J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)176–178
000–000

Spectroscopic Measurement to Study Two-Fluid Relaxationin an Internal Coil Device Mini-RT
YAMAKOSHI Shigeo, OGAWA Yuichi1, MORIKAWA Junji1, OHKUNI Kotaro1 and KADO Shinichiro1
Graduate School of Frontier Sciences, the University of Tokyo, Tokyo, 113-0032, Japan1
High Temperature Plasma Center, the University of Tokyo, Tokyo, 113-8656, Japan(Received: 9 December 2003 / Accepted: 20 February 2004)

Abstract
Mahajan-Yoshida has developed a new relaxation theory, by taking two-fluid effect into account. This theory
indicates that the plasma flow confines high beta plasma. We have constructed an internal coil device Mini-RT withhigh temperature superconductor (HTS) coil, and are expecting the high beta plasma with the fast toroidal plasma
flow by inducing the radial electric field. In order to measure the radial profile of the plasma flow we introduced aspectroscopy. By setting up two cylindrical lenses between a monochromator and a charge-coupled device (CCD)
detector, we could not only correct astigmatism of the monochromator but also increase the resolution of wavelength
up to 2.55 pm/pixel which is equal to the measurement of the plasma flow up to 1.6 × 103 m/s. Additionally we aresetting up an opposed fiber array for an accurate measurement. In the Mini-RT device the plasma was produced by
2.45 GHz ECH (Electron Cyclotron Heating) system with the power of 2.6 kW. Typical electron density andtemperature are more than 1016 m-3 and 10–20 eV, respectively. The ion temperature measured by this spectroscopy
system was 1.0 ± 0.3 eV and the plasma flow velocity was comparable to the resolution of this spectroscopic system.
Although the plasma should flow to the toroidal direction by the ∇B/curvature drift in the internal coil device, thedrift velocity of 1.3 × 103 m/s is not detectable with this spectroscopy. If the radial electric field of 160 V/m or moreis induced in the plasma, the plasma flow due to the E × B drift could be measured with this system.
Keywords:
two-fluid relaxation theory, Mini-RT, spectroscopy, plasma flow, ion temperature

1. Introduction

2. Spectroscopic measurement in theMini-RT device

Spectroscopy is generally used in plasma experiments asnoncontact diagnostic instrument to measure plasma flow
velocity and ion temperature and so on. This measurement isso important because plasma flow is playing an important rolein plasma confinement properties. For example it is widely
accepted in tokamak transport that the H-mode is strongly
related to a shear of the electric field profile at the edge.
A two-fluid relaxation theory developed by Mahajan andYoshida indicates that the fast plasma flow in the range ofAlfvén velocity confines high beta plasma [1]. The Mini-RT
device which has poloidal magnetic field is suitable to drive
fast plasma flow in the toroidal direction, when the radial
electric field is induced in the plasma. The electric field will
be produced by inserting an electrode in the plasma directlyor non-neutralizing with orbit loss of high-energy electron [2].
We introduced the spectroscopy to measure radial profileof the plasma flow velocity and ion temperature simultaneously. Since the spectroscopic measurement does not cool
down the plasma, we consider that non-neutralizing by orbit
loss of high-energy electron is easy to occur.

The spectroscopy in the Mini-RT device is set up formeasurements of various plasma parameters as plasma flow
velocity, ion temperature, electron density and electron
temperature and so on. The schematic drawing of thespectroscopy in the Mini-RT device is shown in Fig. 1. The
light from the plasma is collected to an optical fiber arrayseeing tangentially. In present experiments only one side
optical fiber array is set up. Therefore an absolute wavelengthis identified by standard source such as Ne lamp. The fiberarray transmits light to an 1 m Czerny-Turner spectrometer.
The basic parameters of the monochromator and the CCD
detector are shown in Table 1.
In order to correct astigmatism, we set two cylindricallenses between the monochromator and the CCD detector.
The schematic figure of this cylindrical lens system is shownin Fig. 2. The difference of focal point between in the vertical(spatial) direction and in the horizontal (spectral) direction is
7 mm due to the astigmatism of spherical mirrors in theCorresponding author’s e-mail: yamakosi@plasma.q.t.u-tokyo.ac.jp1176©2004 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchYamakoshi S. et al., Spectroscopic Measurement to Study Two-Fluid Relaxation in an Internal Coil Device Mini-RT

800400Fig. 3Fig. 1Table 1 The list for basic parameters of the monochromatorand the CCD detector.

CCD detector
Wave length
The number of pixel
Pixel size
Dark current

480500520
540
Spectral direction (pixel)

1600
1200
800
400
480500520
540
Spectral direction (pixel)

Broadened spectrum due to the spherical aberration ofthe monochromator, measured line profile (dot) andmulti-gaussian fitting curve (line).

determined as (a, b, f, a + b, m) = (300 mm, 150 mm,100 mm, 450 mm, 0.5) and (71 mm, 386 mm, 60 mm,457 mm, 5.4), respectively. The astigmatism is corrected bythis 7 mm difference of a + b in this calculation. At the sametime, we get high resolution in the spectral direction bymagnification of image m. Therefore we can measure theplasma flow velocity up to 1.6 × 103 m/s. Furthermore we
obtain several magnifications of image by changing focal
length of the lens. So when we measure the slow plasma flow,
we use large magnification of this lens system and in the caseof the fast flow we use low magnification of the lens.
Image from the monochromator is distorted by sphericalmirrors in the monochromator. This distortion is called
spherical aberration. Broadened spectrum caused by influenceof spherical aberration is shown in Fig. 3, where a backgroundof this spectrum is a lead noise of the CCD detector. In thisexperiment we put the light intensity ahead of the effect ofspherical aberration. Because we integrated the data in thespatial direction on the CCD detector for strong light intensity,measured spectrum included the aberration. The effect of theaberration in full width at half maximum (FWHM) is 0.029
nm corresponding to temperature 2.6 eV, and the instrumental
width is 0.0397 nm (slit width: 50 µm) corresponding totemperature 4.9 eV.

(A) The schematic drawing of the spectroscopy. (B) Topview of the Mini-RT with optics collecting the light
distributed radially.

Monochromator
Focal length
Grating
Instrumental width(at 50 µm slit width)
astigmatism

Addingsphericalaberration

Light intensity (count)

Light intensity (count)

12001m1800 grooves/mm
0.0397 nm
7 mm

250 nm ~ 950 nm
256 (vertical) ×1024 (horizontal) pixel
26 µm
2.8 e/pixel/hr at –80°C

3. Experimetal results

Fig. 2The Mini-RT device consists of the vacuum chamber(diameter: 1.0 m, height: 0.7 m), the HTS floating coil (major/minor radius: 150 mm /28 mm, total coil current: 50 kAT,
total weight: 20 kg), a levitation coil, cooling and exciting
instruments. The floating coil produces the dipole magnetic
field and the typical field strength is 0.1 T near the floatingcoil. In the Mini-RT device the plasma is produced by 2.45
GHz ECH and operated for over ten seconds normally. In thisexperiment the floating coil is supported by posts, notlevitating. The plasma parameters of Mini-RT are that electron
density and temperature are more than 1016 m-3 and 10–20eV, respectively.
The measured line profile at He II around 468.57 nm andfitting curve is shown in Fig. 4. We obtained fitting curve byusing multi-gaussian fitting (We used 4 lines 468.538 nm,468.541 nm, 468.570 nm, 468.580 nm out of 13 lines of He:n = 3–4) [3]. Ion temperature is estimated to be 1.0 ± 0.3 eV,
where we deducted the effect of aberration and instrument
width from measurement value. Plasma flow velocity

The cylindrical lens system compensating forastigmatism and expanding spectrum.

monochromator. The two cylindrical lenses focusing light on
different point in the each direction correct this astigmatism.
With length between image and lens a and b, focal length oflens f, magnification of image m, and a corrected thin lensequation 1/a + 1/b = 1/f, vertical and horizontal optics can be2
177Yamakoshi S. et al., Spectroscopic Measurement to Study Two-Fluid Relaxation in an Internal Coil Device Mini-RT

Light intensity (count)

Monochromator side

3000

N
Plasma side

2500
20m

S

2000
250

1500

200

1000

m
N11.5mm
S1468.52

Fig. 4468.54468.58
Wavelength (nm)Optical fiber

N2468.62m

S 2 19.6mm

37mm

Multi-gaussian fitting curve (line) and measured line
profile (dot).
Fig. 5 The schematic of the opposed fiber array.

calculated from Doppler shift has margin of error which iscomparable to measurement value. So we obtained thatplasma flow velocity is less than 1.6 × 103 m/s.
∇B drift and curvature drift are considered as toroidal
plasma flow in the Mini-RT device with the dipole magnetic
field. ∇B drift and curvature drift are expressed as follows:v∇B + vR =⎞m R × B ⎛⎜ 1 22⎟
v+v
⎜⎟,
⊥
||
⎟q R 2 B 2 ⎜⎝ 2⎠

By changing the focal length of lens we can measure theplasma flow velocity up to 6.0 × 102 m/s. So we will be ableto obtain ∇B and curvature drift velocity.
We have to apply an electric field to plasma more than
160 V/m to measure E × B drift. Additionally in order todrive plasma up to Alfvén velocity, we need to charge up
plasma to 260 kV which is equivalent to electric field
860 kV/m, where the electron density is 4.2 × 1016 m-3 andpoloidal magnetic field is 0.09 T. When we measure theplasma flow velocity up to Alfvén velocity, Doppler shift is
too large to detect to the contrary. Hence, we have to change
the magnification of image in the cylindrical lens system to0.3 times for exposing the shifted spectrum on the acceptancesurface of the CCD detector.
Since the line-integrated emission is measured in thespectroscopy except for active diagnostics such as chargeexchange spectroscopy, some techniques might be required.
Especially, we cannot apply the Abel inversion on the flow
velocity measurements, because the velocity component of theline-of-sight in the toroidal flow velocity is measured. We
need to use a parameter-fitting technique due to necessity forcompensation of the flow direction at the non-focal point.
We could measure the plasma flow velocity up to 1.6 ×
103 m/s by using the expander optics which consists of two
cylindrical lenses. We obtained that ion temperature is 1.0 ±0.3 eV and the flow velocity is comparable to maximum
resolution of spectroscopy in the Mini-RT plasma. We aresetting up the opposed optical fiber array which could
eliminate the error of spectral identification and increase theresolution of the spectroscopy system. Accordingly we canmeasure the plasma flow velocity up to 6.0 × 102 m/s.

(1)where v∇B and vR are ∇B drift and curvature drift velocity
respectively, R is curvature radius of poloidal magnetic field,m and q are ion mass and quantum of electricity, ⊥ and ||indicate perpendicular and parallel to poloidal magnetic field,respectively. We obtain that this drift velocity is up to 1.3 ×
103 m/s with magnetic field 0.003 T and ion temperature
1.0 eV in the Mini-RT device. Because of these drift speeds,
it is reasonable that Doppler shift is comparable to themaximum spectral resolution of this spectroscopy system.
We consider the E × B drift velocity expressed vE×B =E/B from radial electric field and magnetic field. The radial
profile of the plasma potential from probe measurements isthat the potential is flat at about 60 V from the coil to thechamber wall. It is due to the support interrupting to produce
the high-energy electron. Therefore we regarded that theradial electric field is too small to generate measurable
E × B drift.

4. Discussion and summary
We are installing the opposed optical fiber array shownin Fig. 5.
By using this fiber array we can eliminate the error ofspectral identification of standard source and improve theresolution of the spectroscopy system. The space between theoptical fibers on the plasma side is designed for measuring
the radial distribution of plasma parameters all at once. Also
the space on the monochromator side is made for decreasinga cross-talk between optical fibers. The optical fibers ofdifferent view side are alternately arranged on themonochromator side for correcting the spherical aberration.

References[1] S.M. Mahajan and Z. Yoshida, Phys. Rev. Lett. 63, 4836
(1998).
[2] Y. Ogawa, Trans. Fusion Sci. Technol. 43, 203 (2003).
[3] S. Kado, J. Plasma Fusion Res. 79, 839 (2003).

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