
the intersection point of the measurement line of sight and the
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FIG. 4. Predicted spectra [(a) line integral value and (b) normalized value] of 3 He+
visible and bremsstrahlung (line integral value) at vertical (#0) and tangential (#6)
line of sight. Solid lines correspond to 3 He+ visible spectra with deuterium beam
injection and broken lines correspond to 3 He+ visible spectra without deuterium
beam injection. Dashed lines represent bremsstrahlung.

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FIG. 5. The weight function for (a) ζ = 0○ ,(b) ζ = 30○ , (c) ζ = 60○ , (d) ζ = 90○ . ζ isthe angle of the diagnostic beam with thetangent to flux surface at the point wherecharge exchange is occurring.

only 1.2 times. In contrast, the difference in the high electron density
case is three times. It is necessary to have a large neutral hydrogendensity to increase the emissivity. For the same r/a (in particular,
plasma center where has high 3 He density), the density of neutralhydrogen will be larger if the side closer to the injection port of
the NBI is selected. This is an important factor in determining themeasurement geometry.
We have examined the geometry by focusing on three points.
We will discuss to what extent these factors affect emissivity andits uncertainty. Figure 10 shows the statistical uncertainty in thepeak value of the spectra of fast 3 He+ for different electron densities. The φNBI are (a) 90○ , (b) 80○ , (c) 70○ , and (d) 60○ , respectively.

FIG. 6. Relationship between the injection angle φNBI of the diagnostic beam andthe angle ζ to the tangent to flux surface at the point the point where charge
exchange is occurring for each line of sight.

FIG. 7. The spatial distribution of the density of fast 3 He2+ with the electron density
as a parameter when T e0 = 25 keV, T d0 = 20 keV, E NBI = 1.0 MeV, PNBI = 33 MW(deuterium beam).

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φNBI is 90○ , it passes through the plasma center only once. In othercases, it passes through the plasma center twice. When the φNBI
becomes small, the difference in neutral hydrogen density between
the two points becomes large because it takes a long distance to passthrough the plasma center again. This is not a problem for small
electron densities, but it significantly impacts the determination ofgeometry for high electron densities. Since high electron density
promotes ionization of neutral hydrogen, the difference in neutralhydrogen density between two points passing through the plasma
center becomes larger than in the case of low electron density. Comparing the low and high electron density cases at φNBI = 60○ , thedifference between the two points in the low electron density case is

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As calculation conditions, we assumed T e0 = 25 keV, T d0 = 20 keV,
ENBI = 1.0 MeV, PNBI = 16.5 MW (hydrogen beam). Statistical uncertainty is defined as the inverse of SNR. We assume that the limit ofapplication of the proposed method to correspond to an uncertainty
of 5% or less in emissivity of the peak value. The emissivity of thebremsstrahlung is proportional to the square of electron density, andthe emissivity of the visible spectra of 3 He+ decreases with increasing electron density. As a result, the uncertainty in visible spectraof 3 He+ increases monotonically with increasing electron density.
In the case of φNBI = 90○ and a vertical line of sight (#0, #1, #2),
the uncertainty is within 5% up to 8 × 1019 m−3 , which is good formeasurement. This is because the ζ is sufficiently small, and the lineof sight looks over the vicinity of the plasma center, as mentioned
earlier. As a result, the uncertainty is small. In the oblique line ofsight (#3, #4), good measurements can be expected from 3 × 1019 to
5 × 1019 m−3 . The uncertainty is a little more because the line ofsight passes a little farther from the plasma center than the verticalline of sight. In the tangential line of sight (#5, #6), the uncertainty
is larger because it has the opposite characteristics of the other linesof sight. #5 can only measure up to 2 × 1019 m−3 , and #6 can only bemeasured if the uncertainty is reduced in some way (e.g., by increasing the exposure time or increasing the wavelength bin). When φNBI
is 80○ , the trend is almost unchanged for #0. In the other vertical lines of sight (#1, 2), the allowed electron density is reduced to
5 × 1019 m−3 . This is because the intersections of these lines of sightand the diagnostic beam are moving away from the plasma centeras shown in Fig. 8. The uncertainty in #4 is significantly reduced in
the oblique line of sight. This is because the intersection of the lineof sight and the diagnostic beam is close to the plasma center, incontrast to the case of vertical lines of sight. Moreover, as shown in
Fig. 5, ζ is decreasing, and the weight function is increasing. Since
these values do not change as much in #3 as in #4, the uncertainty
is almost the same even if φNBI changes. A large decrease in uncertainty for the same reason as #4 is also seen in #5. As the electron
density increases, the uncertainty in #5 is smaller than in #3. Thisis due to the neutral hydrogen density. #5 differs from #3 in thatthe intersection of the line of sight and the diagnostic beam is closer
to the injection port of the diagnostic beam. The closer to the injection port, the smaller the decrease in neutral hydrogen density due toRev. Sci. Instrum. 94, 063502 (2023); doi: 10.1063/5.0110088
Published under an exclusive license by AIP Publishing

FIG. 9. The density distribution of neutral hydrogen in the diagnostic hydrogen beam for (a) ne(d)0 = 2.0 × 1019 m−3 , (b) ne(d)0 = 10 × 1019 m−3 when
T e0 = 25 keV, T d0 = 20 keV, E NBI = 1.0 MeV, PNBI = 16.5 MW.

increase in the electron density, as shown in Fig. 9. When φNBI is 70○ ,there is little change in uncertainty in the vertical line of sight (#0, #1,#2). The oblique line of sight (#3, #4) has a higher uncertainty thanwhen φNBI is 80○ . The intersection point of the oblique line of sightand the diagnostic beam is more sensitive to changes in φNBI thanthe vertical line of sight. This trend is reflected in the electron density
dependence of the uncertainty. The uncertainty in #5 is significantly
smaller than in the other lines of sight. This can be understoodfrom the three factors mentioned above. The first is the weight function, which can be discussed from the value of ζ shown in Fig. 6.
When φNBI is 70○ , and ζ is 20○ , the weight function does not havea significantly lower value. Next, we focus on the energetic 3 He2+
density. This is a direct determinant of the emissivity of 3 He2+ visible spectra. When φNBI is 70○ , the intersection of the line of sightand the diagnostic beam is r/a = 0, and the energetic 3 He2+ density
is very large. Finally, we focus on the neutral hydrogen density. Thisis also a direct determinant of the emissivity of 3 He2+ visible spectra, as is the energetic 3 He2+ density. As mentioned above, in #5,
the neutral hydrogen density is not sensitive to changes in the electron density. This is the most significant factor. When φNBI is 60○ ,the uncertainty increases for all lines of sight except #0. When φNBI
becomes 60○ , all the lines of sight except #0 do not pass near theplasma center, as shown in Fig. 8. Moreover, ζ is larger than that for

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FIG. 8. The position of plasma at the intersection of diagnostic beam and line ofsight as a function of the injection angle φNBI of the diagnostic beam.

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FIG. 10. Dependence of statistical uncertainty in the peak value of the visible
spectrum of fast 3 He+ on electron densities when T e0 = 25 keV, T d0 = 20 keV,E NBI = 1.0 MeV, PNBI = 33 MW (deuterium beam), PNBI = 16.5 MW (hydrogenbeam). The φNBI are (a) 90○ , (b) 80○ , (c) 70○ , and (d) 60○ , respectively.

φNBI = 70○ . These factors reduce the emissivity of the energetic 3 He+
and increase the uncertainty. Figure 11 shows the visible spectrumof energetic 3 He+ and bremsstrahlung that would be measured inlines of sight #5. As calculation conditions, we assumed φNBI is 90○ ,T e0 = 25 keV, T d0 = 20 keV, ne(d)0 = 1020 m−3 , ENBI = 1.0 MeV,PNBI = 33 MW (deuterium beam), PNBI = 16.5 MW (hydrogenbeam). The solid line indicates the injection of the deuterium beam
for heating. The expected intensity of bremsstrahlung emission isrepresented by a dashed line. The emissivity ratio of the spectrumof 3 He+ and bremsstrahlung calculated at this measurement geometry is comparable to the emissivity ratio at other measurement
geometries.
To summarize the results, the measurement geometry with adiagnostic beam injection angle of 70○ and a measurement line ofsight of #5 has the largest electron density independencies. For thisgeometry, (1) the value of the weight function is high, (2) the lineof sight passes through the plasma center where the 3 He density
is very high, and (3) the neutral hydrogen density is not sensitive
to changes in the electron density because the measurement pointis near NBI injection port. This means accurate measurement ispossible even under high electron density operation. The ability toperform measurements in ITER and DEMO reactors, where the electron density exceeds 1020 m−3 , will be a major difference from FIDA.
Note, however, that it is difficult to obtain the radial spatial profile ofthe beam deuteron. Furthermore, the time resolution can be further
improved under low electron density. The spatial profile of beam
deuteron changes as the incident angle of deuterium NBI changes,
and we expect that the unevenly distributed beam deuteron nearRev. Sci. Instrum. 94, 063502 (2023); doi: 10.1063/5.0110088
Published under an exclusive license by AIP Publishing

the center will be mitigated. Therefore, it may be possible to diagnose the spatial profile of beam deuteron, although the choice ofgeometry is necessary. The measurement of bremsstrahlung does
not necessarily have to be the same shot as the measurement of
3
He+ (including information on the velocity distribution functionof fast D), but multiple shots may be used. The bremsstrahlung
emissivity value with high accuracy will be obtained from the integrated value of these measurement data. Similarly, the measurementof 3 He+ will be possible with high accuracy by integrating multiple measurement data. If the uncertainty of the bremsstrahlung
measurements is small enough, it may be possible to extract theburied 3 He+ information. To obtain the 3 He+ spectrum from thebremsstrahlung (which also has a superimposed 3 He+ spectrum)by subtraction, the dynamic range of the instrument should befour digits.
IV. CONCLUSION
This paper shows how to improve the uncertainty of the 3 He
visible spectra under high electron density by varying the line of sightand the injection angle of the diagnostic beam. As a result, the proposed method can be applied to high electron densities such as ne =1020 m−3 in ITER and DEMO. The proposed method was previously
applicable only at low electron densities such as ne = 2 × 1019 m−3 .
This study has increased the applicability of the proposed methodby a factor of 5. We focused on the weight function of the charge
exchange reaction in velocity space and the fast 3 He2+ and neutralhydrogen density in real space. The diagnostic beam incidence angle
that optimizes the weight function is 80○ –90○ . The injection angle ofthe diagnostic beam that increases the fast 3 He2+ density in the lineof sight is 90○ in the vertical line of sight and 70○ in the tangential lineof sight. It is preferable to use the tangential line of sight rather thanthe vertical line of sight to maximize the neutral hydrogen density inthe line of sight. In the tangential line of sight, the neutral hydrogendensity is less likely to decrease as the electron density increases. For
various viewing geometries, the electron density dependence of the94, 063502-8

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FIG. 11. Predicted spectra of 3 He+ visible and bremsstrahlung at LOS#5 for φNBI
= 70○ , ne(d)0 = 1020 m−3 when T e0 = 25 keV, T d0 = 20 keV, E NBI = 1.0 MeV,PNBI = 16.5 MW. Solid lines are 3 He+ visible spectra with deuterium beam injection
and dashed lines are bremsstrahlung.

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uncertainty of the visible spectra of 3 He+ is compared. The electron
density dependence of the uncertainty was the smallest when theinjection angle of the diagnostic beam was 70○ and the measurement
line of sight was 50○ (#5).
What we have discussed in this paper is relevant not only to
3
He visible light spectra but also to other fast ions produced by
nuclear reaction, for example, DT alpha or DD triton diagnostics.
The discussion in this study can be used as a guide for determining the measurement geometry in these diagnostics. In particular,
it will contribute to improving the accuracy of charge exchange
spectroscopy measurements of DT alpha in ITER.

ACKNOWLEDGMENTS

AUTHOR DECLARATIONSConflict of Interest
The authors have no conflicts to disclose.
Author Contributions
K. Kimura: Conceptualization (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Writing – original draft (lead).
H. Matsuura: Conceptualization (equal); Investigation (equal);
Methodology (equal); Project administration (lead); Validation(equal); Writing – review & editing (equal). C. Itoh: Investigation (equal); Methodology (equal); Validation (equal); Writing –review & editing (equal). Y. Kawamoto: Conceptualization (equal);
Investigation (equal); Methodology (equal); Validation (equal);
Writing – review & editing (equal). T. Oishi: Validation (equal);
Writing – review & editing (equal). M. Goto: Validation (equal);
Writing – review & editing (equal). K. Ogawa: Validation (equal);
Writing – review & editing (equal). T. Nishitani: Validation (equal);
Writing – review & editing (equal). M. Isobe: Validation (equal);
Writing – review & editing (equal). M. Osakabe: Validation (equal);
Writing – review & editing (equal).
DATA AVAILABILITY
The data that support the findings of this study are available
from the corresponding author upon reasonable request.
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