Plasma and Fusion Research: Regular Articles

Volume 18, 2402056 (2023)

Study on Knock-on Tail Formation in Deuteron Velocity
Distribution Function Due to ICRF-Heated Energetic Proton by
Using Neutron Diagnostics in the Large Helical Device∗)
Daisuke UMEZAKI, Hideaki MATSUURA, Kento KIMURA, Takahito FUKUDA,
Kunihiro OGAWA1,2) , Mitsutaka ISOBE1,2) , Shuji KAMIO3) ,Yasuko KAWAMOTO1) and Tetsutaro OISHI1,2)
Department of Applied Quantum Physics and Nuclear Engineering, Kyushu University, Fukuoka 819-0395, Japan
1)
National Institute for Fusion Science, National Institutes of Natural Sciences, Toki 509-5292, Japan
2)
The Graduate University for Advanced Studies, SOKENDAI, Toki 509-5292, Japan3)
Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA(Received 9 January 2023 / Accepted 16 May 2023)
In fusion plasmas, energetic ions play a crucial role in plasma heating. Nuclear elastic scattering (NES) is a
non-Coulombic scattering process that aﬀects the energy transport between energetic and bulk ions. In the Large
Helical Device (LHD), energetic protons produced by neutral beam injection (180 keV) formed a knock-on tail(KT) in deuterons via NES, and the DD neutron emission rate increased by one order of magnitude in relatively
high-electron-temperature plasmas. Furthermore, the eﬀect of NES among ion cyclotron range of frequency(ICRF) tail protons and bulk deuterons was investigated at high-electron-temperature plasmas in the LHD. It was
found that DD neutron emission rate was increased by a factor of 2 to 4. Changes in ion temperature and plasma
density cannot be the only reasons for the increase in DD neutron emission rate. The increment in DD neutron
emission rate was reproduced by the Fokker-Planck simulation using the Boltzmann collision integral for NES
by assuming the ICRF-tail protons having a high-temperature Maxwellian.
© 2023 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords: nuclear elastic scattering, NES eﬀect, LHD, knock-on tail, ICRF heating
DOI: 10.1585/pfr.18.2402056

1. Introduction
In fusion plasmas, energetic ions play a crucial rolein plasma heating. Nuclear elastic scattering (NES) [1, 2]
is a scattering process between ions with high relative energy. In NES, a relatively large fraction of energy is transferred in a single scattering event in contrast to Coulomb
scattering. Energetic ions produced through nuclear reactions, neutral beam (NB) injection, and others contribute toa formation of a knock-on tail (KT) in an ion velocity distribution function via NES. In an experiment of Joint European Torus (JET), a non-Gaussian energetic component
in the D-T neutron emission spectrum was observed [3].
In another JET experiment [4], a KT was measured using a neutral particle analyzer (NPA). The beam protons
formed the KT in deuteron velocity distribution function,
which resulted in a one order of magnitude increase in
the neutron emission rate of high-electron-temperature (8 10 keV) plasmas in the Large Helical Device (LHD) [5, 6].
The NES induced enhancement in the slowing-down timeof beam deuterons in the LHD [7]. In another JET experiment, energetic deuterium ﬂux was observed using an NPA
author’s e-mail: umezaki.daisuke.786@s.kyushu-u.ac.jp∗) This article is based on the presentation at the 31st International Toki
Conference on Plasma and Fusion Research (ITC31).

in the 3 He-minority heating deuterium plasma [8]. The
NES between bulk deuterons and ion cyclotron range of
frequency (ICRF)-tail 3 He ions was discussed in Ref. [8];however, the measured suprathermal tail of deuterium isan order of magnitude larger than that given by the simulation. The reason for this discrepancy has not been clariﬁed
yet. The eﬀect of deuterons KT formed by the NES with
ICRF-tail 3 He ions on the neutron emission spectrum wasalso investigated by numerical simulation [9].
In the LHD, the ICRF heating systems have been developed [10, 11]. The energy of beam ions is up to 180
keV and the energy of ICRF-tail protons can reach MeV
range [12]. In the previous ICRF heating deuterium plasma
experiment with a second harmonic scenario performedon the LHD [13], an extra increase in neutron emission
rate over the change in ion temperature has not been observed. A KT might not have been formed, because thecentral electron temperature was not suﬃciently increased,i.e., T e (0) ∼ 5 keV. As discussed in Ref. [6], an apparent
increase in neutron emission rate due to the formationof a KT requires a high-central-electron-temperature ∼8 10 keV. Hence, it is necessary to perform experiments ofhigh-electron-temperature plasmas to observe an increasein neutron emission rate due to a KT.

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In this research, we attempted to observe the KT effect on the D-D neutron emission rate by ICRF-tail protons
in high-electron-temperature LHD plasmas. The ICRF-tailproton spectrum was estimated using a single crystal diamond neutral particle analyzer (DNPA) [14]. The time
evolution of neutral emission rate was reproduced throughFokker-Planck (FP) simulation with the Boltzmann collision integral term for the NES. We also compared the FP
simulation results with Stix’s theoretical model. Furthermore, an ICRF tail in a deuteron velocity distribution function might have been created by second harmonic heating.
Hence it is necessary to validate that any increase in theneutron emission rate is indeed due to the KT by checking
the absorption power of the second harmonic heating. We
report the experimental and simulated results in this paper.

2. Experimental Apparatus
Figure 1 shows a schematic of NBs in LHD experiments reported in this paper. In the experiments, deuterium plasmas were initiated by electron cyclotron resonance heating (ECH). Negative-ion-source-based highpurity hydrogen beam NB#1 was tangentially injected into
the deuterium plasma. The beam energy and port throughpower of NB#1 were approximately 180 keV and 3.5 MW,
respectively. The deuteron ratio in NB#1 was suppressed
to be less than 1 ppm. Positive-ion-source-based deuterium
beam NB#5 was perpendicularly injected. The beam energy and port through power of NB#5 were about 50 keV
and 4.5 MW, respectively. NBs #2, #3, and #4 were notused. Two pairs of ICRF antennas were utilized. They
are the HAS antenna [15] and the FAIT antenna [16].
The ICRF heating frequency was 38.47 MHz. Other details were the same as in Ref. [12]. The neutron emission
rate was measured by 235 U ﬁssion chambers (FC) and 10 B

counters of the neutron ﬂux monitor [17]. In the experiments, the preset magnetic axis position Rax was 3.60 m,
and the toroidal magnetic ﬁeld strength BT was 2.75 T withcounterclockwise direction from the top view.
In the FP simulation [18], a uniform deuteron plasma
accompanied by the deuterium and hydrogen NBs was
assumed. As the background Maxwellian plasmas, deuterons, protons, and electrons were considered. In thisstudy, the KT formed in the deuteron velocity distributionfunction via the NES between bulk deuterons and ICRFtail protons. To assess the eﬀect of NES on the DD neutron
emission rate, we solved the deuteron velocity distributionfunction through FP simulation including the Boltzmann
collision integral term [6, 18–20]. The background particle’s density and temperature were given in reference to experimental values at r/a = 1/2 (a is averaged LHD plasma
minor radius). However, only the electron density ne wasmeasured, and the experimental deuteron density nD was
unknown. By assuming nD = X×ne and calculating the DD
neutron emission rate with consideration of plasma proﬁlesin the LHD, the neutron emission rate can be reproduced
when X = 0.4 - 0.5. Therefore, in this study, we assumed
nD = 0.5 × ne for simplicity. The NES cross section can beassumed an isotropic scattering in the center of mass system [21]. In this study, the ICRF-tail protons velocity distribution function was assumed as an isotropic Maxwellianof an eﬀective temperature T peﬀ . T peﬀ was changed as a parameter to reproduce the increase in experimental neutron
emission rate. The density of ICRF-tail protons was determined with reference to the experimental DNPA data
discussed in Sec. 3.2.
In several studies, proton density was estimated using
experimental Hα and Dα spectroscopic measurement dataDα /(Dα + Hα ) [13]. In this study, the ICRF-tail proton velocity distribution function was assumed by two methods.
1) First, the ICRF-tail proton velocity distribution function was assumed as a Maxwellian of eﬀective temperature T peﬀ , and its spectrum was estimated using the DNPA.
2) Second, the ICRF-tail protons density was estimated using Dα /(Dα +Hα ) data, and its temperature was determinedfrom Stix’s theory [22] as described below. The results ofthese method were compared. The Stix’s theoretical temperature T ptheo is written as follows [12, 22]:
pabs τ s,(1)
T ptheo =2n p
where pabs is the ICRF absorption power density, τ s =6.28 × 108 T e3/2 [eV]/(ne [cm−3 ] × ln Λ) is the Spitzer
slowing-down time, and n p is proton density. The resultsof the ﬁrst and second methods are described in Sections
3.2 and 3.3, respectively.

3. Result and Discussion
3.1
Fig. 1 Schematic view of the NBs and the location of DNPA
around the LHD.

Experimental results

Figure 2 shows the typical waveforms of a deuterium
plasma discharge, i.e., #172058, including the time evolu-

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Fig. 3 Relationship between the change ratio of the neutron
emission rate before and after the ICRF heating, and thechange ratio of the neutron emission rate calculated fromthe experimental ion temperature and electron density before and after the ICRF heating.

Fig. 2 Time evolutions of deuteron plasma discharge (shot no.
#172058). (a) Electron densities at r = 0 and r = a/2; (b)electron temperatures at r = 0 and r = a/2 ; (c) NB#5,
ECH and ICRF injection power; (d) neutron emission
rate; (e) ion temperature proﬁles at t ∼ 3.5 and t ∼ 5.1 s.

tion of, (a) electron density at radii r = 0, a/2, (b) electron
temperature at radii r = 0, a/2, (c) NB#5(D), ECH andICRF injection power, (d) neutral emission rate, and (e) ion

temperature proﬁles at t ∼ 3.5, 5.1 s. Deuteron plasma wasinitiated at 3.3 s. The ion temperature was measured by the
charge exchange recombination spectroscopy at 3.5 (5.1) s
before (after) the ICRF heating and after steady-state attainment of neutron emission rate. To clearly observe an
increase in the neutron emission rate due to the formationof KT, the ICRF heating was started at 4.5 s after the decayof the neutron emission rate caused by NB#5(D). In several discharges (such as Fig. 2), the neutron emission rateincreased in spite of the decrease or slight change in ion
temperature. In addition, the central electron temperaturewas ∼10 keV which is signiﬁcantly higher than in the previous experiments [13].
In Fig. 3, the change ratio of the neutron emission rate
before and after the ICRF heating, S nafter /S nbefore , is plottedon the vertical axis, while the change ratio of the neutron
emission rate calculated from the experimentally obtained
ion temperature and electron density before and after the
ICRF heating, n2e ⟨σv⟩after /n2e ⟨σv⟩before , is displayed on thehorizontal axis. The electron density ne and ion temperature used in the calculation are the experimental values at
r = a/2. The deuteron density is assumed to be equal to ne ,and ⟨σv⟩ is calculated from the measured ion temperature.
The shots shown in Fig. 3 are ion temperatures that did notchange signiﬁcantly before and after ICRF injection. After ICRF heating, the experimental neutron emission rateincreased by a factor of 2 - 4, and the increment was larger
than that of the change ratio calculated from the experimental ion temperature and plasma density. The ICRFtail protons knocked the bulk deuteron, and KT might havebeen formed in the deuteron velocity distribution function.

3.2

Measurement of ICRF-tail energetic
protons by DNPA

The number of ICRF-tail protons was estimated witha DNPA. Figure 4 shows the lines of sight of DNPA channels 1 and 7. As the energetic protons heated by the ICRF
wave were trapped in the helical ripple, channels 1 and 7,

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Fig. 6 DNPA count rates of NB + ICRF heating (red points);
only NB (black points) and the data produced by subtraction of only NB from NB + ICRF heating (blue points).

Fig. 4 Lines of sight of DNPA channels 1 and 7.

integrated counting rates of type-1, type-2, and subtracted
data. Within 90 - 180 keV, ICRF-tail protons might havebeen present in almost the same amount as NB#1(H). Over180 keV, ICRF-tail protons might have been present considerably more than the NB#1(H) alone. The calculated
NB#1(H) absorption power was approximately 1.8 MW.

3.3

Fig. 5 Typical waveform of the shot #172059 for DNPA measurement.

which measured the bottom and upper helical ripples, respectively. In this study, only the signals from channel 1
is utilized. Additionally, the eﬀect of neutron on DNPA
counts can be ignored [23] in this experiment. To ensure
suﬃcient NPA counts, we needed a neutral particle supply,
such as an NB, for a charge exchange with ions. In thisstudy, we compared two types of NPA counts: 1) the integrated counts of DNPA during NB#1(H) only, 2) the integrated counts of DNPA during NB#1(H) and ICRF heating. Figure 5 shows the typical waveform of shot #172059
for DNPA measurement. In #172059, NB#1(H) was injected after 3.8 s, and the ICRF wave was injected after
4.5 s. The DNPA counts at 3.8 - 4.3 (4.6 - 5.0) s were integrated as the only time zone for NB#1(H) (NB#1(H) +ICRF heating). The same data integration was performedin other similar shots to improve the DNPA measurement
accuracy.
We estimated the number of ICRF-tail protons by subtracting type-1 from type-2 data. Figure 6 shows the DNPA

FP and Boltzmann collision integral
simulation

The ICRF-tail proton velocity distribution function
for the Boltzmann collision integral was assumed as theMaxwellian of temperature T peﬀ , which intersected theNB#1(H)’s velocity distribution function with reference tothe DNPA data. The NB#1(H)’s velocity distribution function was calculated by the DELTA5D code [24], in thesame manner as that in Ref. [25], and its absorption power
was 1.8 MW. The time evolution of deuteron velocity distribution function was calculated via the FP simulation
with the Boltzmann collision integral using the assumed
ICRF-tail proton velocity distribution function. Moreover,
the time evolution of the neutron emission rate was also
calculated. To reproduce the experimental time evolutionof the neutron emission rate, the proton’s temperature T peﬀ
was changed as a parameter. Here we focused on #172058
as a typical example to reproduce the neutron emission
rate. Figure 7 shows the simulated and experimental time
evolutions of the neutron emission rate. The neutron emission rate was normalized at the ICRF heating injected timeof 4.4 s. When T peﬀ = 50 keV, time evolution of the neutron
emission rate was reproduced. Figure 8 show the deuteron,assumed ICRF-tail proton, and NB#1(H)’s proton velocity
distribution functions. The temperature T peﬀ = 50 keV obtained by the FP simulation was smaller than the eﬀective
ICRF-tail temperatures (70 - 250 keV) measured by NPAs
in other LHD experiments [26]. As a possible explanation,

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Fig. 9 Time evolution of Dα /(Dα + Hα ).

Fig. 7 Time evolution of experimental (black dots) and simulated neutron emission calculated by assuming T peﬀ = 45
(green line), 50 (red line), 55 (blue line) keV.

in order to reproduce the observed increase in experimental
neutron emission rate. This is consistent with the experimental eﬀective temperature that has been measured by an
NPA in previous studies [26]. The density calculated fromthe assumed ICRF-tail proton velocity distribution function was 2.38×1018 m−3 , which was larger than the density
estimated by Dα /(Dα + Hα ) data, and it is approximatelyn p = 6/25 × ne .

3.4

Fig. 8 Deuteron velocity distribution function (black line) calculated via the FP simulation, the assumed ICRF-tailproton velocity distribution function (red line), andNB#1(H)’s velocity distribution function calculated via
the Delta5d code.

our FP simulation assumed uniform plasmas. However, theICRF-tail ion velocity distribution function generally has
an anisotropy in a heating direction, and the KT may exhibit anisotropy in the same direction. The assumption of a
uniform plasma was expected to be a cause of overestimation of the KT and neutron emission rate increment, which
can lead to underestimation of the ICRF-tail proton’s temperature in this simulation. Furthermore, as described in
section 2, we assumed nD /ne as 0.5 for the FP simulation. If the plasma contains many impurities, the actual
nD /ne may be smaller than 0.5. In such low nD /ne plasmas, it is expected that T peﬀ should be higher than 50 keV

Estimation of theoretical ICRF-tail ion
temperature

To calculate the theoretical ICRF-tail ion temperature using Eq. (1), we estimated the proton density using
the Dα /(Dα + Hα ) data. Figure 9 shows the time evolution of Dα /(Dα + Hα ) in #172058. The ratio changed toaround 90%, and thus, the proton density was estimatedas n p = nD /9 = ne /18. The ICRF absorption powerpabs was assumed 75% with reference to Ref. [13] and[26]. The theoretical ICRF-tail proton temperature T ptheo
was approximately 1.2 MeV using the above discussed values. If the similar calculation of Sec. 3.2 was performed
with the proton Maxwellian, which has n p = ne /18 andT ptheo = 1.2 MeV, the increase in neutron emission rate wasapproximately 500 times, and the experimental increment
cannot be reproduced because the simpliﬁed theory ignores
ion loss and overestimates the number of energetic ions.
The deuteron 2nd harmonic heating absorption power
was also calculated through the same way in Ref. [26]. The
deuteron 2nd absorption power was less than 5% in thisexperimental condition.

4. Conclusions
The eﬀect of NES between ICRF-tail protons and bulk
deuterons on the D-D neutron emission rate in the LHD
was investigated. In the several high-electron-temperatureplasmas, the increase in neutron emission rate by a factor of 2 to 4 was observed after the ICRF proton heating,which cannot be explained by changes in ion temperatureand plasma density alone. The KT in the deuteron ve-

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locity distribution function may be formed via the NES
with the ICRF-tail energetic protons. Moreover, the number of ICRF-tail protons was estimated using the DNPA.
Within 90 - 180 keV, the ICRF-tail protons might have beenpresent in almost the same amount as NB#1(H). In over
180 keV, the ICRF-tail protons might have been present
considerably more than NB#1(H). The FP simulation using the Boltzmann collision integral for the NES was performed, and the time evolution of deuteron velocity distribution function was solved. The ICRF-tail protons velocity distribution function was assumed as a Maxwellian oftemperature T peﬀ with reference to the DNPA counts, andthe experimental neutron emission rate was reproduced by
T peﬀ = 50 keV. By this method, using the NES eﬀect on
the neutron emission rate, ICRF-tail proton velocity distribution function can be possibly estimated. Furthermore,
Stix’s theoretical temperature was calculated by inferring
the proton density from the Dα /(Dα + Hα ) measurements.
However, the FP simulation was not able to reproduce
the experimental neutron emission rate using Stix’s theoretical temperature and the proton density estimated by
Dα /(Dα + Hα ). This was because the simpliﬁed theory ignores particle loss and overestimates the number of energetic ions.
Future works should be aimed at validating the formation of KT by ICRF-tail energetic particles and the increase in neutron emission rate in high-ion-temperature(T i > 2 keV) plasmas, where the neutron emission rate
hardly changes with the ion temperature.

Acknowledgment
This work was supported by JST SPRING, Grant
Number JPMJSP2136. The authors would like to thankDr. K. Saito for discussing the ICRF absorption power and
Dr. D.A. Spong for allowing them to use his code.

Data availability statement
The LHD data can be accessed from the LHD
data repository at https://www-lhd.nifs.ac.jp/pub/Reposi
tory_en.html.
[1] J.J. Devany and M.L. Stein, Nucl. Sci. Eng. 46, 323 (1971).
[2] S.T. Perkins and D.E. Cullen, Nucl. Sci. Eng. 77, 20 (1981).
[3] J. Källne et al., Phys. Rev. Lett. 85, 3358 (1997).
[4] A.A. Korotkov et al., Phys. Plasmas 7, 957 (2000).
[5] H. Matsuura et al., Nucl. Fusion 61, 094001 (2021).
[6] H. Matsuura et al., Phys. Plasmas 29, 092502 (2022).
[7] H. Matsuura et al., Nucl. Fusion 60, 066007 (2020).
[8] F.S. Zaitsev et al., Plasma Phys. Control. Fusion 49, 1747
(2007).
[9] M. Nocente et al., Nucl. Fusion 53, 053010 (2013).
[10] T. Mutoh et al., Phys. Rev. Lett. 85, 4530 (2000).
[11] R. Kumazawa et al., Plasma Phys. Control. Fusion 45, 1037
(2003).
[12] K. Saito et al., Fusion Sci. Technol. 58, 515 (2010).
[13] R. Seki et al., Plasma Fusion Res. 15, 1202088 (2020).
[14] S. Kamio et al., J. Inst. 14, C08002 (2019).
[15] H. Kasahara et al., 38th EPS Conf. Plasma Physics 35, 897(2011).
[16] K. Saito et al., Fusion Eng. Des. 96-7, 583 (2015).
[17] M. Isobe et al., IEEE Trans. Plasma Sci. 46, 2050 (2018).
[18] M.M. Rosenbluth et al., Phys. Rev. 107, 1 (1957).
[19] H. Matsuura and Y. Nakao, Phys. Plasmas 13, 062507(2006).
[20] M. Nakamura et al., J. Phys. Soc. Jpn. 75, 024801 (2006).
[21] D.E. Cullen and S.T. Perkins, Nucl. Sci. Eng. 81, 75 (1982).
[22] T.H. Stix et al., Nucl. Fusion 15, 737 (1975).
[23] S. Kamio et al., Rev. Sci. Instrum. 91, 113304 (2020).
[24] D.A. Spong, Phys. Plasmas 18, 056109 (2011).
[25] S. Sugiyama et al., Plasma Phys. Control. Fusion 60,
105003 (2018).
[26] S. Kamio et al., Nucl. Fusion 62, 016004 (2022).

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