Proceedings of ITC/ISHW2007

Simulation of Angle and Energy Resolved Fluxes of Escaping
Neutral Particles from Fusion Plasmas with Anisotropic Ion
Distributions
E.A.Veshchev1, P.R. Goncharov1, T. Ozaki1, S. Sudo1 and LHD Experimental Group11) National Institute forFfusion Science, Toki, Gifu 509-5292, Japan
Multidirectional diagnostics employing high resolution atomic energy spectrometers [1,2] are being used tostudy the ion component heating mechanisms and fast ion confinement in helical plasmas. Since the natural atomic
flux source is not localized in contrast to pellet charge exchange [3,4] or diagnostic neutral beam methods [5], thecorrect interpretation of such measurements in a complex toroidally asymmetric geometry requires a carefulnumerical modeling of the neutral flux formation and the knowledge of the charge exchange target distributions,relevant cross-sections and the magnetic surface structure. The measured neutral flux calculation scheme for LHD
geometry was given in [6] and the influence of the geometry effect on the interpretation of measured data wasshown. In the current work angular dependence of fast ion distribution function is taken into account. Experimental
signals for all 20 channels of the Angular-Resolved Multi-Sightline Neutral Particle Analyzer (ARMS-NPA) weresimulated for different cases of fast ion distribution functions. Calculation results are shown forheating-induced fast ion distribution tails obtained from Fokker-Planck modeling. The behavior ofcalculated and experimental ion spectra from NBI is discussed.
Keywords: neutral particles, fast ions, angle resolved measurements, fast particle flux simulation, ion distribution,
angular distribution, energy resolved measurements, distribution function, diagnostic, analyzer.

1. Introduction
Multi-directional neutral particle analyzer beside highresolution energy spectra of fast particles can provide theinformation about their angular distribution during scan ofplasma column in tangential direction. Vertical scan ofplasma column by multi-directional diagnostic can provide
information about the radial distribution of fast particles.
Such measurements are required for the understanding of
the fast ions behavior in plasma, for checking of the fast
particle loss-cone presence, for studying if the heating
mechanisms, etc. Such information is important for the fast
particle confinement and ignition of the future fusion
reactor. For this purpose the novel ARMS-NPA has beendeveloped [1] which can measure plasma in vertical andtangential directions. As the magnetic field geometry of
LHD has a very complex 3D structure, simulation of theexperimental signal of the flux of fast particles is requiredwith taking into account the attenuation of fast particles on
the way to the detector due to the charge-exchange, and theinfluence path length of the particle along every scanning
chord in order to understand how does geometry ofmeasurements influences in the angular fast particle
distribution. The difference in the geometry ofmeasurements can be clearly seen on the illustration of thevertical cross-section plane of every detector sightline on
Fig.1. Detector 1 corresponds to the most tangential
author’s e-mail:veshchev.evgeny@lhd.nifs.ac.jp

direction and detector 20 is the direction close to theperpendicular one. The sheaf of sightlines was adjusted insuch a way that all the channels to observe as closer as
possible to the central region of plasma.

2. The Calculation Scheme.
The escaping neutral flux formulation has been madein [6] for passive diagnostics and the atomic flax can bewritten as:
1Q − ( ρ ') d ρ '∫ λ ( E , ρ ') ΩSρΓ( E ,ϑ ) = e minmfp

14π ρ∫minag ( E ,ϑ , ρ ) ×ρρ
⎡Q − ( ρ ') d ρ ' ⎤
Q + ( ρ ') d ρ '− ∫− ∫λmfp ( E , ρ ') ⎥λmfp ( E , ρ ')⎢× ⎢Q + ( ρ ) e ρmin
− Q − ( ρ ) e ρmin⎥dρ⎢⎥⎦⎣+Q ( ρ ) = dX d ρ > 0whereandQ − ( ρ ) = dX d ρ < 0 on the two intervals between
ρ = 1 and ρ = ρmin .

In order to check the geometry influence simulation ofexperimental signal was made for the isotropic
Maxwellian plasma ion energy probability density uld beProceedings of ITC/ISHW2007

Fig.1 Vertical cross-section plane of every ARMS-NPA sightline. Red color of the line correspond to the scanned part ofplasma close to the LHD center. Blue color is the part of sightline close to the detector. Detector 1 corresponds to the mosttangential direction and detector 20 is the direction close to the perpendicular one.
function:fi ( M ) ( E , ρ ) =2 E
exp ( − E Ti ( ρ ) )π Ti 3/ 2 ( ρ )1/ 2

It has already been shown that the geometry effect may
influence on the fast particles spectra [6] but not assignificantly as in experiment. That could be due to the notsignificant difference of the compared magnetic
configurations Rax = 3.6m and Rax = 3.53m. Thus the new
calculations were made for much more different magnetic
axis configurations (Rax = 3.6m and Rax = 3.9m) for all 20
sightlines. The results of simulation can be seen on theFig.2. Both cases demonstrate angular anisotropy due tothe geometry influence and in both cases fast particle
population is reduced in perpendicular region.

3. Experimental Results
Angular resolved measurements were made for bothmagnetic axis configuration (Rax = 3.6m and Rax =3.9m). Angular resolved spectra plotted on Fig.3 Bothcases demonstrate angular anisotropy and both cases

demonstrate the reduceing of fas particle population inperpendicular direction. In order to understand if such abehavior of fast particle spectra is due to the geometryeffect, it must be subtracted from experimental data. The
geometry of measurements influences only on the relativevalues of fast particles but not on the shape of spectra,thus for the geometry effect subtraction it will be enoughto divide experimental spectra along every sightline byrelative values obtained from calculation results.
Angular resolved spectra plotted Fig.4 represent
experimental data of angular distribution of fast particles
after the geometry effect subtracting for Rax = 3.6 m andRax = 3.9 m correspondingly. Both cases still demonstrateangular anisotropy. Fast particle population in Rax =3.6m configuration measured along four perpendicular
sightlines are plotted on Fig.5 and demonstrate reducingof spectra. The case of Rax = 3.9 m in addition to thereducing of the fast particle flux in perpendicular
direction (Fig.103) still demonstrate the drop of fast
particle population in the region of the 8th channel. Sucha behavior can be due to the presence of the loss-coneregion.

Proceedings of ITC/ISHW2007

Ch.20a)Ch.20b)Ch.1

Ch.1

Fig.2 Calculated angular resolved spectra of fast particles a) for Rax = 3.6 m magnetic axis position and b) for Rax = 3.9 m
magnetic axis position.

Ch.20a)Ch.20b)

Ch.8
Ch.1

Ch.1

Fig.3 Experimental results of angular distribution of fast particles a) for Rax = 3.6 m magnetic axis position and b) for Rax= 3.9 m magnetic axis position.

Ch.20a)Ch.20b)

Ch.8
Ch.1

Ch.1

Fig.4 Experimental data of angular distribution of fast particles after the geometry effect subtracting a) for Rax =3.6magnetic axis position and b) for Rax = 3.9 m magnetic axis position.

Proceedings of ITC/ISHW2007

sightline 20
sightline 19
sightline 18
sightline 17

Γ(E)

100

10

120

25

30
E, keV

3540

Fig.5 Fast particle spectra for four of the sightlines
close to perpendicular direction (sightline 20
is the most perpendicular one) during
perpendicularly-injecting NBI4 operation thecase of Rax = 3.6 m BT = 2.75T magnetic
field after the geometry effect subtracting.

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10F129-1 (2006).
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P.R. Goncharov, T.Ozaki, et al., Rev. Sci. Instrum., 77,
10F119-1 (2006).
P.R.Goncharov, T.Saida, et.al., Rev. Sci. Instr., 74, 1869
H. Matsushita and K.Ida et al., Rev. Sci. Instrum., 75,3607 (2004).
E.A. Veshchev, P.R.Goncharov, et al., Rev. Sci. Instrum.,77, 10F116-1 (2006).