VOLUME 78, NUMBER 20 P H Y S I C A L R E V I E W L E T T E R S 19 MAY 1997

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Rotation of Cylindrical Plasmas in the GAMMA 10 Tandem Mirror

K. Ikeda,1 Y. Nagayama,2 T. Aota,1 M. Ichimura,1 K. Ishii,1 T. Ishijima,1 Y. Kiwamoto,1 A. Mase,1 T. Saito,1

T. Tamano,1 T. Tokuzawa,1 N. Yamaguchi,3 and M. Yoshikawa11Plasma Research Center, University of Tsukuba, Tsukuba 305, Japan

2National Institute for Fusion Science, Toki 509-52, Japan3Toyota Technological Institute, Nagoya 468, Japan

(Received 10 September 1996)

Plasma rotation of cylindrical plasmas has been investigated using the visible spectroscopy in theGAMMA 10 tandem mirror. Significant observations are as follows: (1) Radial profiles of an electro-static potential obtained from rotations of various ions are identical; (2) A radial profile of a diamagneticflow velocity varies with ion species, which indicates that diamagnetic drift is different for different ionspecies. This is the first clear experiment observing a diamagnetic drift in high temperature plasmas.[S0031-9007(97)03173-6]

PACS numbers: 52.30.–q, 52.25.Vy, 52.55.Jd, 52.70.Kz

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The effect on plasma confinement of an electric fiehas been intensively investigated in tandem mirrors [Recently, the electric field has become a more importmatter due to its role for improved confinement in torsystems [2]. The electric field profiles are often obtainby the use of plasma rotation and pressure profile measments with visible spectroscopy [3–7]. The basic equatof the plasma rotation velocityva for each ion speciesais as follows:

va ­E 3 B

B2 2=pa 3 BnaZaeB2 , (1)

wherepa, na , andZa are the pressure, the density, and tcharge of each ion species, respectively,e is the electroncharge,E is the electric field, andB is the magneticfield. The first term represents anE 3 B drift, and thesecond term a diamagnetic drift. The radial electric fieis recently considered to play an important role of timproved confinement in torus plasmas [5]. The ideaas follows: In the torus system, the ion poloidal rotatiis often damped with many reasons, so the electric fielcreated in order to cancel the ion diamagnetic rotationEq. (1). The created electric field drives the shearedE 3

B rotation of the plasma, which suppresses turbulencethen causes the improved confinement such as the H m

There are two basic questions: One is whetherE 3 B drift is identical for different ion species; anotheis whether the diamagnetic drift is different for differenion species. These questions are so important to theperiment and theory of improved confinement that thshould be examined experimentally. It has been obserthat the electric field measured from the main ion rotatiand that from the impurity ion rotation are identical in thD-IIID tokamak [7]. This is an answer to the first quetion. However, some assumptions are required to calate the friction between the poloidal flow and the toroidflow for the data analysis in torus plasmas. Simpler eperiment with fewer assumptions would be requiredconfirm this result. In most spectroscopic measureme

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of the radial electric field, the diamagnetic drift is sometimes neglected or sometimes estimated from plasmarameters [4]. In spite of its importance, the momentubalance equation (1) has not been well examined expmentally. Especially, experimental studies about diamanetic drift have been so inconclusive in high temperatuplasmas.

In this paper, we will investigate rotations of cylindrical plasmas by the use of a UV-visible TV spectrograsystem [8] in the GAMMA 10 tandem mirror [9]. In-terpretation of an ion rotation in cylindrical plasmasrather straightforward. The rotation of variously chargeions can be measured because the electron temperaturather low (70 100 eV). This paper will present two ex-amples: In one case theE 3 B drift is dominant, andin another case the diamagnetic drift is dominant.significant result is that the above two questions on tE 3 B drift and the diamagnetic drift are exactly confirmed. Also, this is the first clear experimental verification of the diamagnetic drift in high temperature plasma

The GAMMA 10 is a 20 m long tandem mirror consisting of a 5.6 m long axisymmetric central cell, anchor cefor suppressing MHD instabilities and axisymmetric enmirrors for forming plug–thermal-barrier potentials [9]A plasma in the central cell is produced and heated byelectron cyclotron resonance (ECR) heating [10] andby an ion cyclotron range of frequency (ICRF) heatin[11]. The magnetic field at the center is 0.4 T in the caof ICRF heating experiment and 0.48 T in the caseECR heating experiment. The mirror ratio is about threThe schematic view of the experimental setup is shownFig. 1. An impurity emission from the cylindrical plasmawhich is confined in the central-cell region, is collected ba quartz lens and is transferred to a spectrometer byuse of a 40 channel quartz fiber array. A light collectiosystem coversx ­ 220 , 120 cm with a channel sepa-ration of 1 cm. A spectrum is detected with an imagintensifier tube coupled with a CCD TV camera at the e

© 1997 The American Physical Society

VOLUME 78, NUMBER 20 P H Y S I C A L R E V I E W L E T T E R S 19 MAY 1997

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FIG. 1. Schematic diagram of the experimental setup onGAMMA 10 tandem mirror for the measurement of the plasmrotation. The coordinates for the Abel inversion are ashown. Anglex is the angle between the direction of iomotion and the line of sight at the positionsr, ud.

plane of a 1 m Czerny-Turner spectrometer with a gratof 2400 groovesymm. A spatial position and a relativsensitivity of the spectrograph are calibrated using a mcury pen lamp and a 1.2 m long linear fluorescent lamThe spectral resolution is 0.08 nm, and the time resotion is 17 ms [8]. The measured oxygen spectral linare as follows: OII line (441.5 nm) from O1, OIII line(298.4 nm) from O21, OIV line (306.3 nm) from O31,and OV line (278.1 nm) from O41.

The Doppler shift is determined from impurity spetra Sasld, which are fitted to the Gaussian asSasld ­C expf2Dsl 2 Dld2g, whereDl, C, and D are fittingparameters. Here,l ­ lobs 2 la , wherela is a wave-length of the impurity emission andlobs is the observedwavelength. The observed spectraSasld is the integralof impurity emission along the line of sight. AssuminMaxwellian velocity distribution in the cylindrical symmetric system,

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where sr , ud is the polar coordinates,s is the distancealong the line of sightL, x ­ f 2 u is the anglebetween the direction of rotation and the line of sigma is the mass of the impurity ion,c is the lightvelocity, and kB is the Boltzmann constant. In thpresent work, profiles of the impurity density and thelectrostatic potential are obtained using the paramfitting technique [8]. The fitting procedure is as follow(1) Assume fitting parameters for profiles of the io

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density and the electrostatic potentialF; (2) calculatethe ion velocity using Eq. (1); (3) calculate the emissivigasrd assuminggasrd ~ nesrdnasrd; (4) calculateSasldusing Eq. (2); (5) calculate profiles of the Doppler shiand the brightnessIa, of which definition is

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(6) adjust fitting parameters and repeat the process6) until the calculated profiles of the Doppler shift anthe brightness fit to the observed profiles. The impurion temperature, which is obtained from the width of thspectrum, is fixed during this procedure.

Figures 2 and 3 show a typical example of theE 3 Bdrift, which is observed in ECR heated GAMMA 10plasmas. Figure 2 shows comparison of the observprofiles of the Doppler shift and the brightness witcalculated ones from assumed profiles of the impurdensity and the electrostatic potential, which are shoin Fig. 3. These profiles fit well. In this plasma, thobserved impurity ion temperatures from the Dopplwidth are as follows: 20 eV for O1, 40 eV for O21,60 eV for O31, and 80 eV for O41. Those profiles foreach ion species are flat. Figure 2 shows that the Doppshift profile is similar for different ion species. Both

FIG. 2. The radial profiles of (a)–(d) the Doppler shift an(e)–(h) the line spectra from various oxygen ions in the ECheated plasma, where theE 3 B drift is dominant. The solidcurve is obtained by using the parameter fitting technique.

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VOLUME 78, NUMBER 20 P H Y S I C A L R E V I E W L E T T E R S 19 MAY 1997

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FIG. 3. Radial profiles of (a) the electron density, (b) toxygen ion density, and (c) the electrostatic potential inECR heated plasma, where theE 3 B drift is dominant.

the E 3 B drift and the diamagnetic drift are taken intaccount. However,E 3 B drift is 10 times faster thanthe diamagnetic drift. A contribution of the diamagnetdrift is very small due to a lack of ion heating. Thereforthese Doppler shift profiles indicate theE 3 B drift,dominantly. The various ions rotate in a similar manne

The O41 ion density profile is peaked and the othoxygen ion density profiles are hollow, as shown in Fig.Figure 3 also shows the Abel inverted electron denswhich is measured by the use of a multichannel finfrared interferometer [1]. The highly charged oxygeions locate in the region of the high electron temperatubasically. Electrostatic potential profiles obtained frothe differently charged oxygen ions are shown in Fig.The various oxygen ions provide the identical electrostapotential profiles so that theE 3 B drift is identicalfor the different ion species. The potential differenbetween the center and the edge is 900 V with the eof 200 V in this plasma. The gold neutral-beam promeasurement does not work in this particular plasbecause of a slightly different magnetic field, but the beprobe measurement [12] in the similar plasmas providthat the difference between the central-cell potential athe limiter floating potential tends to be1 , 1.2 kV. So,those potential measurements are consistent. This isfirst measurement of the potential profile in tandem mirplasmas. Interestingly, the potential profile is narrowthan the electron density profile.

Figures 4 and 5 show a typical example of thdiamagnetic drift, which is observed in ICRF heatGAMMA 10 plasmas. The observed impurity ion temperatures from the Doppler width are as follows: 120 efor O1, 270 eV for O21, 350 eV for O31, and 400 eV

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FIG. 4. The radial profiles of (a)–(d) the Doppler shift and(e)–(h) the brightness of the line spectra from various oxygeions in the ICRF heated plasma, where the diamagnetic driftdominant. The solid curve is obtained by using the parametfitting technique.

for O41, and those profiles for each ion species are flaFigure 4 shows comparison of the observed profilesthe Doppler shift and the brightness with calculated onefrom assumed profiles of the impurity density and thelectrostatic potential, which are shown in Fig. 5. Thesprofiles fit well. In this fitting, the electrostatic potentialis taken into account. The measured potential from thbeam probe and the space potential at limiter are showin Fig. 5(c). The plasma potential at the center, which imeasured by using the gold neutral-beam probe, is 240and the floating potential at the limiter ofr ­ 18 cmis 330 V, as shown in Fig. 5. Thus the electric field isvery small in this plasma. The width of the brightnesprofiles and width of the electron density profile in ICRFheated plasma are narrower than those in the ECR heaplasma. So the diameter of the ICRF heated plasmcolumn is smaller than that of the ECR heated plasmThe diamagnetic drift in the ICRF heated plasma is muclarger than that in the ECR heated plasma becauseimpurity ion temperature is much higher and the width othe impurity density profile is much narrower in the ICRFheated plasma than in the ECR heated plasma.

A clear difference is observed in rotation characteristicof oxygen ions with different charges. Interesting feature

VOLUME 78, NUMBER 20 P H Y S I C A L R E V I E W L E T T E R S 19 MAY 1997

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FIG. 5. Radial profiles of (a) the electron density, (b) toxygen ion density, and (c) the electrostatic potential inICRF heated plasma, where the diamagnetic drift is domina

of the diamagnetic drift are as follows: The directionthe diamagnetic rotation in the inner region is opposto the direction of theE 3 B drift; the direction of therotation reverses at the particular radius. Any electrostpotential profile cannot give different rotation profiles fodifferent ion species. When the impurity pressure prois hollow, the pressure gradient in the inner regionopposite to that in the outer region. The second teof Eq. (1) indicates that the opposite pressure gradcauses the opposite direction in the diamagnetic rotatThe observed reverse radius of the Doppler shift isfollows: 9 cm for O1, 8 cm for O21, 7 cm for O31, and4 cm for O41. The reverse radius for the ion with highecharge is smaller. The radius of the peak positionthe hollow brightness profiles is smaller for the ion wihigher charge. This tendency is similar to the reveradius of the Doppler shift. The oxygen ion densiprofiles are hollow, as shown in Fig. 5. Radii of the peof the profile are as follows: 12 cm for O1, 11 cm forO21, 9.5 cm for O31, and 7 cm for O41. Those radiiare slightly wider than reverse radii of the Doppler shprofile. This is because the observed Doppler shift prois the line integrated one.

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In GAMMA 10 plasmas, the ion temperature is different among different ion species even at the same potion and each ion species has flat temperature profiles.probable reason is as follows: The H1 ions are heatedby ICRF and the electron is cooled by the end loss. Tcentral H1 ion temperature is 5 keV and the central eletron temperature is 70 eV. The impurity ions are heatby the collision with H1 ions and cooled by the collisionwith electrons. The temperature of each ion species istermined by the balance of the heat transfer. Also, colsion is less frequent due to the low density. For exampthe collision time between O41 ions and the backgroundH1 ions is the order of 100 ms, if the density of O41 ionis 1% of the electron density. Therefore the different iospecies have different temperature at the same position

Experimental results are concluded as follows: (Radial profiles of an electrostatic potential obtained frorotations of various ions are identical; (2) the Doppleshift profile due to the diamagnetic rotation is differenfor the different ion species as is expected from thsecond term of Eq. (1). These results are usefulverify the momentum balance equation (1), and so thexperiment provides a strong foundation for the studythe improvement confinement with the electric field.

The authors would like to acknowledge thGAMMA 10 Group for their operational and diagnosticsupport. They also would like to thank Professor K. Idfor the useful discussions. This work was supporteda Grant-in-Aid for Scientific Research (No. 06452433from the Ministry of Education, Science and CultureJapan.

[1] A. Maseet al., Nucl. Fusion31, 1725 (1991).[2] K. Itoh and S. Itoh, Plasma Phys. Controlled Fusion38, 1

(1997).[3] K. Brau et al., Nucl. Fusion23, 1643 (1983).[4] K. Ida et al., Phys. Rev. Lett.65, 1364 (1990).[5] B. P. Duvalet al., Nucl. Fusion32, 1405 (1992).[6] K. H. Burrell et al., Phys. Plasmas1, 1536 (1994).[7] J. Kim et al., Phys. Rev. Lett.72, 2199 (1994).[8] K. Ikeda et al., Fusion Eng. Design (to be published).[9] T. Tamano, Phys. Plasmas2, 2321 (1995).

[10] T. Kariya et al., Phys. Fluids B31, 1815 (1988).[11] M. Ichimuraet al., Nucl. Fusion28, 799 (1988).[12] K. Ishii et al., Nucl. Fusion30, 1051 (1990).

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