J. Plasma Fusion Res. SERIES, Vol.7 (2006) 5-8

Line Ratios within σ and π Components of Hα Lines from High Energy
Hydrogen Atom with Motional Stark Effect
IDA Katsumi, YOSHINUMA Mikirou, GOTO Motoshi, ATAKE Makoto1and IWAMAE Atsushi1
National Institute for Fusion Science, Toki 509-5292, Japan
1 Department of Engineering Physics and Mechanics, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan（Received: 4 October 2004 / Accepted: 28 April 2005）

Abstract
The Line ratios within σ and π components of Hα lines from high energy hydrogen atom with Motional
Stark Eﬀect are investigated experimentally using the heating beam and plasma in Large Helical Device withthe magnetic field of 2.78 T. The line averaged electron density and central electron temperature in the plasma
are 2 × 1019 m−3 and 1.5 keV, respectively. The emission spectra are measured through four sets of polarizer
which tilted by 0, 45, 90, and 135 degree with respect to the magnetic field at the plasma center using animaging spectrometer. Nine lines of Hα lines ( 0σ, 1σ+, 1σ−, 2π+, 2π−, 3π+, 3π−, 4π+, 4π−) are observedin the spectra emitted from the hydrogen beam with the energy of 150 − 180 keV/amu. The line ratio of
circular polarized components 1σ/0σ, is significantly larger than that caculated although the line ratio of
linear polarized components 4π/3π is consistent with the calculation. The discrepancy of the line ratio of
1σ/0σ, becomes larger when it is observed more perpendicular to the beam line, which suggest the ellipticalpolarization of σ lines due to the non-Maxwell proton excitation by high energy beam.
Keywords:
Motional Stark Eﬀect, plasma, spectroscopyStark spectrum. In this paper, the fine structure of σ andπ lines observed in the MSE spectroscopy is described.

1．Introduction
Since the motional Stark features was observed in
the Balmer spectrum radiated from the neutral hydrogenor deuterium beam injected to the plasma confined bymagnetic field, the Motional Stark Spectroscopy (MSE)
has been a useful tool to measure the radial profile of rotational transform [1-4]. In order to study the fine structure of the σ and π lines the observation from the highenergy neutral beam and strong magnetic field are necessary, because the motional stark shift is proportional
to the beam velocity and magnetic field, In the experiment in PBX-M, where the magnetic field, B, and beamenergy, E, were not high enough (E = 55 keV/amu,
B = 1.3 T), the fine structure of each component, forinstance 0σ and 1σ or 2π, 3π and 4π, was not observed[1]. This is in contrast to the measurements in JET,
where the magnetic field B is 3 T, the fine structure ofeach lines are observed and the ratio of 1σ to 0σ or 2πto 3π and 4π to 3π are measured. There are some discrepancy observed between the measurements and theoretical calculation [3]. The Large Helical Device equips
high energy beam with the energy of 150 − 180 keV andhigh magnetic field of 3 T and is considered to have abig advantage to study the fine structure of the motional

2．Motional stark effect
The neutral beam injected in the plasma is excited
to the upper energy levels through collisions with electrons and ions in the plasma. The line spectrum emitted from a high energy hydrogen beam is dominatedby the motional Stark eﬀect due to the Lorentz electricfield E = vB sin(β), where v is the beam velocity andB is the total magnetic field and β is an angle between
beam line and magnetic field. This Lorentz electric field
causes the Hα line to split into 15 Stark components, 9of which ( 0σ, 1σ+, 1σ-, 2π+, 2π-, 3π+, 3π-, 4π+, 4π-)
are strong enough to be observed. These components
are divided into to polarization groups. The σ lines dueto the transition for which ∆m = −1 or +1, where m isa magnetic quantum number) are circular polarized perpendicular to the Lorentz electric field, while the π lines
due to the transition for which ∆m = 0 ) are linearlypolarized parallel to the Lorentz electric field. Whenviewed nearly perpendicular to the Lorentz electric field
C 2006 by The Japan Society of Plasma

Science and Nuclear Fusion Research

Corresponding author’s e-mail: ida@nifs.ac.jp

5Line Ratios within σ and π Components of Hα Lines from High Energy Hydrogen Atom with Motional Stark Eﬀect(this is the case in this experiment), σ lines are almost
linearly polarized perpendicular to the Lorentz electricfield. Therefore the σ lines and π lines can be measured
separately by inserting the linear polarizer, one is parallel and the other is perpendicular to the Lorentz electricfield, in front of the object lens.

(1340×1300 with 20×20 micron pixel) at the exit plane
is used to measure 100 spectrum.
4．Fine structure of σ lines and π lines
Figure 2 shows the σ lines and π lines measured
with the MSE spectroscopy system. The σ lines aremeasured with the channel with the polarizer parallel tothe horizontal direction (horizontal channel), while theπ lines are measured with the polarizer parallel to thevertical direction(vertical channel). Since the Lorentz
electric field is slightly tilted from the vertical direction
due to the poloidal field produced by the external helicalcoil current, small σ lines appears even in the verticalchannel.

3．Spectroscopy system for the MSE measurements in LHD
Figure 1 shows the experimental set up for Motional
Stark Eﬀect (MSE) spectroscopy installed in the Large
Helical Device. The Large Helical Device (LHD) is atoroidal helical magnetic device (Heliotron device) witha major radius of Rax = 3.5 − 4.1 m and a magnetic field
B of 0.5 − 3 T. The major radius Rax , an average minor
radius, a magnetic field B and the beam energy is 3.6 m,0.6 m, 2.78 T and 170 keV in this experiment.
The MSE system consists of spectrometer, opticalfibers and linear polarizer tilted by 0, 45, 90 and 135 degree with respect to the horizontal direction. The liner
polarizer are arranged in front of object lanes to avoid
the change of polarization angle due to lenses. The
100 optical fibers with a diameter of 200 micron coreand 250 micron clad are arranged at the focal plane ofeach object lens. The optical fibers are divided to 25
groups and each group has optical fibers with the linear polarizer tilted by 0, 45, 90 and 135 with respect tothe horizontal direction. The object lens of each optical fiber arrays are adjusted to make optical fiber in asame group to view an identical observation point (intersection between beam line and line of sight). The
100 optical fibers are arranged at the entrance slit of thehigh throughput spectrometer (Bunkou-Keiki CLP-400)
which consists a pair of f = 400 mm/F = 2.8 camera
lenses and 2160/mm grating. A back illuminated CCD

Fig. 2 σ lines and π lines measured MSE spectroscopy
system.

The asymmetry of σ lines (higher 1σ in larger wavelength) observed is due to the geometric eﬀect. The
motional Stark shift is proportional to v × B cos(β) andthe Doppler shift is proportional to cos(θ), where θ isa angle between the beam line and line of sight. Boththe angle β and θ changes along the line of sight within
the beam width due to the beam divergence with keeping the diﬀerence more or less constant. Therefor when
the Doppler shift increases, the motional Stark shift decreases. When the direction of Doppler shift and motional Stark shift is in the same direction (in the longerwavelength side) the beam divergence causes the increase of the peak of 1σ+ line. On the other hand, in theshorter wavelength side ( 1σ− line), where the directionof motional Stark shift is in the opposite to the Doppler
shift, the beam divergence causes the decrease the peakof line.
5．Line intensity ratio of 1σ and π lines to 0σlineAs seen in Fig. 3, the beam divergence causes thediﬀerence of peak height between 1σ− and 1σ+ or π−and π+ lines. Three component of σ lines and π lines

Fig. 1 Experimental setup for Motional Stark Effect spectroscopy in LHD.

6

Line Ratios within σ and π Components of Hα Lines from High Energy Hydrogen Atom with Motional Stark Eﬀect

3000

Intensity

2500(a)0σ20001500

1σ−1000
500
06672

Here the viewing angle is parallel to the magnetic fieldand perpendicular to the Lorentz electric field. The calculated line ratios are tends to increase as the Lorentz
electric field decreases for low Lorentz electric field below 2 MV/m, where the Zeeman eﬀect becomes important. At higher Lorentz electric field above 2 MV/m, theZeeman eﬀect can be neglected and the line ratios arealmost constant does not depend on the magnitude ofLorentz electric field. At higher Lorentz electric field,
the line ratio does not depend on the magnitude of magnetic field as seen in Fig. 4(b).
The line ratios of 1σ and π lines to 0σ line measured
are significantly larger than that predicted by calculations. The mechanism causing the discrepancy of measured ratio to that calculated is not clear yet, although
the discrepancy itself have been observed in the previous work.

1σ+


0.46

0.60
6674
6676
6678
wavelength(angstrom)

6680

Fig. 3 The spectrum measured and calculated for (a) σand (b)(c) π lines. The open circles are spectra
measured with MSE spectroscopy, while the solidlines are fitting curves with multi Gaussian.

are fitted with three Gaussian profiles. The discrepancy at the longer wavelength tail is due to the overlapping of σ lines to the measurements of π lines measured with the liner polarizer parallel to the vertical direction, because of the tilting of Lorentz electric field
due to poloidal magnetic field. In order to eliminate theeﬀect of beam divergence on the estimate of line ratios,
the peak heights of 1σ− and 1σ+ or π− and π+ lines areaveraged. The averaged values are compared with that
calculated with magnetic field of 3 T for various magnitude of Lorentz electric field as shown in Fig. 4(a).

Fig. 4 Comparison of line ratios measured to that calculated (solid line for the emission viewing parallel tothe magnetic field and dotted line for the emission
viewing perpendicular to the magnetic field as afunction of Lorentz electric field with a magnetic
field of 3 T and (b) magnetic field with a Lorentz
electric field of 5.3 MV/m.

7

Line Ratios within σ and π Components of Hα Lines from High Energy Hydrogen Atom with Motional Stark Eﬀect

0σ and 1σlines in the MSE spectrum, where the excitation process is dominated by the collision between theproton in the plasma and neutral beam. When the beamenergy is low, the excitation is mainly due to electron
impact, which can be treated as Maxwell distribution.
However, when the beam energy is high, the proton impact becomes dominant in the excitation process. It
should be noted that the discrepancy of line ratios between the measurements and calculation becomes significant for the MSE spectra from the high energy ofbeam of 150 – 180 keV/amu in LHD. The orientation in
the excitation process due to the non-Maxwell ion impact, which is not included in this calculation should
be taken into account. The calculation including theseeﬀect will be developed in future.
The authors would like to thank the LHD technicalstaﬀ for their eﬀort to support the experiments in LHD.
This work is partly supported by a grant-in-aid for scientific research of MEXT Japan.

Fig. 5 Viewing angle dependence of line ratio 1σ / 0σ
for the plasma with magnetic field of 2.78 T andLorentz electric field of 5.3 MV/m in LHD.

6．Discussions
As discussed in the previous section, the measured
line ratio of 1σ/0σ is significant larger than that calculated.
The line ratio of circular polarized components1σ/0σ, is significantly larger than that calculated although the line ratio of linear polarized components
4π/3π is consistent with the calculation. The intensity
ratio of 1σ/0σ has viewing angle (intersection angle
between line of sight and beam line ) dependence asshown in Fig. 5. It should be noted that 1) the discrepancy is significant in the circular polarized line and not
the linear polarized line, 2) a degree of the discrepancy
strongly depends on the viewing angle with respect tothe direction of neutral beam exciting the Hα line.
This data suggests that σ lines are elliptical polarized and there is a diﬀerence of the ellipticity between

[1]

[2]

[3]

[4]

8

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