ELSEVIER Fusion Engineering and Design 34-35 (1997) 257-260

Fusion Engineering and Design

Measurement of plasma rotation in a tandem mirror

K. Ikeda a, y . N a g a y a m a b N. Yamaguchi °, M. Yoshikawa a, T. Ao ta ~, T. Ishijima a, Y. Okamoto ~, K. Ishii a, A. Mase a, T. Tamano ~

a Plasma Research Centre, University of Tsukuba, Tsukuba 305, Japan b National Institute for Fusion Science, Nagoya 464-01 , Japan

c Toyota Technological Institute, Nagoya 468, Japan

Abstract

Diamagnetic rotation of a cylindrical plasma has been investigated in the GAMMA 10 tandem mirror by using a UV-visible TV spectrograph system. A parameter-fitting technique is developed for obtaining spectra of local impurity emission profiles and diamagnetic rotation is determined from the impurity density profile. © 1997 Elsevier Science B.V.

Measurement of plasma rotation using visible impurity emission is widely used for determining the electric field in a plasma. The measured plasma rotation is E x B drift plus diamagnetic drift; both of which are obtained from the ion momentum balance equation [1]:

E x B V p ~ x B

v ~ - B2 n"Z~eB 2 (1)

where p~, n~ and Z~ are the impurity pressure, density and charge respectively, e is the electron charge, B is the magnetic field and v~ is the plasma rotation velocity. Therefore, the radial electric field E and impurity pressure p~ can be obtained from measurement of plasma rotation velocity v~ when the magnetic field B is already known. In torus systems, diamagnetic drift is small and the radial electric field is estimated at the peak of emission, where diamagnetic drift is zero. Plasma rotation due to the diamagnetic drift has not been sufficiently studied in experiments.

In this paper, we will investigate diamagnetic rotations of a cylindrical plasma in the G A M M A 10 tandem mirror [2]. Measurement of diamag- netic rotation in cylindrical plasmas is much eas- ier than that in torus plasmas. First, we will describe the UV-visible TV spectrograph system. Then, we will discuss a parameter-fitting tech- nique for obtaining spectra of local impurity emis- sion profiles. Finally, we will present a diamagnetic drift velocity profile determined from an impurity density profile.

In the G A M M A 10 tandem mirror, the plasma potential plays an important role in plasma confi- nement. Doppler shifts of spectral lines from vari- ous charged ions including ions in low ionization states are measured by a 40-channel UV-visible spectrograph system covering x = - 20 to + 20 cm with a channel separation of 1 cm. The spec- trograph system views the plasma column verti- cally, as illustrated in Fig. 1. The visible light is transmitted from the plasma to the spectrometer

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258 K. Ikeda et aL / Fusion Engineering and Design 34-35 (1996) 257-260

through an 8 m long bundled optical fibre array. Each optical fibre consists of a quartz core with a diameter of 400 /zm and a clad glass with a thickness of 50 •m. The optical fibres are led to the entrance slit of the 1 m Czerny-Turner spec- trometer with a grating of 2400 grooves mm-1. The observable wavelength is in the range from 200 nm to 530 nm. At the exit plane the light from each fibre gives the spectrum from each spatial position. The dispersed light from the fibre optics is focused onto an image intensifier tube coupled with a charge-coupled device (CCD) TV camera with a time resolution of 16.7 ms. The output of the CCD camera is a standard TV composite video signal, and it is digitized by an 8-bit video capture board installed in a personal computer. An example of an image detected by the TV camera is shown in Fig. 2; the vertical axis is the spatial position and the horizontal axis is the wavelength. Then the digitized image is analysed with a personal computer (Macintosh 8100/80AV) and a workstation, which are con- nected by an Ethernet network. Determination of the spatial position and the calibration of the relative sensitivity of the spectrograph are carried out using a mercury pen lamp and a 1.2 m long linear fluorescent lamp. This leads to a spectral resolution of 0.08 nm. The absolute sensitivity of the system is calibrated by using a tungsten rib- bon lamp calibrated by NIST as a spectral radi- ance standard source.

The detected signal is a line-integrated emis- sion. Here, we use a parameter-fitting technique

0.1

~o

-0.1

276 277 278 279 280 Wavelength [nm]

Fig. 2. An inverted image of a spatially resolved UV-visible spectrum taken in an ICRF-heated plasma on the G A M M A 10 central cell.

for obtaining the spectrum of the local emission. A pressure gradient can be described by an equa- tion of state. The diamagnetic drift velocity de- pends on density and temperature profiles. Since the observed impurity temperature gradient and the electric field are estimated to be negligibly small in this plasma, the rotation velocity (Eq. (1)) becomes

kBT~(r, O) l gnu(r, O) v~(r, O)- (2)

Z~eB no(r, O) 6r

where ks is Boltzmann's constant and the impu- rity temperature T~ is constant.

The brightness of impurity emission is roughly proportional to the product of electron density and impurity density provided that the excitation

~ 4 0 c h Optical Fiber

/ ~ < ~ / / 1 ~ ~ ~ - ~ r \ , L;.;es

Image Intensifier [..r - Plasma CaCgeVaideol

I I I I I Camera Controller

Fig. 1. Schematic diagram of the experimental set-up on the G A M M A 10 tandem mirror for measurement of plasma rota- tion.

P, s

I

i

Fig. 3. Geometry and coordinate system for the analysis.

K. Ikeda et al . / Fusion Engineering and Design 34-35 (I996) 257-260 259

6 2

n -

4 ~ g-"

'd' 2 =~ D Dm 1

0 -0.2 R 0 0.2 top

Radius [m]

Fig. 4. Elect ron densi ty profile (thin line) m e a s u r e d with a in ter ferometer and the radial profile ( thick line) o f the impu- rity densi ty func t ion for pa rame te r fitting. The fit t ing pa r am e- ters are also indicated.

rate has a weak temperature dependence for the measured emission line. We calculate the bright- ness if impurity emission I(r, O) from I(r, O)ocn~(r,O) ne(r , 0). The geometry and the coordinate system for this analysis are shown in Fig. 3. The impurity density profiles n~(r, O) are assumed to be as follows:

where Rtop , g t o p , H i n , Din and D o u t a r e fitting parameters shown in Fig. 4. Here a is the radius of the plasma column. The local impurity emis- sion Q(r, O) at position (r, 0) is written

Q(r, O) = I(r, O) { lm~.[v-v~(r,O)cosz] 2}

x exp 2 lcB-~(r, 0-)

(4) where Z is the angle between the direction of rotation velocity and the line of sight. Now, we assume axial symmetry. The integrated spectrum S(p, 2) of impurity emission along the line of sight is given by

S(p, 2) = .}r ds I(r, 0)

x exp 2kBT~(r, 0)

x ds (5)

where L is the line of sight, c is the light veloc- ity, 2~ is the wavelength of the impurity emis- sion and A 2 = 2 - 2 ~ . Both the diamagnetic rotation and the brightness of impurity emission

~ (Hto p - - //in ) exp [ - (r - Rtop) 2 in 2/D~j + H~n n~(r,O) = l H t ° p exp [ - ( r - Rtop) 2 I n 2/D2out]

0 _ r </~top Rto p ~ r < a a_<r

(3)

20 ~ . . . . I . , ,I . . . . , . . . . , . . . . I, ,~ I,... / . . . .

? 10) 02+ o ~ 0 0 0

o = -10

'~ o E I:~ -20 ,,

-0.2 -0.1 0 0.1 0.2 Radius [m]

Fig. 5. 0 2 + ro ta t ion velocity m e a s u r e d for the G A M M A 10 t a n d e m mirror : - - , d i amagne t i c drift velocity calcula ted by us ing the parameter - f i t t ing technique.

are calculated by fitting the observed spectrum to this equation.

Fig. 5 shows a radial profile of the diamag- netic rotation velocity, both measured and cal- culated values, in the ICRF-heated plasma. The core plasma potential ~bc which was measured by a gold neutral beam probe was nearly equal to the floating potential of a central cell limiter with 36 cm diameter. Therefore, the electric field is negligibly small in this plasma. The plasma rotation velocity was measured by using the O III line (298.4 nm). The direction of the 02+ diamagnetic rotation and the E x B drift direc- tion are equal in the region outside the peak position of the impurity density profile, and are

260 K. Ikeda et al./Fusion Engineering and Design 34-35 (1996) 257-260

opposite in the inner region between the peaks of the impurity density profile.

In conclusion, diamagnetic rotations have been investigated in a cylindrical ICRF-heated plasma with a negligible electric field in the G A M M A 10 tandem mirror. Diamagnetic drift velocity profiles are measured by using a space- and wavelength- resolving UV-visible TV spectrograph system. A parameter-fitting technique is developed for ob- taining a spectrum of the local impurity emission profile. The diamagnetic rotation profile is deter- mined from the density of both impurity and electrons.

Acknowledgements

The authors would like to acknowledge the G A M M A 10 group members for their operational and diagnostic support and for useful discussions.

References

[1] F.F. Chen, Introduction to Plasma Physics, Plenum, New York, 1974.

[2] M. Inutake et al., Proc. 14th Int. Conf. on Plasma Physics and Controlled Nuclear Fusion Research, W/irzburg, 1992, Vol. 2, IAEA, 1993, p. 651.