Plasma and Fusion Research: Regular Articles

Volume 16, 2405064 (2021)

Estimation of Anisotropic Neutron Emission Spectrum Using
Spatial Neutron Flux Profile Outside Vacuum Vessel∗)
Tomoki URAKAWA and Hideaki MATSUURA
Department of Applied Quantum Physics and Nuclear Engineering,
Kyushu University, 744 Motooka, Fukuoka 819-0395, Japan(Received 13 November 2020 / Accepted 9 March 2021)
It is known that emission spectrum of fusion products is anisotropically distorted from Gaussian distribution
when fuel ion velocity distribution function is anisotropic non-Maxwellian distribution. Previously, anisotropic
neutron emission has been measured in experiments with the Large Helical Device (LHD). In this study, as anapplication, a method for evaluating anisotropic neutron emission spectra by measuring the spatial profiles of theneutron flux is presented. Assuming beam-heated deuterium plasma in a JT-60SA class tokamak device, it was
confirmed that the eﬀect of neutron flux emission appears in the neutron flux spatial profile outside the vacuum
vessel when the energy region to be measured is set to the high energy side. In addition, it was shown that thecharacteristic change of the anisotropic emission spectrum is reflected in the spatial profile of the neutron flux.
Estimating the neutron anisotropic emission spectrum by this measurement method can lead to new proposals forfast ion diagnosis such as analysis of velocity distribution functions.
c 2021 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: anisotropic neutron emission spectrum, neutron measurement, spatial neutron flux profile
DOI: 10.1585/pfr.16.2405064

1. Introduction
When fast ions are produced by fusion reaction andexternal heating, energetic non-Maxwellian component isformed in the ion velocity distribution function [1–6]. Asa consequence of this non-Maxwellian component formation, the emission spectra of fusion-produced particles are
distorted from the Gaussian distributions to high (low) energy sides [7]. Previously, measurement of the distorted
neutron emission spectrum was used for fast ion diagnosis
aimed at understanding the energetic ion characteristics incore plasma. Hence, it reflects characteristic of the nonMaxwellian component on the fuel ion velocity distribution function. In JET, the distortion component of neutron
emission spectrum was measured to observe the fast ion
distribution in third harmonic ICRF heating on deuterium
beams, as well as α “knock-on” process in DT plasma, byusing high-resolution neutron spectroscopy [8–10].
The anisotropic non-Maxwellian component formedin the velocity distribution function leads to anisotropic
distortion in the emission spectrum of fusion products. In
the tangential deuteron-beam-injected DT plasma, the neutron emission spectrum is largely distorted from Gaussian
to the higher (lower) energy side toward (opposite to) the
NBI direction [11, 12]. In Ref. [13], the emission spectrum of neutrons produced by the D(d,n)3 He reactions in
the proton-beam-injected deuterium plasma has been analyzed. In such plasmas, the anisotropic non-Maxwellian
author’s e-mail: urakawa-0804@nucl.kyushu-u.ac.jp∗) This article is based on the presentation at the 29th International Toki
Conference on Plasma and Fusion Research (ITC29).

component (knock-on tail) formed on the deuteron velocity distribution function due to nuclear elastic scattering(NES) [14] with the proton beam. The NES eﬀect due toproton beam injection was actually observed using neutron
measurement in the large helical device (LHD)-based deuterium plasma experiments [15]. The anisotropic neutron
emission is also caused by the diﬀerential cross-section of
the D(d,n)3 He reaction [16]. Higher energy beam injection
induces the emission of neutrons produced by D(d,n)3 Hereaction toward NBI direction.
The large anisotropy of neutron emission caused wasactually observed in the LHD-based deuterium plasma experiments using tangential NBI. It was reported that theanisotropic neutron emission spectrum during NBI heating appears as a diﬀerence in the neutron flux measured
by neutron flux monitor which installed near the equatorial
port and center axis, or neutron activation system which
installed at outside port and lower vertical port [17, 18].
This diﬀerence was used to ascertain the neutron emission
anisotropy and was used for fast ion diagnostic. In addition
to the observation of anisotropic neutron emission on a fusion reactor scale, the above experiments in LHD suggestthat their anisotropy aﬀects the spatial distribution of theneutron flux. Therefore, there is a possibility to estimate
the anisotropic neutron emission spectrum in detail basedon the measurement the spatial neutron flux profile outside
the vacuum vessel. Especially in beam-injected deuterium
plasma experiments conducted in LHD and JT-60SA [19],this measurement can be realized, because neutron produced by D(d,n)3 He reaction provide suﬃcient anisotropy.

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c 2021 The Japan Society of Plasma
Science and Nuclear Fusion Research

Plasma and Fusion Research: Regular Articles

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This leads to the proposal a new fast ion diagnostic method
such as analysis of velocity distribution functions, which
will be a much easier method technically than that using
a neutron spectroscopy. It is first necessary to confirm
whether the neutron flux measured outside the vacuum vessel retains suﬃcient information to reproduce the neutron
emission spectrum in plasma.
In this study, a method for evaluating anisotropic neutron emission spectra by measuring the spatial profiles of
the neutron flux is presented. We evaluated the correlation between the anisotropic neutron emission spectra andthe spatial profiles of the neutron flux outside the vacuum vessel. As an example of anisotropic fast-ion generation, proton-beam-injected deuterium plasma was assumed and the neutrons produced by the D(d,n)3 He reaction were measured. The neutron transport model was simulated JT-60SA class tokamak device. Section 2 describes
the method of calculation and the model for transporting
neutrons. Results and discussion are shown in section 3.
Finally, the concluding remarks are given in Section 4.

Fig. 1 Eng emission direction dependence when κ = 0.1, 0.5, 1.0
and 2.0.

2. Analysis Model
2.1

Double diﬀerential neutron emission
spectrum

In this study, we simulated a distorted neutron emission spectrum from the Gaussian distribution by superimposing two Gaussian distribution. In addition, neutron produced by D(d,n)3 He fusion reaction is assumed. The double diﬀerential neutron emission spectrum is written as follows:⎡⎞⎛ ⎛⎜⎜⎜ ⎜⎜ E − E 0 ⎞⎟⎟2 ⎟⎟⎟d2 Nn
S ⎢⎢⎢⎢ 1 − αNG ⎟ ⎟⎜⎜⎟⎠ ⎟⎟⎠(E, θn ) = 1/2 ⎢⎢⎣exp ⎜⎜⎝− ⎜⎝dEdΩlab
ΔNG
ΔNG
n
⎞⎤
⎛ ⎛
⎜⎜⎜ ⎜⎜ E − E 0 ⎞⎟⎟2 ⎟⎟⎟⎥⎥⎥αG⎟⎟⎠ ⎟⎟⎠⎟⎥⎥⎦⎥ . (1)exp ⎜⎜⎝⎜− ⎜⎜⎝+ΔGΔGHere, ΔG(NG) is

ΔG(NG) =0of the E NG
at various κ. When κ is around 1.0, the direction
0
reflects the characteristics of tanh.
dependence of the E NG
On the other hand, when κ = 0.1, the average energy andthe emission direction are proportional.

2.2 Neutron transport calculation
04mn EG(NG)
TG(NG)

m3 He + mn

,

(2)

0
E NG
shows the average energy of Gaussian component introduced to simulate the distortion component0(θn ) =E NG

Fig. 2 The model used for MVP neutron transport calculations
assuming the JT60-SA class tokamak device.

−0.25tanh(κ(2θn − π))+ 2.52.
tanh(−κπ)(3)0Here, E NG
is a function of emission direction θn to simulate the anisotropy of the distortion component. Where
S is neutron total emission rate, α is intensity ratio of
Gauss component to total emission, EG0 is average energyof Gaussian component (2.45 MeV), mn(3 He) is neutron (3helium) mass and TG(NG) is temperature of Gauss (distortion) component. θn represents the angle between the direction of the emitted neutron and that of the toroidal axis
in the laboratory system. κ is a coeﬃcient that determines
the direction dependence of the average energy of distortion component. Figure 1 shows the direction dependence

Figure 2 shows the computational schema of the
3D-torus form with the neutron flux measurement region
which placed outside of vacuum vessel (VV). In this study,
the JT-60SA class tokamak device (major radius 2.97 m,
minor radius 1.16 m) is assumed. θwall represents poloidal
angle, which is the angle between the measurement regions
and the equatorial direction (See Fig. 2). In this study, themultiple torus form (minor radius 10 cm) neutron measurement regions were placed along the vacuum vessel andwere wrapped around the tokamak device. These measurement regions were arranged with an equal angle width(9◦ ) in the range of 0◦  θwall  90◦ , and evaluate thepoloidal angle dependence of the neutron flux. Table 1
shows the layer structure from the core plasma to the VV
and its thickness [19].
The neutron flux in the measurement regions is calculated using the Monte Carlo transport code MVP [20] withreference to the JENDL-4.0 [21] nuclear data library. The
neutron emission spectra were used as the point source in

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Table 1 the layer structure.

Fig. 4 Double diﬀerential neutron emission spectra at the θn =0◦ when T ng = 4.0, 10, 20 keV.

Fig. 5 Double diﬀerential neutron emission spectra at the θn =0◦ when T ng = 4.0, 10, 20 keV.

Fig. 3 Double diﬀerential neutron emission spectrum: (a) all
emission directions and (b) in the directions of θn = 0◦ ,30◦ , 45◦ and 180◦ .

the neutron transport calculations, which is placed in thecenter of plasma. For neutron sources, the angle and energy mesh sizes are Δθ = 3◦ , ΔE = 5 keV, respectively.

3. Result and Discussion
3.1

Anisotropic neutron emission spectrum

In this section, we describe the characteristics of the
double diﬀerential neutron emission spectrum which was
calculated using eq. (1). First, we reproduce the double
diﬀerential neutron emission spectrum (deuteron densitynd (0) = 1019 m−3 , electron temperature T e (0) = 2 keV,
proton beam energy and power E NBI = 200 keV, PNBI =33 MW) presented in Ref. [13]. We discuss the validityof the two Gauss distribution superposition models. In
Fig. 3, the double diﬀerential neutron emission spectrum
was shown as a function of both the energy and the direction ((a) all emission direction, (b) in the direction of
θn = 0◦ , 30◦ , 45◦ and 180◦ ). The solid lines in Fig. 3 (b)shows the neutron emission spectra which were calculatedusing eq. (1). The broken lines show the neutron emission

spectra presented in Ref. [13]. When reproducing, each parameter is as follow; S = 8.58 × 1011 m−3 s−1 , α = 0.972,
κ = 0.5, T g = 1.4 keV, T ng = 4.0 keV. In Fig. 3 (a), it canbe confirmed that the double diﬀerential neutron emission
spectrum reproduces the characteristics of it presented inRef. [13]. When comparing each solid line and broken line
in Fig. 3 (b), the energy regions of the distortion components are approximately the same in each emission direction. However, the strength of the distortion component at
θn = 180◦ is overestimated.
Figure 4 shows double diﬀerential neutron emission
spectra at θn = 0◦ when T ng = 4.0, 10, 20 keV. The distortion component spreads to the high energy side as T ng
increase. This is because the half width increases based oneq. (2). When T ng = 20.0 keV, the total number of neutrons
emitted with energies exceeding 2.7 MeV increases by afactor of 1.19 compared to the case where T ng = 4.0 keV.
Figure 5 shows the total number of neutrons emitted withenergies more than 2.7 MeV as a function of emission direction when T ng = 4, 10, 20 keV. The spread of the distortion component toward the high energy side increases
the emission rate of neutrons with energies more than 2.7
MeV in all emission direction. Therefore, the anisotropyof the neutron emission rate is relaxed as T ng increases.

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Fig. 6 Neutron flux spatial profile as a function of poloidal angle, which evaluated using anisotropic emission spectrum(T g = 1.4 keV, T ng = 4.0 keV, κ = 0.5 and α = 0.972 areassumed).

3.2

Anisotropic neutron emission spectra
estimation using the spatial neutron
flux profile outside vacuum vessel

In this section, we describe the characteristics of thespatial neutron flux profile outside the vacuum vessel whenusing the anisotropic neutron source. Figure 6 shows
the spatial neutron flux profile outside the vacuum vessel
which is evaluated using double diﬀerential neutron emission spectrum in Fig. 2 (T g = 1.4, T ng = 4.0, κ = 0.5 andα = 0.972). The neutron flux profile obtained by using theisotropic neutron source (mono energy, 2.45 MeV) is also
shown. For isotropic neutron source, the neutron flux ishighest around θwall = 0◦ and 90◦ . This is considered a geometric eﬀect. In the case of anisotropic neutron source,
the neutron flux profile diﬀers depending on the energy
range to be measured. When measuring a total neutron
flux or neutron flux with energies more than 1.0 MeV, theneutron flux profile is the same as that of isotropic neutron
emission. In other word, the eﬀect of anisotropic neutron
emission cannot be confirmed. On the other hand, whenmeasurement energy region is set to the higher energy side
(En > 2.4 or 2.7 MeV), the eﬀect of anisotropic neutron
emission on the neutron flux spatial profile appears. The
neutron flux near the equatorial port (θwall = 0◦ ) is about
50% larger than of that measured above the tokamak apex
(θwall = 90◦ ) due to anisotropic neutron emission whenmeasuring neutron flux with energies more than 2.7 MeV.
In addition, this confirmed that the emission direction distributions of neutron emission rate shown in Fig. 5 and thespatial neutron flux profile outside the vacuum vessel havethe same tendency. Therefore, the spatial neutron flux profile outside the vacuum vessel holds suﬃcient informationon the anisotropic neutron emission spectrum. However,the spatial neutron flux profile is less anisotropy than theneutron emission rate directional distribution because thesize of device is large enough to diﬀuse neutrons.
Figure 7 shows the spatial neutron flux profile whichis evaluated using the anisotropic emission spectra when
T ng = 4.0, 10, 20 keV. It is confirmed that the diﬀerence

Fig. 7 Neutron flux spatial profile evaluated using anisotropic
emission spectra when T ng = 4.0, 10, 20 keV.

in the anisotropic neutron emission spectrum appears as
the diﬀerence in the spatial neutron flux profile outside thevacuum vessel. When T ng increases, the eﬀect on the neutron flux profile is mitigated. This is because the emission
rate of high energy neutrons (En > 2.7 MeV) increased
in all emission direction in Fig. 5. This result indicatesthat diﬀerences in neutron flux profile can lead to the estimation of anisotropic neutron emission spectra. Whenthe spread of the distortion component can be measured, it
may lead to the diagnostic of the energy range of the nonMaxwellian component formed in the velocity distributionfunction.

4. Conclusion Remarks
In this study, we presented a method for evaluating
anisotropic neutron emission spectra by measuring the spatial profiles of the neutron flux. It was assumed thatthe neutrons were produced by the D(d,n)3 He reactionin proton-beam injected deuterium plasma. The neutrontransport model was simulated JT-60SA class tokamak device. We evaluated the correlation between the neutron
emission spectra and the spatial neutron flux profiles outside the vacuum vessel. Due to the anisotropic neutron
emission spectrum, the neutron flux on the tokamak equatorial plane is the highest, which has the attenuation that
decreases toward the apex. When the measurement energy region is fixed at above 2.7 MeV, the neutron flux on
the tokamak equatorial plane was about 50% higher thanthat at the torus apex and the attenuation distribution was
clearly appeared. It is observed that the neutron flux profilereflects the characteristic of anisotropic neutron emission
spectra. When the energy region of distortion component
expands, the diﬀerences also appeared in the neutron flux
profile. Therefore, it can be possible to estimate the characteristics of the anisotropic neutron emission spectra bymeasuring this profile, which can be used to analyze thevelocity distribution function of the fast ions.
In this study, we assumed proton-beam-injected
deuterium plasma, which formed the anisotropic non-

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Maxwellian component on the deuteron velocity distribution function due to nuclear elastic scattering with theproton beam. Since the eﬀect on the neutron flux spatial
distribution could be confirmed under the conditions, thismeasurement method would be more feasible when large
anisotropic neutron emission such as the deuteron-beaminjected deuterium plasma.
In this study, the double diﬀerential neutron emission
spectrum was simulated by superimposing two Gaussian
distributions. It is necessary to evaluate the neutron emission spectrum based on the velocity distribution functionof fuel ions. Moreover, in this study, we only confirm
the eﬀect of anisotropic neutron emission on the neutron
flux spatial profile. In the future, it will be necessary toconsider the selection of a neutron detector (e.g., radiation
foil with a threshold value) that can identify high-energy
neutrons suitable for this measurement method. Finally,
the actual fusion reactor is elliptical, and even when neutrons are emitted isotropically, the neutron wall load showsa distribution (specific to each tokamak device). Therefore,
in order to use this diagnostic method, a simulation is required in advance for each device.
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