Plasma and Fusion Research: Regular Articles

Volume 11, 2403049 (2016)

Neutron Incident Angle and Energy Distribution at Vacuum Vesselfor Beam-Injected Deuterium Plasmas in the Large Helical Device∗)
Shota SUGIYAMA, Hideaki MATSUURA and Takuya GOTO1)
Department of Applied Quantum Physics and Nuclear Engineering,
Kyushu University, 744 Motooka, Fukuoka 819-0395, Japan1)
National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292, Japan(Received 30 November 2015 / Accepted 26 January 2016)
Assuming a deuterium-beam-injected deuterium plasma confined in the Large Helical Device (LHD), theincident angle distribution and energy spectra of neutrons at various wall positions are evaluated by considering
the complex shape of the vacuum vessel and the deuteron velocity distribution function. The eﬀect of anisotropyof this function on the incident flux, the energy spectra, and the incident angle distribution of the neutrons to thevacuum vessel, are examined. In this paper, the neutron spectra are shown to depend on the wall position and theincident direction because of the formation of anisotropic high-energy tail in the deuteron velocity distributionfunction and the characteristic shape of the vacuum vessel of the LHD.
c 2016 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords: fast-ion velocity distribution function, neutron emission spectrum, beam-injected deuterium plasma,neutron incident angle distribution, neutron incident energy spectrum, Large Helical Device
DOI: 10.1585/pfr.11.2403049

1. Introduction
In toroidal devices, neutron wall loading and incident
flux to the first wall depend on the poloidal angular wall
position because of the shape of the torus wall [1, 2]. Theshape of the first wall may cause an additional nonuniformity of the neutron incident flux because the vacuum vessel of helical devices has a dumbell-shaped poloidal crosssection. The neutron flux has been evaluated for neutron
measurement, e.g., for in situ calibration of neutron monitor [3], use of Monte Carlo simulation in the Large Helical
Device (LHD) by approximately considering the complex
shape of the vacuum vessel. Neutron emission profiles canbe considered for these calculations [4]. However, the neutron incident energy spectrum and the incident angle distribution to the first wall as a diﬀerential amount of the neutron flux have not been evaluated. In order to improve theeﬃciency of neutron measurements [5] and maintenance ofdiagnostics equipment, the neutron energy spectra for every incident angle at all wall positions should be grasped.
Energetic ions contribute to the formation of highenergy ion tails in ion velocity distribution functions [6,7].
As a result of this formation, the neutron emission spectrum is modified from a Gaussian distribution [6, 7]. In
neutral-beam-injection (NBI) heated plasmas, the highenergy ion tail and the non-Gaussian component in theneutron emission spectrum have anisotropic distributions
because beam particles are injected in a particular direction. An eﬀect of the anisotropy of emitted neutrons apauthor’s e-mail: s-sugi@nucl.kyushu-u.ac.jp∗) This article is based on the presentation at the 25th International Toki
Conference (ITC25).

pears when they collide with the first wall. Because incident neutrons produced by suprathermal reactions have ananisotropic spectrum, the incident directions of neutrons
to the first wall are also anisotropic when the high-energy
ion tail is formed. This trend could be seen in all toroidal
devices. In addition to the geometrical eﬀects of the firstwall, anisotropic high-energy ion tail formation in the fuelion velocity distribution function aﬀects the neutron flux
distribution, the energy spectra, and the incident angle distribution.
In this paper, assuming deuterium-beam-injected deuterium plasmas confined in the LHD, the incident angle
distribution and energy spectra of neutrons at all wall positions are evaluated by considering the complex shape ofthe vacuum vessel and the deuteron velocity distributionfunction. The neutron spectra diﬀer significantly depending on the wall position and the incident direction.

2. Analysis Model
We suppose that the position of the magnetic axis isRax = 3.6 m, which is shifted inward from the major radius of the device R = 3.9 m. The bulk deuteron density nd (ρ) = 2 × 1019 m−3 , and the deuteron temperature
T d (ρ) = 10(1 − ρ2 ) keV, where ρ is the normalized radius, are assumed. The position of the magnetic axis corresponds to ρ = 0. We assumed that the deuterium beam
is tangentially injected at the magnetic axis, and that thehigh-energy ion tail in the deuteron velocity distributionfunction is formed in the beam-injected direction. An NBI
power of 5 MW and energy of 180 keV are also assumed.
We used the sum of the Maxwellian and the slowing-down

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c 2016 The Japan Society of Plasma
Science and Nuclear Fusion ResearchPlasma and Fusion Research: Regular Articles

Volume 11, 2403049 (2016)

Fig. 1 The deuteron velocity distribution function on a magneticaxis. A beam energy of 180 keV, power of 5 MW, a bulk
deuteron density nd = 2 × 1019 m−3 and temperature T d =10 keV, are assumed.

Fig. 3 The first wall shape (a) in the poloidal cross section and(b) in the horizontal cross section, and incident angle ι.

1m3 HeEn = mn v20 +(Q + Er )2
m3 He + mn

2m3 He mn+v0 cos ζ(Q + Er ),m3 He + mn

Fig. 2 Bulk deuteron temperature and density profiles. The averaged deuteron density nd = 2 × 1019 m−3 and temperature T d = 5 keV, are assumed.

distribution for the deuteron velocity distribution function. The deuteron velocity distribution function used inthis calculation is shown in Fig. 1 while the assumed bulk
deuteron profile is shown in Fig. 2.
The positions and directions of the energetic deuteronat the instant when the D(d, n)3 He reaction occurs are calculated by the orbit calculation with the LHD field. The
cross section for the D(d, n)3 He reaction is taken from
Bosch et al. [8] and Drosg et al. [9]. The orbit of a 180keV deuteron for 200 toroidal turns after generated at themagnetic axis with pitch angle 0◦ is used as a test particle
for this calculation.
The neutron emission direction and energy are calculated using the positions, directions, and energies of the energetic deuterons. The thermal motions of bulk deuterons
are assumed to be isotropic. The neutron emission energy
by the D(d, n)3 He reaction in the laboratory system is asfollows [10]:(1)

where mn(3 He) is the neutron (3 He) mass, v0 is the centerof-mass velocity of the reacting deuterons, ζ is the angle
between the center-of-mass velocity and the neutron velocity vectors in the center-of-mass system, Q is the reaction Q-value, and Er is the relative energy of the reacting
deuterons.
The neutron incident points on the first wall and theneutron incident angles are calculated using the neutron
emission direction and a mathematical expression of thefirst wall’s shape. The incident angle ι of the neutron to
the first wall is calculated as the angle between the neutron
emission direction and the wall surface in the horizontal
cross section. The first wall shape and the definition of theincident angle are shown in Fig. 3. In this paper, we define
two parts, the trench part and the torus part in the poloidal
cross section of the vacuum vessel of the LHD. The former
is the part where helical coils are placed in, and the latteris the remaining part.

3. Result and Discussion
3.1 Neutron emission spectrum
The volume-averaged neutron emission spectrum bythe D(d, n)3 He reaction is shown in Fig. 4 (a), and the double diﬀerential emission spectra are shown in Fig. 4 (b),where χ is the angle between the neutron emission direction and toroidal axis. The neutron emission spectrum does

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Fig. 5 Neutron flux distribution as a function of poloidal angle
θ at ϕ = 0◦ .

Fig. 4 (a) Volume-averaged and (b) double diﬀerential neutron
emission spectra by the D(d, n)3 He reaction when thedeuterium beam is tangentially injected in the deuterium
plasma.

not obey the Gaussian distribution and the non-Gaussiancomponent is formed with a range of energies from approximately 1.7 to 3.2 MeV. From Fig. 4 (b), the neutronthat has the maximum energy can only be emitted in theχ = 0◦ direction, because the deuterium beam is tangentially injected, and the neutron emitted in the same
direction as the center-of-mass velocity of the reacting
deuterons has the maximum energy from Eq. (1). Thisanisotropy of the neutron emission aﬀects the neutron incident spectra to the first wall.

3.2

Neutron flux distribution

The flux distribution of the non-Gaussian neutrons as
the function of poloidal angle θ at the toroidal angle ϕ = 0◦
is shown in Fig. 5. The flux in the trench part is muchhigher than that in the torus part. Because the trench partis closer to the plasma than the torus part, the neutrons caneasily enter the trench part before they reach the torus part.
The flux at θ = 180◦ is higher than that at θ = 0◦ because
the vacuum vessel has a complex shape, and the distance
between the vacuum vessel and the center of the plasma at
θ = 180◦ is shorter than that at θ = 0◦ . When we assume
an isotropic plasma without beam injection in the magnetic
configuration, the ratio of the flux at θ = 180◦ to that atFig. 6 Neutron incident energy spectra at ϕ = 0◦ and θ = 0◦ ,ϕ = 0◦ and θ = 180◦ , ϕ = 18◦ and θ = 0◦ , and ϕ = 18◦
and θ = 180◦ .

θ = 0◦ becomes approximately 20% larger as comparedwith the beam-injected plasma. This is because neutrons
emitted in the χ = 0 and 180◦ directions, i.e., neutrons
reaching the point θ = 0◦ on the vacuum vessel, increases
because of anisotropic beam injection.

3.3 Neutron incident energy spectra to thefirst wall
The incident energy spectra of the non-Gaussian neutrons at ϕ = 0◦ and θ = 0◦ , ϕ = 0◦ and θ = 180◦ , ϕ = 18◦
and θ = 0◦ , and ϕ = 18◦ and θ = 180◦ are shown in Fig. 6.
The neutron incident spectra depend on the wall position.
Similar to the flux distribution, the spectra at ϕ = 0◦ in
the trench parts are larger than those at ϕ = 18◦ in thetorus parts. At θ = 180◦ , neutrons with the maximum andminimum energy are not observed. In this calculation, neutrons emitted in the same direction as the NBI have maximum energy, whereas those emitted in the opposite direction have minimum energy. These neutrons can only enterat wall position θ = 0◦ from the geometric relationship between the neutron emission vector and the torus shape ofthe first wall.

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Fig. 7 Double diﬀerential neutron incident energy spectra at θ = 0◦ and ϕ = 0◦ for (a) all incident angles, (b) ι = 35, 90, and 145◦ , and at
ϕ = 18◦ for (c) all incident angles, and (d) ι = 50, 90, and 130◦ .

3.4

Neutron energy spectra for each incident
angle to the first wall

The incident angle and energy spectra of the nonGaussian neutrons at θ = 0◦ and (a) ϕ = 0◦ at all incident
angles, (b) ϕ = 0◦ at ι = 35, 90, and 145◦ , (c) ϕ = 18◦
at all incident angles, and (d) ϕ = 18◦ at ι = 50, 90, and130◦ are shown in Fig. 7. The neutron incident angle correlates closely with the neutron energy. The neutron incident
angle is determined by the geometric relationship between
the shape of the first wall and the neutron emission direction. The neutrons emitted in the direction χ = 0◦ enter
the first wall at an incident angle ι = 35◦ at wall positionϕ = 0◦ . Similarly, the neutrons emitted in the direction
χ = 180◦ enter the first wall at an incident angle ι = 145◦
at the wall position ϕ = 0◦ .
The neutron spectrum at ϕ = 18◦ and ι = 50◦ isapproximately 1.5 times larger than that at ϕ = 0◦ andι = 35◦ . However, at ι = 90◦ the spectrum at ϕ = 18◦
is smaller than that at ϕ = 0◦ . This dependence of toroidal
angle at the same poloidal angular position is not observedin tokamak devices.
As shown in Figs. 6 and 7, the neutron incident spectradepend on the wall position and the incident angle becauseof anisotropic neutron emission and the complex shape ofthe vacuum vessel of the LHD. This dependence is not observed in isotropic plasmas and uniform toroidal devices

without trenches for helical coils. For accurate analysesof the spectra of non-Gaussian neutrons in the LHD, theanisotropic fuel ion velocity distribution function, orbit ofenergetic ion, and the complex shape of the vacuum vessel
should be considered.

4. Conclusion
Assuming a deuterium-beam-injected deuterium
plasma confined in the LHD, the neutron incident angle
and energy spectra are examined by considering the complex shape of the vacuum vessel and the deuteron velocity
distribution function. We presented the dependence ofthe neutron incident spectra on the wall position andthe incident angle because of the anisotropic deuteronvelocity distribution function and the shape of the vacuum
vessel. The neutron spectrum at ϕ = 18◦ and ι = 50◦ isapproximately 1.5 times larger than that at ϕ = 0◦ andι = 35◦ at the same poloidal angular position θ = 0◦ .
This dependence of toroidal angle on the neutron incidentspectra is a distinct feature of the helical device. Our
results are important for improving the eﬃciency ofneutron measurements and the maintenance of diagnostics
equipment.
In this paper, we assumed that the high-energy ion tailis formed only in the NBI direction, and calculated thedeuteron orbit without collisions. A more detailed calcu-2403049-4

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lation with modifications to this analysis model (e.g., byconsidering the spatial and pitch-angle distribution of energetic ions) is the subject of a future study.

Acknowledgement

The authors are grateful to Prof. T. Watanabe for providing data of orbit calculation, fruitful discussion and hisencouragement.
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