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.

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