J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)310–313
000–000

Temperature, Density, Magnetic Field and Pitch Angle
Dependence of Neutral Particle Spectrum inLarge Helical Device
OZAKI Tetsuo, GONCHAROV Pavel, MURAKAMI Sadayoshi1, SANUKI Heiji, OKAMURA Shoichi,
SUDO Shigeru, KUBO Shin, SHIMOZUMA Takashi, OHKUBO Kunizo, NOTAKE Takashi2, IDA Katsumi,
TANAKA Kenji, OKA Yoshihide, OSAKABE Masaki, TAKEIRI Yasuhiko, TSUMORI Katsuyoshi,
IKEDA Katsunori, KANEKO Osamu, NARIHARA Kazumichi, NAGAYAMA Yoshio, SAKAKIBARA Satoru,
SHOJI Mamoru, NAKANISHI Hideya, KOJIMA Mamoru, YAMAUCHI Kenji, KAWAHATA Kazuo,KOMORI Akio, MOTOJIMA Osamu and LHD Experimental Group
National Institute for Fusion Science, Toki 509-5292, Japan
Department of Nuclear Engineering, Kyoto University, Kyoto 606-8501, Japan2
Department of Energy and Science, Nagoya University, Nagoya 464-8603, Japan
1(Received: 9 December 2003 / Accepted: 23 March 2004)

Abstract
In a helical device, the particle loss by the resonance between the ∇B drift and the E × B drift is well known as aresonant loss. The behavior is observed as a dip in the charge exchange neutral particle spectrum. It is not easy
directly nor experimentally to observe the loss cone itself, which is the characteristic effect in the helical device,because it appears in the velocity space. However the experimental observation of resonant loss suggests the evidenceof the loss cone. The depth of the dip is strongly dependent on the electric field. It is difficult to observe in an NBI
plasma in LHD since the NBI is tangentially injected in order to avoid inserting of the particles in a loss cone region.
Since an electron is strongly heated by ECH at low plasma density, the positive electric field can be easily obtained.
Therefore it is easy to observe a change of the spectrum by the strength of ECH power. In this paper, the dependenceof the resonant loss on the density, the temperature, the magnetic field, the magnetic axis and the pitch angle isclarified. According to the present analysis, the dip in the spectrum becomes deeper with the outer shift of the magneticaxis. The dependence of the dip depth on the density or temperature, i.e., the electric field is in accord with theoreticalprediction.
Keywords:
resonant loss, loss cone, electric field, helical ripple, time-of-flight neutral particle analyzer

1. Introduction

not exist. Moreover, most of the particles heated by tangential
NBI (Neutral Beam Injection) do not have a pitch angle
perpendicular to a magnetic field. However, if the slowing
down of the incident particle by electron collision occurs, notonly in ICH (Ion Cyclotron resonance frequency Heating)heating but also in NBI heating, the particle with a large pitch
angle actually will be generated due to the scattering between
the particle and a plasma ion at several times the plasma
temperature. These particles cause the drift motion and rotate
poloidally. They can almost be confined in the plasma because
the energy of these particles is not so large. However part ofthem are not confined by balance with the electric field E. It
is known for helical devices that the particle with a specificenergy is lost by cancellation of the ∇B drift and the E × B

On helical devices, particle orbits in plasma are very
complicated due to the magnetic field ripple. The particle istrapped by the helical or/and the toroidal ripples. When theseorbits are drawn in velocity space, some particles with large
pitch angles are lost. This phenomenon is known as a loss
cone and it express well the features of particle confinement
in helical device. One of the main subjects in helical devices
and the future fusion reactor with the helical system is, how
this loss cone can be reduced. This phenomenon can bereduced by the control of the magnetic configuration, theheating method and the electric field etc. In the Large HelicalDevice (LHD), the device design is devised so that the loss
cone at ρ (radial position on the magnetic surface) < 1/2 may©2004 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Corresponding author’s e-mail: ozaki@nifs.ac.jp1310

Ozaki T. et al., Temperature, Density, Magnetic Field and Pitch Angle Dependence of Neutral Particle Spectrum in Large Helical Devic

drift resulting from the electric field E [1]. This phenomenon
occurs at the negative radial electric field. The reason why
we are interested in the resonant loss is that we can find it
from the dip in the high-energy particle spectra measured by
the neutral particle analyzer. (We can find only the decreasing
flux in the loss cone, therefore it is very difficult to distinguishthe effect of the loss cone from other effects).

this paper is defined as the angle between the magnetic axis
and the sight line, not the actual pitch angle for each particle
because it is difficult to find the generation point of eachparticle. About the vertical scan, it is possible from –12 to+15 degrees. A very high-speed scan of one degree per secondin the vertical system is possible since a counter weight isused to compensate the weight of the analyzer (700 kg).
LHD has the toroidal mode number of m = 10 andhelical mode number of l = 2. The major radius and minor
radius are 3.9 m, 0.6 m, respectively. The helical ripple is0.25 and a magnetic field is a maximum of 3 T. Although thestandard magnetic axis is 3.75 m, it can be changed from 3.4
m to 4.1 m by applying a vertical magnetic field. There arethree kinds of heating system of ECH (10 MW), NBI (15MW) and ICH (3 MW). As for electron temperature, amaximum of 10 keV is observed by using Thomson scatteringand ECE (Electron Cyclotron Emission). Electron density canbe changed from 0.1 to 4 × 1019 m-3. The density profile ismeasured with the multi-channel interferometer.

2. Theoretical prediction
The conditions under which degradation of confinement
occur have been made clear by the theory [2]. The resonanceoccurs when the following condition is satisfied,µB/eφ = –1 / εh ,(1)where, µ , B, e, φ and ε h are the magnetic moment, themagnetic field, the electron charge and the helical ripple,respectively. According to eq. (1), the degradation is strongly
related to the helical ripple and the plasma potential (theelectric field). Since εh is 0.25 in LHD, the equivalent energy
is roughly 4 times the potential. Here, we describe how theresonant loss depends on various kinds of plasma parameters,and compared it with theory. The helical ripple increases if
the magnetic axis is shifted outward and it will become
smaller with an inward shift. If the helical ripple is small, it
is inevitably expected that the dip on the spectrum becomesalso small since the degree of resonance is small. At positive
radial electric field, since resonance for ion cannot take place
easily, the dip becomes small too.
To obtain the positive electric field, if all other conditions
are same, lower density and higher electron temperature etc.
are required [3]. Another way is using the central heating ofECH (Electron Cyclotron resonance frequency Heating).
Moreover, pitch angle dependence is also an interesting
subject. Theoretically the resonant loss cannot take place forthe particle with lower pitch angle. However, the number ofparticles with lower pitch angle also may be reduced because
certain energetic particles with higher pitch angle are lost due
to the resonant loss. Here, the high-energy particle spectrum
is measured using a neutral particle analyzer, and theresonance loss is shown from the dip on the spectrum. The
various plasma parameter dependences of the resonant loss
are clarified, and compared with theoretical prediction.

4. Experiment results
We start by confirming that the dip on the spectrum isthe resonant loss. The number of energy channels in the TOF
analyzer is restricted since its merit is compactness. Moreover,the detection efficiency error of each channeltron may
produce another dip on the spectrum. Therefore we must
consider carefully that the dip on the spectrum means aresonant loss or a problem of the measurement. To make sureof this, we use a spectrum comparison with/without thepowerful central ECH in the low-density plasma, just as inCompact Helical System experiments [5,6]. It produces apositive radial electric field. In this way, the drift motion dueto the ∇B can be canceled out by the E × B drift originatingfrom this electric field. As a result, the dip in the spectrum
around 5 keV is found as shown in Fig. 1. From the analogyof the CHS experiments, it seems to be the resonant loss. The
dip at the energy of 5 keV is consistent with the expected
potential value and the energy as which the pitch angle
scattering of the NBI particles is dominant. If the slowing
down of the incidence particles by electron collision occurs
even in the tangential injected NBI, particles with large pitch
angle can be actually generated due to the scattering between
the particle and plasma ions at several times the plasma
temperature (typically 5 keV for the plasma temperature of
1–2 keV).
As mentioned above, since it is assumed that the dip
observed near 5 keV is the resonant loss, the comparison of
the spectrum for various plasma parameters is performed at
this energy. Figure 2 shows the density dependence in theplasma whose conditions are similar. From the results ofcharge exchange spectroscopy, the electric field in LHD ispositive at densities less than about 1 × 1019 m-3 and negativeat larger [3]. The critical density depends on the magnetic
axis position and the plasma temperature. The parameter don the vertical axis in Fig. 2 is given by eq. (2) as the degreeof the dip near 5 keV.

3. Experimental arrangement
The time-of-flight (TOF) type neutral particle analyzer
has a large S/N ratio for various kinds of radiation noise fromsoft X-rays. Its detail and experimental configuration aredescribed in ref. [4]. The analyzer with its driving stage isinstalled on the plasma mid-plane (port 10-O). As for theposition of 10-O, NBI#1 and NBI#2 are installed at the rightand left sides of the analyzer sight line, and especially thebeam path of NBI#1, which crosses the sight line near theplasma center, can be expected to generate neutral particles
because of charge exchange in the central part of the plasma.
The possible scanning angle is equivalent to the pitch
angles from 40 degrees to 100 degrees. The pitch angle in2311

Ozaki T. et al., Temperature, Density, Magnetic Field and Pitch Angle Dependence of Neutral Particle Spectrum in Large Helical Devic

Fig. 1Fig. 2

The density dependence of the dip depth.
The shadow emphasizes the dependence between dand density. Deep dip at high density is due to thenegative electric field.

Fig. 3

The temperature dependence of the dip depth.
The shadow emphasizes the dependence between dand temperature. The shallow dip at high temperatureis due to the positive electric field.

The spectra without (a)/with (b) ECH.
During ECH, the dip around 5 keV disappeared.

d = log(Real Flux) – log(Expected Flux) ,(2)where ‘Expected Flux’ is the flux at the dip point, obtained
from the polynomial fitted spectrum excluding the flux at thedip. The magnitude of the negative electric field around ρ =0.9 slightly increases when the density becomes high [7]. Thismeans two things. One is that the resonant energy, at whichthe ∇B drift compensates the E × B drift, increases. Anotheris that if we consider the same energy, the region with theequivalent potential is shifted inward where the backgroundneutral is poor (back ground neutral density decays in theplasma center), that is, the neutral flux at that energy
decreases. The extension of the dip at high density can beexplained by this effect. Figure 3 shows the dependence of don the electron temperature in three different density region
cases because the electric fields are strongly dependent on
the density. When the electron temperature increases, theradial electric field becomes positive. Therefore the dip depth(absolute value of d ) decreases as the temperature increase.
In the low-density region, the correlation between thetemperature and the d looks weak since the electric field issensitive against the density. Figure 4(a) shows thedependence of d on the magnetic axis position. Plasma
parameters also change as a function of the magnetic axis
position or the magnetic field strength in many cases. We

choose similar plasma parameter shots. When the magnetic
axis is shifted outward, the particle loss increases because thehelical ripple increases. The increase of the dip depth
indicates the effect. If the magnetic axis is shifted outside,although it will become stable in the magnetic hydrodynamics(MHD), from the viewpoint of particle confinement, it is notdesirable theoretically. Figure 4(b) shows the dependence ofthe d against the magnetic field strength. The increase of thedip depth at the lower magnetic field indicates bad particle
confinement. Finally, the dependence of the d on the pitch
angle is studied as shown in Fig. 5. According to theexperimental results, the dependence of the pitch angle is not
so remarkable. The typical time scale of the pitch angle
scattering TDii isTDii = 4.53 × 10−3

3312

3/2
A1/2i Ti

Zi4 (ni / 1020 ) lnΛ

[sec] ,(3)Ozaki T. et al., Temperature, Density, Magnetic Field and Pitch Angle Dependence of Neutral Particle Spectrum in Large Helical Devic
Table IThe dependence of /d /.
/d / is the amplitude of d given by eq.(2).

densitytemperaturemagnetic axis shift
magnetic field strength
pitch angle

prediction
enlargesmallerenlargesmallerenlarge

experiments
enlargesmallerenlargesmaller
not clear

where Ai , Ti , Zi , ni and lnΛ are the mass number, the ion
temperature, the ion density and the Coulomb logarithm,respectively. TDii is a few milliseconds for the actual LHD
plasma although the NPA detection duration is several tensof milliseconds. Since pitch angle scattering is dominant andreaches equilibrium at the energy of 5 keV, the number ofparticles with lower pitch angle also decrease if the particle
with higher pitch angle are lost.

5. SummaryFig. 4

The resonant loss, which is a certain phenomenon in
the loss cone, is studied under various plasma conditions. The
results are summarized in Table I. To verify if the dip on theenergy spectrum is due to the resonant loss, the comparisonof spectra with and without strong ECH has been performed.
The dip depth is introduced to compare the strength of theresonant loss. The various dependencies on density,temperature, magnetic axis position, magnetic field strengthand pitch angle, have been obtained. The results can becompared with theoretical prediction. However the actual
effect of the loss cone on the plasma performance is not so
serious in LHD due to the magnetic configuration design andthe tangential NBI heating.

Magnetic axis dependence (upper) and magnetic fieldstrength dependence (lower).
The shadow emphasizes the dependence between dand magnetic axis/ magnetic field. When the magnetic
axis is shifted outward, the dip depth becomes
extended due to the large ripple.

References

Fig. 5[1] K. Hanatani et al., Nucl. Fusion 25, 259 (1985).
[2] M. Wakatani, Stellarator and Heliotron Devices, (Oxford
University Press, 1998) p.262.
[3] K. Ida et al., ,IAEA-CN-77/EX9/4 (2002).
[4] T. Ozaki et al., V. Zanza et al., Rev. Sci. Instrum. 71(7),2698 (2000).
[5] M.Osakabe et al., Change of loss-cone due to the electricfield on CHS, Proc. 6th IAEA TM, (JAERI, 2000).
[6] T. Notake et al., Additional ECRH effects on energetic
ions in NBI-sustained plasma on LHD, Proc. 8th IAEA
TM, (San Diego, 2003).
[7] K. Ida et al., Phys. Rev. Lett. 86(23), 5297 (2001).

The pitch angle dependence.
The pitch angle dependence is not so remarkable.

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