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Incident neutron spectra on the first wall and their application to energetic iondiagnostics in beam-injected deuterium–tritium tokamak plasmasS. Sugiyama, H. Matsuura, and D. Uchiyama
Citation: Physics of Plasmas 24, 092517 (2017); doi: 10.1063/1.4986859View online: http://dx.doi.org/10.1063/1.4986859View Table of Contents: http://aip.scitation.org/toc/php/24/9Published by the American Institute of Physics
Incident neutron spectra on the first wall and their application to energeticion diagnostics in beam-injected deuterium–tritium tokamak plasmas
S. Sugiyama,a) H. Matsuura, and D. UchiyamaDepartment of Applied Quantum Physics and Nuclear Engineering, Kyushu University, 744 Motooka,Fukuoka 819-0395, Japan
(Received 7 June 2017; accepted 6 September 2017; published online 28 September 2017)
A diagnostic method for small non-Maxwellian tails in fuel-ion velocity distribution functions is
proposed; this method uses the anisotropy of neutron emissions, and it is based on the numerical
analysis of the incident fast neutron spectrum on the first wall of a fusion device. Neutron energy
spectra are investigated for each incident position along the first wall and each angle of incidence
assuming an ITER-like deuterium–tritium plasma; it is heated by tangential-neutral-beam injection.
Evaluating the incident neutron spectra at all wall positions and angles of incidence enables the
selective measurement of non-Gaussian components in the neutron emission spectrum for energetic
ion diagnostics; in addition, the optimal detector position and orientation can be determined. At the
optimal detector position and orientation, the ratio of non-Gaussian components to the Gaussian
peak can be two orders of magnitude greater than the ratio in the neutron emission spectrum. This
result can improve the accuracy of energetic ion diagnostics in plasmas when small, anisotropic
non-Maxwellian tails are formed in fuel ion velocity distribution functions. We focus on the non-
Gaussian components greater than 14 MeV, where the effect of the background noise (i.e., slowing-
down neutrons by scattering throughout the machine structure) can be ignored. Published by AIPPublishing. [http://dx.doi.org/10.1063/1.4986859]
I. INTRODUCTION
In burning plasmas, energetic ions are generated by exter-
nal heating and fusion reactions. Energetic ions form non-
Maxwellian tails in the ion velocity distribution functions.1–5
As a consequence of this non-Maxwellian tail formation, the
emission spectra of fusion-produced particles are modified
from the Gaussian distributions;3,5,6 the tail modifies the
fusion reactivity and the emission spectra of the particles pro-
duced by the fusion reactions, i.e., the fusion power. Energetic
ion diagnostics is important for understanding the physics of
energetic ions, such as their effects on fusion power, current
drive, and instabilities.7,8 Non-Maxwellian tails have been
measured using a variety of different techniques and equip-
ment, such as collective Thomson scattering9 and neutral par-
ticle analyzers.10 By detecting the non-Gaussian component in
a neutron emission spectrum, one can indirectly determine a
non-Maxwellian tail.11 In next-generation fusion devices, e.g.,
ITER and DEMO reactors, the plasmas are made up of a small
number of fast ions and a large number of thermal ions. It is
important to understand the effects of the small non-
Maxwellian tail in these plasmas. The accuracy of energetic
ion diagnostics must be improved so that when the non-
Maxwellian tails are several orders of magnitude smaller than
the thermal component of the ion velocity distribution func-
tion (or when the non-Gaussian component is much smaller
than the Gaussian component of the neutron emission spec-
trum), they can still be detected.
Neutral beam injection (NBI) is a method for heating
plasma whereby energetic particles are injected into a plasma
in a particular direction and transfer their energy to the bulk
plasma. Radio-frequency waves in the ion cyclotron range of
frequencies (ICRF) can also heat a plasma by accelerating
ions perpendicular to magnetic field lines. Based on these
techniques, anisotropic non-Maxwellian tails can be formed
in externally heated plasmas. The non-Gaussian components
in the emission spectra of particles produced by fusion
exhibit anisotropic distributions when anisotropic non-
Maxwellian tails are created in fuel-ion distribution func-
tions;12,13 this is a consequence of the dependence of the
emission direction of the particles on the direction of motion
and energies of the reacting ions. The neutrons emitted by
fusion reactions travel in a straight line in a magnetic field;
therefore, the anisotropy of neutron emission affects the inci-
dent neutron spectra on the first wall of a fusion device.
In tokamak devices, it is known that the neutron flux
and wall loading for isotropic neutron emissions depend on
the wall position.14,15 For anisotropic neutron emissions, the
neutron energy spectrum depends on the wall position and
angle of incidence in addition to flux distributions.16,17
Therefore, it is necessary to evaluate the neutron spectrum
observed at the detector in order to perform energetic ion
diagnostics, as the diagnostics work by measuring the non-
Gaussian neutrons. The neutron energy spectra in the line-
of-sight of a fixed-position neutron spectrometer have been
calculated for beam-injected deuterium plasmas;18,19 good
agreement with the experimental data has been reported. The
observation of the neutron spectrum has been performed for
plasmas in which the fusion reaction is dominated by fast
ions. Ideally, in order to detect a small non-Gaussian compo-
nent with high accuracy, a detector will be positioned and
oriented in a manner that would allow it to observe thea)Electronic mail: s-sugi@nucl.kyushu-u.ac.jp
1070-664X/2017/24(9)/092517/8/$30.00 Published by AIP Publishing.24, 092517-1
PHYSICS OF PLASMAS 24, 092517 (2017)
largest number of non-Gaussian neutrons; the suitable detec-
tor position and orientation can be determined by knowing
the dependence of the neutron energy spectrum on the wall
position and angle of incidence. Previously, we have shown
the existence of a combination of the angle of incidence and
the wall position that the ratio of non-Gaussian components
to a Gaussian peak is two orders of magnitude greater than
the ratio in the neutron emission spectrum.16 The evaluation
was conducted so as to verify the effects of nuclear plus
interference (NI) scattering20,21 [in other words, nuclear elas-
tic scattering (NES)] for a 3He-beam-injected deuterium
plasma confined in the Large Helical Device. Increasing this
ratio can improve the measurement precision of anisotropic
knock-on tail formation3–5 due to NI scattering since the
knock-on tails are several orders of magnitude smaller than
the bulk components in the ion velocity distribution function.
This advantage is also expected when small, anisotropic
non-Maxwellian tails are created by other phenomena.
In this paper, we propose a method for diagnosing small
non-Maxwellian tails by using the anisotropy of a neutron
emission. The neutron energy spectra incident at each position
on the first wall and each angle of incidence is examined
assuming an ITER-like deuterium–tritium plasma heated by
tangential NBI. The characteristic correlation between the
neutron energy and the angle of incidence is shown. The
energy components in the neutron emission spectrum can be
selectively detected by grasping the dependence of the inci-
dent neutron spectra on the wall position and the angle of inci-
dence. The ratio of non-Gaussian components to the Gaussian
peak (located at a neutron energy of 14 MeV) in the neutron
emission spectrum is found to increase by several orders of
magnitude when a suitable detector position and orientation
are selected. In our discussion of the measurement accuracy
of the non-Gaussian components, we focus our attention on
the energy components that are greater than 14 MeV, as this is
where the effect of the background noise (a slowing-down
component in the measured neutron spectrum formed by the
scattering throughout the machine structure) is no longer sig-
nificant.22 The proposed method determines the optimal posi-
tion and orientation of neutron detectors based on the
dependence of the neutron energy spectra on the position
along the first wall and the angle of incidence.
II. ANALYSIS MODEL
A. Computational methods
In order to incorporate the behavior of energetic ions
into the calculations of the neutron spectra incident on the
first wall, we first calculate energetic-ion orbits using the
ORBIT code.23 We use the analytical model of a magnetic
surface that was proposed by Yavorskij et al.24 for the parti-
cle orbit analyses
x ¼ Rmaj þ r cos h� dr sin2 h� �
cos u;y ¼ Rmaj þ r cos h� dr sin2 h
� �sin u;
z ¼ jr sin h;(1)
where Rmaj is the major radius of a plasma, r is the minor
radius, d is the triangularity, j is the elongation, h is the
poloidal angle, and u is the toroidal angle. We assume that
the path of NBI in a plasma is a zero-width straight line
through the center of the plasma. The beam deposition pro-
file is considered by generating test particles on the beam
line weighting with the following equation:
W lð Þ ¼ nertotSNBI exp �nertotlð Þ; (2)
where
rtot ¼hrevivNBI
þ nd
ne
hrdCXvi þ hrdvi
vNBI
þ nt
ne
hrtCXvi þ hrtvi
vNBI
; (3)
W(l) is the weight of the beam ion generation per unit length
at a distance l from the beam-injected position, SNBI¼PNBI/
ENBI, PNBI is the NBI power, ENBI is the NBI energy, vNBI is
the speed of the beam particles, and ne(d,t) is the electron
(deuteron and triton) density. re(d,t) is the cross-section of the
ionization by background electrons (deuterons and tritons),
and rdðtÞCX is the cross-section for the charge exchange by the
deuterons (tritons); these cross-sections are adopted from the
results of a previous study.25 We assume a Maxwellian dis-
tribution for the velocity distribution functions of the back-
ground ions and electrons. The particle orbit analyses predict
the position, direction, and energy of an ion at the instant
when a T(d,n)4He reaction occurs. Although the gyro-motion
is not considered by the particle orbit analyses, it is taken
into account at the emitted position of neutrons, as a gyro-
phase from 0 to 2p is randomly assigned. The cross-section
of the T(d,n)4He reaction is taken from two earlier stud-
ies.26,27 The total number of fusion reactions is determined
by using the slowing-down distribution function of the beam
ions, which is obtained by counting the results of the particle
orbit analysis as follows:
ftail v; qð ÞdvdV ¼XNp
i¼1
XNt
j¼1
SNBI
Dt
Np
d v� vi;jð Þd q� qi;jð Þ; (4)
where Nt is the number of time steps of the particle orbit
analysis, Np is the number of test particles, q is the normal-
ized poloidal flux, V(q) is the plasma volume at q, Dt is the
time step interval, and v is the velocity of a test particle. The
subscripts i and j represent the i-th test particle and the j-thtime step, respectively. The orbit of each test particle was
followed until the particle either reaches the last flux surface
or slows down to 1.5 times that of the ion temperature.
The direction and energy of the emitted neutrons are
determined using the results of the particle orbit analyses.
The neutron energy emitted by the T(d, n)4He reaction in the
laboratory system was derived28
En ¼1
2mnv
20 þ
ma
mn þ maQþ Erð Þ
þ v0 cos ~f2mnma
mn þ maQþ Erð Þ
� �1=2
; (5)
where mn(a) is the neutron (alpha-particle) mass, v0 is the
center-of-mass velocity of the reacting ions, Q is the reaction
Q-value, and Er is the relative energy of the reacting ions. ~f
092517-2 Sugiyama, Matsuura, and Uchiyama Phys. Plasmas 24, 092517 (2017)
represents the angle of the emitted-neutron velocity vector
relative to the direction of the center-of-mass velocity in the
center-of-mass system (ions move in various directions in
the plasma); it is needed to obtain the neutron emission angle
v relative to the toroidal axis. The geometric relationship
between the vectors and the angles is shown in Fig. 1. The
vector representation of the emitted-neutron velocity vn in
the Cartesian coordinate system, considering rotation about
the magnetic vector retaining the pitch angle of hp and cen-
ter-of-mass motion keeping the neutron emission angle f rel-
ative to the center-of-mass direction, enables the calculation
of the position at which neutrons are incident on the first
wall from the relationship in Fig. 1.
The positions of the neutrons incident on the first wall
are calculated using vn and the wall-shape function. We
defined the wall-shape function by shifting and expanding
the last flux surface described by Eq. (1). The angle of inci-
dence for the neutrons on the first wall is calculated as the
angle between the neutron emission vector vn and the tangent
to the surface of the first wall. We defined the angle of inci-
dence in the poloidal plane as the poloidal incident angle, ip;
in the horizontal plane, we defined it as the toroidal incident
angle, it. The shape of the first wall and the angles of inci-
dence in the poloidal and horizontal planes are shown in
Figs. 2(a) and 2(b), respectively.
B. Calculation conditions and assumptions
The conditions of the plasma are adopted from an induc-
tive operation scenario for ITER.29 We examine the neutron
spectra incident on the first wall for a deuterium-beam-injected
plasma. The NBI energy and power are ENBI¼ 1 MeV and
PNBI¼ 33 MW, respectively; the mean deuteron and triton
densities are 5.05� 1019 m�3, the mean ion temperature is
8 keV, and the mean electron temperature is 8.8 keV. The cal-
culations assume both a uniform density distribution and a par-
abolic temperature distribution. The radial profiles of the
electron and ion temperature, deuteron density, and safety fac-
tor that were used for the calculations are shown in Fig. 3 as
functions of the normalized poloidal flux, q. For the magnetic
surface, Rmaj¼ 6.2 m, d(r)¼ 0.48(r/a)2, j¼ 1.85, and the
minor radius of the last flux surface is a¼ 2 m. The wall-shape
parameters include the major radius Rwall¼ 6.25 m, minor
radius awall¼ 2.25 m, triangularity dwall¼ 0.5, and elongation
jwall¼ 2 of the first wall. The assumed magnetic surface and
shape of the first wall are shown in Fig. 4. The volume-
averaged total deuteron distribution function which is the sum
of the Maxwellian and slowing-down distribution obtained by
the particle orbit analysis and Eq. (4) is shown in Fig. 5 as a
function of both (a) energy and (b) parallel and perpendicular
components of velocity.
III. RESULTS AND DISCUSSION
A. Neutron emission spectra
The volume-averaged neutron emission spectrum result-
ing from the T(d,n)4He reaction is shown in Fig. 6. The dis-
tribution function in Fig. 5 was used to calculate the neutron
emission spectrum. The non-Gaussian components in the
neutron emission spectra are due to the formation of the non-
Maxwellian tails; they range in energy from approximately
11.5 to 17.4 MeV. For the T(d,n)4He reaction, neutron
energy is determined by how the sum of energies of two
reacting ions and reaction Q-value is distributed to the neu-
tron and alpha particle. Neutron energy depends on the
FIG. 1. Geometric relationship between the neutron-emission direction, the
toroidal axis, the magnetic vector, and the direction of the center-of-mass
motion.
FIG. 2. Shape of the first wall and the definition of the angles of incidence
in (a) the poloidal plane and (b) the horizontal plane.
FIG. 3. Radial profiles of electron temperature Te, ion temperature Ti, deu-
teron density nd, and safety factor q.
092517-3 Sugiyama, Matsuura, and Uchiyama Phys. Plasmas 24, 092517 (2017)
emission angle relative to the center-of-mass velocity, ~f, as
can be seen from Eq. (5). In this case, when a beam deuteron
with an injected energy of 1 MeV reacts with a triton in
Maxwellian distribution, a maximum energy of 17.4 MeV is
obtained for a neutron if it is emitted in the same direction as
the center-of-mass velocity of reacting ions (~f ¼ 0�). In the
same situation, a minimum energy of 11.5 MeV is obtained
if a neutron is emitted in the opposite direction as the center-
of-mass velocity (~f ¼ 180�). The non-Gaussian components
are several orders of magnitude smaller than the 14 MeV
peak of the Gaussian. At a neutron energy of 16 MeV, the
non-Gaussian components are approximately 3 orders of
magnitude lower than the Gaussian peak. In order to obtain
the magnitude and energy range of the non-Maxwellian tails,
the neutron energy spectra must be measured as accurately
as possible.
The volume-averaged double differential emission spec-
tra of the neutrons are shown in Fig. 7(a) as functions of both
the energy and the direction for all the neutron-emission
angles. The double differential spectra are shown in Fig. 7(b)
at neutron-emission angles of v¼ 0�, 90�, and 180�; here, vis the neutron-emission angle relative to the toroidal axis, as
defined in Fig. 1. These spectra are the derivatives of the
spectrum in Fig. 6 with respect to the emission angle, v. The
non-Gaussian components depend on the emission angle
because of the anisotropy of the non-Maxwellian tails. If we
consider the reaction by an energetic deuteron at the center
of the plasma that is moving along the line of the magnetic
force, then v is almost identical to the pitch angle for the
charged particles. As can be found from Eq. (5), neutrons
with maximum energy are emitted only in the direction
v¼ 0�, while neutrons with the minimum energy are emitted
only in the direction v¼ 180� in tangentially beam-injected
plasmas.
FIG. 4. Magnetic flux surfaces and the first wall.
FIG. 5. Distribution functions of the deuteron as functions of (a) energy and (b) parallel and perpendicular components of the velocity in a NBI-heated plasma.
FIG. 6. Volume-averaged neutron emission spectra from the T(d,n)4He reac-
tion in the NBI-heated plasma.
092517-4 Sugiyama, Matsuura, and Uchiyama Phys. Plasmas 24, 092517 (2017)
The neutron energy spectra differ depending on the emis-
sion direction of the neutrons; as such, the neutron spectra
observed by the detectors differ from the volume-averaged emis-
sion spectrum shown in Fig. 6. It is useful to grasp the incident
spectra at all positions and angles of incidence along the first
wall; this enables the determination of the most suitable position
and orientation of the detector for energetic ion diagnostics.
B. Neutron energy spectra incident on a wall position
The neutron energy spectra incident on all wall positions
are shown in Fig. 8(a), while the spectra at selected wall
positions (h¼ 0�, 90�, and 180�) are shown in Fig. 8(b). The
wall position is denoted by the poloidal angle h (see Fig. 2),
and the incident neutron spectra are integrated with respect
to the toroidal direction u. The spectra depend on the wall
position due to the anisotropic non-Maxwellian tail. The neu-
tron energies range from approximately 11.6 to 17.3 at
h¼ 0� and from about 11.8 to 17.1 MeV at h¼ 180�. Based
on the geometric relationship between the shape of the first
wall, the position, and direction of the ionized beam deute-
rium, neutrons emitted in the directions v¼ 0� and 180� with
the maximum and minimum energies can enter the first wall
only at h¼ 0�, respectively.
The largest number of neutrons in the non-Gaussian
components in the neutron emission spectrum is observed at
h¼ 0�; therefore, the ratio of non-Gaussian to Gaussian neu-
trons increases at this position, which is advantageous for
measuring non-Gaussian neutrons. As more neutrons with
energies greater than the Gaussian components are emitted
both parallel and anti-parallel to the toroidal axis, the ratio of
non-Gaussian to Gaussian neutrons is expected to increase;
the measurement accuracy of non-Gaussian neutrons can be
improved by optimizing the detector position. Hence, in this
condition, placing the detector at h¼ 0� is optimal for ener-
getic ion diagnostics.
FIG. 7. Volume-averaged double differential neutron emission spectra: (a) all emission directions and (b) in the directions of v¼ 0�, 90�, and 180�. The neu-
tron emission angle v is defined as the angle between the neutron-emission direction and the toroidal axis.
FIG. 8. Neutron incident spectra: (a) at all wall positions and (b) at h¼ 0�, 90�, and 180�. The poloidal angle h denotes the wall position (see Fig. 2).
092517-5 Sugiyama, Matsuura, and Uchiyama Phys. Plasmas 24, 092517 (2017)
C. Neutron energy spectra at different angles ofincidence
The distribution of the poloidal incident angles of the
neutrons at h¼ 0� is shown in Fig. 9. The incident angles are
defined in Fig. 2. The relationship between the poloidal inci-
dent angle, the plasma edge, and the first-wall shape is shown
in Fig. 10. Most of the non-Gaussian neutrons enter the first
wall at this position with a poloidal incident angle ip ¼ 90�
since the most energetic deuterons are found, and these neu-
trons are generated near the center of the plasma. Although
non-Gaussian neutrons have a peak at ip ¼ 90�, Gaussian neu-
trons are distributed widely over a range of poloidal incident
angles, from approximately 30� to 150�. As is shown in Fig.
10, the poloidal incident angle can be geometrically allowed
from approximately 23� to 157�; however, the observed neu-
trons with the maximum and minimum poloidal incident
angles are very few (dN=dip � 1014 m�2s�1rad�1) because
of the assumed ion temperature profile (Gaussian-neutron
emission profile). It is expected that the ratio of non-Gaussian
to Gaussian neutrons will increase if the neutrons are mea-
sured at h¼ 0� and ip ¼ 90�.The neutron incident spectra at h¼ 0� for ip ¼ 90� are
shown in Fig. 11(a) for all the toroidal incident angles, it.
Figure 11(b) shows the spectra for it ¼ 43� and 137�.Different spectra are observed at each toroidal incident angle
due to the effect of the anisotropic non-Maxwellian tail. The
toroidal incident angle of the neutrons correlates closely
with the direction of the neutron emissions. The geometric
relationship between the toroidal incident angle, the assumed
NBI line, the plasma edge, and the first-wall shape is shown
in Fig. 12. For the case of the assumed NBI line, neutrons
having maximum energy that enter at h¼ 0� with ip ¼ 90�
are geometrically limited to neutrons that are emitted by the
reaction of the 1-MeV deuteron moving with a pitch angle of
0� at the center of the plasma and emitted in the same direc-
tion as NBI (v¼ 0�). Because the tangential line to the
toroidal axis through the center of the plasma intersects the
first wall only at angles corresponding to it ¼ 43� and 137�
at h¼ 0� (see Fig. 12), the neutrons emitted from the center
of the plasma in the direction v¼ 0� enter the first wall at
h¼ 0� only at it ¼ 137�. The neutrons with maximum
energy can be observed only at it ¼ 137�, and neutrons with
minimum energy can only enter at it ¼ 43� at h¼ 0�.The Gaussian neutrons are distributed across all the wall
positions and all the possible angles of incidence. By contrast,
the non-Gaussian neutrons that have a particular energy tend
to concentrate at specific combinations of the wall position
and the angle of incidence. By determining the position and
direction of the neutron detector with knowledge of this com-
bination, it is expected that the accuracy of the measurement
of non-Gaussian neutrons can be improved. The full width at
half maximum of the neutron spectra must be measured to a
sufficient degree of accuracy because the data are used to
calculate the ion temperature profile.30,31 For this reason, we
discuss the measurement accuracy of the non-Gaussian neu-
trons; the 14 MeV peak in the neutron spectrum is taken as
being the basis for a sufficient level of accuracy. The ratio of
non-Gaussian components to the peak of the Gaussian com-
ponents in the emission spectrum, �emission, and the ratio in
the incident spectrum, �incident, can be obtained by normaliz-
ing each spectrum by the value of the 14 MeV peak,
�emission ¼dN
dEn
dN
dEn
� ��1
peak
; (6)
�incident ¼d3N
dEnditdip
d3N
dEnditdip
!�1
peak
; (7)
where dN/dEn is the neutron emission spectrum,
d3N=dEnditdip is the incident spectrum as a function of the
neutron energy, En, and the subscript “peak” represents the
value of the 14 MeV Gaussian peak in each spectrum. Figure
11 shows that there exists a combination of the position and
the angle of incidence such that the ratio of non-GaussianFIG. 9. Distribution of the poloidal incident angle for neutrons at h¼ 0�.The poloidal incident angle ip is defined in Fig. 2.
FIG. 10. Geometric relationship between the poloidal incident angle, the
plasma edge, and the first wall.
092517-6 Sugiyama, Matsuura, and Uchiyama Phys. Plasmas 24, 092517 (2017)
components to 14 MeV neutrons in the neutron emission
spectrum can be increased. We introduce a parameter, g� �incident/�emission, that compares the ratio of the incident
spectrum to the ratio of the emission spectrum. In order to
discuss the possibility of using this for diagnostics, we must
first consider the effect of scattering of neutrons throughout
the machine structure (i.e., background noise).22 However,
since we focus our attention onto the energy component
above 14 MeV in the neutron spectrum (i.e., where the effect
of the wall scattering of neutrons is not so significant because
the background noise consists of the slowed-down neutrons),
we can exclude this effect from the discussion. The parame-
ters g, �emission, and �incident at h¼ 0� for ip ¼ 90� and it
¼ 137� are shown in Fig. 13. The value of g is larger than
102 at neutron energies greater than 16 MeV; this result is
highly favorable for energetic ion diagnostics when small
non-Maxwellian tails are formed. The non-Gaussian neutrons
can be measured to a higher degree of accuracy by under-
standing the incident neutron spectra at all positions and
angles of incidence on the first wall before the measurements.
The characteristics of the parameter g strongly depend
on the spatial profile and the pitch-angle distribution of ener-
getic ions. For instance, non-Maxwellian tails are formed
perpendicular to the lines of the magnetic force due to
perpendicular-NBI or ICRF heatings. The parameter for the
neutrons emitted by the D(d,n)3He reaction must also show a
different feature from the case of the T(d, n)4He reaction
because of the large anisotropy of its double differential
cross-section.26 In such cases, the most suitable detector
position and orientation for the diagnostics are different from
the case of the tangential NBI.
IV. CONCLUSION
We have proposed a method for diagnosing small non-
Maxwellian tails; our method utilizes the anisotropy of neu-
tron emissions to determine a suitable detector position and
FIG. 11. Neutron incident spectra at h¼ 0� for ip ¼ 90�: (a) for all toroidal incident angles it and (b) for it ¼ 43� and 137�. The toroidal incident angle it is
defined in Fig. 2.
FIG. 12. Geometric relationship between the toroidal incident angle, the
NBI line, the plasma edge, and the first wall.
FIG. 13. Parameters g, �emission, and �incident at h¼ 0� for ip ¼ 90� for
it ¼ 137�.
092517-7 Sugiyama, Matsuura, and Uchiyama Phys. Plasmas 24, 092517 (2017)
orientation based on the dependence of the neutron incident
spectra on the wall position and angle of incidence. We
examined the incident neutron spectra for each wall position
and angle of incidence on the first wall of a fusion device by
assuming an ITER-like deuterium–tritium plasma heated by
tangential NBI. Differentiating the neutron emission spec-
trum with respect to the wall position and angle of incidence,
we found that the ratio of the non-Gaussian components to
the 14 MeV components at the wall position h¼ 0� for inci-
dent angles ip ¼ 90� and it ¼ 137� became approximately
two orders of magnitude greater than the ratio in the emis-
sion spectrum. As such, the accuracy of energetic ion diag-
nostics can be improved by installing a detector at this
position and orientation in order to more accurately measure
non-Gaussian neutrons. The incident neutron spectra differed
significantly depending on the direction of motion of the
reacting energetic ions. Although we focused on tangential-
NBI heating being the cause of the formation of the non-
Maxwellian tails, the method can be applied to diagnostics
and experimental validations of any phenomena that create
non-Maxwellian tails.
ACKNOWLEDGMENTS
The authors are grateful to Dr. R. B. White for
permitting the use of the ORBIT code.
1J. G. Cordey and M. J. Houghton, Nucl. Fusion 13, 215 (1973).2T. H. Stix, Nucl. Fusion 15, 737 (1975).3L. Ballabio, G. Gorini, and J. K€allne, Phys. Rev. E 55, 3358 (1997).4H. Matsuura and Y. Nakao, Phys. Plasmas 13, 062507 (2006).5H. Matsuura, M. Nakamura, O. Mitarai, and Y. Nakao, Plasma Phys.
Controlled Fusion 53, 035023 (2011).6H. Henriksson, S. Conroy, G. Ericsson, L. Giacomelli, G. Gorini, A.
Hjalmarsson, J. K€allne, M. Tardocchi, and M. Weiszflog, Plasma Phys.
Controlled Fusion 47, 1763 (2005).7A. Fasoli, C. Gormenzano, H. L. Berk, B. Breizman, S. Briguglio, D. S.
Darrow, N. Gorelenkov, W. W. Heidbrink, A. Jaun, S. V. Konovalov, R.
Nazikian, J. M. Noterdaeme, S. Sharapov, K. Shinohara, D. Testa, K.
Tobita, Y. Todo, G. Vlad, and F. Zonca, Nucl. Fusion 47, S264 (2007).8S. E. Sharapov, B. Alper, H. L. Berk, D. N. Borba, B. N. Breizman, C. D.
Challis, I. G. J. Classen, E. M. Edlund, J. Eriksson, A. Fasoli, E. D.
Fredrickson, G. Y. Fu, M. Garcia-Munoz, T. Gassner, K. Ghantous, V.
Goloborodko, N. N. Gorelenkov, M. P. Gryaznevich, S. Hacquin, W. W.
Heidbrink, C. Hellesen, V. G. Kiptily, G. J. Kramer, P. Lauber, M. K.
Lilley, M. Lisak, F. Nabais, R. Nazikian, R. Nyqvist, M. Osakabe, C. P.
von Thun, S. D. Pinches, M. Podesta, M. Porkolab, K. Shinohara, K.
Schoepf, Y. Todo, K. Toi, M. A. V. Zeeland, I. Voitsekhovich, R. B.
White, V. Yavorskij, ITPA EP TG, and JET-EFDA Contributors, Nucl.
Fusion 53, 104022 (2013).9H. Bindslev, J. A. Hoekzema, J. Egedal, J. A. Fessey, T. P. Hughes, and J.
S. Machuzak, Phys. Rev. Lett. 83, 3206 (1999).10S. S. Medley, A. J. H. Donn�e, R. Kaita, A. I. Kislyakov, M. P. Petrov, and
A. L. Roquemore, Rev. Sci. Instrum. 79, 011101 (2008).11C. Hellesen, M. G. Johnson, E. A. Sund�en, S. Conroy, G. Ericsson, E.
Ronchi, H. Sj€ostrand, M. Weiszflog, G. Gorini, M. Tardocchi, T. Johnson,
V. G. Kiptily, S. D. Pinches, S. E. Sharapov, and JET-EFDA Contributors,
Nucl. Fusion 50, 022001 (2010).12H. Matsuura and Y. Nakao, J. Plasma Fusion Res. Series 9, 48 (2010);
http://www.jspf.or.jp/JPFRS/index_vol9.html.13P. R. Goncharov, Nucl. Fusion 55, 063012 (2015).14P. P. H. Wilson, R. Feder, U. Fischer, M. Loughlin, L. Petrizzi, Y. Wu,
and M. Youssef, Fusion Eng. Des. 83, 824 (2008).15J. C. Rivas, A. de Blas, J. Dies, and L. Sedano, Fusion Sci. Technol. 64,
687 (2013).16S. Sugiyama, H. Matsuura, D. Uchiyama, D. Sawada, T. Watanabe, O.
Mitarai, and T. Goto, Plasma Fusion Res. 10, 3403055 (2015).17S. Sugiyama, H. Matsuura, and T. Goto, Plasma Fusion Res. 11, 2403049
(2016).18C. Hellesen, M. Albergante, E. A. Sund�en, L. Ballabio, S. Conroy, G.
Ericsson, M. G. Johnson, L. Giacomelli, G. Gorini, A. Hjalmarsson, I.
Jenkins, J. K€allne, E. Ronchi, H. Sj€ostrand, M. Tardocchi, I.
Voitsekhovitch, M. Weiszflog, and JET-EFDA Contributors, Plasma Phys.
Controlled Fusion 52, 085013 (2010).19Z. Chen, M. Nocente, M. Tardocchi, T. Fan, and G. Gorini, Nucl. Fusion
53, 063023 (2013).20J. J. Devaney and M. L. Stein, Nucl. Sci. Eng. 46, 323 (1971).21S. T. Perkins and D. E. Cullen, Nucl. Sci. Eng. 77, 20 (1981).22P. Antozzi, G. Gorini, J. K€allne, and E. Ramstr€om, Nucl. Instrum.
Methods Phys. Res., Sect. A 368, 457 (1996).23R. B. White and M. S. Chance, Phys. Fluids 27, 2455 (1984).24V. A. Yavorskij, K. Schoepf, Z. N. Andrushchenko, B. H. Cho, V. Y.
Goloborod’ko, and S. N. Reznyk, Plasma Phys. Controlled Fusion 43, 249
(2001).25A. C. Riviere, Nucl. Fusion 11, 363 (1971).26M. Drosg and O. Schwerer, “Production of monoenergetic neutrons between
0.1 and 23 MeV: neutron energies and cross-sections,” in Handbook onNuclear Activation Data STI/DOC/10/273 (IAEA, Vienna, 1987).
27H. S. Bosch and G. M. Hale, Nucl. Fusion 32, 611 (1992).28H. Brysk, Plasma Phys. 15, 611 (1973).29B. J. Green, Plasma Phys. Controlled Fusion 45, 687 (2003).30M. Sasao, A. V. Krasilnikov, T. Nishitani, P. Batistoni, V. Zaveryaev, Y.
A. Kaschuc, S. Popovichev, T. Iguchi, O. N. Jarvis, J. K€allne, C. L. Fiore,
L. Roquemore, W. W. Heidbrink, A. J. H. Donne, A. E. Costley, and C.
Walker, Plasma Phys. Controlled Fusion 46, S107 (2004).31A. V. Krasilnikov, M. Sasao, Y. A. Kaschuck, T. Nishitani, P. Batistoni,
V. S. Zaveryaev, S. Popvichev, T. Iguchi, O. N. Jarvis, J. K€allne, C. L.
Fiore, A. L. Roquemore, W. W. Heidbrink, R. Fisher, G. Gorini, D. V.
Prosvirin, A. Y. Tsutskikh, A. J. H. Donn�e, A. E. Costley, and C. I.
Walker, Nucl. Fusion 45, 1503 (2005).
092517-8 Sugiyama, Matsuura, and Uchiyama Phys. Plasmas 24, 092517 (2017)
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