LETTER

Effect of nuclear elastic scattering on the D(d,n)3He fusion reactivity
induced by energetic protons observed in the large helical device
To cite this article: H. Matsuura et al 2021 Nucl. Fusion 61 094001

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International Atomic Energy Agency

Nuclear Fusion

Nucl. Fusion 61 (2021) 094001 (5pp)

https://doi.org/10.1088/1741-4326/ac13e6

LetterEffect of nuclear elastic scattering on theD(d,n)3He fusion reactivity induced byenergetic protons observed in the large
helical device
H. Matsuura1,∗ , K. Kimura1 , D. Umezaki1 , K. Ogawa2,3 , M. Isobe2,3 ,T. Nishitani4 , Y. Kawamoto2 , T. Oishi2,3 , M. Goto2,3 , M. Osakabe2,3
and S. Sugiyama5
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, Japan
3
The Graduate University for Advanced Studies, SOKENDAI, 322-6 Oroshi-cho, Toki 509-5292, Japan
4
Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan
5
National Institutes for Quantum and Radiological Science and Technology, Rokkasho, Aomori
039-3212, Japan
E-mail: matsuura@kyudai.jp
Received 8 May 2021, revised 21 June 2021
Accepted for publication 13 July 2021
Published 30 July 2021
Abstract

The enhancement of the fusion reaction rate coefficient induced by energetic protons, which isone of the typical nuclear elastic scattering (NES) effects, was observed in the large helicaldevice (LHD) located at the National Institute for Fusion Science. An intense high purity
hydrogen beam (the atomic ratio of the contained deuterium was less than 1 ppm) with∼170 keV-energy and ∼10 MW-power was injected into a deuterium plasma with the electron
temperature ∼9 keV and density ∼1019 m−3 . After the hydrogen beam injection, the neutron
generation rate by the D(d,n)3He fusion reaction immediately increased, and an increment ofover one order of magnitude was observed, even though there was no meaningful ion
temperature variation. The reasons for the increment in the neutron generation rate are
discussed with reference to the Boltzmann–Fokker–Planck analysis along with LHD
experimental data. It is concluded that the increment was induced by the production ofenergetic deuterons due to the NES of energetic protons.
Keywords: large angle scattering, nuclear elastic scattering, fusion reaction rate coefficient,
DD neutrons, large helical device(Some figures may appear in colour only in the online journal)∗

Author to whom any correspondence should be addressed.

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Nucl. Fusion 61 (2021) 094001

H. Matsuura et al

In thermonuclear plasma, energetic ions exhibiting a nonMaxwellian velocity distribution are always present and, during their slowing-down process, these energetic fuel ionsreact with thermal ions. Since the fusion cross sections
strongly depend on the relative energy between the reactants,
the velocity-averaged reaction rate coefficient is influenced by
the shape of the fuel ion velocity distribution function. Nuclear
elastic scattering (NES) [1, 2] contributes to the decelerationof energetic ions. NES is a non-Coulombic scattering process
through which a large fraction of ion energy is transferred during a single scattering event. Because of the accumulation of
the discrete high energy transfer processes from energetic tothermal ions via NES, energetic ions are continuously produced via the recoil process of thermal fuel ions. The resulting
distortion of the distribution function induces a modificationin the velocity-averaged reaction rate coefficient.
It is well known that, when a fuel ion velocity distribution function is modified from being Maxwellian, the emission spectrum of the fusion products also changes its shapefrom that of a Gaussian distribution [3]. A non-Gaussianenergetic component in the T(d,n)α neutron emission spectrum was observed in JET [4, 5]. This component may
be created by the T(d,n)α reactions between the energetic
recoil components in both the deuteron and triton distribution functions due to NES. Recently, the NES effect on
the fast ion slowing-down process was also observed in
the large helical device (LHD), by measuring a delay inthe decay (attenuation) time of the D(d,n)3He neutron generation rate due to NES of beam-injected energetic protons by thermal deuterons [6]. Thus far, several NES effects
that will be important for the sustainment of nuclear burning have also been predicted. Several numerical estimations
have indicated that the transferred power ratio from energetic
to bulk ions can be enhanced due to NES depending on thefast ion energy and species compared with the case in which
only the energy transfer via Coulomb collisions is considered[7, 8]. The effect of NES on the fusion reaction rate coefficients has also been predicted [9]. Some of the NES effects, i.e.
modification of the neutron emission spectrum [4] and slowing down of energetic ions, have already been confirmed [6],however, the experimental confirmations for other phenomena
remain limited. This work reports an experiment to observe the
NES effect on the D(d,n)3He fusion reaction rate coefficientinduced by the externally injected protons. The experiment
was conducted in the LHD [10, 11] at the National Institutefor Fusion Science (NIFS).
Figure 1 depicts a schematic of the set of neutral beam injectors (NBIs) in the LHD. In the experiment, deuterium plasma
was formed, and the plasma was heated via the NBIs andelectron cyclotron resonance heating (ECH). Three negativehydrogen (H) beam (NBI#1, 2, and 3) and two positivedeuterium (D) beam (NBI#4 and 5) injectors were used.
Injectors NBI#1, 2, and 3 are directed tangentially toward
the axis of the toroidal magnetic field, with the negative-ion
sources providing fast hydrogens at an energy of 160–175 keVwith powers of ∼2.4 MW (NBI#1) and ∼3.8 MW (NBI#2, 3).
Injectors NBI#4 and 5 are perpendicular to the magnetic

Figure 1. Schematic of the NBI systems around the LHD.

axis, with positive-ion sources of deuterium at energy of∼60 keV and with powers of ∼8 and ∼3.6 MW, respectively.
For this experiment, high purity (enriched) H was prepared inthree injectors (NBI#1, 2, and 3), where the deuterium atomic
ratio contained in the H beam as an impurity was suppressed toless than 1 ppm. Throughout the experiment, a magnetic axis
(Rax ) of 3.6 m and a toroidal magnetic field (Bt ) of 2.75 T (inthe counter clockwise direction) were adopted.
In the experiment, after a period of 3.8 s from the beginning of the plasma discharge, three high purity H beams(NBI#1, 2, and 3) were injected into the deuterium plasma.
The total power of the three beams was ∼10 MW, and theaverage energy was ∼170 keV. To precisely measure the ion
temperature, a spectroscopic measurement method utilizing
charge exchange recombination was adopted by providing
electrons to thermal deuterons from the deuterium beam. For
this purpose, the D beam (NBI#5) was injected before andafter the H beam injections, i.e. 3.5 and 4.7 s from the beginning of the plasma discharge, with a short pulse (of 40 msduration) modulation. Figure 2 shows the typical waveform ofa deuterium plasma discharge, including the time evolutions of(a) the neutral beam heating powers for injectors NBI#1, 2, 3,
and 5, (b) the electron temperature at the radius r = 0 and a/2(a is a minor radius of the LHD plasma), (c) the electron density at the radius r = 0 and a/2, and (d) the neutron generation
rate. During the discharge, deuterium plasma was heated by the
ECH with 4.1 MW power; the electron temperature increases
T e (0) ≈ 9 keV at the equilibrium state. As a neutron detector, three 235 U fission chambers (FCs) alongside 10 B and 3 He
counters were prepared. One of the FCs and the 10 B counterare placed on the center axis, whereas the remaining two
FCs are placed on different sides of the LHD vacuum vesselalong with the 3 He counter (the sensitivity of the 3 He and 10 B
counters is several hundred and ∼60 times larger comparedwith the FC in the 1011 n/s range, respectively [11]). It was
found that, immediately after the high purity H beam injection
at 3.8 s, the neutron generation rate began to increase gradually, almost reaching an equilibrium value at ∼2 × 1012 s−1 ;an increment in the neutron generation rate of over one orderof magnitude was observed. While the neutron generation rate2

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three shots, i.e. #164867, #164868, and #164870. For comparison, we add the electron temperature and neutron production
rate from 3.6 to 4.8 s for #164874 (shown in figure 2) with thedotted lines in figures 3(b) and (d). Because there is no ECH,
the electron temperature is lower compared with figure 2, i.e.
T e (0) = 3–4 keV. The neutron generation rates measured by
the FC, 10 B, and 3 He counters are almost the same; however,the values obtained by the 3 He counters were adopted andindicated as the corresponding count rates were small. For all
shots shown in figure 3, the neutron generation rate is foundto be less than 1011 s−1 . In general, LHD plasma operation,
the neutron generation rate due to negative-deuterium (100%D) beam (NBI#1, 2, or 3) injection in low electron temperature plasma (T e (0) = ∼3 keV) is in the 0.5–1.0 × 1015 s−1
range. This implies that, even if a small number of deuterons
were accelerated and injected into the deuterium plasma
unintentionally with the high purity H beams (in figure 2),
the D/H atomic ratio would be 0.02% at most. To examine
the correlation between the neutron generation rate and electron temperature, Boltzmann–Fokker–Planck (BFP) simulations [12] were performed. In the BFP simulations we assumed
a uniform plasma, and the NES was assumed to be isotropic
in the center-of-mass frame [9, 12]. The temporal trends ofthe neutron generation rate by the D(d,n)3He reaction between
energetic and thermal deuterons after D or H beam injection
are shown in figure 4(a) for several electron temperatures. The
dotted curves indicate the results when only the 100% D beam
is injected into the deuterium plasma, whereas the solid curves
denote the case when only the high purity H beam is injected.
In all simulations, the D and H beams were assumed to haveenergy of 170 keV and a power of 10 MW. The BFP equations
for protons and deuterons were solved simultaneously considering the non-linear Coulomb scattering and NES processes[9, 12]. In the simulations, the ion temperature, electron density, and particle confinement time were assumed to be 2 keV,
1019 m−3 , and 0.5 s, respectively. When the high purity H
beam is injected, the proton distribution is formed gradually;
subsequently, because of the continuous energetic deuteronproductions via the NES induced by the energetic protons,
the energetic component, i.e. so called the knock-on tail, isformed in the deuteron velocity distribution function. Thus, it
can be noticed that the time required to reach the equilibrium
states is longer when high purity H beams are injected compared with the 100% D injections. The fast deuteron distribution functions at an equilibrium state are shown in figure 4(b)for the 100% D injections (dotted lines) and high purity H
beams are injected (solid lines). Each neutron generation rate
at 2 s shown in figure 4(a) was obtained using the distribution function in the same conditions shown in figure 4(b).
When the external D beam is adopted, the injection rate isalmost constant, whereas, when the H beam is injected, thedeuteron recoil rate itself, which corresponds to the beam
injection rate, is also influenced by the electron temperature.
This is because the formation process of the proton distribution function depends on the electron temperature strongly.
This is the reason why the neutron generation rate via NES
is more sensitive to the electron temperature in this case compared with the situation with external D beam injections. From

Figure 2. Time evolution of the deuterium plasma discharge (shotno. #164874). (a) Neutral beam heating powers for injectors NBI#1,
2, 3, and 5; (b) electron temperatures at r = 0 and a/2; (c) electron
density at r = 0 and a/2; (d) neutron generation rate detected by the
FC and 10 B counters.

increased, the electron density and the electron central temperature gradually decreased. The ion temperatures before andafter the H beam injection at the radius a/2 were obtained
as 2.11 and 2.37 keV, respectively. The ratio of the thermal D(d,n)3He reactivities between 2.11 and 2.37 keV, i.e.
DD(n)σvDD(n)2.37 keV /σv2.11 keV , was ∼1.6; thus, the neutron increment cannot be explained from the viewpoint of the thermal
fusion. Regarding the shape of the neutron increment curve(figure 2(d)), the fusion reaction seems to be induced by theenergetic ions.
Figure 3 shows the neutron generation rate due to H beam
injections in low electron temperature (without ECH) plasma.
The waveform of (a) the neutral beam heating powers forinjectors NBI#1, 2, or 3, (b) the electron temperatures at theradius r = 0, (c) the electron densities at the radius r =a/2, and (d) the neutron generation rates are presented for3

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H. Matsuura et al

Figure 4. Numerical BFP simulations for (a) the time evolution of

the neutron generation rate and (b) the equilibrium fast deuteron
distribution functions when 100% D and high purity H beams with170 keV energy and 10 MW power are injected for several electron
temperatures along with the D(d,n)3 He fusion cross section. In thesimulations, T i = 2 keV, ne = 1019 m−3 , and τ p = 0.5 s are assumed.

Figure 3. Time evolution of the deuterium plasma discharges

without ECH (shot no. #164867, #164868, and #164870).
(a) Neutral beam heating powers for injectors NBI#1, 2, 3; (b)electron temperatures at r = 0; (c) electron densities at r = a/2; (d)neutron generation rates detected by the 3 He counter.

degree of increase in the neutron generation rate becomeslarger by a factor of 20–50 compared with that illustrated infigure 4. The ion temperature before and after the high purity
H beam injection is 2.73 and 2.39 keV, respectively, and theratio of the thermal D(d,n)3He reactivities is ∼0.6. Figure 5(b)shows the increment in the neutron generation rate in an evenhigher electron density (2.4 × 1019 m−3 ) and lower electron
temperature (5.7 keV) plasma. In this case, only NBI#3 isinjected. The increment in the neutron generation rate is lessthan one order of magnitude. The ion temperature before andafter the high purity H beam injection is 1.53 and 1.42 keV,
respectively, and the ratio of the thermal D(d,n)3He reactivities is ∼0.7. In both cases, the reactivity enhancement canbe attributed to the energetic deuteron productions via the
NES caused by the energetic protons. Throughout the experiments, we measured the ion temperature at r/a = 0.5. This isbecause most of the D(d,n)3He neutrons are produced aroundthis region. Since a volume of layer between flux surfaces
decreases as approaching the magnetic axis, the ion temperature variation at the center plasma region would not be a crucial
factor in our experimental condition.
In this work, the NES effect on the D(d,n)3He reaction
rate coefficient was observed in the LHD. It was found

figure 4(a), it can be seen that the neutron generation rateincreases almost by a factor of two at most due to the electron
temperature increment from 3 to 9 keV; thus, the incrementin the neutron generation rate illustrated in figure 2 still cannot be explained through the small amount of D containment.
However, the increment in the neutron generation rate can bequantitatively explained by considering that the neutron generation is caused by the energetic recoil deuteron component
created by NES.
Similar neutron generations due to high purity H beam
injection have been observed in several plasma conditions. As
an example, figure 5(a) displays the increment in the numberof neutrons due to a H beam injection when plasma with alower electron density (0.8 × 1019 m−3 ) and a higher electron temperature (13.6 keV) is observed. As discussed infigure 4, the knock-on tail tends to grow in high electron temperature plasma. From figure 5(a), it can be seen that the4

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H. Matsuura et al

predict the NES effects induced by fusion-born energetic ionsin the future reactor, a further confirmation using such large
beam injection energies would be necessary.

Acknowledgments
The authors would like to thank the cooperative program of
NIFS20KLPH047 and the LHD experimental team for theircontribution. The first author is grateful to Emer. Professor Y.
Nakao for long years of discussion and encouragement.

ORCID iDs
H. Matsuura https://orcid.org/0000-0002-7498-4191
K. Kimura https://orcid.org/0000-0003-3198-042X
K. Ogawa https://orcid.org/0000-0003-4555-1837
M. Isobe https://orcid.org/0000-0002-3572-1882
T. Nishitani https://orcid.org/0000-0003-2254-3164
Y. Kawamoto https://orcid.org/0000-0002-6337-4080
T. Oishi https://orcid.org/0000-0002-1171-8603
M. Goto https://orcid.org/0000-0002-9160-682X
M. Osakabe https://orcid.org/0000-0001-5220-947X
S. Sugiyama https://orcid.org/0000-0002-0010-6310

References
Figure 5. Time evolution of the neutron generation rates (a) after

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NBI#3 is injected (shot no. #164891, time averaged electron density
ne = 2.4 × 1019 m−3 , and temperature T e (0) = 5.7 keV).

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that the degree of increment is consistent with BFP simulations [12]. In the experiment, we used the hydrogen beam(∼170 keV) to distinguish the recoil deuterons from beaminjected protons. In our LHD experimental condition, therecoil component is very small compared with the beam component [6]. Thus, if we had used a deuterium beam insteadof hydrogen beam, the recoil component would be buried
under the beam component (we could not observe the NES
effect). To observe the NES effect for deuterium beam (which
would be used in the future fusion reactor), an experimentusing much higher beam-injection energy is required. The
NES effect essentially becomes important not only for beaminjected ions but also for further energetic fusion-born ions. To

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