Plasma and Fusion Research: Regular Articles

Volume 14, 3402075 (2019)

Analysis of Energetic Particle Confinement in LHD Using Neutron
Measurement and Simulation Codes∗)Hideo NUGA1) , Ryosuke SEKI1,2) , Kunihiro OGAWA1,2) , Shuji KAMIO1) , Yutaka FUJIWARA1) ,Masaki OSAKABE1,2) , Mitsutaka ISOBE1,2) , Takeo NISHITANI1) , Masayuki YOKOYAMA1,2)and LHD Experiment Group
1)

National Institute for Fusion Science, National Institutes of Natural Sciences, Toki 509-5292, Japan
2)
SOKENDAI (The Graduate University for Advanced Studies), Toki 509-5292, Japan(Received 10 January 2019 / Accepted 7 March 2019)

The fast ion confinement time in the Large Helical Device (LHD) is investigated by using the neutron measurement and simulations. To estimate the fast ion confinement time, a series of short pulse neutral beam (NB)
injection experiments have been performed. Additionally, the NB heating simulation code, CONV_FIT3D, hasbeen extended to estimate the neutron emission rate in LHD. We estimate the fast ion confinement time from thediﬀerences between the measured and the simulated neutron decay times after the NB is turned oﬀ. It is foundthat the fast ion confinement time of three tangential NBs have similar values τc ∼ 0.5 sec and the confinement
time of the perpendicular NB is approximately τc ∼ 0.06 sec. Additionally, by using the confinement time andthe ion ratio data estimated from the simulation result, we can obtain a simulation result similar to the measureddata.
c 2019 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: fast ion confinement, neutron emission rate, LHD
DOI: 10.1585/pfr.14.3402075

1. Introduction
In magnetic confinement fusion devices, the plasma
heating is achieved by the kinetic energy transfer from thefast ions, which is generated by the neutral beam injection, radio frequency waves, and fusion reactions, to thebulk plasmas. Therefore, the high performance of the fastion confinement leads to the high eﬃciency of the plasma
heating. For this reason, the confinement of the fast ionshas been investigated in several magnetic confinement fusion devices and in simulations.
The deuterium plasma experiment in the Large Helical Device (LHD) started in March 2017 [1–4]. In general, deuterium fusion plasmas yield fast neutrons due tothe deuterium-deuterium (DD) fusion reaction. Because
the neutron measurement plays an important role in thestudies of fast ion confinement, LHD is equipped with theneutron diagnostics systems [5]. In the present fusion devices, such as LHD, the fusion reaction between thermal
ion and accelerated fast ion is dominant instead of the reaction between thermal ions. The DD fusion cross-section
monotonically increases with the increase of the fast ion
velocity within the range of the typical neutral beam (NB)
energy ( 200) in LHD. Therefore, the neutron emission
rate reflects the fast ion density profile and the fast ion velocity distribution. In other words, we can investigate theauthor’s e-mail: nuga.hideo@nifs.ac.jp∗) This article is based on the presentation at the 27th International Toki
Conference (ITC27) & the 13th Asia Pacific Plasma Theory Conference(APPTC2018).

fast ion transport and the slowing down from the neutron
measurement.
In this paper, we investigate the fast ion confinement
time in LHD by using the neutron measurement. Generally, the fast ion transport mechanism is very complex.
This is because the transport mechanisms consist of several physics, such as the classical Coulomb collisional diffusion, the neo-classical transport due to inhomogeneous
magnetic field, and the wave-induced transport. The accurate simulation including these phenomena requires immense computational resources. In this research, instead ofan accurate analysis, we estimate the fast ion confinement
time from the analysis of the experiment data. As noted
above, the neutron emission rate has information about thefast ion transport and the slowing down. Although the estimation of the fast ion transport is diﬃcult due to its complexity, the fast ion slowing down process can be estimatedby using several simulation codes. Therefore, we estimate
the fast ion confinement time from the diﬀerences between
the neutron measurement and the simulation result, which
ignores the fast ion transport during fast ion slowing down
process.
The rest of this paper consists of the following sections. The introduction of the experiment scenario and the
setup are provided in section 2. Analysis tools and simulation models used in this paper are explained in section 3. A
benchmark test is also provided in section 3. Experimentand analysis results are shown in section 4. The conclusion

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Plasma and Fusion Research: Regular Articles

Volume 14, 3402075 (2019)of this paper appears in section 5.

2. Experimental Setup
2.1

Scenario

To estimate the fast ion confinement time, a seriesof short pulse NB injection experiments have been performed. We have observed the fusion-born fast neutrons
and the decay time of the neutron emission rate after the
NBIs have been turned oﬀ. Because short pulse NBs haveinsignificant impact on the bulk plasma, fluctuations of theplasma parameters can be suppressed and fast deuterons
will slow down under constant conditions. Figure 1 shows
the typical waveforms of this experiment. Neutral beam
port-through power and injection energy in each beam,electron temperature and density on axis, and the neutron
emission rate are displayed. NB#1 to NB#4 are injectedwith the pulse width of 40 ms. In addition, plasmas areheated by 2.5 MW electron cyclotron heating system from3.25 sec to 5.25 sec in order to sustain the plasmas.
It can be considered that the decay of the neutron
emission rate after the NBIs are turned oﬀ comes from two
factors. One is the reduction of the fusion cross-section
due to the slowing down of the fast deuteron, and the otheris the reduction of the fast deuteron density due to the fast
deuteron transport. Therefore, the neutron decay time τncan be expressed as below:
−1
−1
τ−1
n = τ s + τc ,(1)

where τ s is the e-folding time of the neutron emission rate
owing to the fast deuteron slowing down and τc is the fastion confinement time. Conventionally, the classical neucltron decay time τcln is often used [6, 7] for τ s . τn is expressed as:
⎛ 3/2
3/2 ⎞
τ se ⎜⎜⎜⎜ E0 + EC ⎟⎟⎟⎟
ln
=
τcl
(2)
⎜⎝ 3/2⎟⎠ ,n
3
E1 + EC3/2
τ se =

3(2π)3/2 02 mD T e3/2
ne e4 m1/2
e ln Λ

,(3)

where E0 is the injection energy, EC is the critical energy
where the ion drag force is equal to the electron drag force,me and mD are the rest mass of electron and deuteron, andτ se is the Spitzer slowing down time on electron. E1 is the
kinetic energy satisfying the following relation:√
σ(E1 ) E1 1
(4)
√ = ,
e
σ(E0 ) E0
where σ indicates the fusion cross section. In the following analysis, the neutron decay time simulated by
CONV_FIT3D, which is introduced in section 3, is usedfor τ s . The simulated neutron decay time can take theplasma profiles into account.
In the present paper, we focus on the neutron decay
time instead of the neutron emission rate itself. This isbecause the absolute value of the neutron emission rate issensitive to uncertain parameters. In general, fusion reaction rate R can be described as:

(5)
R=
σ(Eab )v̄ fa (ua ) fb (ub )dua dub ,where Eab = 0.5ma mb /(ma + mb )v̄2 is the relative kinetic
energy, v̄ = |ua − ub | is the relative velocity, and subscripts aand b indicate the particle species, respectively. When the
beam-thermal fusion reaction is dominant, the expressionof the fusion reaction rate can be reduced as(6)Rbt = nD σvbt (T i , Ea ) fa (ua )dua ,where nD indicates the bulk deuteron density, T i is the ion
temperature, and Ea is the kinetic energy of species “a.”Although the fusion reaction rate is proportional to the bulk
deuteron density, it is diﬃcult to estimate the bulk deuterondensity profile accurately due to the lack of impurity measurements. Therefore, the estimation of the absolute valueof the neutron emission rate has an ambiguity. On the other
hand, the neutron decay time has fewer ambiguities. Since
fast deuterons slow down due to the fast deuteron-electron
Coulomb collision, the slowing down of fast deuterons is
not sensitive to the plasma eﬀective charge [8]. Becauseof these reasons, we planned to perform the short pulse
NB injection experiment and focused on the neutron decaytime.

2.2 Apparatus

Fig. 1 Typical waveform of this series of experiments(SN139591). Neutral beam port-through power in eachbeam, electron temperature and density on axis, and theneutron emission rate are displayed.

Figure 2 shows the top view of the NBI system in
LHD. LHD is equipped with three tangential NBIs (NB#1 NB#3) and two perpendicular NBIs (NB#4 and NB#5).
Beam ion species is deuteron. Typical value of beam injection energy and the port through power of NB#1 - NB#4 areillustrated in Fig. 2. In this paper, NB#5 is not used. In thefollowing experiments, the toroidal magnetic field strengthis |B| = 2.75 T, whose direction is counter-clockwise fromthe top view and the preset of the magnetic axis position is
Raxis = 3.6 m. Therefore, NB#1 and NB#3 are co-directionof the magnetic field and NB#2 is counter-direction. The

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Volume 14, 3402075 (2019)is taken as input. By accumulating the test ions until anarbitrary time t, the energy distribution at the time can beobtained roughly. The kinetic energy of test ions obeys
the fast ion slowing down equation based on the classicalCoulomb collision theory [14]:
E 1.5
E
dE
=
1 + c1.5 ,dt
τ se /2E√ 2/3
3 π
mb T e Z 2/3
,
Ec =
4
m eﬀ
m1/3
e
n j Z 2jZ=,m eﬀ
ne m jjFig. 2 Top view of NBI system in LHD is shown. NB#1 to
NB#3 are tangential NBIs and NB#4 and NB#5 are perpendicular NBIs. In the present paper, NB#5 is not injected.

averaged plasma minor radius is approximately 0.6 m. The
plasma temperature and density profiles have been measured by the Thomson scattering diagnostics and the neutron emission rate has been measured by Neutron Flux
Monitor [9].

3. Analysis Tools
In this paper, simulation analyses of the neutron emission rate consist of two steps. The first step is the fast ion
birth process and the second step is the fast ion slowing
down process, respectively. The first step is simulated by
FIT3D code [10–12]. FIT3D calculates the ionization of
NB particles and the radial redistribution of fast ions dueto the prompt orbit loss eﬀect. This code takes the threedimensional magnetic equilibrium, the plasma density andtemperature, the beam injection energy, and the beam portthrough power as input. The second step is simulated by
CONV_FIT3D code. CONV_FIT3D code calculates theslowing down of NB fast ions in each normalized minor
radius ρ. This code takes the fast ion birth profile, which is
calculated by FIT3D, and plasma temperature and density
as input. By using CONV_FIT3D, the energy distribution
of NB fast deuterons can be obtained. Originally, this code
has been developed to obtain NB heating profile. In thepresent paper, we have extended this code to calculate theneutron emission rate. The details of this code are provided
in section 3.1.
These two codes are components of the integrated
transport analysis suite, TASK3D-a [13].

(7)
(8)
(9)

where E is the kinetic energy of test ions, Ec is the criticalkinetic energy where ion drag force is equal to the electrondrag force, and the subscript “ j ” indicates ion species, respectively.
In this paper, CONV_FIT3D is extended to calculate
the neutron emission rate in LHD experiments. Within the
typical plasma parameters on LHD, the fusion reaction between NB fast deuteron and thermal deuteron is dominant.
Therefore we adopt the beam-thermal fusion cross-section
σvbt derived by Mikkelsen [15]. The first term of eq. (7)in Ref. [15] is implemented in CONV_FIT3D. Since thetypical plasma temperature in LHD is less than 10 keV, thereduced implementation is suﬃciently accurate. The fitting
coeﬃcients for the astrophysical S function used in σvbt
are chosen from Ref. [16].
There are two notifications regarding the simulation
model. At first, since CONV_FIT3D is a code to calculate the kinetic energy dissipation due to the fast ion
slowing down, the pitch angle scattering and distribution
are ignored. In general, this lack of information causes
under-estimation of the neutron emission rate. This is because this model can not consider the fusion reaction between non-thermal particles. For example, if there are twotangential NBs which have an opposite direction to eachother, the fusion reaction between two NB fast ions can
not be ignored. However, in the present experiment, the fusion reaction between non-thermal ions can be neglected.
This is because NBs are injected one by one, as shown in
Fig. 1. The second notification is that the Coulomb collision model used in eq. (7) assumes that the velocity of testions is suﬃciently faster than that of thermal ion velocity.
This assumption is broken in low energy region. Since thefusion cross-section in such a low energy region can be
negligible, however, the Coulomb collision model is valid
for the neutron estimation.

3.2 Benchmark of the neutron estimation
3.1

CONV_FIT3D

CONV_FIT3D calculates the time evolution of the
kinetic energy of the test ions, which are injected everyΔt ∼ 2 ms. The test ion has information regarding thenumber of NB ions absorbed during Δt. This information, which is obtained as the simulation result of FIT3D,

A benchmark test among a measurement in LHD
and three simulation codes has been performed to validate the neutron emission rate estimation implemented in
CONV_FIT3D. Here, FBURN [17] and TASK/FP [8] arechosen for benchmark codes. FBURN code has been developed for the time dependent analysis of DD and DT

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Volume 14, 3402075 (2019)neutron emission rate. The Coulomb collision term implemented in FBURN is based on the classical fast ion
slowing down theory, which is similar to CONV_FIT3D.
TASK/FP is a three-dimensional (two dimensional inmomentum space and one dimensional in radial direction) Fokker-Planck code. TASK/FP implements relativistic non-linear Coulomb collision model [18], whichis the more rigorous model than the model implemented
in CONV_FIT3D and FBURN. This Coulomb collisionmodel can include the Coulomb collision eﬀect between
non-thermal ions and this model does not assume that thefast ion velocity is suﬃciently faster than thermal ion velocity. In addition, TASK/FP can estimate the fusion reaction between non-thermal ions because TASK/FP can consider the pitch angle distribution.
Figure 3-(a) shows the waveform of NB port throughpower and Fig. 3-(b) shows the evolutions of measured andsimulated neutron emission rates. In Fig. 3-(b), blue solid,
green dotted, red dashed, and yellow dash-dotted curves
denote the simulation results of FBURN, CONV_FIT3D,
and two kinds of TASK/FP, respectively. The result of“TASK/FP full” uses eq. (5) for the fusion reaction rate.
On the contrary, the result of “TASK/FP bt” uses eq. (6)for the fusion reaction rate. The diﬀerence between these
two results comes from two contributions. One is the fusion reaction between thermal ions and the other is thefusion reaction between non-thermal ions. In this case,the fusion reaction rate between thermal ions is negligibly
small. Therefore, the diﬀerence between “TASK/FP full”
and “TASK/FP bt” indicates the contribution from the fusion reaction between non-thermal ions. This non-thermal
contribution can not be estimated by CONV_FIT3D and
FBURN. In this benchmark, it is assumed that the eﬀective
charge of the plasma is Zeﬀ = 1, the plasma is a fully ion-Fig. 3 The waveform of NB port through power and evolutionsof the measured and simulated neutron emission rates
are shown (SN140924). In figure (b), blue solid, green
dotted, red dashed, and yellow dash-dotted curves denote the simulation results of FBURN, CONV_FIT3D,
two kinds of TASK/FP, respectively. “TASK/FP full” includes beam-thermal and beam-beam fusion components
and “TASK/FP bt” includes only beam-thermal component.

ized pure deuteron plasma, and the ion temperature is equal
to the electron temperature T i = T e . The absolute values ofsimulated neutron emission rate is over-estimated becauseof these assumptions and the lack of the fast ion transport.
From Fig. 3-(b) it is found that the results of FBURN
and CONV_FIT3D have a good agreement. On the other
hand, the results of TASK/FP are slightly smaller thanthat of CONV_FIT3D. In this benchmark, CONV_FIT,FBURN and “TASK/FP bt” use the same model [15] of
the beam-thermal fusion cross section. Therefore, the differences of the neutron emission rate come from the differences of the fast deuteron energy distribution. It canbe considered that the diﬀerence of the Coulomb collisionmodel causes the the diﬀerence of the neutron estimation.

4. Analysis Results
Figure 4, which is the example of the analysis result,shows the NB port-through power and the time evolutionof the measured (solid curve) and simulated (dotted curve)
neutron emission rate. As noted in eq. (1), the simulated
neutron decay time is longer than the measured neutron
decay time due to the lack of the fast ion transport. Since
the diﬀerence of these two neutron decay times indicate
the fast ion confinement time, we investigated the relationof these two neutron decay times over 18 shots having different temperature and density. In these shots, the plasma
temperature on ρ = 0.5 has a range of 2 < T e [keV] <4.5 and the electron density on ρ = 0.5 has a range of
0.5 × 1019 < ne [m−3 ] < 2.5 × 1019 . Figure 5 shows therelation between measured and simulated neutron decay
times. The horizontal and vertical axes denote the simexp
and τn .
ulated and measured neutron decay times, τsim
n
exp
sim
These neutron decay times, τn and τn , are estimated bypeak
the weighted least-square fitting in S n exp(−t/τn ), which
is weighted by the variance of the measured neutron emispeaksion rate [5], where S n is the peak value of the neutron
emission rate. The y error-bars displayed in Fig. 5 indicate
exp
the standard deviation of τn . As the simulated neutron
decay time increases, the simulated neutron decay times
separate from the measured values. This is because in highτsimn region the contribution of the fast deuteron transport

Fig. 4 The waveform of NB port through power and evolutionsof the measured and simulated neutron emission rates areshown (SN139601).

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Fig. 5 The measured neutron decay times are plotted against
the simulated decay times. The simulated decay time isroughly proportional to T e1.5 n−1
e as shown in eq. (2).

to the neutron decay time can not be ignored. The auxiliary curves and the confinement time τc displayed in Fig. 5
are obtained by the weighted least-square method fitting in
expsimτn = τsimn τc /(τn + τc ). From Fig. 5, it is found that thefast ion confinement time of three tangential NBs (NB#1- #3) are longer than that of perpendicular beam (NB#4).
This is because the perpendicular NB fast ions have a poorconfinement due to the strong ripple-induced diﬀusion in
LHD [19].
Next, we investigate the relation of the two peakvalues of the measured and simulated neutron emission
peak
peak
rate, S n (exp) and S n (sim). For simplicity, we assume the plasma parameters and the fast ion birth rate,r f [m−3 s−1 ], are constant in time. The kinetic energyof the test fast ion is highest immediately after birth.
Therefore, the neutron emission rate, which is made by
the test fast ion, is also highest at the time. Fromeq. (6), the neutron emission rate generated by the test ion,
which has the injection energy E0 , can be expressed as
dVnD r f dt σvbt (E0 , T i ), where dV indicates the volume integration and the velocity distribution is assumed tobe the delta function. Since this value decays exponentiallyexpwith the time constant τn , the neutron emission rate at t0 ,at t becomeswhich is yielded by the test fast ion injectedexp
dVnD r f dt σvbt (E0 , T i ) exp[(t0 −t)/τn ]. Therefore, thepeak
peak value S n (exp) can be expressed as t0
t0 − tpeak
S n (exp) = Cexp
exp simdt,
τn τc /(τsim
0n + τc )(10)Cexp ≡
nD r f σvbt (E0 , T i )dV,
(11)
where t0 indicate the duration of the short pulse NB injection. In the present case, t0 = 0.04 sec.
peak
Similarly, simulated peak value S n (sim) can be expressed as: t0
t0 − tpeak
exp sim dt,
S n (sim) = Csim
(12)
τn
0

ne r f σvbt (E0 , T i )dV,
(13)
Csim ≡
where the electron density ne appears instead of theFig. 6 The measured peak value of the neutron emission rate
S npeak (exp) is plotted against F S npeak (sim).

Fig. 7 Evolutions of the measured and simulated neutron emission rates are shown. Simulation assumes nD /ne = 0.5,
nHe /ne = 0.056, and nC /ne = 0.065. In addition, three
tangential NBs decay with τc = 0.5 sec and the perpendicular NB decays with τc = 0.06 sec.

deuteron density nD because of the assumption of the pureD plasma. With the assumption that the deuteron density
ratio to the electron density is uniform, from eqs. (10) and(13) the ratio of two peak values have the following relation:
peak

Sn

(exp)

peak
S n (sim)

F ≡

=

nD
F,
ne

sim
1 − exp(−t0 /[τsimτcn τc /(τn + τc )]).
τsim
1 − exp(−t0 /τsimn + τc
n )
(14)
peak

Figure 6 shows the relation between S n (exp) andpeak
The horizontal axis denotes F S n (sim) andpeak
the vertical axis denotes S n (exp). From eq. (14), thegradient of the fitting line, which is shown in Fig. 6, indicates nD /ne . The measured value of H-He ratio is approximately (nH + nD )/(nH + nD + nHe ) ∼ 0.9. Here, it
is assumed that there are only two impurities, 42 He and
12
6 C, there are no protons, and that nD /(nD + nHe ) = 0.9.
From these assumptions and nD /ne = 0.5, we can estimate
nHe /ne ∼ 0.056, nC /ne ∼ 0.065, and Zeﬀ ∼ 3.1. Since
the typical value of Zeﬀ in LHD plasmas (ne ∼ 1019 m−3 )measured by the extreme ultraviolet (EUV) spectrometer[20, 21] is Zeﬀ ∼ 2 − 4, it can be considered that the estimation of Zeﬀ is valid.
By using these ion ratios, the neutron emission rate is
re-calculated by CONV_FIT3D.
Figure 7 shows the evolutions of the measured andpeak
S n (sim).

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simulated neutron emission rates. Solid and dotted curvesindicate the experiment and the simulated neutron emission rate. Simulation assumes nD /ne = 0.5, nHe /ne =0.056, and nC /ne = 0.065 (Zeﬀ ∼ 3.1). Additionally, fastions from three tangential NBs decay with time constantτc = 0.5 sec and the perpendicular NB decays with τc =0.06 sec. With these assumptions, we can obtain a consistent result with the experiment result. It is noted that since
the ion ratios are not always constant in this series of experiments, an accurate prediction can not be obtained bythis estimation.

5. Conclusion
In this paper, a series of experiments and simulation
analyses have been performed to investigate the confinement time of NB fast ions in LHD. We observed the neutron emission rate itself and the decay time of the neutron
emission rate, which is generated by DD fusion reaction,in the short-pulse NB injection experiments. In addition,
to analyze the LHD experiment data, CONV_FIT3D code,
which is a NB heating component of TASK3D-a, has been
extended. In LHD, since the beam-thermal fusion reaction
is dominant, CONV_FIT3D code implements the beamthermal fusion cross-section derived by Mikkelsen [15].
The validity of the simulation result of the neutron estimation has been checked through a benchmark test withFBURN [17] code and TASK/FP [8].
The decay of the neutron emission rate after the NB
is turned oﬀ comes from two physics factors. One is the
reduction of the DD fusion cross-section due to the slowing
down of the NB fast ions. The other is the reduction of
the fast deuteron density due to the fast deuteron transport.
CONV_FIT3D, which is based on the classical Coulomb
collision theory, can only describe the contribution of thefast ion slowing down. Therefore, the diﬀerences between
measured and simulated neutron decay time indicate thefast ion confinement time as shown in eq. (1).
Figure 5 shows the relation between the measured
and the simulated neutron decay times. Owing to the fast
deuteron transport, the simulated neutron decay times separate from the measured values as the fast deuteron slowing down time increases. From these data, the fast deuteronconfinement time in each beam can be roughly estimated asshown in Fig. 5. Additionally, from the measured and simulated peak values of the neutron emission rate, ion density ratio can be roughly estimated as shown in eq. (14).
Finally, by using the estimated fast ion confinement timeand ion density ratio, we can obtain a simulation result of
the neutron emission rate similar to the measured emission

rate as shown in Fig. 7. It is noted that this estimation includes the assumption that the deuteron density ratio is thesame in each shot.
In this paper, the results for single magnetic configuration are shown. Through analyses with several magnetic
configurations, the magnetic configuration dependence ofthe fast ion confinement time will be investigated in future
works.

Acknowledgments
This work is supported partly by LHD project budgets (NIFS07KLPH004 and NIFS14KNTT025). This
work has been performed on “Plasma Simulator” (FUJITSU FX100) of NIFS with the support and under the
auspices of the NIFS Collaboration Research program(NIFS16KNSR005).
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