IAEA-TECDOC-519

RESEARCH USING SMALL TOKAMAKS

PROCEEDINGS OF A TECHNICAL COMMITTEE MEETING ORGANIZED BY THE INTERNATIONAL ATOMIC ENERGY AGENCY AND HEL NICEDN I , FRANCE, 10-11 OCTOBER 1988

ATECHNICAL DOCUMENT ISSUED BY THE INTERNATIONAL ATOMIC ENERGY AGENCY, VIENNA, 1989 RESEARCH USING SMALL TOKAMAKS IAEA, VIENNA, 1989 IAEA-TECDOC-519 ISSN 1011-4289

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A significant fraction of the worldwide efforts to demonstrate scientific breakeven for controlled fusion in a magnetically confined plasma is directed towar presene th d t generatio largf no e tokamak devices. However, other plasma physics programmes continu plao et activn a y quese th r fusiorol fo tn i e n power generation. These programmes perform a variety of functions, both directly and indirectly complementing the large tokamaks research. Some laboratories are engaged in "small" tokamak projects or work on alternative magnetic confinement concepts, testin w idea gne technologiesd san , optimizing existing techniques, performing basic plasma physics studies, etc. Many countrie eagee ar sparticipato t r thesn i e e existing "support" activities examino T . e facedepte on e internationath f to f h o l magnetic fusion research outside the scope of large tokamaks, the IAEA sponsored a serie Technicaf so l Committee Meeting Researcn so h Using Small Tokamakse Th . meetings highlighte dachievemente somth f eo smalf so l tokamaks d specia,an l efforts were mad asseso et suitabilite sth startinf yo w programmegne thin i s s area, particularly in developing countries. The last meeting was held on 1 Octobe10-1 r 198 Nice8n i , attendes Franc wa participant0 4 d ean y d b s fro6 1 m countries,

The programme of the meeting includes 21 reports and was arranged by reference to the main topics of research: MHD plasma equilibrium and stability in tokamaks, diagnostic development, computational plasma physics. Each topic was covered by papers which were either in the nature of a review or were a detailed description of a particular experiment or concept.

These proceedings contai manuscripte nth s whic reproducee har d directly from the author's copy. It is hoped that the present publication will provide e fusioth n specialist countriel al f so s wit materiae hth l which definee sth main direction ongoinf so d futuran g e activitie e fiel th smalf o n di s l tokamak research. EDITORIAL NOTE

In preparing this material for the press, staff of the International Atomic Energy Agency have mounted paginatedand originalthe manuscripts submittedas authorsthe givenby and some attention to the presentation. The views expressed papers,the statementsin the general madethe and style adoptedthe are responsibility of the named authors. The views do not necessarily reflect those of the governments of the Member States or organizations under whose auspices the manuscripts were produced. thisin The bookuse of particular designations countriesof territoriesor does implynot any judgement by the publisher, the IAEA, as to the legal status of such countries or territories, of their authorities institutions delimitationand the of or theirof boundaries. The mention of specific companies or of their products or brand names does not imply any endorsement or recommendation on the part of the IAEA. Authors are themselves responsible for obtaining the necessary permission to reproduce copyright material from other sources. CONTENTS

Summary ...... 7

High beta plasmasecone th d dan s stability regime ...... 1 1 . D. C. Robinson The production of high poloidal beta tokamak equilibria in the Versator II tokamak by means of RF current drive ...... 23 S.C. Luckhardt, K.I. Chen, Kesner,J. Kirkwood,R. Lane,B. Porkolab,M. SquireJ. Second regime tokamak operation at large aspect ratio ...... 29 G.A. Navratil Tokamak experiment JIPn o s P T-IIU ...... 3 4 . Y. Ogawa, J. Fujita, Y. Hamada, NTX-Group, GA-Group Stud f plasmyo a passage throug htoroidaa l slo T-1n i t 3 tokamak ...... 1 5 . V.I. Belashov, A. V. Bortnikov, N.N. Brevnov MHD activity under the influence of helical external magnetic fields ...... 61 /. C. Nascimento, A. Vannucci Equilibrium poloidal beta limit in tokamaks ...... 67 P.K. Raw, R.M. Kulsrud, S.C. Cowley Stabilit f ballooninyo g modepresence th n toroidaa i s f eo l flow ...... 1 7 . Sen,A. A.K. Sundaram High beta plasma self-stabilizatio accesd secone th an n o t sd stability regime ...... 1 8 . V.V. Demchenko Phaedrus-Statue th f o s T tokamaPhaedrue th d kan s program ...... 3 10 . Hershkowitz,N. Phaedrus Group Preliminary desig smala f no l aspect ratio tokamak ...... l Il . G.O. Ludwig, Montes,A. SakanakaH. P. TMR — A tokamak for Alfven heating and current drive research ...... 125 A.G. Kirov, V.D. Medun, L.F. Ruchko, G.I. Astapenko, D.A. Vojtenko, A.V. Sukachev, A.Z. Rakhel'kin, V.P. Sidorov, A.G. Elfimov, K.G. Komoshvili, M.A. Stotland, S.E. Il'inskij, N.I. Malykh, I.S. Ledneva, L.L. Kalayjyan, L.B. Kislova, M.Sh. Burdiashvili, V.A. Miloserdov, S.N. Mordik, R.A. Terteryan, V.I. Kuznetsov, V.Sh. Gamgia, V.H. Zharikov, V.V. Onishchenko, A.G. Nagornyj, L.Ya. Malykh, Yu.N. Gubin, M.V. Lomtatidze, I.S. Fursa, T.P. Bochikashvili, M.V. Dmitrieva, G.A. Pestryakova, I.F. Potapenko, S.Yu. Medvedev, V.P. Boyun, V.F. Gubarev, Yu.G. Krivonos, A.I. Nebookin, I.K. Rubin, B.K. Ostapchenko, G.F. Gusev Lithium beam activated edge plasma spectroscopy — recent results arid atomic database for quantitative studies ...... 135 F. Aumayr, R.K. Janev, Schneider,M. Schweinzer,J. WinterH. Design and test of a time-of-flight analyzer ...... 141 J. Stöckel, P. Vetesnik, K. Jakubka, F. Zâcek, E.L. Berezovskij, A.B. Izvozchikov Tokamak edge plasma investigatio lasey nb r blow-off ...... 9 14 . J.S. Bakos, G. Bürger, I.B. Földes, P.E. Giese, D. Hildebrandt, L.N. Khimchenko, P.N. Ignacz, Koltai,L. Paszti,F. Petravich,G. SzigetiJ. Atomic iron concentration measurements by laser induced fluorescence in TO-2 ...... 171 Vukolov,Yu. K. N.N. Shvindt, Lider,G. VenzelU. neutraV ke 0 l4 lithiuA m beam sourc r tokamaefo k CASTOR ...... 7 17 . F. Zâcek, Stocket,J. Jakubka,K. Badalec,J. Valovic,M. KolâcekK. Recent results from SK/CG-1 machine ...... 185 A. Sinman, S. Sinman Preliminary results of the investigation of slow minor radius compression on HT-6B tokamak ...... 197 Yexi He, Cheng Zhang, Jikang Xie, Linzhong Li, Pinjian Qin, Dequan Guo, Zhixuan Pan, Chuanbao Deng, Guoxiang Li, Hengyu Fan, Junyu Zhao, Rang Huang

List of Participants ...... 207 SUMMARY

Fusion scienc presentls ei y approachin criticaa g lneae stageth r n I . future it is expected that the scientific feasibility of fusion will be demonstrated. Also planned are experiments to study the physics of ignited plasmas.

The leading concept in the magnetic confinement approach to fusion is the tokamak majoe Th . r fusio tokamae basie th their th n e fo s block a us r l al s research leading to an eventual fusion power plant.

Nuclear fusion is still in the stage of intensive scientific research and many "supporting" plasma physics programmes continu plao t en importan a y t role e solutio imaie nth th n f probleo n constructio- m commerciaa f no l fusion power reactor. A considerable number of plasma physics laboratories participate in the aspects of fusion research outside of the large tokamak programmes. Man f thesyo e smaller programmee founb developinn o i dt e ar s g Member States and in countries outside of the 4 major fusion blocs. Some of these are involved in small tokamak projects or programmes on alternative fusion concepts (inertial confinement, stellarator's type devices, etc.). They carry out basic plasma physics studies, develop new diagnostic techniques and study many aspects of plasma technology.

To support this wor Agence kth s instituteyha seriea d Technicaf so l Committee Meetings on Research Using Small Tokamaks. The major goals of these meetings are to provide an overview of plasma physics programmes at small laboratories and to foster collaboration between the smaller programmes themselves and between them and the larger programmes. Participants at these meetings strongly supported such scientific cooperation and the establishment oconferenca f e that would concentrate effort smalf o s l laboratoriee th n o s most interesting direction plasmf o s a research.

The last IAEA TCM on Research Using Small Tokamaks was held 10-11 October 1988 at Nice, France. Since the results of these meetings are important and useful to a wide range of specialists involved in fusion research the IAEA Secretariat has prepared this TECDOC as an IAEA publication. s attendewa M abouy TC b d e participant0 4 tTh havo swh e actually been involved inte relevanth o t experimenta theoreticad lan l works programme Th . e meetine forth g include reports1 2 s .

The meetin mainls gwa y devote higo t d h beta tokamak operatione Th . fundamental objective to high beta tokamak research is to gain understanding physice oth f equilibriumf so , stabilit d confinementan y permio ,t e desigtth n of reliabl d economicallean y competitive tokamak power reactors. Since eth cos f fusioto n powe proportionas i r e averagth o lt e volum toroidaf eo l beta maximizatioe th achievable th f no e tokamaa bet n majoa i a s i kr goaf o l controlled fusion research.

Extensive analytica d computationalan l wor s establishekha d s i tha t i t likely tha tokamata achievn ca k establa D equilibriueMH averagn a t a m e toroidal beta operatioy valub e regimexces% n i eth 10 n "seconf f i neo so d stability". High beta together with moderate magnetic fiel resuln ca d n ti more compact reactors for a given power output. The optimal range of beta, from the point of view of minimizing capital cost per kW is (12-18%). In a test reactor with ITER-sized plasma and magnetic field, operation at beta % wil~10 l permit sufficiently large densit o insuryt „ ent thae th t require r ignitio fo e achieveddb n nca .

Three papers (D.C. Robinson, Culham Laboratory, UK; G.A. Navratil, Columbia University, USA; V.V. Demchenko, IAEA) reviewed the experimental and theoretical research on tokamak behaviour at high plasma pressure and second regime operation. Several method bees sha n discusse e start-uth r higf fo do p h beta tokamaknecessare th d san y transition from firs secono t d stability regimes f indente.o e Amonus de g th cross-section thee mar , current density profile, sheared toroidal plasma rotation, plasma self-stabilization effects, etc. The results obtained on the TOSCA and CLEO devices (UK), tokamaks HBT, TORUS-II, VERSATOR-II, PBX-M and DI1I-D (USA) were summarized. Specifically, three useful experimental methods of obtaining the second stability regime were outlined: 1) the increase of the central q value to reduce the shear in the central region of the plasma, 2) bean-shaped plasma cross-section, and 3) energetic electron population trapped in regions of bad curvature. Specifically, experiment VERSATOn so tokamaI I R . Luckhardt(S k show) a. st ,e tha currenF tR t usee b drivproduco t dn ca e e high poloidal beta plasmas with the pressure and current supplied by the RF driven energetic electron component. Stability analysis indicates that these plasmas are near the transition to the second stability region. Low-n external modes have been observe severan i d l experiment hara t dn se i bet o „ st q a w limitlo t :a D-Ili, in the Columbia HBT tokamak. High-n ballooning modes have been identified in very high beta equilibria produced in the TORUS II tokamak and were inferre apparenn a s a d t limi D-IIn i t higt . Ia hq O

n somI eSundaram. A paper d Navratil. an (G sDemchenkon . ,V Se . ,A , P. Kaw, et al) an approach to the theoretical study of the key questions on beta limi describeds i t stabilite Th . y analysi higf ) ideao s (n h l ballooning presence modeth n i storoidaf eo l plasma rotation indicate that rotatioa s nha stabilizing influence on those modes. The effect is associated with the equilibrium modificatio flue th xn ni surface s arising frocentrifugae mth l force n recenI . t times there have been several experimental observationf so toroidal plasma rotation (e.g .tokamakn i s TFTJET)d an R n idea.A l ballooning mode transport mode bees lha n describe explaio t d mann i n y tokamaks degradatio confinemenf no t with increas auxiliarf eo y heating modee Th . l provide seIf-consistena s t descriptio profilf no e evolution that incorporates both stabilit transportd an y modee Th s employe. lwa examino t d e confinement in a tokamak plasma that can access the second stability regime by means of different stabilization mechanisms.

The influence of externally induced magnetic fields on magnetic strure activitD andMH tokamakn i y performes swa JIPn i d Pd an T-II Ogawa. ) (Y al U t ,e TBR-1 (J. Nascimento, A. Vannucci) tokamaks. Experiments have shown that under certain circumstance e interactiosth resonanf no t magnetic helical fields with MHD magnetic islands produces a strong attenuation of the amplitudes of the modes.

preliminare Th y conceptual desig somf no e small-scale tokamaks were presented. The TMR tokamak (A. Kinov, et al) is intended for Alfven heating and driving current researches PROTO-ETe Th . A tokamak desig bases i n d upon e sphericath l torus concept which should allo investigatioe wth higf no h beta tokamak operation. The PHAEDRUS-T tokamak (with operation expected in 1989) is devoted to study edge effects, ponderomotive force stabilizing effects for mode control, ICRF plasma heating.

Several report Bakos. , Stöckel. J . AnmayerJ al , (F s, t al ,e al t ,t e ,e K. Vukolov, et al, F. Zacek, et al) discussed the recent progress in the developmen diagnostif to c technique varietA . methodf yo s have been developed or improved at recent time. The already acquired experience with Li beam-activated plasma diagnostics show greae sth t promis thesf eo e methodr sfo measurin rathea g r complet datf fusior o fo at ese n plasma (plasma density, current density distribution, impurity concentration, etc.). A diagnostic technique for the measurement of the energy of the fast charge-exchange atoms from plasma was presented. On this basis the analyzer is proposed to determine the ion temperature;. The characteristic measusurements of the impurity atoms in a plasma by means of the laser-induced fluorescence are described for large-scale fusion devices.

Overall, the IAEA TCM on Research Using Small Tokamaks (Nice, 1988) demonstrated an increasing activity of the groups working on small-sized plasma devices, which provide foundatioa s testinr nfo w ideasgne , sucs ha access to and operation at the second stability regime, installing modern RF and neutral beam heating systems, developin w diagnostigne c techniques, etc. They also provide useful scaling experiments that allow extrapolation of results from small to larger devices.

10 HIGH BETA PLASMAS AND THE SECOND STABILITY REGIME

D.C. ROBINSON UKAEA-Euratom Fusion Association, Culham Laboratory, Abingdon, Oxfordshire, United Kingdom

Abstract

y tokamake A e numbeth k f probleme o e raddressefuturb th n r ca efo sn o d small devices. Amon ge accestheth d operatio- man s e seconth t a dn stability regime. An extensive small tokamak research programme (CLEO, TOSCA and COMPASS devices) has been conducted at Culham Laboratory which includes, as part beta limits, where issues such as access to the second stability region, more extreme form f plasmo s a shaping e influencth , f superthermao e l particles e addressedb n ca e methodTh . f obtainino s e seconth g d stability regims i e considere n detaili d .

Introduction There is good agreement between theory and experiment for the boundary of the first regime where the Troyon ß limit is given by ß = (2.8 - 3.5) %. This formula was developed for the low n kink instability a(m)B.(T) but Sykes [1] has shown that it also applies to high n ballooning modes if the coefficient is replaced by 4. He has also shown that this formula applies equally well for very tight aspect ratio devices such as STX as r non-circulafo wel s a l r tight aspect ratio systemd an T s JE suc s a h COMPAS d beaan S n shape e noteb d o plasmasdt s thai e optimisatio th t I . n is for central q values of 1.05 and applies for elongations only up to about 2. Unfortunately for a number of reactor applications, the Troyon ß limi s stili t l uncomfortably low, particularl r largfo y e aspect ratio systems without strong shaping (which can generate axisymmetric instability). It has also been observed in many experiments that the confinement degrades when the ß value exceeds some 80% of this limit. Accordingly ther s greai e t interes n definini t d attaininan g e seconth g d stability regime.

ß limits s interestini t I o loot g t balloonina k g mode calculation r tighfo s t aspect ratio tokamaks, which hav naturalla e y stabl. 2 e^ elongatio o t p u f o n In this boundard casr centraan fo e5 1. valueq q yl ^ f o ^ 4.5s , % coul30 obtaine e averago b dt p u edf o valuevalu* wit ^ ß ß f a hf o e o s e firs % th eve 60 n ti n regim f stabilityo e .

11 In highly elongated equilibria such as those for the crescent shaped EST, ballooning mode stability is also possible with much larger aspect ratios avalueß t 45%f o s .

Ther s gooi e d evidence thaaspece th t t rati oß limi scaline s i th t f o g correct. Experiment e TOSCth An o s device, wit n aspeca hd an t5 rati3. f o on CLEO, with an aspect ratio of 7, both agree with the Troyon ß limit expression, Fig l C2]. In both cases substantial MHO activity occurred e confinementh d ß limian e 1 clos th tt^ wito degradet eß e h . 2 - Figd .

o,5 Q 3. TOSC= a R/ A 7 = a * CLER/ O 10

05

01 02 03

I (MA)/(a(m) B0(T))

Fig 1. Average ß value as a function of I/(aB.) for ECRH plasmas on CLEO and TOSCA. The theoretical limit ß(%) = 2.8 I{MA)/a(m)B,(T) is shown.

The box point for TOSCA was obtainedc by decompressing an ohmically heated plasma, thus obtaining a higher value of I/(aBJ.

!„ = 5 4 kA, B., = 5 1 kG, n„ = 1 5 x 10

(gaussB 6 )

Fig 2. Confinement time, poloidal beta (ßy), and amplitude of magnetic fluctuations observed inside the vacuum vessel on the outer equatorial plane as a function of the ratio of RF power to initial ohmic power on CLEO. The maximum RF power was 180 kW.

12 Observed ß limits and theory

DIII-D

ß%

1 -

Fig 3. Observed ß limits and theory on a variety of circular and non-circular tokamaks.

However with strong ECR heating off axis, it was not possible to further increase the ß limit though this should have been possible if access to the second stability regime had been obtained. Figure 3 shows the observe ß dlimit s compared wite Troyoth h a rangß nlimi r f circulao efo t r and non-circular tokamaks and includes the latest maximum ß values obtained from the Doublet III-D device - in the region of 6% C3]. It is to be noted that even on non-tokamak devices such as REPUTE [4], operating at low and ultra low q values, the toroidal ß value scales as I/aB even up to ß values in excess of 10%.

It is clear that access to the second stability regime would give a much greater choic f aspeco e t ratio o reactot s r designers n additioI . woult i n d permi e optimisatioth t e thermonucleath f o n r yield, a particlwher e th e e powe s proportionai r n existino , 2 ß o gt l devices sucr exampls JETa Fo h . e X poin A M ß tlimite 4 s discharg a thermai a o T t dt JE Q valu lno n o ef o e more than 0.76 assuming a pure plasma, but at 6 MA an X point H mode discharge could achieve a Q value of up to 2. It is interesting to note that comparable values of Q can be obtained at the ß limit by using a lower current discharge of 4.5 MA and compressing it in major radius. The required confinement tim s consisteni e t with present empirical scaling laws. Such calculations do not include non-thermal effects.

13 A particular problem in operating in the first regime of stability, is the appearanc ß limi f o et disruptions whic e fas d harar d happeae an tb an d o t r impossible to control. Operation beyond this limit might improve the flexibility of operation against this particularly difficult problem.

Operation in the second regime of stability would make D-He3 or advanced fuel operation with reduced environmental impact much more attractive particularl s mora y e direct energy conversio y wel e possiblma nb l n suci e h cases.

Methods of obtaining the second stability regime The first method, which was pursued in electron cyclotron resonant heating experiment e TOSCth An o s devic d reporte e an Oxfore th t a d conferencn i e 1979 o raist [5]e centra s th e, wa q valul o reduct ee e sheath th en i r central region of the plasma and then heat the plasma strongly. Figure 4 shows the stability boundary in the central q value - ß space, indicating thar centra fo tt thi a s5 q valuel 1. aspec f o s t ß rati value, d 2 an of o s access shoul e possibleb d e equilibriuTh . m curren d pressuran t e distribution is also shown.

- o Z

005 - -o 6

20

1 61-

Fig 4. (1) Flux contours, (2) current and (3) pressure distribution for marginally stable equilibrium with ß = 7. (4) Ballooning mode stable region in the q(0), ß plane.

14 Mender and colleagues [71 have also looked at the access to second stabilit d heryan eT regim founJE n i ed thae centrath t o t q valul d ha e increas8 befor 1. s muc a s a ho e t ee secon accesth o dt s regime coule b d obtained (Fig 5).

10

UNSTABLE

%

2 1 1 A 1 6

Fig 5. Limiting ß value for ballooning modes as a function of q(o) for JET. The second method, which is particularly important in that it may have a bearin n H-modo g e discharges thas i , t e seconaccesth o dt s e regimb n ca e obtaine y usinb d g plasmas bounde e X pointregioth y n f b favourabldi o sn e curvature. For example Bishop [6] showed that stability could be obtained with significant current flow near the edge of the plasma as shown in Fig . 6 Separatrix configuration e inboarsX poin th wit e n o tth hd side ar e planneCOMPASe th n o dS , FigurdevickA , wher0 t current7 ea e 10 th e% f o s limitin ß valug e wil e exploreb l df axiwitof sd h electroan bot n o h n cyclotron resonant heating at the 1MW level. Sabbagh et al [8] have investigated access to the second regime as a function of aspect ratio, finding thar centrafo t q valuel s significantly abov , acces1 e t larga s e aspect ratios can be obtained at relatively modest values of ß (< 2%). In addition for aspect ratios less than 2 this becomes possible even at zero r centrafo ß q valuel . 2 > s Indentation or triangularity (leading to bean shaped plasmas) is very helpful in providing access to the second regime, though the existence of a conducting wall would seem to be an essential pre-requisite for low n stability.

The third technique is to exploit hot electron plasmas such as suggested colleagued an m . Da ] n C9 sb Va y

15 A = 0 8 20

5 l

I 0 UNSTABLE

0 5

00 1 1 i 7 0 6 0 0 5, 0 8 09 10

Fi. 6 g Marginally stabl a e(pressur e gradient a functio s a )k (shap f o n e of magnetic surfaces) for f = 3n/4 (angle of X point relative to outer horizontal axis) and A = 0.8 (toroidal current density parameter), showing the absence of the unstable region near the edge of the plasma.

q versus radius

03 04 05 OS 07 08 J versus radius

8 0 7 0 6 0 5 0 4 0 3 0 P versus radius

03 04 05 06 07 08

Fig 7. Inboard X-point equilibrium for the COMPASS device with its initial circular vacuum vessel.

16 A fourth approach s deployea , mirron i d r machine experimentso t s i , exploit the ponderomotive force.

Finally a fift, h area, which seem o makt e probles th e m easiero t s i , operate at larger values of the boundary safety factor - q.

Problems Ther e substantiaar e l problems associated with e seconaccesth o dt s regime f stabilityo n particulai , e achievementh r f profilo t e controd an l low shear leads to "infernal modes". An example of this problem was investigated for JET - Fig 8 shows the q profile and growth rates as a function of central q value for a low shear peaked pressure profile case.

12 1 3

to) (b) Fig 8. Ca) Pressure and q profiles (b) Growth rate of the n = 3,4,5, Infernal modes as a function of q(o) for the equilibrium shown in (a).

Here the first regime critical ß value decreases because of these internal low n modes to less than 8% C7]. By introducing more shear in the core it becomes possible to stabilise these modes and higher values of ß can be obtained. It is also important to note that resistively stable q profiles with central q values less than 1, such as the one shown in Fig 9, permit highe d rals an value oß avoif o s d infernal modes. y problemke e th s f wito e h On these configuration m tearin w lo s tha i sf g o t modes, particularly near the S-a (shear-pressure gradient) boundaries. JET equilibria which are ballooning mode and n=l kink stable at average values of ß ^ 3% are found to be n=l tearing mode unstable, though the growth rate does decrease substantially with increasing Lundquis r magnetio t c Reynold o favourablt s e numbedu , S r e average curvature effects. Neae th r ideal stability limits the tearing mode stability becomes significantly

17 8 2

2 4

2 0

1 6

1 2

0 8

0 4

0 0 0 1 8 0 6 0 4 0 2 0 10 r

toroidaA Fi. 9 g l resistively stabl profilq e e with q(o. 1 )<

q(r)

30

20

A' 2/1 10

0 0-5 1-5 ß (•/. l ) 0 /2

-10

-20L

Fig 10. AJ,i as a function of pressure for a flattened q profile with a single resonant surface.

worse. Hasti d colleaguean e s [10] have , thashown 10 1 becomeA tg Fi , s destabilising before the ideal limit is reached. In the conventional S-a diagram the n=4 tearing mode is unstable before the ballooning mode limit is reached, as shown in Fig 11. An essential requirement for low n kink modes is the presence of a close conducting wall as in the reversed field pinch. This will however produce its own problems associated with the finite resistivit e wallth f , o ymod e lockin d modean g s whice h th gro n o w timescales at which the helical fields penetrate the conducting wall. Active contro f suco l h mode y wel e necessarma sb l r lonfo y g sustainmenf o t second stability regime plasmas.

18 resistiv4 = n — e — — ———— n = oo ideal idea4 = n l — - —

j_ I 0 0-2 0-4 0-6 0-8 1-0 1-2 1-4 a a stabilitS- . Fi11 g y diagra r balloonin4 ideafo mn= ld an ) g» » mode- n ( s and resistive modes.

It is also worth noting that the problem of confinement in the second regime may be an issue, as the gradient region is substantially smaller than thos n conventionai e l equilibria, althoug e neo-classicath h l confinemen s theoreticalli t y better.

Experimental Access The problem of access to the second regime is analogous to that of access r q ultroperatioo w q lo aw a tokamak lo n i no t . Thi s difficuli s t because it is necessary to achieve the right conditions for the current profile in e outeth r regione edgd boundarth an ee i s y region includin e limiterth g s where the plasma is strongly turbulent. It is worth noting that it is possibl e first closth ge o to t et eregim e boundary with ohmic heating alone. The ratio of the ß value obtained with neo Alcator scaling for ohmic heating and the ß value associated with the Troyon limit is proportional to the loop voltage x nR/B, x q- . The voltage tends to be approximately constant whereas nR/B, can be optimised by operating in Helium with gettering r examplfo , e with titanium, chromium etc. Thus with careful conditionin s possibli t i g o achievt ß elimi e ß closth ta eo t e n ohmia eve n i nc plasma, thoug he densitclosth o t ey limit which presumably produces non-optimum profiles. There are two techniques which can be employed for investigating access to the second stability regime:- (1) to use fast programming such as in the high ß screw pinch experiments where plasmas wit e ß seconvalueh th n i ds regim f stabilito e e b n ca y obtained, eg TPE2 [11], but sustainment of such plasmas is difficult.

19 (2) the more conventional way is to provide access using slow profile control from radio frequency heating, beams, or rate of change of current etc. In this case the access appears to be difficult and indeed many code calculations suggest that stabilit d fielyan d diffusiot no e ar n compatible. In principle with this technique sustainment should be somewhat easier A numbe. f experimento r w tantalisinglno e ar s y closo t e the region where e seconaccesth o dt s regime shoul e possibldb e th t ebu issues of anisotropy and fast ion pressure confuse the picture somewhat. It is also important to note that the access could become quite difficult with radio frequency control because in such equilibria there may be multiple resonances due to plasma paramagnetism distorting the IB I contours.

-TF Core

.Solenoid Octupole Winding

1m -Vessel and limiter

'Axis Vessel-

Fig 12. Sequence of equilibrium for the production of a tight aspect ratio tokama k< 1.2 wita .R/ h

20 We at Cul ham will pursue an active programme on beta limits and control on the new COMPASS device, which is now in an advanced state of construction. We are exploring the issue of disruption control at both the density and ß limits using internal (and external) helical coils with fast feedbacke W . are also pursuing a route to higher values of ß in the first regime of stability by exploring a novel approach to producing a tokamak configuratio n aspeca t s 1.2a a n t w .2 ratilo 1 Thig s a s showoFi i s n i n for a small tight aspect ratio tokamak, START, where a sequence of equilibria are compressed to provide naturally stable elongated configuration whose central electron temperature could be ^ 1 KeV with a plasm. kA a0 curren20 ^ f o t

Conclusions It is clear that at this stage in the development of tokamaks, the small o mediut m scale experiments hav n importana e t rol o pla t en guidin i y e th g present and future large experiments on plasma pressure optimisation since ther s considerabli e e evidence thae gros th D tbehaviou MH s f tokamako r s has remained independent of their size and temperature as long as the Lundquist number, S, is > 103.

REFERENCES

Cl] A Sykes et al, Proc EPS Conf, Aachen, 1983 Part II, p363 [2] D C Robinson et al, Proc of IAEA Conf, London, 1984, Vol 1, p205 [33 T Simonen et al, Proc of IAEA Conf, Nice, 1988, to be published (pape o E-III-6n r ) Pro, N Inouf IAEal o c t Ae ] ConfC4 , Nice, e publishe1988b o t , d (paper no C-V-8) C5] R Birch et al, Proc of EPS Conf, Oxford, 1979, Vol 1, p43 [6] C Bishop, Nuclear Fusion, Vol 26 No 8(1986) p!063 ConfS EP Pro, MendeC , f al T o c Madrid t e r ] [7 , 1987, Par p23, I t 1 A Sabbag, S 'Transitiod regioal 2n t ] e hf e idea C8 o nD th MH lo t n stability1, submitted for publication in Nuclear Fusion also Proc of IAEA Conf, Nice, 1988 publishee b o ,t d (pape o D-IV-14n r ) [9] M N Rosenbluth et al, Phys Rev Lett, Vol 51, No 21, p!967 (1983) [10ProJ , Conno ]f IAEal o c t Ae r Conf, Nice, 1988 e publisheb o t , d (pape D-l-4o n r ) [11Pro, HayasK f ]IAEal o c t Ae Conf, Kyoto p56, , 11 19863 l Vo ,

Next page(s) left blank PRODUCTIOE TH HIGF NO H POLOIDAL BETA TOKAMAK EQUILIBRI VERSATOE TH N AI TOKAMAI RI MEANY KB S CURRENF R F O T DRIVE

S.C. LUCKHARDT, K.I. CHEN . KESNERJ , . KIRKWOODR , , B. LANE, M. PORKOLAB, J. SQUIRE Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts, United State f Americso a

Abstract Experiments on the Versator II tokamak have been carried plasmw a regim oulo n i tf ao e curren f reachino m tai wite g th h high poloidal beta, ß . Lower-hybrid RF current drive was used to produc n energetia e c electron population which carrie e plasmth d a curren d pressurean t n thiI . s mod f operationo e , plasmas wit3 e/ h approaching or exceeding unity could be produced. Data from equilibrium magnetic analysis, hard x-ray, and density profiles displa n outwara y d magnetic axis shif n agreemeni t t with equilibrium theory, and analysis of the x-ray profile data indicates that q(0. PES6 )= T rangeo codt p eu s modelin f theso g e experiments suggests that some of these plasmas may be near or beyond the transition to the second stability region for ballooning modes.

INTRODUCTION In lower-hybrid current sustained plasmas the energetic electron component produce n anisotropia s c pressure (P..>P.) which can sustain high values of poloidal beta if the total plasma curren s comparabli t r leso o st e thae Alfveth n n current I ^ITkAiTpVp/c where v~ is the maximum velocity in the rf driven plateau distribution function. In particular, the poloidal beta for such an anisotropic plasma may be written as

p /(B=i ß 2/2fi )+ip. ,/(B2/2f) i ' 'o a v 1 1 4 ' o a * 2

v e +V overba( I/(2Trai th f =j ) d B m ,= an r ). . . P , v f m wher= P e 2 22 Q

23 Typically in the Versator II experiment. the above formula indicates that ß = 20kA/I where I is the total steady state RF RF RF driven current. Hence thF R e driven distribution provides current a higdriv d h an eparalle l pressure component which allows e tb o raised significantly above the ohmic value.

LHCD EXPERIMENTS WITH f=0.8GH d 2.45GHzan z Experiment o investigatt s e higth eh poloidal beta regime were carried out on the Versator II tokamak (R=0.40m. a=0.13m, e=a/R=0.31) with lower hybrid current driv t f=800MHa e d zan 2.45GHz e invers.Th e current scaling predicte e abovth ey b d analysis was confirmed as shown in Fig. 1, where the equilibrium quany t ti ß*=ß - l,/2 is plotted against the RF driven current for P P steady stat F driveR e n plasmas. In these discharge w plasmlo s a so that Hard x-ray profile curren s maintainewa t d IRF

TES9 0. U • 800 MHZ 0.7 800 MHZ

0 2 5 1 0 1 25

RF CURRENT (kA)

1 FigCompariso. driveF R f o n equilibriu mß +1/2(- value ß f ) o s K wit P hpredicte d froe modeth mdistributioF R l n function.

At high poloidal beta D equilibriuMH , m theory predicta s large outward shift of the magnetic axis, and such shifts can result in measurable outward shifts of the density profile. In e observeth Fig 2 . d outwar ddensite shifth f o ty profile peak, N A , s measurea a vertica y b d l microwave interferometer s comparei , o t d the magnetic axis shift, AMAr,(ß ), predicted by MHD equilibrium theory e outwarTh . de densit shifth f o ty profile peak appearo t s agree well with the equilibrium shift of the magnetic axis, within the experimental uncertainty.

Experiments with LHC t a Df=2.45GH z have also been carriet ou d to extend the density of high poloidal beta operation up to 3 — 8 1 6 prob3 A e. poloida m 5x10 l field magnetic probe arra s usewa yd o determint e evolutioth ee magnetith f o n c surface n thii s s case.

24 0.6 DENSITY PEAK THEOR . FREIDBERGJ Y . R«v. Mod. Phys. (1982) MHD CODE

Fig. 2 Comparision between the outward shift of the density profile peak, A„, and the MHD equilibrium theory prediction of the magnetic axis shift, 'MAG' at higß h 1./2 =1.0 is used here.

see Fig. 3. In the initial ohtnic phase of the shot shown in Fig. e plasmth s wel, wa a3 l centered. Then afte F currenR r t drivs wa e initiated, the plasma moved to the outside and hit the outer limiter, this resulted in a continued decay of the plasma current during this stage. Subsequently, the equilibrium field system recentered the plasma. Fig. 3c, and a large outward shift of the magnetic axis appeared. The equilibrium flux surfaces during the current flattop phas e showear n Figi n . Thi.3d s flux plot also indicates a large magnetic axis shift.

20 30 40 50 TIME (MSEC)

Fig. 3 Time evolution of the magnetic flux during inductive and RF current driv s measurea e a poloida y b d l 6 arra3 f o y magnetic probes.

25 STABILITY ANALYSIS AND PEST CODE RESULTS Idea D theorMH l y predict a sstabl e secone th pat o t dh stability regime of high toroidal mode number ballooning modes if q(0) can be raised sufficiently.2 '3 Usually the stability to these modes is simply estimated using the Troyon criterion. In figure 4 the full data bas f theso e e experiment s showi s n wit ß e hplotte d vs. ß[%]/(I[MA]/a[m]B[T]£Z. Z is the Troyon factor. However, the simple Troyon criterion which assumes q(0)=l canno e useb to t d asses e stabilitth s f theso y F driveR e n plasmas whers ei q(0) e rango anotheS th f 4-6o n e.believe i re b proceedur o t d s wa e followed. Model MHD equilibriH a were constructed which best fit the experimental data for ß , magnetic probe signals, plasma and coil currents d densitan , d x-raan y y profiles. These model equilibria were then teste r stabilitfo d y against idea D ballooninMH l g modes (hig ) usinn he th g 5 PE ST code.

1.5

n _ B=0.9T A _ • f=0.8 GHz * n 8=0.7 T 1.0 Tk £1 • f=O.B GHz .4. 1 . B=O.B5T A ** O • f=2.*5GHz p 4>p & ° 60 0.5 ••.t

n n 0.0 0.5 1.0 1.5 2.0 0%/(l[MA]/a[M]B[T])

Fig. 4 Data base of RF driven plasmas plotted with &ß vs. the Troyon parameter.

e resultPESe Th th T f codo s e analysir fo e show 5 ar sn Figi n. five model equilibrium points. Four of the points (1-4) are from the sequence of four equilibria shown in Fig. 3. A fifth point is from earlier experiment t f=0.8GHza s .

HIG HBALLOONINN G STABILITY (PEST)

0.5

Fig. 5 Stability diagram for high n ballooning modes. Data points 1-4 represent model equilibria corresponding to the flux plot. Dat 3 n Figi sa. s fropoini a modem5 # t l equilibium obtained in an earlier run with f=800MHz.

26 In Fig. 5, points lying below the dashed line are stable to ballooning modes, above are unstable. The solid curves indicate sequences of flux conserving equilibria generated-numerically. As ß increases these curves rise and cross the instability boundary at the first instability transition, then as ß continues to increas e curveth e s turn oved restabilizan r e seconth t da e stability transition e resultTh . s presente n Figi d .5 sygges t that the three data points 3,4,5 are near or beyond the second stability transition.

CONCLUSION In conclusion, these experiments show that RF current drive can be used to produce high poloidal beta plasmas (aß =1) with the pressure and current supplied by the RF driven energetic electron component. Magnetic measurements indicat a eseparatri t no d di x enter the plasma as ß was increased from its initial value in the ohmi cmaximus phasit o t em F drivedurinR e th gne phasth f o e discharge. Major disruptions wert observedno e d equilibrian , a wit2 wer ß 1. e hrangin e o t produced p u g . Stability analysis using the PEST code indicates that these plasma e nea ar r sbeyono r e th d transitio e seconth o dt n stability region.

REFERENCES

1. A. Mondelli and E. Ott. Phys. Fluids 17.. 5. 1017 (1974) 2.B. Coppi et al. Comments on Plasma Physics 6. 109 (1980) 3. M. Gerver et al. Phys. Fluids 31.. 2674 (1988).

Next page(s) left blank 27 SECOND REGIME TOKAMAK OPERATION LARGT A E ASPECT RATIO*

G.A. NAVRATIL Department of Applied Physics, Plasma Physics Laboratory, Columbia University, New York, N.Y., United States of America

Abstract This paper reviews the need for high beta in economic tokamak reactors and summarizes recent results on the scaling of the second regime beta limit for high-« ballooning modes using optimized pressure profiles as well as results on low-n mode stability at the first regime beta limit fro Columbie mth tokamakT aHB . While several experiments have studied ballooning limits

using hig p plasmasheß mose th , t importan secone th f o d e stabilitt us questio e th yr nregimfo r efo tokamak reactor improvement is how to achieve these high values of eßp while at the same time increasin value gth betf eo severao at l time Troyoe sth n beta limitapproacn A stude . th thif yo o ht s key question on beta limits using modest sized, large aspect ratio tokamaks is described.

1. INTRODUCTION

neee higr Th dfo h bet orden ai achievo rt economicalln ea y practical forf mo fusion power reactor based on the tokamak has been recognized for some time. The most recent fusion reactor design study which tried to quantify this point was the 'Generomak' study led by Sheffield [1] which defined a level of beta for a generic toroidal devic economicalle b o et y attractive. This resul shows i t Fign ni 1 . and indicates that value f volumso e averaged beta, <ß>, greater thane abouar % 9 t needed. This 'attractive' leve f betstrona o l s ai g functio f aspeco n t ratio witha minimum valu scalinR ee 1/ 7.5= th aboue reaso e f a Th go .th r thi R/ t nfo s i s toroidal magnetic toroidaa fiel n i d l e stronsysteth d gm an scalin e fusioth f ngo power density, Pf, with magnetic field for a given value of beta. This can be expressed simpl: yas

) (1 . PB ß coi ~ B l = p P« f

where A is the thickness of the inboard blanket and shield (usually taken as about 1.3 meters). Since the value of magnetic field at the toroidal coil has a maximum technologe th y valub t se ey employed (take e SheffielTesl9 th s na n ai d study),

Researc* h supporte Unitey db d States Departmen f Energo t y Grant DE-FG02-86ER53222.

29 0.2

Sheffield's "Attractive" <ß> Level 0.16

0.12

A Q. V 0.08 / '' Troyo7 n1. = Limi K t Constana , t2 « * q t "--... / 0.04 -Tröyon Limit '',, ^ U* na\ I t '"""--.„.

10 12 R/a

Figur . e1 Attractiv e volume averaged bet r economiafo c toroidal fusion reactor from the Generomak study by Sheffield et al. [1]. Also shown is the Troyon beta limit assuming q* = 2 and K = 1.7 and the curve for the minimum required curren a-particlr fo t e confinement.

this leads to a lower beta requirement as R/a is increased due to the improved toroidal field utilization efficiency. However, at some point the discrete coil effects, which result in a separation between the coils on the inboard side as R/a is increased, will limi maximue th t m toroidae valuth f eo l field utilization efficiency (taken in the Sheffield study as 0.6). This causes the curve to turn upward again at the point where the field utilization predicted by Eq. (1) approximately equals this assumed maximum practical value. Given thabete th ta necessar r economiyfo c fusion powe e s givei rth y nb curve in Fig. 1, we compare this with the Troyon beta limit [2] for the first stability regime assumin elongationd an cylindricaga 2 = 1.7cleas = i * t K ,q I . r , thaq l t there is a substantial gap in beta at all values of R/a between what we can presently achiev tokamaa n ei whad kan requireds i t . Whil increasee eth d plasma curren tyield a permitteR/ largesa w lo t dra first regime beta limit requiree th , d beta due to the poor toroidal field utilization efficiency is also much higher. In fact, the most easily achievabl e larg e founa valueb th e R/ t ey beta d sma a where th e absolute value of required beta is lowest and the ratio between the Troyon beta requiree th limi d an td bet s alsai o minimized. Thipartls r basiou e wa s yr th fo s proposa n 198i l 6 that large aspec t exploio t rati bese y oth wa tsystem e b y ma s the possibility of the second stability regime for improved tokamak reactor design [3]. In the sections which follow we first discuss the scaling of the ideal MHD instability limit ballooninr sfo kind gan k modes which overcome neeb o dt orden ei r to produc establa e plasm secone th n ai d regim thed ean n describ advantagee eth s

30 of large aspect ratio tokamaks for carrying out key experiments to test methods of instability control which may permit stable access to the second regime.

. BARRIER2 OPERATIOO ST HIGT NA H BETA

dividn ca typee e eth modef D idea W limio sa expece t n MH lw so se t o t t the achievable beta into three categories: Low-n External Modes, High-n Internal Modes or Ballooning Modes, and Low-« Internal Modes (Ballooning or 'Infernal'). Each of these is discussed briefly below. Low-n External Modes. These are the external kink modes which are believe responsible b o dt experimentalle th r efo y observed operational beta limin i t conventional tokamaks describe Troyoe th y db n beta limit. Scalin Ip/aBjs ga , they were propose limitine th s Troyoa y dgb . numericaal s mod t hi ne n ei l study which led to this widely accepted semi-empirical scaling law for the beta limit. These modes have been observed in several experiments to set a hard beta limit usually resultin rapie th dn g i disruptio plasme th f no a stored energ currentd yan . These

were believe responsible b o dt bete th D-IIa n r i limi ea fo q I t[4]w seelo , t werna e identified as the limiting mechanism in PBX [5], and have been identified at the Troyon limit in the Columbia HBT tokamak [6]. In all these cases the n=l mode was identified or believed to represent the most serious limiting instability. At the present time it is this mode which is limiting the achievement of larger beta values

in machines operating wit a nea hq minimue rth m values allowed (typically from just unde abouo t . r2 3) t High-n Internal Modes (Ballooning). s theswa et I mode s which were originally predicted to set the beta limit in tokamaks [7, 8]. However, they have proved more elusive in experiments and have only been identified in very high beta equilibria produced transientl Columbie th n yi a Toru I tokamaI swerd an e] k[9

inferre apparenn a s da t limi D-IIn i t t hig a I effec e a [4]hq Th f thes.o t e moden si experiments attemptin reaco gt h high beta remains unclear e expectatioTh . s i n o theit thate r du shor, t wavelength, they will appea a 'soft s a r ' beta limiy b t causing enhanced cross-field energy transport. These modes have beee th n subjec f considerablo t e theoretical investigation (being more analytically tractable than the low-n external kinks) and were observed to have the exciting property that they would re-stabilize at high beta in some equilibria, hence the introduction e teroth fm "second stability regime describo "t e this re-stabilization [10-16]. Whil e seconth e d stability regim s normalli e y though a synony e f o th t r mfo achievement of high beta, in fact these modes and the phenomenon of second

stability is governed by eßp not <ß>. Since the relation between these two is \ 7 , 2 * a given by £P> -

V(TT^} <2)

31 t showi s t sufficientlthaa > t hig <ß p experiment heß w y lo carrie e t b a n t dca ou s high q. Experiments of this type are presently being carried out to test ballooning limit describes a s d briefly late s importanSection i i r t I . n 4 kee o t t minn pi d that while balloonin second gan d stability need only deal with equilibri t higa h values of eßp, reactor relevant beta values, as described previously in Section 1, require that high (no> value<ß t onlf o s y eßp achievede b ) . This will necessarily require control of both ballooning and the low-n kink modes. Low-n Internal Mode (Ballooning or 'Infernal'). These modes have recently been predicte occuo dt regionn sheari w lo rf so (typicall y nea centee rth f ro the tokamak equilibrium) wher finita e existsp V e thes n I . e region s beeha nt si shown that the standard high-« ballooning theory breaks down and a new class of low to intermediate-« internal ballooning modes, sometimes called 'infernal' lowese th t modestse betn ca a, threshol r stabilitdfo y [17]. These modey ma s

already have been seen as an eßp limit of 0.7 in TFTR supershots which are characterize highly b d y peaked pressure profiles [18]. They blocy ma yan k attemp puso t te cor th he e plasmregioth f o na inte seconoth d stability regime where it has direct stable access due to the low shear typically found near the center of the tokamak q-profile, while leaving the edge region, where the shear is high, in the first stability regime. Such modes are a particular concern whenever a low shear configuratio proposes ni permio dt t improved stabilit high-o yt n modes for high beta operation.

. SCALIN3 BETF GO A LIMIT INSTABILITD SAN Y CONTROL

High-n Modes recentla n I y published parameterizatioe studth f yo accesd e th an f o t sno second regim r high-efo « ballooning mode Sabbaghy sb . [19al t databasa e ], f eo marginally stably equilibria with varying aspect ratio, edg , centeeq , q-profilq r e shape elongatiod an , n were use determino dt behavioe eth threshole th f o r> d<ß anabovp deß e whic hsecona d stability regim ef thes o exists e e Us 'optimized. ' pressure profiles eliminates the pressure profile shape from the set of predictor variables and provides insight into the parametric dependence of the stability boundaries. Show scaline optimizee Fign plote nth i th ar f f o .s2 g o d second regime boundar threr yfo e centravaluee th f o s(1.01q functiola s a , ) f aspec2 1.5no d ,an t ratio for a circular cross-section with an edge q of 4.1. Several very important generalization e seeb nn immediatelca s y from these aspecw curveslo t tA rati. o with a central q near 1, the second regime only exists at very high beta values.

32 CO. 10

Figur . e2 Secon d regime boundary using 'optimized' pressure profilea s a s

function of aspect ratio for three values of the central q0: 1.01, 1.5, and

havl Al e2.0 fixe.4.1 = a d.q

Since thesaspecw lo e t ratio equilibri e seconth n i ad regime also require substantial curren e plasmt th flo n wo a boundary e practicallb t no , they yma y achievable. At large aspect ratio the required beta drops to values below 5% with more realistic current profiles effece Th f increasin.o t centrae value th gth s i f eo q l

very strong and for q0 = 2 the second regime beta threshold begins to drop to 0 at aspecw lo t ratioe consequencTh . openine f th thi e o completela s i s f go y stable

path from low to high beta against high-« ballooning modes. As the value of q0 is further increased the point of stable access moves up to larger aspect ratio values

with q0 = 2.3 necessary to stabilize R/a = 3 and q0 = 2.6 needed to stabilize R/a = 7.5.

While the value of q0 needed to allow stable access to the second regime is somewhat lowe t lowea r r aspect ratio importano tw , t facts shoul kepe db mindn i t . First, sinc centrae tokamaa eth n i q l k naturally drop valueo t s s belo , somw1 e for f currenmo t driv r curreneo t programming needdevelopee b o st generato dt e these high central q equilibria. Since the central current density for a given q easiee scaleb y modifo a/Rs t ra s ma curren e t ,i th y t profil t largea e r aspect ratio valu0 q e eveeth needef ni s somewhadi t larger. Secondly mord an , e significantly,

the elevated value of q0 must be maintained indefinitely in low aspect ratio configurations, sinc secone eth d regime doe t exissno tl practica (foal r l purposesf i )

the q0 is allowed to relax back to 1. At large aspect ratio, the option exists to

allow a relaxation of q0 to 1 after achieving the modest <ß> needed to remain in e seconth d regime a practica e . b Thiy l ma sconsideratio f curreni n t drive efficiencie e poo ar r scurren o r t driv f afteeof accest centee r th fusiocu o s t i sr n ignition. The overall effect of shaping and q-profile modification, leads to the following conclusions regarding the optimization of access to the second stability regime: • q0 > 1 reduces <ß> and eßp thresholds for all parameters.

• At small R/a require q0 > 2 at all times for second regime operation with moderate shaping.

33 afte1 t larg~ r requironlA a 2 0 relan r acces q eR/ > • yca fo o x0 t eq s— second regime is achieved. • Elongation without triangularity is unfavorable. • Combinatio f elongationo triangularitd nan s favorablyi r sufficientlfo e y large 0 and/or large edge q. If the favorable effects identified in the study are then combined to produce the lowest beta threshold resulte sth elongates shown si a r Fign nfo i 3 . d 'dee' shaped

plasma 8.1= wit a .q h This show 2.5= 0 sq , thacompletelr fo t y stable access i s

l aspecfounal r dfo t ratios lowe l aspecal r 2 tha t= , whil ration0 9 q t ea s larger than stil3 l hav residuaea l regio f ballooninno g instability.

12 15

Figur . e3 Secon d regime boundary using 'optimized* pressure profilea s a s functio f aspeco n tn elongate a rati r 2 'dee ofo = K d' shape1 = d8

equilibriu four mfo r valuecentrae th : f 1.010 so q l , 1.5, 2.0 l 2.5d Al ,an .

have fixe8.1= a d.q

The general conclusion from these studies is that control of the central q e besvaluth t s i eavailabl e techniqu r high-fo e « mode control given thae th t experimental techniques needed to effect such control (such as neutral beam and rf current drive appea w practicale b no ) o modestlt ra n I . y shaped tokamak, access secone th o t d regio possibls ni e ove wida r e rang f aspeceo t ratior fo s9 froo t m2

values of q0 larger than 2.

Low-n Modes e controe low-th Th f «o l kink mode propey b s r choic f equilibriuo e m parameters at high beta has not been as successful as the control of high-« modes described above and no true 'second stability' regime has been found for kink mode higs sa h betaonle Th y. well established techniqu r stabilizatioefo f thesno e instabilitie s bee e prescriptioha sth n a perfectl f o n y conducting wall neae th r plasma boundary. As part of the design study for an experiment called SRX [20] to investigate access to the second regime, the stabilizing effect of such a conducting wall for the lowest three toroidal modes was studied as a function of eßp for two 'dee' shaped equilibria: one at R/a = 8 and one at R/a = 3. This is

34 show bot n FigI n ni h . possibl s 4 .case wa modt 1 si stabiliz o et = en wite eth ha conducting wall placed about 25% of the plasma minor radius beyond the edge of the plasm mose th t taa unstabl e valu f betaeo . Highe moden r s require closer wall placement reaching 15% for the n — 3 mode. In the large aspect ratio example of

Fig , interestinthern 4 a . s ei g feature whicafte9 0. rh> secon appearp eß r d fo s stabilit achieves yi r high-dfo n modes kine Th k. modes partially re-stabiliz thin ei s region as indicated by the relaxed wall placement distance as beta is increased. e significanb Thiy ma sr reacto fo t r design sinc e stabilizinth e ge effecth f o t conducting wall is only expected to be completely effective on a time scale shorter conductine timR th f L/ thae o e nth edde g th wal yr currenfo l t pattern inducee th y db

mode. 0.7

0.6- (a)

0.5- -a- n=1 0.4- -*- n=2 -a- n=3 0.3-

0.2-

0.1 0.2 0.4 0.6 0.8 1.0 1.2

0.6

0.5- (b)

0.2

0.1 —i— —I——i- —,— —i— 0.5 0.6 0.7 o.a 0.9 1.0

Figur . e4 Minimu m conducting wall distanc stabilizo et e low-n external modes sa

valueo tw aspecf r so fo functioa p t eß ratio f nR/a=8) o (a : , K=1.6, 5=0.5,

q0=2.4, qa=6.74, and (b) R/a=3, K=1.4, 5=0.3, q0=2.0, qa=7.22. The ratio distance ratie th th (b/af oo s i )e betwee plasme nth wale a th edg ld ean plasme th o t a minor radius.

These low-n kink modes have been observed at the Troyon beta limit and showstable th unstabld summara t Fign ean ni s i se 5 a . ef yo discharge e th n i s Columbi tokamaT HB a k compared wit e Troyoth h n limit taken from Ref. [6].

35 1.00

0.00 q* Figure 5. Gross stability of several HBT discharges. Open circles indicate measured parameters during the stable period of the discharge; solid circles indicate values just prior to the onset of instability.

These unstable discharges have been observed to show a growing n = 1 external mode whose mode structur s measureei d with internal magneticn i probe e b o t s qualitative agreement with the predicted mode structure from the PEST code stability analysis of a numerical best fit equilibrium to the experimental measurements. This figure also show e routth s o secont e d stability without exceeding the Troyon limit at large q* mentioned earlier: when q* > 6, the value of p approacheeß e sufficien b whic1 s y r seconma hfo t d stability against high-« modes.

4. TOKAMAK EXPERIMENTS TO INVESTIGATE BETA LIMITS: WHAT CAN 'SMALL' TOKAMAKS DO?

High eßp Experiments In the past two years there have been a number of experiments which have

studied tokamak plasmas at high values of eßp to study ballooning properties of tokamaks using a variety of techniques: Small shor t Columbita pulse] 21 , da [6 device UniversitT HB se sucth ys ha TPE-e th e 2 th Electrotechnicae [22r th o t a ] l Laborator t Tsukubaya , Japae nus ohmically heated plasmas whose density is substantially above the Murakami density limi permio t t operation nea Troyoe rth n beta limit. A large tokamak, DIII-D, has used tangential neutral beam current drive to create an elevated central q and high poloidal beta plasma [23] in a manner similar thao t t originally propose r higdfo h bet, StudX 20 a , studieSR y[6 e th pars sa f o t

, 25]24 . This result plasman si s with e verth yo t large du 1.2e ~ t valuep ,bu eß f so , thes30 large~ equilibri* eq substantialle aar y belo Troyoe wth n limit.

36 otheo Tw r form f curreno s t drive have been use smallen do r machiner fo s

the production of high eßp plasmas. On the CDX machine at Princeton [21], an electron beam generated plasma current is used to sustain a high q* discharge near the Troyon limit. On the Versator II tokamak at MIT [26] lower hybrid current drive has been used to create a high q* = 30 discharge with a beta supported by energetic electron f scurrenr createe th ty db drive . These Versator equilibrie ar a nea secone th r d regime ballooning limi t considerablbu t y belo Troyoe wth n beta limit. Those experiments which operate near the Troyon limit have reported observation f instabilityo s , while those belo Troyoe wth n limi neat secone bu tth r d regime boundary witrepor1 h~ higtp loneß h g lived plasmas wit cleao n h r observation of any instability.

High ß/ßc Experiments In order to study not only the high-« modes at high eßp, but also the more reactor relevant issu f low-o e « mode stabilit t higa y h <ß> s necessari t ,i o t y provid a significane t amoun f auxiliaro t y heating power e onlTh y. tokamak experiment presently operating with sufficient power and with a properly designed conducting shell near the plasma boundary for low-« mode control is PBX-M [27]. However, this devic s beeeha n designe teso stabilite dt th t y propertie f stronglso y shaped 'bean' cross-section equilibria conductine Th . g shel optimizes i l r sucdfo h plasmas and, eve f successfulni , wilneee w knolo dt l likel al t wtel s no u ylabou t capabilite th r moryfo e modestly shaped plasmas with q-profile contro acceso t l s the high beta, second regime. Can smaller tokamaks make a contribution in this area? We believe the answer is yes, and the present tokamak scaling laws show that the lowest level of auxiliary powe givea for rn size devic obtaineis e largdat e aspect ratio. Thiis s shown in Fig. 6 in the context of an SRX sized device with R/a = 9 and a comparable volume low aspect ratio device with R/a = 3. Shown in this figure are the calculated values of <ß> (assuming L-mode scaling) for three power levels

(1 MW, 2 MW and 3 MW) divided by the Troyon beta value, ßc as well as curves

of constant eßp. For the Kaye-Goldston [28] version of L-mode scaling of the energy confinemen thae tcombinatioe timese th t e w , f currenno majod an t r radius

scaling shows that the largest values of <ß>/ßc are obtained at the lowest possible value of q*. This provides a partial explanation of why a machine like DIII- challengn Dca t usin Troyoe bu , geth neutraq* n w limilo lt a beat m current drive at high q*, it falls well short of this limit while still setting record values of eßp.

37 (a)

(b)

Figur . e6 Calculate r threfo e> value<ß d f auxiliarso y heatin2 , g poweMW 1 ( r MW, and 3 MW) assuming Kaye-Goldston L-mode scaling for two value f aspeco s t ratio ) R/a=3(a : ) R/a=9,(b a=0.d ,, an B=1T 3m l K= , , K=lT l . a=0.B= Als , 2m o Troyoe showth e nnar limi curved an t f o s

constan referencer fo p eß t .

Also significant is the comparison of the low and high aspect ratio result in Fig. 6 which shows that for comparable volumes, we can expect to do a factor of 2 better with larg a respec Troyoe n i e th * aspecq o t t n w limilo t t ratia t o machine. This fact, together with the reduced neutral beam current drive requirements for larga o t e s aspecu d achievinle t, rati2 > o 0 configuratiogq n wit insidn ha e null divertor and an adjustable conducting shell, shown schematically in Fig, 7, in the SRX design study [20] of an optimal device for high beta tokamak research.

38 Figur . e7 Schemati c cross-sectio tokamaX SR e kth desigf no n showin insidn ga e null diverto adjustabld an r e conducting stabilizer with carbon limiter tiles.

We are presently designing an upgrade to our HBT tokamak at Columbia University which will incorporate desige manth f yo n features discussed abovr efo the SRX device. The preliminary design parameters are shown in Table I.

Tabl . eI HBT-E P Preliminary Design Parameters______R = 90 cm 10 cm < a < 15 cm 9 < a R/ < 6 TeslB1 T= a 13 3 15 3 tpulse ^ 10 msec 10 cnr < ne < 10 cm ' ______PICRF ~ 3 MW______

We expect to retain the capability of the present HBT to operate with a rapid ohmic start-up substantially above the Murakami density limit to allow ohmically

heate f ICRo dn FW i plasmaM 3 o additiot n exceeo I t sp u . c wile e ß dnw us l eithe fasa r t Bernstein wavio r eo n wave configuratio heao t n t both high density

and conventional density discharges to values above ßc. In order to control the low-« kink modes, an adjustable conducting shell similar to the one shown in Fig. 7 wil e useb l quantifo dt e effecth yf walo t l stabilizatio e Troyoth s a nn limis i t approached. In this way we hope to be able to provide some important information

not only on the behavior of high-« ballooning modes at high eßp but also whether

the low-« kinks can be controlled sufficiently to allow us to exceed ßc.

39 5. CONCLUSION

Thera numbe e ar ef importano r t issues connected wit e desigth h f o n improved tokamak reactor t higa s h beta which require experimental input. Specifically we need to know whether or not ballooning modes can be avoided by proper programming of the q-profile in a tokamak to reach the theoretically predicted second regime e alsW o. nee possibls i knoo dt t i wf i significantlo et y exceed the Troyon beta limit in order to take advantage of this second regime for improved reactor performance. While some of this data will necessarily come from the larger tokamaks, there are several opportunities which have been described in this pape r smallefo r r device mako t s contributionea f particularn o I .e us e th , virtuall fory f yan currenmo t driv smallea n ei r devic alloy ema e w studa th f yo

stabilit f hig yo p plasmas heß orden I . bea o Troyort e th t ndevicy limian n ei t with limited resources, the optimal approach is to use a larger aspect ratio than conventiona plae builW o nt . l 9 machinda design o t range 6 th f f thin eso i o s type at Columbia University, called HBT-EP, as a successor to our HBT short pulsed, high beta tokamak.

REFERENCES

[1 ] Sheffield, J. et al. Fusion Technology 9,199 (1986). [2] Troyon, Phys. Gruber d al (1985 9 t an e ,2 . , Lett.F , A R. )Plasma, 11 Physics Controlledd an Fusion 26 1A, 209 (1984), and Ecole Polytechnique Federale Lausanne Report, CRPP 239/84, June 1984. [ 3 ] Marshalld Navratil an , Comments. C. A . . ,T ,G Plasman o Physics Controlledd an Fusion 10,185 (1986). [4] Bernard, L.C., Helton, F.J., Moore, R.W., Todd, T.N., Nuclear Fusion 23,1475 (1984). [5] Bol al.t e , , Phys. Rev. Lett. , 18957 1 (1986). [6] Mauel, M.E., Ivers, T.H., Che, H.Y., et al., Plasma Physics and Controlled Nuclear Fusion Research 1988, (Proc. 12th Int. Conf., Nice, 1988) IAEA, Vienna, to be published. [7] Coppi, B. Phys. Rev. Lett 39, 939 (1977). ] Todd[8 , A.M.M., Manikam Okabayashi, ,J. al.t e ,, Nuclear,M. Fusion 19,743 (1979). [9] Machida, M. and Navratil, G.A., Phys. Rev. Lett. 51,992 (1983). [10] Coppi, B., Ferreira, A., Mark, J.W., Ramos, J.J., Nuclear Fusion 19,715 (1979). [11] Coppi, B., Ferreira, A., Ramos, J.J., Phys. Rev. Lett. 44, 990 (1980). [12] Fielding, P.J., Mass, F.A., Phys. Rev. Lett. 41,801(1978). [13] Greene, J.M., Chance, M.S., Nuclear Fusion 21,453 (1981). [14] Lortz Nuhrenberg, ,D. . Phys./ , ,J. Lett. 68a (1978)9 ,4 ; Nuclear Fusion 19,1207 (1979). [15] Mercier, C., Plasma Physics and Controlled Nuclear Fusion Research 1978, (Proc. 7th Int. Conf., Innsbruck, 1978) IAEA, Vienna (1979), Vol p701, 1 . .

40 [16] Strauss, H.R., Park Monticello, ,W. , D.A. al.t e ,, Nuclear (1980)Fusion8 63 , .20 [17] Manickam Pomphrey, ,J. Toddd an , , A.M.M.,N. , Nuclear Fusion 27,1461 (1987). [18] Todd, A.M.M., private communication. [19] Sabbagh, S.A., Mauel, M.E., Navratil, G.A. t al.e ,, Plasma Physics Controlledd an Nuclear Fusion Research 1988, (Proc. 12th Int. Conf., Nice, 1988) IAEA, Vienna publishede b o t , . [20] Bhattacharjee lacono, A. , Marshall, ,R. , T.C., Mauel, M.E., Navratil, G.A., Paranicas , Sabbagh,C. , S.A., Sen, DamA.K.n Va , J.W., Wang, X-H., Hughes, M.H., Phillips, M.W., Todd, A.M.M., Columbia Plasma Physics Laboratory Repor . 109tNo , June 1987. [21] Navratil, G.A., Baransky , BhattacharjeeY. , t al.e ,, PlasmaA. , Physics Controlledd an Nuclear Fusion Research 1986, (Proc. 11th Int. Conf., Kyoto, 1986) IAEA, Vienna (1987), Vol p299, 1 . . [22] Hayase, K., Hirota, I., Kiyama, H., et al., Plasma Physics and Controlled Nuclear Fusion Research 1986, (Proc. 11th Int. Conf., Kyoto, 1986) IAEA, Vienna (1987), Vol. 2, p563. [23] Simonen, T.C., Bhadra, D.K., Groebner, R.J. al.t e ,, Bull. Phys.. Am Soc. 32,1900 (1987); Simonen, T.C., Matsuoka, M., Chance, M.S., et al., Plasma Physics and Controlled Nuclear Fusion Research 1988, (Proc. 12th Int. Conf., Nice, 1988) IAEA, Vienna, to be published. [24] SRX Proposal, Columbia Plasma Physics Laboratory Report No. 100, August 1985. [25] Sabbagh, S.A., Hughes, M.H., Phillips, M.W., Todd, A.M.M., Navratil, G.A., to be published in Nuclear Fusion, March 1989. [26] Porkolab, M., Bonoli, P., Chen, K.I., et al., Plasma Physics and Controlled Nuclear Fusion Research 1988, (Proc. 12th Int. Conf., Nice, 1988) IAEA, Vienna publishede b o ,t . [27] Okabayashi , AsakuraM. , t al., Belle ,, N. , PlasmaR. , Physics Controlledd an Nuclear Fusion Research 1988, (Proc. 12th Int. Conf., Nice, 1988) IAEA, Vienna publishede b o ,t . [28] Kaye, S.M.Goldstond an , , R.J., Nuclear Fusion 25,65 (1985).

Next page(s1 ) 4 left blank TOKAMAK EXPERIMENT JIPN SO P T-IIU

Y. OGAWA, J. FUJITA, Y. HAMADA, NTX-GROUP, GA-GROUP* Institut f Plasmeo a Physics, Nagoya University, Nagoya, Japan

Abstract

Wit a medium-sizeh d tokamak JIPP T-IIU (R/a=0.91m/0.23m, Br=3T and Ip=300kA), confinement stud r ohmi fo d yauxiliaril an c y heated plasmas (P/c/?F=2MW, Pwe/=0.7MW) has been conducted. To study plasma microturbulences R lase,FI r scattering syste bees ha mn developed with heterodyna e detection hign I .h density ohmically heated plasmasw ,lo frequency density fluctuations propagating in the ion diamagnetic drift direction ( ion mode ) have been observed in addition to the electron mode. The injection of ICRF power remarkably enhances both components e densitoth f y fluctuations e pelle Th s .als wa to injected into auxiliarily heate dbees plasmasha nt i observe d ,an d thadecae th tf yo the ion mode just after the pellet injection is much faster than that of the electron mode. This would suggest a stabilization of the ion peakee modth t dea density profile produce pellee th y tb d injection. In the JIPP T-IIU tokamak, two toroidally localized m=3 multipole coil equippede sar o demonstratT . concepe helicae eth th f o tl island divertor a pum, p limite s insertewa r d inte magnetith o c island. Experimentally, it is found that, when an island 0-point surrounds the graphite limiter blade, the heat load and plasma recycling at the neutralizer surface behind the limiter increases, and high Z impurities in the plasma are reduced.

I. Density Fluctuations [1] Stud anomaloun yo s transpor bees tha lonna carrier g fo timet dou . Recentl s pointei t t theoreticalli you d y tha a dissipativt e trapped electron (DTE) mode and an ion temperature gradient mode (r?i mode) would play an important role[2,3,4]. In ohmic plasma experiments on a TEXT tokamak, density fluctuations propagating to ion diamagnetic drift directio s beeha nn observe n higi d h density regime, suggestinn a g

Genera* l Atomics Diegon Sa , , California, United State f Americaso .

43 existence of 77; mode, but without experimental informations about ion temperature profile[5] e JIPth P n I T-II. U tokamak u modr s i ee th , observed in high density ohmic and also in auxiliarily heated (NBI and ICRF) plasmas, and its influence on temperature profile is investigated.

Spatia temporad lan l behavior densite th f so y ne(r,t) electroe ,th n

Ttemperaturen e(r,tio d )an s Tj(r,t e measure)ar d with 6-C N laseHHC r interferometer system, 10-CH grating polychromator (ECEd )an charge-exchange recombination spectroscopy (CXRS), respectivelyn I . orde o studt r y plasma microturbulences e havw , e develope R laseFI d r scattering system wit a heterodynh e detection e maiTh .n radiation lonm laseN sourc5 g HC a r s ewhici h deliver slinearla y polarized beam of 0.5 W with a wave length /li^SST^m. For the heterodyne detection another HCN laser is operated as a local oscillator with the beat frequency of 2 MHz. w frequencLo y density fluctuations whichn io propagat e th n i e diamagnetic drift direction have been observe n higi d h density ohmically heated plasmas. Figur 1 showe s typical power spectrf o a density fluctuations with fce=9.9cm~'. Thee observeo ar ytw t a d different scattering regions whose center e locatear s t z=+30ca d m (Fig.l(a) and (b)) and z=-30ctn ((c) and (d)). The uppper(/>0) and lower (/<0) sideband Fig.l(a)n i s ) correspon(b , directione th e o t dth f o s electron diamagnetic drift and the ion diamagnetic drift, respectively, and vice vers Fig.t(c)n i a w densit,lo (d)e th y .n regimeI maie th ,n e densitth par f o ty fluctuations propagate e directioth e n th i s f no electron diamagnetic drift (Fig.l(a), (c)), havin lineaga r dispersion relation for various wavenumber. In the high density regime, the ion mode propagating in the ion diamagnetic drift direction is observed (Fig.l(b), (d)). To evaluate the ion temperature profile for ohmic plasmas, we have employed CXRS data just after the injection of the neutral beam, which would give informations of ohmic plasmas if t «T slow-down- Fortunately the time resolutio r CXRou S f o nsyste s veri m y good (At=1.5msed an c Tstou>-doum=10~20msec) r ohmiFo . c plasma e valuth sf Tji(=dZnTi/cunn,o e ) s beeha n evaluated with profile dat n temperaturef densito aio d an y , resultin n r? 1.0~1.i ig= t r/a~0.2a r hig5fo h density plasmas. This valu s comparabli ee thresholth o t e d value (~0.95) estimated

theoreticall e instabilitth r yfo y with fcpi A

44 (à) (c) loe n w

Fig l . Power spectral distributions of the density fluctuations wit fce=9.9cnf• h ' for ohmic plasmas, where Ip-2UQkA. Sr-2.97 and (a), (c) n.-^.SxlO'V3, and

ai/2* (400kHz/d.)

Density fluctuations for auxiliarily heated plasmas have been examined. Figure 2 shows the temporal behaviors of plasma parameters

ICRe ith nF heated discharge (P/~0.8,W). Durin ohmie th g c phase th e r stored energy increases with the increase in the line averaged electron densito 4zl0t p 13u ycm~ d saturate3an , n higi s h density regiof o n

____, I O __O M e electroTh n e>4rl. nm c Omod e component ne(e) increases wite th h electron density. On the other hand, the ion mode component n(i) keeps

13 3 e

the constant level in low density region (ne<4xl0 cm~ ) and starts to

3

rise clearly when n increases above 4xl0cm~13 , as pointed out in e previous section. The injection of ICRF power at t=255ms remarkably enhances both component densite th f so y fluctuations. Her shoule ew d remark that density fluctuations at the ICRF phase are about 4 times

as high as at the ohmic phase for the ion mode n(i), while those are e

2 times for the electron mode ne(e), suggesting that TH mode is playing an importan deterioratioe tth rol r efo energe th f yno confinement time in auxiliarily heated plasmas. e pelleA ic ns bee ha tn injected durin e ICRth gF heating, since pellethe eic vers ti y usefu modifo lt densite yth y profile drastically. e injectio Th e pelle th s brough f ha to n t abou e increaseth te th f o s amplitudes for both components just after the injection. A few

milliseconds later, n howevermodio e e componenth , t ne(i) rapidly returns to the level just prior to the injection in contrast to the

behaviou electroe th f o r n mode component ne(e). These phenomena seem

45 300. 200.

0. 1.0 .ru. 0.0

2 8. o

v A *-s * l* 0.

S 10. a? 0. ~ 2.0 -5 S 1.0 Vrf' % C l

0.0

4.0 3.0 2.0 1.0 0.0 . 0 125. 250. 375. 500. time (ms )

Fig. 2 Temporal evolutions of plasma parameters; i.e., plasma current

Ip, ICRF power P/, line averaged electron density n, total r e

stored energy Wp, electron density fluctuations n«(ed nean (i)) ,

where n«(e) and ne(i) are the electron density fluctuations propagating in the direction of the electron diamagnetic drift and that propagating in the direction of the ion diamagnetic drift, respectively. Durin ICRn ga F heating pulse pellee th , s injectei t d at i-300msec, indicated by arrows.

to be closely related to the temporal behaviour of the electron density profile injectee Th .e pelleic d .Omm*1 ( t >xl .3mm' ,v~400m/s s i ablate) d around r/a~0.5. The broad density profile formed just after the injection makes the ion mode unstable, which may cause the increase of the inward flow. This enhanced inward flow makes the density profile peaked in 3ms after the injection, which is favorable to reduce the resultd e reductioan th i e valufluctuation J? i th s f f o eo n n levef o l

the ion mode ne(i)/n<>.

46 II. Pump Limiter Experiment] s[6 e fusioIth n n reactor, divertor functio s indispensabli n e from the viewpoints of not only particle/heat removal but also the achievemen n improvea f o t d confinement like H-modes n existinI . g tokamak devices, stud poloidan o y l diverto s beerha n conducted, while Karge d Lacknean r s proposeha r a concepd a resonan f o t t helical divertor, where divertor function is held by helical islands produced bweaa y k helical coil currenplasme th t ata edge[7) e JIPTh .P T-IIU tokamak is equipped with two sets of toroidally localized m=3 multipole field coils Helicae Th . l Island Divertor Experiment (HIDEX bees )ha n then conducted, insertin a pumg p limiter insid e helicath e l island. The HIDEX pump limiter head has a curved graphite blade ( 10 mm thick, 220 mm poloidal by 160 mm toroidal) which is designed to fit inside these islands and acts as the main limiter for the plasma. When the blade of the pump limiter is inserted into the 0-point of the magnetic island, it is expected that particles flowing along magnetic field lines can be removed by pumping, resulting in the reduction of the heat load to the limiter blade. Rough measurements of the island widths are in agreement with numerical field line mappings that predict values of 15~25mm for m/n=3/l or m/n=4/l islands for typical operationing condition Ip=250fcA,ßr=2.7f so helicaa d Tan l current Ih=6fcA. The temperature of the HIDEX limiter blade edge has been measured with an infrared video camera. Figure 3(a) compares the temperatures operationr fo s wit hwitA IhQk h =±d ohmi6an c heatin valuq ga onl ed yan at the blade of qi=3. It is clear that the temperature rise is much less when the 0-point of an island surrounds the blade than when IH is zero or reversed to produce an island X-point at the blade. Figure 3(b) i comparisosa n betwee shoto 5 ntw 0. s t wit ne additionan ha f o s m 0 l10 MW NBI auxiliary heating. The 0-point operation again results in a lower blade temperature althoug e differencth h e wite X-pointh h s i t smaller r operatioFo . n wite bladth h e between islands (e.g., Qi=3.5), little or no difference in temperature is observed. The plasma densit d carboan y n radiation strongly increase durin e timth ge the X-point is on the limiter, probably due to ablation of carbon from the limiter. The lack of a corresponding increase in oxygen radiation also indicates that the carbon is coming from the pump limiter rather thaimpurite th n y gases adsorbe othee th rn o dsurface vacuue th f mso chamber othen I . r cases, however, thero significann s ei t changn i e the amount of carbon in the plasma. These results verify that the heat load to the blade is minimized when the blade is set inside the 0-point.

47 o 90°- - n l o x'*/*"*"*helle») fiel^d x 10 i 11,or 850 ' ''•t lea" y d 800 X \ r / / " °' y ° (10°~*"*\ he8'n llo t a \ 5 750 / \ ^x_ at a « 3 résonance g 700 • • V^ 5 650 / / \ -x g 600 •Al \ ^ -x S SSO 7 X v g 500 (/ ° \ "\" " vx S 450 0 ' „/ * °^ -°-o-o-0 """"•—-...... *~*~*- -'400 ————————— ——————— - —————• — -• —————————• ————————— • 0 200 400 600 900 1000 TIM Emse• c

~ 1300- x x - X-po1nt on head _ 1200- • o-po1no hean o t d - yt ~x%x N résonanc3 • q »t e g 1100- x * / f~°~\ * with N8I S 1000- II O w N b ) £ 900- / / \ x t \ N ' x' § 800- / / °-° \ V / \ \ 58 700- oi * I °V X ut / V -x-x E 600- X s 1 °-n-n 'X-X .0 . . ~0-„.0.„-... 0 80 100 0 60 0 0 40 0 20 0 TIM E- mse c

Fig. 3 A comparison of the surface temperatures of the limiter blade edge (ion 0-point1 d islan drif3/ an e = - th dX t n n ssideo m/ r )fo limiter blade and for Ih=0. ohmie th cn i heatin ) (a g case blade ,th e temperatur mucs ei h higher for the X-point or Ih=0 cases than for the 0-point case. (b) in the NBI heating case, X-point operation is again hotter although differences are not so large.

A high speed video camera with various interference filters is also use o e viet HIDEdth w X limiter head during plasma discharge. Photograph Fig.n si e take4 ar n tota i n l visibl caseso e tw ligh r ;fo t 1 islan0-poine 4/ th centeres a i dlimitere ) ) f o tth (b (a n d o d an , th e same th eX-poin n o location s i t e visiblTh . e light signas i l brightes e middlth e X-poin t e th a ebladt th n par i ef to t case, confirming thapattere th t f outwaro n d power flo plasmy b w a particles changes e formatioi th y b d f islano n d concentratean d e regioth n ni d around the X-point.

A Da detector viewing the limiter blade from the rear shows a noticeably signal (i.e., greater recycling at the neutralizer surface behind the limiter) for the 4/1 island 0-point on the blade than for an 0-point whic s slightli h y displaced radially inward e plasmTh . a

temperatures (Te,Ti) and their profiles are not greatly different for operations with and without the helical field perturbation. When the HIDEX limite /\V-line F d inserteds ri an er C intensitie , ,Ti s become very weak probably due to less interaction between the core plasma and the vessel wall.

48 { a ) 0-polnt on limiter head ( b ) X-po1nt on limiter head

4 HigFig. h speed video photograph e HIDEth f Xo s limiter hea n totai d l visible light froelectroe mth n drift limitesidee Th . r blads i e 1 island4/ = n .centere m/ ) 0-poin (a n ) X-poina (b n f i d o ( t ) t For the X-point case, the light is much brighter at the middle part of the head.

In conclusion, large magnetic islands are formed in the edge of e JIPth P T-IIU e resonanplasmth y b a t interactio e externath f o n l helicaflu4 d x an surfacesl3 fielq= t da . Surroundin HIDEe gth X limiter blade with the 0-point of one of these islands changes the outward power flow frocore mth e plasma, resultin lesn gi s hea blade t loath eo dt than when t presentislandno e ar s .

REFERENCES

[1] Kawahata , Adati K. , ,Akiyama K. , , Andot al.,e , R. Ando, , A. , R. , in Plasma Physics and Controlled Nuclear Fusion Research, 12th IAEA Conf. in Nice, 1988, IAEA-CN-50/A-5-3-1. ] Tang[2 , W.M., Bishop, C.M., Coppi , KayeB. , , S.M., Perkins, F.W., Redi, M.H., Rewoldt n Plasmi , G. a, Physic Controlled an s d Nuclear Fusion Research (Proc. llth Int. Conf. Kyoto, 1986) Vol.1, IAEA, Vienna (1987) 325. ] Waltz[3 , R.E., Dominguez, R.R., Wong, S.K., Diamond, P.H., Lee, G.S., Hahm, T.S., Matter , ibid.N. , , 345. (4] Kadomtsev, B.B., Pogutse, O.P., Reviews of Plasma Physics, Vol.5, Consultants Bureau, New York, (1970) 308. ] Brower[5 , D.L., Peebles, W.A., Kirn, S.K., Luhmann, N.C., Tang, W.M., Phillips, P.E., Phys. Rev. Lett. 9 (19875 ,. 48 ) [6] Evans, T.E., Adati, K., Ando, A., Baker, D.R., DeGrassie, J.S., et al., n Plasmi a Physic Controlled an s d Nuclear Fusion Research, 12th IAEA Conf. in Nice, 1988, IAEA-CN-50/A-6-2-2. . . fTLacknerKargeF K ] d an r , Phys. Lett.,61A, (1978) 385.

Next page(s) left blank 49 STUDY OF PLASMA PASSAGE THROUGH TOROIDAA L SLO T-1N TI 3 TOKAMAK

V.I. BELASHOV, A.V. BORTNIKOV, N.N. BREVNOV I.V. Kurchatov Institut f Atomieo c Energy, Moscow, Unio f Sovieno t Socialist Republics

Abstract

A short survey of experimental activity on small tokamak T-13 is given. The wor s i relatek a schem o dt f quasi-continouo e s tokamak operatione Th . experimental dat plasmn o a a column behaviou e proces s th passagit n i f r o s e through a toroidal slot are presented.

A schem f quasi-continuouo e s tokamak-reactor operations wa , proposed in £1J . According to it, a plasma, after the fuel burn-out, is ejected into an auxiliary chamber having the developed internal surface and a high-power evacuation. The chambers are connected with each other through a narrow, toroidal slot to reduce a revers flow of neutral gas into an operating chamber. As a result of plasma eje- ction e operatinth , g chambe r e excitatiowil th reade b lr yfo a f no new discharge» Then, the cycles are repeated. One of the unknown problems in this approach is the absence of experimenta le plasm datth n ao a column behaviou e procesth n i f r o s its passage through a toroidal slot. Some experimental data on this problem are given in this paper. An experimental e plasmstudth f yo a column passage througha rather narrow toroidal slot was performed on T—13 tokamak [23 with toroidal partition withi s operatinnit g chamber (Fig.1) pare Th -. tition includes four semiring f triangulao s r cross-section extended toroidae th n i l direction. Each semiring mad f aluminiuo e ms insui - lated from the chamber and from other semirings« The toroidal slot, e experimentTh . " wide s variecm "h 7 wa , so dt wer m froc em2 carri- e followinth t a t egdou parameters: maximum plasma current» J ,

, toroidakA 5 1 la magnetic field t Bn motioRa i T «1o; «t4G 0k e cm 0nth

51 Fig.1. Geometr experimene th f yo dispositiod an t diagnosticf no s at T-13.

major radius was varied in the range R « 48-65 cm, plasma density —n~ 1 x 10 11-•'era , 3The minor plasma radius, a » 7.5 cm was preset with rail limitera. necessare Th y conditio plasme th r an fo passag e without magne- tic structure violatio plasme th n ani columfollowss a s ni :

<£* — -,< ^ ^ where V is the plasma column velocity y K A^$ n SK )

alon e majogth r radius, SA, is the plasma skin time, °C^ is the skin time of the partition with the slot. Under T-13 conditions this requiremen satisfieds ti , whe 1Crcm/s> nV .cono Thern -s ewa ducting facilitycasine plasmth e th n g i d a,an equilibriu pros mwa - vided by the time coded currents through the poloidal turns. Such a rapid plasma motion by changes in the currents through poloidal turns only cannot be technically - provided in T-13 tokamak. There- fore, a horizontal plasma column instability in the confining mag- netic field with the high decay index, n = | || > 3/2, within the slot has been used. The plasma column was produced within the zone (R < 48 cm) with quasi-resonance confining magnetic field. Then, it was slowly shifted along the major radius and entered an unstable re- gion (R>50 cm) plasme .Th a column velocity withi unstable nth - ere gio s determinenwa deceleratioe th y db ninduceo t forc e du ed currents

52 vacuue th partitione n mi th chamben i positioe d .Th an r plasma f no a column ceatr measurea ewa d with magnetic probes (Fig.1). Langmuir probes were locatepartitioe th n o d n surfac measuro et periphee th e - ry plasma parameters at a time of plasma column passage through the slot. Optical measurement visibla n si espectrue rangth f d o e man measuremente th fasf so t neutral fluxes were performed durine gth whole time of plasma motion. lin- V eG intensitied an I GU s measured acros directioe sth n of the plasma column motion in front of the separating wall (I - R » 54 cm), at the centre of the wall (2-R- 58 cm) and beyond the wall (3-R=62 cm) are given in Pig.2. The plasma column motion wels i l observed wit signalse hth s spee. It estimates di s a d 3-5x10~ V 4 cm/s.

50 » 5 ov

4.5 S t[mS]

Pig . «GUI2 , CV-optical line intensity oacillograms acros plase th s - ma column motioe vicinit th e gap n th ni o .yt

The discharge parameters during the plasma column passage thro- ugh the slot withS=^x100#«4C$ of relative wideness, where h is the distance between the upper and lower semirings (Fig.1), are o show n ffig«3i n » Withi e regionth f plasmno a productio *nV * 10^cm/s,

53 o.s

Pig . .Discharg3 e parameter e plasmth t a as motion acros e gapth s , e plasmth s i aS **4.Q% majoe currentI th ( rs i radius,R , ^ is the loop voltage, I is 0V - line intensity at R «= 58 cm,

Langmuie th s bi r- prob centrep ega currene ,th t ta I is the hard X-ray radiation intensity.

withi partitioe th e slo nth n i t3x1Crcm/s » nv . Spectroscopic mea- surements and the data from Langrauir probes coincide with the data from magnetic probes on the plasma position along the major radius. The Langmuir probes were installed on the surface of the wall to make measurements at the plasma periphery at a time of the plasma column passage throug e slothth movabla , e Langmuir probe (Pig.4) was use measuro t d e plasmth e a parameters alon e Z-axise gth th n i , saturation slotio e middl th e chang A f th , o e n ni e current sa j t from the Langrauir probes on the wall surface during the plasma co- lumn motion through the slot with varied width, S **3Q% and O »4055,

Pig.4. Langmuir probe dispositioregionp ga e .th n ni is shown in Pigs. 5,6. One can see that at £«0 Jsat in the range of 54-6« R doem slo0e depent c sth no t n widthdo e th othet , a " r"£ saturation current rises with a reduction in b . A change in Jsat along the vertical axis measured with the movable Langmuir probe - shows i Pigsn ni . basi e 7,8 th thesf so n , O e measurementn ca e son build up the dependence laat » f (Z) at the fixad major radius

(1^=5 variouRr , 2 =5R^=62fo , cm 8) cm (Pigs.9,10)sE 4cm botn ,I h cases the distribution can be represented by the power function ot Y « 1-(x/h) , when o( %. 4, where h is the slot width* The electron density distribution in a moving plasma column - measured with an interferometer in operation without separating wall - is close to the parabolic one. A signal from the interferometer ( /I «2.3 mm), when the measurements are done from the gap centre (R «= 58 cm) in vertical direction, is shown in Pig,11.

5=3*7

foa

5* Si 62 Pig.5. Saturation currents from Langmuir probes at a time of plasma column passage through the gap at 5 =30%.

too.

Si SI 42 Pig.6. The same for 5 040$.

55 m A]

/oo :

/?£•*. I

Fig.7. Saturation current from a movable Langmuir probe (R « 58 cm) at a time of plasma column passage through the gap for va- ~ S riou t a sZ

too

£Z Pig. 8. The same for S

10 20 Pig.9. Relative distributio saturatiof no n current alon movablga e Langmuir probe for different plasma column positions at S »30% ( A =t>R = 52 cm^ * =c> R « 58 cm, a =* R = 64 cm).

56 ots

0,2

10 20

Pig.10ô sam e r Th fo e.

KCc»] 6t 60 56 Fig.11. Interferometric phase incremen e plasmth t a at passage through the gap o~ » 3Q% wide (R = 58 cm).

The presence of a plasma column in the auxiliary chamber after passage throug confirmp ga a he optica th s l line intensity measure- ments (GUI, 0V, CV) and those of fast charge-exchange atomic flu- e T-1th 3 n i auxiliar s xe y chamber e horTh .d measurement f o sopti - l lineca s CIII alon V e majo0 , gth r radiu fasy b s t scanning acrosa s narrow gap along the 2-axis allow one to watch a vertical motion of the expanding plasma edge in the auxiliary chamber (Pig.12).

Z C

60

62 $& S4

Fig.12. Vertical plasma column edge position found wit e spechth - tral line IIIC s. ,0V When the plasma column reaches the middel of the gap the line inten- sity border touche raisa tha) lmm t 5 limiteprobabl7 B Z ( r y reve- dumb-bella s al s like configuratio plasme th f nao colum thit na s instant of time. A relative change in the plasma current in the plasma column motion through the slot with the varied width is shown in Fig.13« A plasme changth n aei current, whe plasme nth a colum shiftes ni d in the absence of partition, within the T-13 chamber is also shown there. The loss of charged particles due to diffusion onto the par- tition was estimated by the saturated ion current to one semiring.

06

0,1.

52 SO

Pig. 13« Plasma current change at the passage through the gap wit variee hth d width.

The flux of charged particles in the process of motion through the slot is reduced the stronger, the higher is the velocity of motion (Fig.14) powee .Th plasme r th cos y ab t through this channel doet sno exceed 10% of that spent on Joule heating.

10 v-3-ro*?

4 Ctn

5J? ^ SO

Pig. 14. Saturation current from one semiring at the motion with different apeed.

58 A sloe widtth t f hdetermineo naturplasme e sth th f eo a column passage throug Whe. 30%« hit n% , passageo n ther s plasme ewa ,th a column waa destroyed in front of the partition. When 30%.£ o < 40%, the plasma passed through the slot, but the plasma column disruption resulting in a slight deceleration of the plasma column and in some energy loss (15%) took place very often. When B?-40%, the plasma co- lumn passe slote rulea dth s ,a , without disruption. experimente basie Thusth th f so n , o s don T-1n ei 3 tokamae kon concludn ca e thaplasme th t a ejection throug toroidaha l slot with widta h sufficiently-loss thaplasme nth a column diamete possibs ri - le. REFERENCES

1. Degtyarev L.M., Pistunovich V.l., Shafranov V.D. Nucl. Fus.,1980, v. 20, N 1. 2. Bortnikov A.V., Brevnov N.N. Preprint IAE-3277/8, 1980.

Next page(s) left blank MHD ACTIVITY UNDE INFLUENCE RTH F EO HELICAL EXTERNAL MAGNETIC FIELDS

I.C. NASCIMENTO, A. VANNUCCI Institute of Physics, University of Sâo Paulo, Sào Paulo, Brazil

Abstract

e configuratioTh e intersectioth f o n f magnetino c field lines wit poloidaha l surfaca r fo e plasma colum equilibriun i smale th mn li torus TBR- obtaines Ii d befor afted applicatioe ean th r n resonan2 ofm= t helical fields (RHF) resulte .Th s suppor interpretatioe th t actuatF n RH thae e th t on the m = 2 mode causing a strong decrease in the MHD activity.

I - INTRODUCTION

Experiments using resonant magnetic helical fields (RHF) have shown that under certain circumstances they can strongly influence the MHD activity in tokamaks and even trigger or inhibit the disruptive instability.

Sinc firse eth t wor 1974Kargen y i k b l a (1t )e r man y experiments were performe severan di l laboratories to investigate the effect of RHF on the plasma equilibrium*2"4'.

Investigatio differenf no usinF gRH t helicities were also done recentl TBR-1e th n yo smala , l tokama operatiokin Institutthe nat Physic eof Universit the Paul of sSâo oof ywhos e main

parameters are: R = 0.30m, a = 0.08m. B= 0.40T. T -\-200eV, I = 12kA, plasma duration • * p ( ITI3p X 6IT19X O A uo 7mst p n TBR-I . 1 discharge s alreadwa t i sy verifie d e activit D stronglb tha n MH t ca y y attenuated by RHF(5>. In this paper we study the configuration of the magnetic surfaces for different intensitie compositiod s an influence modeD th d MH s an f RHFf neo o .

II - EXPERIMENTAL ARRANGEMENTS

The RHF at the TBR-1 is created by a set of copper mesh helicoidally installed at the outside toroidae ofth l chamber coiline continuoust .Th no s gi r eac.Fo h half-tur windinge nth attachee sar d to a panel so the desirable helicity can be easily obtained by setting the right connections as it is show fign i . 1 .

61 CONNECTIONS PANEL CONNECTIONS PANEL

Fig Helica- l . l coil connectiod san n system.

currene Th windinge t pulsth squara n s eo sha e wave like amplituds formait d o t an t 0 e( 700A), duration (1 to 10ms) and instant of firing (concerning a specific tokamak discharge) can be properly adjusted. Variations in the intensity value is practically negligible reaching ^2% only for longer pulse conditions.

plasm e influence activitD th Th n applieobservee s o aMH th y F wa f eo dRH d througf o t se ha twenty Mirnov coils placed insid vessele th e avoio t , d field attenuation. Sixtee f theno m were equally space poloidae th n di l directio fixea t na d toroidal positio foud nan r coils separaten i ° d90 the toroidal direction at a fixed poloidal position*6*. The coils output signals were digitalised by two eight-channe moduleC lAD recorded san a microcomputer n di .

ANALYSI- l Il EXPERIMENTAF SO L RESULTS

presentes i figt n i I .2 exampln da whicn ei m/n=2/e hth l windin activates gwa d about 450/is afte beginnine th r plasme th f go a discharge helicae .Th l puls 260s ha fign amplitud f eAi b o .2 d ean duratio 3msf neasils o i t .I y identifie stronfiga n di c .2 gactivit D attenuatioMH ye whilth f e no eth current pulse is on. When the pulse ends the intensity of the Mirnov oscillations rapidly increases'51. The q(a) value was measured to be -v4.

Calculating the relative amplitude of the perturbed magnetic poloidal field in the three interval f thio s s discharge (before, unde afted influence an rth re RHF th s obtaine f wa o e ) t i d BQ/BQ %0.7%, 0.3% and 1.7%, respectively. Fourier analyzing the MHD signals before the verifies wa applicatio t i d F thadominane RH smalleth td f no an 3 tr modcontributionm= s ewa f so Afterwards. =4 m d an ,2 durin m= dominan e applicatioe th g th F RH tf nmodo essentialls ei . =3 ym

62 ^_^ 1C. (a)J * 6 l/^ o. - 1-1 0 L ———— ,—————— — |————— — ,————— — |—————— —h (b) - 300 o - C - / — \ 0 ——— U- ——— | — s — i ——— | ——— j. 0.10 (c)- £ 0 r lH*Ylty» X- .':$$}$^*'^fttä$^ X -0.10 v r- - , i , ' |' , — ICÛ 0 1.0 2.0 3.0 t(ms)

Fig. 2 - Profiles of plasma (a) and 2/1 helical windings currents (b) during a discharge in the TBR-1. In (c) the corresponding mhd activity is presented.

Finally, it is observed mainly a saturated m=2 component when the MHD amplitude increases wit helicae hth l pulse ending. These dat showe aar Tabln ni . e1

TABLE 1.

AMPLITUDE OF MHO DOMINANT MODES (T)

RHF condition Ip(kA) B /B B9(T) 2 = m m* 3 i m = 4 qa e 9 l Before 10.3 r 4.0 0. 7 % 15x105 3.9x10"5 50 1 x 7.3 3.9x10"5

During (260A) 10.5 3.9% 3 . 0 6.2 xia5 1.6x10"* 3.6x10'5 1.0x10'5

After 10.5 3.9 1.7% 4 Ox105 23x105 12 x 105 4. 5x105

Constructing the Poincaré maps for the equilibrium field lines distribution^, before and afte pulseF applicatioe diagramth re RH th , e th f nso presente , respectively4 d figsn dan i 3 . , were obtained. Comparing these figures we can see that after the influence of RHF has ceased the q = 2 island associate activitD d MH witmucs yi e hth h bigger than befor activatioe eth e RHFf no th n I . island3 regio observeq= s i d t si nan existenc e betwee2 dth ergodiq= n a e f nth eo c region without any minor disruptio e havw es na identifie mann di y other discharge TBR-1n si (8).

During the application of the RHF the approximation made to construct the Poincaré diagrams are poorer. In fig. 5 we present for comparison purposes the result obtained for the Poincaré map considering only the MHD measured modes. We can see that the equivalent island width decrease ergodie th d scan region betwee islande nth s increases.

By other taksidee w ef i , into mod3 accounm= ee witth t hintensits halit f fo yn o befor F eRH islanF obtaie RH d w 2 resule nth m= te islanlarga show2 th = e d edfigm se n an ni n wher.6 ca e ew and a large ergodic region overlapping the islands showing the destruction of magnetic surfaces.

63 .08

.04

*v-\ l Ê 0

"

-.04 \ •

-.08 -.04 0 .04 .08 X(m)

Fig Intersection- .3 magnetif so c field lines wit poloidaha l surfac plasmr efo a puls Figf eo , .2 before the application of RHF and for data of Table 1.

.08

» '* * * • . * >;,-, >

.04 «'• *{„•'<.f ' ,••'' ' ' •''•'•?:,• ' ','•. ' .. « <*.'" ' ' '"t^i ' s • -

0

- V

-.04

-.08 -.08 -.04 0 .04 O8 X(m)

Fig. 4 - Same as Fig. 3 after the application of RHF.

64 .08

.04

• A -/ . {

E. o

. i " 'ir

-04 ,'- • ' ' '" C •'•> s Ss ' x

-08 i -OS -04 .04 08

Sam- 5 Figs eg a durinFi .3 applicatioe gth RHFf n o calculatio e date . Th Tabl f th t ao r bu fo e 1 s ni only the plasma parameters are taken into account (see text).

-.08 -.08 -.04

Fig 6 - Same äs Fig. 3 during the application of RHF (m=2) and considering only the m=3 mode with half of its value.

65 RHFe th f , o figd show4 . Afteen calculate e resule e th sth th r fo t d islands associated with activitD MH y islan2 e observedth q= muctha e s di e se th t e h largeW . r than befor applicatioe eth n of the RHF. It is seen also the increased ergodic region between q = 2 and q=3 islands.

comparisoe Th n betwee show4 d nevidence sfigan th 3 . e thaD attenuatioe th t MH e th f no modes is caused by the influence of the m=2 RHF.

CONCLUSION

The interaction of the RHF of helicity 2 with MHD magnetic islands produces a strong attenuation of the amplitudes of the modes. In the discharge investigated the RHF seems to actuate mainly on the m = 2 mode since after the ending of the RHF pulse there is a sudden increase in the m = 2 mode amplitude and a growth of the q=2 island.

ACKNOWLEDGEMENT

We thank Dr. M.V.A.P. Heller for calculating the Poincaré's maps of this paper.

REFERENCES

. Karger,HF ) (1 . Wobig Cortî. S , . Gernhardt,J Klubler. O , Lisitano. G , McCormick. K , . MeiseSesni. D ,S d klan - "Influenc Resonanf o e t Helical Field n Tokamao s k Discharges "Proc- h Intt 5 . . Conf. Plasma Phys. Contr. Nucl. Fus. Res., Toky oJapan- , IAEA-CN33/PD-2(19747 )20

(2) Z. Yoshida, K. Okano, Y. Seike, M. Nakanishi, M. Kikushi, N. Inoue and T. Uchida - "Suppression of Disruptive Instabilit Low-n yi q Regim Externay eb l Ergodizatio f (2.1no ) Island h Intt 9 , . Conf.Plasma Phys. Contr. Fus. Res., Baltimore - USA, IAEA-CN-41/S-5 (1982).

(3) K. Yamazaki, K. Kawahata, R. Ando, K. Matsuoka, S. Hirokura, S. Kitagawa, A. Mohri, S. Tanahashi, Y. Taniguchi - "Quic i To k. K Profile-Reorganizatio, n Drive Helicay nb l Field Perturbatio Suppressinr nfo g Tokamak Major Disruptions" - Nagoya University - Report IPPJ-796 (1986).

(4) J.Y. Chen, Y.P. Huo, J.K. Xie, Q.CL.Z, Li .. Zhao, G.Q. Zhang, M.Q. Wang, D.Q. Guo . QinPJ , , G.X, Li . H.Y. Fan, C.B. Deng - "MHD Studies on HT-6B and HT-6M Tokamak by Active Magnetic Probes" - to be published.

. VannucciA ) (5 , O.W. Bender, I.L. Caldas, I.H. Tan, I.C. Nascimento, E.K. Sanad a- "Influenc Resonanf o e t Helical Windings on the Mirnov Oscillations in a Small Tokamak" - II Nuovo Cimento, to be published.

) I.H(6 . Tan, I.L. Caldas, I.C. Nascimenlo, R.PSilvaa d . , E.K. Sanada . BruhR , - a"Mirno v Oscillationa n i s Small Tokamak" - IEEE Trans. Plas. Sei., PS-14 (1986) 279.

) A.S(7 . Fernandes, M.V.A.P. Helle I.Ld .an r Calda s- "Th e Destructio f Magnetino c Surface Resonany b s t Helical Windings" - to be published in Plasma Phys. and Contr. Fusion (October, 1988).

(8) A. Vannucci, I.C. Nascimento and I.L. Caldas - "Disruptive Instabilities in the Discharges of the TBR-1 Small Tokamak "- Plasm a Phys Contrd an . . Fusion publishede b o t , .

66 EQUILIBRIUM POLOIDAL BETA LIMI TOKAMAKN TI S

P.K. KAW Institut r Plasmefo a Research, Bhat, Gandhinagar District, India R.M. KULSRUD, S.C. COWLEY Plasma Physics Laboratory, Princeton University, Princeton, New Jersey, United State f Americso a

Abstract

The analytical investigatio e fluth xf no conservin g tokamak equilibrium proble larga r efo m inverse aspect ratio tokama presenteds i k e Th . Grad-Shafranov equatio uses ni demonstrato t d e that beta poloida uppen a s riha limit of the order of the inverse aspect ratio.

e poloida a tokamaTh f o ß ik plasm defines e expressioi a th y b d n y i2

where the numerator is the pressure averaged over the minor crossection e totath ls i an plasmI d a current. Flux conserving tokamak (FCT) theory s showha ne safet th tha f yi t factor profile s q(\|maintainei j) d constant as p(\|O is increased, then there is no upper limit on $ . However, this 1 conclusion is based on the use of a model equilibrium with shifted cir- n equilibriuculaa n o r t surfaceno m d obtainean s a solutioe y th b d f o n Grad-Shafranov equation n thiI . s pape n analytica a e carr w rt ou y l investi- gation of the FCT equilibrium problem for a large inverse aspect ratio circular crossection tokamak. We solve the Grad-Shafranov equation analy- ticall a boundar y b y y layer techniqu d demonstratan e n a s eha tha ß t upper limit of order the inverse aspect ratio R/a, in contrast to the predictions of the usual FCT theory.

In dimensionless variables e Grad-Shafranoth , v equatioe writteb y ma nn

1 ... 2 dp d ,F2. ex) 4() Y Y e z 3 x 3 a (2) •*••*• 2 where x = (R - R )/a , z = Z/a, £ = a/R , V\|j/R = B , F = a ( 1 + ex) B , , a is the o op (p minor and R the major radius of the conducting torus surrounding the plasma e safetTh . y factor probleo Ou t r. jßdlF(\| s Vi)= i ] | mq(ty ) ) | j [(ex / 1)) +

67 determin e axisymmetrith e c tokamak equilibriu r givefo m n

the boundary conditions ty (r=a) = 0, matyx = , $ being the total stored poloidal flux.

whic1 W et , yequivalens ~ introduci h1 ~ F orderine , phyo 1 th et ~ - p g Notcontrase . 1 eth ~ ^ t ~ wit e Y th h, 1 sica ~ q l. 1 statement ~ , B ~ p s 4> 2 conventional ordering in which p/B is ordered small in £.

To orders E- 2 , £ -1 we find

2 p + (F /2)Q = c (3a)

2 x = -(F /2)2/2(||) E x (\\i) (3b)

Eqs. (3a,b) determin ea cor e solutio n whici n = 4*' * h4 x) - Knowledg f p(ijj}eo , usee b e cordetermino t dy th q(4 ema n i 0 ee equatio x(\|>th y b ) n

x /———2 _3/2 \j; dty q(\|>) ) 4 ( / " J .-r- 2 .= x d x - 1 / / p(ty- c )o/ -1

where c is determined by the boundary condition ty = 4>fx = 1-

The above core solution ty= ty (x) corresponds to a poloidal field dominated t obviouslI . bB y y doet satisfno s e boundarth y y condition e conth -n o s ducting wall everywhere o finT . d e \|;(x,zneighbourhooth n i )e conth f -o d ducting wall, we carry out a boundary layer analysis in the coordinates p,6 definey b d sinÖ) p £ . +/ 1 { cos6 ) p = £ z ,/ + 1 ( = x

£ / scaline radia e th Th f lo g variabl ep correspond a squashin o e t s th f o g poloidal field neae conductinth r n gals ca wallo e demonstratOn . e that the contributio f boundaro n y laye Ë o q(^/ smallet r s i ) r thae corth ne contributio hencs i d e an nnegligible .

The lowest order boundary layer equation (we expand i|j in a series \JJ = gives i , y nb ) . . . £i+ . bb \ £ / + \\)

= - 2tt [coso - x (fy ) ] (5) dp

where a = dp/d^ is assumed to be constant for simplicity and x(ip ) is

68 determined by the core equation (4). Note that 6 enters equation (5) only as a parameter. Eqn. (5) may be solved by quadratures to give the solution

= P

where V(\p ,9)=2a / °o [cos6 -x(i^ ) ] d\|) is an effective 'nonlinear poten- t= y ) a = (cos9)r ( . tial4 d = T\> an ' u ob o o

Eqn. (6) satisfies the boundary conditions \|> (p =0} =0, \p (p-* -°° ) = \(j (cos6) and demonstrates that as p -*• - °°

= K 1/2 *o *ob+ exp[(+2a f| | ) p] (7) Yo Yob

i.ee boundarth . y layer solution matche e corth se solution wit n expoa h - nentially dampe n dsho ca termw e thae On solution. th t o next s t orden i r /£ also match beautifully. In the boundary layer, constant \|J contours are constant p contours i.e. the magnetic surfaces in the layer take the shape of the conducting vessel until they smoothly join with the vertical B lines in the core-region. The overall shape of the magnetic surfaces is therefor r froD fa eshape m d circularan d e magnetiTh . c axi s alsi s o situated in the boundary layer. A more careful boundary layer analysis is neede o investigatt d e elongatee th shapth ef o e d surfaces neae th r magnetic axis.

The above detailed solutions can be utilised to demonstrate the scaling

2 ) (8 (/4!§,

numbea s i ordethaf e o r se R t re Notin w unit, , d/dgä ya / thap~ ~ p t independent of the magnitude of pressure. ß only depends on the forms of p{4> } , q(\|> ) and the shape of the boundary. Effectively, one finds that o providt p e pressurv n equilibriua th a ess a p u eI mus o goe, g tm up s such tha ß tremain s limited.

Our conclusion is that even for an FCT equilibrium eß is limited to a 1 2 valu f ordeo e r unity. More detailed report wil e publisheb l d elsewher. e

REFERENCES

1. J.F.Clark d D.J.Sigmarean , Phys. Rev. 0 (1977)7 Lett , 38 ..

2. P.K.Kaw, R.M.Kulsru S.C.Cowled an d published)e b o (t y .

Next page(s) left blank 59 STABILITY OF BALLOONING MODES IN THE PRESENCE OF A TOROIDAL FLOW

A. SEN, A.K. SUNDARAM Institute for Plasma Research, Bhat, Gandhinagar District, India

Abstract e stabilitTh higf yo h (ra,n) ideal ballooning presenc e modeth n si e of a rigid toroidal flow is examined. Equilibrium modifications induced by centrifugal forces are found to stabilize the ballooning modes in all but the outer regions of the plasma. Plasm helf ao gainin n rotatiope i b n e g ca th n acces o t s second stability regime.

1. Introduction Ideal ballooning modes have been extensively studiee pasth tn i d [1-12 their 3fo r importanc settinn ei ß limi e tokamakn gth ti t (f s is the ratio of plasma pressure to magnetic field pressure) Much of this work has been carried out for static plasmas and problee th ballooninf mo g mode e presencstabilitth f n o ei y equilibrium flows has received limited attention [13 ~ 193- In recent times there have been several experimental observationf o s toroidal plasma rotation e orde th sounf o f rso d speed during neutral beam heating of tokamaks (e.g. on ISX [203, PDX [213 and currentl TFTn yo T [233)RJE [22 .d 3an Suc h rotation ca n affect the position and form of the magnetic surfaces as well as alte densite rth pressurd yan f importanco e s profilesi t I e . therefore to investigate the resultant modification in the ballooning stabilit sucf yo magnetia h c configuration worr Ou k. is motivate sucy b d hconsideratio a furthed an n r stimulatey b d some recent experimental interest [24 usinn 3i g toroidal rotation to gain access into the second stability regime.

. Equilibriu2 m We conside a plasmr a confine a perfectl n i d y conducting axisymmetric toru whicd san h obey e ideas th equations.I D lMH e nth case whe plasme nth s rotatinai g rigidly abou s it axitf o s symmetry with a constant angular velocity O = V / R (where V

71 is the flow velocity and R is the major radius). the equilibrium force balance equatio writtee b n nca n dows na

e magnetith e ar c field p , ,p , wherJ plasm , B e a current, pressure and density respectively and the subscript o denotes equilibrium quantities0 x cleas i p rt V .I • tha) fro (1 o tmE a surfac t sno oe thas i t unlikp stati e , eth 0) c - cas O e( quantity. The surfaces of constant pressure and constant magnetic o n longeflu e rxar coinciden e separatear o t t e bu tdu d centrifugal force effects. Assumin e temperaturth a g e b o t e surface quantity (in view of the high thermal conductivity along field lines wit d furthee )an hth r choicf eo

O2 02 T R r = constant ( 2 )

{where CT - -^j- is the square of the sound velocity) the parallel component of ( 1 ) can be solved to obtain a simple expressio equilibriue th r nfo m pressure [25]:

n { ——— — } (3) 0 0 n 2

arbitrarn a s i ) y wher y functio ( e poloidaep th f no l flu. y x Notice that rotation induces a poloidal asymmetry in the equilibrium pressur a flu n xo e surface (the exponential > functioa poloidaVy e s i th e ) f Th 3 n o facto l ( . angln ) i r e& component of (1) yields the equilibrium equation

I a Ü d p ~ 9 A \y + R —— exp { —— - } + I —— = 0 (4) d y 2 CT ô \f> 9 wher equilibriue eth m magnetic fiel bees dha n expresses a d

\ - -jjpC + V C X 7 y (5)

(£ is the unit vector in the toroidal direction) and Û is

72 e usuath l Grad-Shafranov operato cylindrican I r l coordinates

Z m & 1 d y d y ) (6 — —— + ——R —= — — —v —— A Z a s d R R a

The equilibrium given by (6) is characterized by three flux functions p , O / C and I. Analytic and numerical solutions of (6) have been obtained in the past [25,26] for specific choice thesf o s e flux functions principae .Th l changes seen i n these equilibria (compare e statith o dt c equilibriae th e ar ) separatio constanf o nd constan an tp v tsurfaces , additional Shafranov shift of the magnetic axis, ellipticity in the shape of magnetic surface sinfluence etcshale th W .e l se som f e o thes f eo e features on the stability of ballooning perturbations for these equilibria.

STABILIT. 3 Y Following Frieman and Rotenberg [13] we will formulate the linear stability a proble n Lagrangiai termf o m s n displacement vecto aboue f ri th equilibriut m trajectory. Linearisin e th ideag l MEID equation d an e usinth s g boundaryconditione n-vth = , s (wherE 0 i =nx n = e B > sn e boundarynormath o t e lobtain on ) s after some standard algebra,the equation [13,17,19]:

2 - w po ? + 2 i o> po ÎQ • V ? - F { ? } = 0 (7)

( normal mode solutions of the form if (r,t) = Jf (r) exp(-twt) have been e assumedlaborator th s givei n operatoi e } n)f Th j y { rF frame by

o -Sp 7 o• -$£ + )+ E o ? -V • $7 O P r ( v = } ? { F

(8) + * ' * fto + 7 • ( po Mo • 7 »o - p0 *0 *o - * ? ) Hermitiae ar F d nan wit V operatore - h Th respec$ e th p o si tt inner product =jdrâ-È, but the total operator is non-Hermitian in general. This is a characteristic difficulty of analysing stability problem presence th n si flowf eo prevent d san s (unlike in the static case ) the use of general Energy Principle techniques generan i s i l» , o complex2 , unless certain conditions thesf holdo e e. On condition gives si y nb S^Jdr?*F<) (9 0

73 f conditioI ) e hold(9 nth systes s s read i thei man lo n c stableconstitute) (9 . .Eq sa sufficien t conditio r stabilitfo n y and has been used in the past to examine the linear stability of equilibria with flows [18,19]. « is also real at the marginal stabilit choose yw sucr poinanalyso d t fo a e casehan ) t (7 e. e addeth Thi ds advantagsha f affordino e a direcg t comparison with the various analytic results available for the static limit studies of the marginal stability of the ballooning mode. The marginal stability point can be found as follows. Taking the inner t ge produc e ) w wit (7 f h* f o t

2 F {?} , >* 2 o P£ $- 0 " o?-+ v > e imaginarth , . co giveo ) •» c 0 y£ •1 = par{ s> o f to r Fo

2 co. [ - cor < ?*, P0? > + t < ?*, P0V V ? > ] = 0 (11)

If co. is different from z:ero the mode is unstable. Letting co. tend to zero, one gets the following condition, if the limiting mode exists.

where f is now a solution of (7) with to = co (real). Condition a (12bees necessar e ha )b n w [27 o showt Lo ] y ynb conditior fo n marginal stability of the» mode Jf , to We will therefore analyse equn. (7) for co = co . Wcs consider large n modes (where n is the toroidal mode number) in the ballooning limit (i.e. long parallel wavelength and short wavelength perpendicular to the field lines) ys. **. and adopt the eikonal description,? - Ç exp ( i n W ) , where Ç ia sslowl y varying amplitude e phasth ed an ,facto W rsatisfie s Unde. 0 r= thiW V s • description È e rea,th l frequencs i o c y

found from (12) to be o>o a: - n ( $o ? W ).We further express Ç and the perturbed field Q in terms of its components parallel to orden I . o avoiB rt e fasx th dW t V magnetosonid an VW B , c wave w e assume tha e plasmth t s nearli a y incompressibl| j Ç e- [7]V t , VW • Ç ! « I VW | | Ç | . This assumption is not equivalent to strict incompressibilit d retainan y sloe sth w soune d th wave n i s system e systefacn i .Th ts i mrepresente o coupletw y db d second order equations correspondin e sheath Alfve- ro gt d sloan nw sound

74 waves. For finite growth rate modes the effects of compressibility and parallel inertia can then be taken into account by solving the coupled set of equations. Such calculations carried out in the static limit have shown that these effects can reduce the growth rate [7], We do not consider these effects in our calculation, sinc marginat ea l stabilite t th pla yno a d roly the o an d ey equations infact become uncoupled [7]. We concentrate therefore on e sheath Alfver- n equation whic obtaines hi x B ( takiny db e th g ) componenVW (7)f to . Substitutin e ideath lw r ballooningfo g mode equatio marginae th t na l stability poin gives ti y nb

ÈX VW ——f-( V V> ?-t L o Ê x VW'Vp B x VW1 (^ -V)$ ———( + -—— —————r-( ~) 0 2= ———, Ç (13-) ) H> H o o firse Th t term represent usuae sth l field line bending whics ha h stabilizina g effect secone .Th d term ,usuae whicth ls h i driving term for the ballooning mode contains the interaction of the curvatur (Ï>-7)- ex S wit pressure hth e gradient thire .Th d term contains the effect of the centrifugal force due to rotation and is usually destabilising. Howeve bees ha n s pointera t beforou d e [19], this terbecomn mca e stabilizin certain i g n regione on f si takes e accounrelativth f o t e centrifugal separatioe th f o n pressur densite th d yean profiles from each othed froan rm flux surfaces. If one considers a flux surface in the intermediate region, lying between the maxima of the pressure and density profiles, the third term can change sign and have a stabilising influence s beeha nt .I shown howeve re basith [19f o sn o ] numerical evidence thar rigifo t toroida• d l rotatione th , stabilising effect of this term is not sufficient to overcome the second term. We have chosen to neglect this stabilising effect in our analysis and for our equilibrium model this term is always destabilisng. We next adopt the ballooning representation and express Eq.(13) in the infinite domain [-00,00] of the ballooning space &, for a given flux surface. To take account of the ellipticity effect flue th x n si surface adope , w metrie tth c

cos(ö+ r A(r o + )R - S) 2 (r= R) cos(ö) (14a)

S r Z = r sin( sin(ö) (14b)

75 Shafranoe th - wher) v(r eA shif t -represent e displacemensth f o t the centr givea f eo n flux surface fromagnetie mth c ) axis(r S . accounts for the ellipticity effects (for S(r) = 0, (14) describe conventionae sth l shifted circle equilibriume th n I ). present model - the shifted elliptical model -the following relation holds(where primes denote differentiation w.r.t) .r A sin(6>) - S sin(2ö) r Vr-Vö = ————— -————— — -— — -, ——————— (15) l + A cos(e) - S2 cos(20)

t « The quantities A , S can be evaluated from the Grad -Shafranov equation (6) by carrying out a perturbative expansion in the large aspect ratio limit. We adopt the high ß tokamak ordering [28] ( ß e ß poloida ~l,th = < s , i , *^wher1 ß £ „l q ),an ~ ß e d p p neglecting quantities r/R , A/R and S /R as compared to A and ' ' ' et ô S we obtain , A ^ - a , S ^ - — 5— where 2 2 ^

2 2 KQq 0 B£ ?{ si S I a < — ) n —a rsi + > - 1 0 (sr - ) —— ? d> J 2 J

cos r> + sin f) (sn ~ « sin rj - a 6 sin 2r) ) Y = 0 (17) 2 J

where r) = sB, s - q(~ )(-srdr ) is the shear parameter and Y is the normalised displacement. The boundary conditions are Y •* 0 as Y) -» ± . (18ooEq . Not) 0 reduceee 6= thath r mode o fo tst l equation [5,28] studied for static plasmas.Rotation introduces two major modifications - Ca!> the (a6/2)sin2r) term arises from the equilibrium modificatio e magnetie th shapth f o n ei n c flux surface, namely ellipticity effects and is associated with the

76 poloidal asymmetr equilibriue th n yi m pressure.Cb e cScosr)th ) term represents the additional destabilizing force arising from centrifugalforce effects. We have solved Eq.(17) numerically to determine the marginal stability boundaries in the (s,ot) space. resulte Th displayee sar Fig.n i differenr d lfo e t Th value . 6 f so stati e c, showfirs th d 0) resulsecon an = st Q t( d stability regimes separate zona instabilitf y eo db y ywa extendine th l gal to the origin. For 6 > 0 we find the instability zone to broaden.

0 1- 9 0- 8 0- 7 0- 6 0- 5 0- 4 0 3 0- 2 0- CH

Figure 1: Marginal stability boundaries for several values of 6. instabilite th 0 < Howeve 6 y r zonrfo e reduce d alsan so moves away from the origin thus providing a stable window which connects the first and second stability regimes. From (16) we see that cS is a function of the radial coordinate and remains negative as long as r < L . Thus flux surfaces located within L are stable p p to ballooning modes in the presence of toroidal rotation. In the outer regions, rotation has a destabilizing effect.

4. Discussion We have investigate e stabilitth d f higo y h (m,n) ideal ballooning modes in the presence of toroidal plasma rotation. Our model calculations indicate that rotatioa stabilizin s ha n g influence on ballooning modes on most flux surfaces except in the outer region e effecTh .s associatei t d wite equilibriuth h m modification in the flux surfaces arising from the centrifugal force - namely an elliptic elongation of the surface. This aspect

77 beet no n s considereha n earliei d r studie f thio s s problem [18,19] wher stabilito en bees yha n found r 'shifte.Ou d ellipse' model allows us to take into account this equilibrium modification of the flux surface and we find it to have a stabilising influence. The stable region is given by r < L , where L is the p p pressure scale length. Typically L ~->-L the density scale length) p n so that this region encompasse e plasm th e bul th sf kao profile. The stabilizatio substantiae b n nca r quitfo l e modest value6 f so as seen by the separation of the finite 6 curves. With observed plasma rotation e ordeth f sounro f s o d speed [20-23]e ,th man f o y present neutral beam heating experiments are in the regime where this stabilization experimentalle effecb n ca t y investigatedn A . additional and important advantage of toroidal rotation is the creatio a stabl f no e window connectin e firsth d gseconan t d stability regimes - the goal of future high ft experiments and for which several approaches are currently being studied [9,24,29]. Toroidal rotation may provide a simple and attractive option, as our model calculations demonstrate d thereforan , e warrants both experimental and further detailed theoretical investigations.

REFERENCES

] Lortz [I Nucl, . ,D . Fusion 13. (1973) 817. [2] Dobrott, D., Nelson, D.B., Greene, J.M., Classer, A.H..Chance.M.S Freemand .an , K.A., Phys. Lett 9 3 . (1977) 943. Coppi] [3 Phys, ,B. . Rev. Lett (1977a .3 ) 939. Pogutse] [4 , D.P Yurchenkd .an o E.I., JETP Lett (19788 .2 ) 318. [5] Connor, J.W., Hastie, R.J. and Taylor J.B., Phys. Rev. Lett. 40 (1978) 398. [6] Coppi, B. Ferreira, A. and Ramos, J. J. , Phys. Rev. Lett. 44 (1980) 990. Antonsen] [7 , T.M., Ferreira Ramosd an . ,A J.J.,Plasma Phys4 2 . (1982) 197. Ramo] [8 s J.J., Phys. Fluid (19841 s2 ) 2313. [9] Sen, A. , Kaw, P.K. and Sundaram, A.K. , in Plasma Phys. and Controlled Nuclear Fusion Research (Proc. llth Int. Conf.,Kyoto, (1986) Vol.2, IAEA Vienna (1987) 101. [10] Todd, A.M.M .Manickam, , Okayabash. J , , Chance. M i , M.S., Grimm, R.C., Greene, J.M. and Johnson, J.L., Nucl. Fusion 19 (1979) 743. [II] Miller, R. and Moore, R.W., Phys. Rev. Lett. 43 (1979) 765. [12] Chance.M.S., Jardin, S.C Stixd .an , T.H., Phys. Rev. Lett1 5 . (1983) 21. [13] Frieman Rotenbergd an . ,E Rev, ,M. . Mod.Phys 2 (19603 . ) 898. [14] Hellsten, T.A.K. and Spies, G.O., Phys. Fluids £2 (1979) 743. [15] Hameiri, E. and Hammer, J.H., Phys. Fluids £2 (1979) 1700. [16] Spies, G.O. Nucl. Fusio 9 1 (1979n ) 1531; Phys. Fluids 25(1980) 2017.

78 [17] Hameiri, E.J., Math. Phys. £2 (1981) 2080. [18] Hameiri Laurenced an . E , , P.J., Math. Phys 5 (1984.2 ) 396. [19] Bondeson, A., lacono, R. and Bhattacharjee, A., Phys. Fluids (1987) 2167 Bhattacharjee n Workshoi , A. , n Theorpo f o y Fusion Plasmas Varenna (1987). [20] Isler, R.C. Murray, L.E., Grume, E.C., Bush, C.E. , Dunlap,L.L., Edmonds, P.B.,, Kasai , Lazarus. S , , E.A., Murakami, ,M. Neilson, G.H., Pape, V.K., Scott, S.D., Thomas, C.E. and Wootoni,, A.J., Nucl. Fusio3 n2 (1983) 1017. [21] Brau, K., Bitter,M. , Goldston, H.J., Manos. D , McGuire, K.and Suckewer, ,S. Nucl. Fusion £3 (1983) 1643. [22] Scott, S.D., Bitter,M., Hsuan, H., Hill, K.W., Goldston, R.JGoelern .Vo . S , d Zarnstorffan e th n i Proc f , o .. M , 14thEuropean Conf. on Controlled Fusion and Plasma Physics,Madrid, 1987, Vol. 11D, . Par65 1 t [23] Core, W.G.F., Bell, P. Van and Sadler, G., in Procs. of the 14th European Conf. on Controlled Fusion and Plasma Physics, Madrid, 1987, Vol. 11D, Par , 1321 t . [24] Navrâ . A Baranskyt . ilG , , BhattacharjeeY. , , ChuA. , , C.K..Deniz, A.V., Grossman, A.A., Holland , IvorsA. , , T. , Li, X.L., Marshall, T.C., Manel, M.E., Sabbagh , Sen. S , , A.K., Van Dam, J.W., Wang, X.B. , Phillips, M., and Todd, A.M.M. in Plasma Physics and Controlled Nuclear Fusion Research (Procs. llth Int. Conf. Kyoto, 1986) Vol., IAEA1 , Vienna (1987) 299. [25] Maschke, E.K d Perrin.an Plasm, . ,H a Phys. . (198022 , ) 579. [26] Semenzato, S., Gruber, R. and Zehrfeld, H.P., Comp.Phys. Reports 1 (1984) 389. [27] Low, F.E., Phys. Fluids 4(1961) 842 [28] Galvao n i Radiatio . R , Plasmasn i n , . B.McNamaraVoled . I . , World Scientific (1984) 280. [29] Gerver, M.J., Kesner, J. and Ramos,J.J., MIT Report PFC/JA -87-34(1987).

Next page(s) left blank 79 HIGH BETA PLASMA SELF-STABILIZATIOD NAN SECONACCESE TH O SDT STABILITY REGIME

V.V. DEMCHENKO Division of Physical and Chemical Sciences, International Atomic Energy Agency, Vienna

Abstract The shear-induced instability of ideal and resistive ballooning MHD modes is studied analytically for closed magnetic traps with an arbitrary shape of the magnetic axis. A stability criteria determining the maximum pressure of a D stablMH e plasmwida r e fo arang toroidaf eo l configuration derivee sar y b d usin methoe th g smalf o d l oscillations.

The simple ballooning mode transport model are used for self-consistent investigation of the self-stabilization effect on the high-pressure plasma confinemen conventionaa n ti l tokamak with auxiliary heating.

1. Introduction. Intensive theoretical studiee ideath D lf MH so internal ballooning modes stability have predicte existencn a d "secona f eo d stability regime tokamar "fo k operatio higt na h beta (see review papers [1,2] and references therein). Tokamak plasma operatin secone th n di g stability regim havn eca e sound benefit compares sa e firs th to t dregim stabilityf eo : a) high beta can result in a more compact reactor for a given power output, b) the lower magnetic field (because of high beta) reduces the difficulty of using liquid-metal blanket coolants, c) plasma current can be significantly same reduceth e r tokamafo d k sizpowed ean r whic advantageous hi s froe mth engineering requirements by simplifying the design (primarily improved access for maintenance).

Several mechanisms thastabilizn tca e ballooning mode provided san sa route by which to access the second stability regime have been proposed, including:

rapid non-uniform and/or sheared toroidal rotation with flow velocitf o y soune ordee th th df r o speed [3], - stabilizatio energetiy nb c (hot) trapped particles [4], raising central q (safety factor) just above unity [5], use of indented cross section [6], current profile control [7].

81 Besides stabilization mechanism mentioned above there exists specific for plasmf mo a self-stabilization [8] plasme :th a stability improves with increasing pressure criterioe Th . idear nfo l ballooning mode toroidan i s l magnetic systems obtained in Refs. [9-11] predicts the second regime of plasma stability which was first found in the numerical calculations of Refs. [12,133.

In the second regime of stability beta practically unlimited only under condition that high beta equilibrium obtaine stabls t onli dno yo et idea t lbu all MHD modes. Presumably resistive ballooning modes will come into play and w betne leadaa limito st e stabilit Th . resistivf yo ballooninD eMH g moden i s tokamaa k plasm analyyzes awa Refn i d . [14] generalizatioe .Th e th f no results obtained in Ref. [14] to the case of confinement systems with three dimensional for magnetif mo c axis (among them various stellarators with helical windings) was done in Ref. [15].

presene th n Sec I f o .t 2 pape comparativra e analysi stabilite th f so f yo small-scal modeD eMH s (namely, Mercier modes, idea resistivd lan e ballooning modes) is performed for toroidal magnetic systems with spatial magnetic axis. Stability criteria are given, stabilization and destabilization mechanisms of modee th s considere indicatede ar d . Using these criteri shale aw l examine analyticall secone yth d stability regim tokamakn ei trapd san s witha complicated magnetic field geometry. In Sec. 3 the auxiliary heating power require tokamar fo d k plasm evolvo at timn i e e self-consistently intoa high-beta, globally self-stabilized equilibriu estimates i m meany a db f so simple theoretical model that incorporates both transpor balloonind tan g stability.

2. Ballooning modes in closed magnetic traps with spatial magnetic axis. In this part of the paper we shall briefly summarize a formalism develope studyinr fo d g ballooning modebroaa n i sd rang three-dimensionaf eo l toroidal magnetic configurations in papers [8-11].

2.1 Derivation of an averaged equation and stability condition for the ideal ballooning modes. The starting equation presents a small-oscillation equation from Ref. 16 [Eq. (2.30) in this paper]:

82 Here the notation is standard:

(2.2)

O. -» y^

& « C*

•«>

»^^-. M / JA , the v\ are the signed minors of the tensor ~ * wYt' 3 ^^ yi s £'1$>V Ä ^/«V, «à- ^^ ^v*, V is the Perturbed radial displacemen plasmae th f to ,

(2.6), (2.7)

I is the equilibrium current density, J u are the transverse (along 6) and longitudinal (along ^ ) magnetic fluxes.

Equation (2.1 writtes )i coordinata n ni e system with straightened lines of force. The quantity v is determined by ,

, (s~i* = \ o o

83 We conside toroidara l magnetic confinement system wit magnetiha c axis whicclosea s hi d curv three-dimensionan i e l space. Parameter thif so s curve torsioe th arcurvature eth d nan ) (K e

By analogy with Ref. 17, we replace the variable Q by u which has an infinite rang writd e eikonaean th en i valu l, for\j e m (2-9)

where F ( ^j^)^) is a slowly varying function of angular variables. Equation writtee b (2.1n ca )n >o » 3 (2.ioM )U U v ^US w ^V )- * 1* v v • (2.11)

^Tf vf>

Her hencefortd ean superscripte denot" hth "1 averagee d eth an d " an ds"0 oscillatin ge correspondin partth f o s g quantities.

The averaging of Eq. (2.10) over the oscillations of the metric is performe techniqua y b d e propose exprese W Refn . i ds .10 F(a,a y,^s a P) series ? * I * ,t, . ~

__ where -v and 4 are the mean and oscillating parts of the function F (a, y, Then averaginn ,o g ove fase rth t oscillations (2.10. Eq , ) take fore th sm

84 Subtracting the averaged Eq. (2.14) from Eq. (2.10), we obtain relations ** determining function: 9 s

where u : il-a .^

L_ 4. l f-j

L^ is the oscillating part of the operator V» ^H . The substitution of the **+* expressions for L into Eq. (2.10) reduces the latter to f { L

t i [ { 1 l i o" Wiu lt^ c n:c u "

firse Th t(2.16. Eq ter n )mi describe stabilizine sth g actio shearf no d ,an secone th d term mea e allowth n r magnetisfo c well. Quadratic ^ termA n i s correspon balloonine th o t d g effect tere ,th m proportiona . describeU o lt s the combined effect of shear and current density inhomogeneity along the magnetic field lines. The quantity A takes into account the plasma self-stabilization effect. Equation (2.16usee b analyso t dn )ca e idea eth l ballooning mode stability in toroidal magnetic configurations of different types.

85 The coefficient sw d ^l^Han enterin \ ,(2.16^f , calculateEq ge )ar d accordin procedure th o t g e suggeste Refn i d . [18]. Omitting cumbersome intermediate calculations write ,w e dowfinite th n e formulas:

where

>* -

A \ * Jf

A A r x v x -** o y i \ ^ ^ f

^ ^v V(.y^vu^/ J H x»^!^ ^ n-v» ^^ AHv vul X

(. • -1_IA. .VJ^"V"-i

( \

(2.18)

where

86 i

W- ntt vl

where

f 1^

-*» ^ i «, - I * , •r „ . _ •—. v - — • - -r Ir ^^ 4. ^ A ^

87 ( *M> /A \ N

— ;.„

where the quantity with subscript v\ denotes the Fourier component of the expansion of the corresponding quantity in the major azimuth of the torus,

rectification functio n. (2.18 h(GuvEq n gives )i *)i y nb

^0\^>t^t*O [ f l _ ^J 1 -*.» N } - T L>v -u % ; j

^ .

The equations for £ and a are the same as those obtained in Ref. [19]. The expressions for \4^ ^ ^ iv^ an<* *"V given above completely describe the solutio equatioe th f no smalr nfo l oscillations (2.16) thereby providing necessare th y stability criterio balloonine th r nfo g mode toroidan si l magnetic traps wit arbitrarn ha y shap magnetie th e c axis.

88 generae Inth l case stabilite ,th y criterio cumbersoms ni thao es e tw confine the analysis of Eq. (2.16) to traps with a parabolic pressure distribution thin I .s case, froequatione magnetic-axie mth th r sfo s displacement Ç and the magnetic surface ellipticity a, we obtain

\I ______+ . i. ———————————*> — . — ———————* — 1I

L v*^ ^^V^^VWA) Q^4,VO where

After the substitution of Eqs (2.20) and (2.21) into relations (2.18) and (2.19), the equation for the small oscillations reduces to the form + t ^ -1 - ^ -i l -o, <2 where

Jfc*1 "I* Tt.v> I _ (2.25) _l-l-V/O> ^> •*

.v> H»A U.WX «.

89 f .1 L ^

Cy*«u>

(2.26)

„ Xv.y XoyvtA^^X F V\-

Su 4- ——————

'l,

r \

L y.^V>4 J'

p -tl _ o « Using the trial function ^ = (1+t ) from Eq (2.22) we derive the necessary stability criterion for ideal ballooning modes:

Here, the first term corresponds to the shear stabilization effect of the flute instability; the second term describes the stabilizing effect of the geometrical magnetic well on plasma stability. The third term in criterion (2.27) for S>0 describes the de-stabilization of a high-pressure plasma

90 (ballooning effect) lase Th .t term correspond plasme th o sat self-stabilization effect.

2.2 The stability of resistive ballooning modes. By generalizing the method for analyzing resistive ballooning modes in a tokamak (see Ref. 14) to devices with an arbitrarily shaped magnetic axis, we can show that the three-dimensional problem reduces to a two-dimension one in terms of the turn whici simplifie, e nb n variablehca ^ d takiny an b d averagn S sga e ovee oscillationrth reducee b metricsecone n a th ca o dt f t so dI . order one-dimensional equation. Nea instabilite rth y threshol growte th s h (a drat e

"$ -*0) and for a parabolic plasma pressure distribution {. 0= ^0 (.4- 0> /CX this equation becomes

where

—y -v^/ A.

91 An analysis of the small-oscillation equation (2.28) reveals that there are two branches of resistive electro-magnetic modes: a "fast" branch (t»l) and a "slow" one (t«l).

Stability conditio "faste th r " nfo mode . n Unde ca conditioe e rth w l nt» ignore ballooning effects in Eq. (2.28). In this case, the question of the stability reduces to one of the stability of the g-mode. A geometry- independent o-mode stability condition for the case of a tokamak is in Ref. thin I s[20] .sectio generalize nw resulte eth Reff so . [20 deviceo ]t s with a spatial magnetic axis. For the "fast" mode Eq. (2.28) reduces to

29)

where

From Eq. (2.28) we find the stability condition for "fast" resistive mode as follows: \^l r> o

(2.30) ^ ^ * S ^ ( ^ fe 5"

where t r p A « v * » f Jt n ^ (.\v>V* ^ ^ ->c^ wS^-1^ VvT " %-

-A

_ t

***

92 Fro e conditiomth n thasolutioe tth q (2.29 E f no ) mus boundede tb fine e ,w th d growt he "fast th rat f e"o

Using condition (2.30), we can analyze the stability of a plasma in a current free confinement system with a three-dimensional magnetic axis (Spitzer 's figure eight design) . The stability condition in this case reduces to

. ^ ,-T„ ^ , ^ where >4^ ~ *v* K ^ 31 Ä *. v/fe^Vv -^ Tl^ ^«^^XfChe curvature of the magnetic axithir fo smodellese b tran ca py b d

where

~

r specifiFo c calculation *afc d 1.5= "^, t wan eithen se I .5 = e 0. s w r case ew e "fastTh . " >0 resistiv hav: "3 e e mod therefors i e e unstabl arbitrart ea y pressure devicen si thif so s type (condition (2.31) never fulfilled).

- Stability condition for the "slow" resistive mode. Assuming that solution of Eq (2.29) localizes in a small region CV^-0 » ^ find the w conditio "slowr nfo " mode stability:

(2.32)

93 Neae instabilitrth y threshol (2.29. Eq d ) becomes •— > )r \L - *- \\ *————— rv^-I/ *~ vV J1 *V ™- v\>) (2-f 33J )"*"*)

where

From the condition that the solution of Eq. (2.33) must be bounded we find the growth rate of "slow" mode resistive instability:

/•

Instability condition (2.32) contrasn ,i t with thaidear fo t l ballooning modes 2 (2.27), does not contain a basic stabilizing term proportional to the S . 4 othee Onth r hand doet i , s contai tera n proportionaf o ma d an a S l The latter corresponds to a plasma self-stabilization. e thesus s eu resultt Le analyzo st e stabiliteth plasmf yo a n i a current-free device (^ =0), when stability conditions transform to: idear fo l- ballooning modes: v»,

(2.34)

94 - for Mercier modes:

(2.35) o

- for "slow" resistive modes:

(2.36)

Let us consider such a device spatial magnetic axis of which constitutes closed curves wit Fourieo htw r harmonie magnetie th f so c axis curvature [21]. Using conditions (2.34) - (2.36), it is possible to find explicit dependence of plasma threshol ^ plasm ß dß> apressurt stabilit(a ^ eß y occurs) on the parameters •& , k and two values (m) and (n) which determines the «x * spatial location of magnetic axis. The results of calculations are presented e tableath t .

.-2/, _t , h 3 Parameters ß -(R/a)

X n m ko kn Mercier Ideal balloon- "Slow" resis- mode modg in e tive mode

0.5 2 I 1.12 k2=l .06 1.08 0.84 0.69 0.1 2 1 1.03 k2=0.5 0.91 1.13 1.1 0.3 3 1 1.05 k3=l .21 1.11 0.89 0.73 2 2 1.5 3 1 1.27 k3=2 .2 5.io- 4.io~ 3.5.10-2 0.4 4 1 1.05 k4=l.68 1.24 0.98 0.76 2 2.4 4 1 1.35 k4=3 .28 1.io- 0.9.10~2 0.6.10~2

It can be concluded from these results that the least value of ß « belongs to "slow" resistive mode. Further increase of plasma pressure leads to the stabilization of either ideal ballooning mode or Mercier mode. The most dangerou e "fasts th mod e founs b "i e o resistivt d e mode, excites sinci t ei d

95 pressurplasme e ith th n s a raiseds ei current-frea n I . e device, this mode is unstabl arbitrart ea y plasma pressure. This conclusion differs qualitatively from the conclusion that this mode can be stabilized in a tokamak .

3. Confinemen self-stabilizef to d tokamak idean Refn a I .2 .l2 balooning mode transport model has been proposed to explain experimentally observed degradation of confinement in tokamaks with auxiliary heating. This model provide singlesa , self-consistent descriptio profilf no e evolution that incorporates both stabilit transportd an y Refn I thi3 ..2 s mode s employelwa d to examine confinement in a tokamak plasma that can access the second stability regime by means of energetic particles stabilization mechanism. In this section we shall use ideal ballooning mode stability condition (2.27) that incorporated both the effects of magnetic well and the self-stabilization. Employing this stability condition conjunction ,i n with the ballooning mode transport model it is possible to investigate how these effects modifies energy confinement in a tokamak.

For a more detailed description of the ballooning mode transport equation. Briefl23 d Refse an ys se 2 stated.2 thin ,i s model plasms ai divided into a transport zone and ballooning zone. In the transport zone, the plasm stabls i a e against ideal balloonin ge therma modeth d lsan conductivity is assumed to have been established for low-beta Ohmic discharges. In this region, the pressure profile is determined by the thermal conduction equation:

(3-D

poloidae anth d l magnetic fiel determines i d Ampere'y db s equatio Ohm'd nan s law from

Equations (3.1) and (3.2) are written in the large-aspect-ration cylindrical approximatio electrod an equar n fo io ln temperature constand san t densit, yn wit e followinhth g normalized quantities :minoe x=r/th rs i aradiu s normalized to the plasma radius a;

96 parameter"^-is relatee energth o t dy confinementy b tim Ç " e

(3.3)

where A. H

also, "\I^ r iC,U / *.3»j _s INTOR confinement time associated with the 1 A j termal conductivitC ^ y ~ S V>~ for low-beta Ohmic discharges.

ballonine Inth g zone wher plasme eth a woul linearle b d y unstablee ,th conductivit consideres i yo larg s e eb thao pressure t d tth e profile adjusts itself to remain marginally stable. Thus the pressure gradient is determined by the condition for ideal MHD ballooning stability. In the large toroidal mode number limit, this stability condition involves onlsheae yth r ^>- eaC'K/O/^ d *an t* 16 quantity

V**- A*. (3.4)

Note that

^ n2. -

approaches the value S = 2 at the plasma edge. The parameter A is the normalized total input powerP

i (3.5)

plasme witth ahI current majoe densitye th th rR ,n radiusd ,an .

Here, we propose to use the following necessary condition for marginal stability of ideal balloonig modes:

97 firse Th t term represents shear stabilization secone ,th de th ter s mi average magnetic well, the third term arises from pressure-gradient-driven destabilization fourte th d h,an term represents self-stabilizatio finitt na e beta. inversee Her th - &/R eC s i . r safete aspecth s yi t factorq rati d oan . e tha . (3.6writtee se b tEq e n W )ca s • na } ' s definW u Q t — \ Le eC i* C,< ^— ^a (3.7)

There is no instability for «V. < «^.« - *^, H .s* t at which point S * «»-a * ^S tjji • larger values, the stability boundary becomes t For « parabolic: v ^ ~ £ U± fixer Fo d powevaluee th rf so paramete e systeth Eqs, f rA mo . (3.1), (3.2), and (3.7) constitutes an eigenvalue system with X as the eigenvalue and p(x) and b(x) as the eigenf unctions. The boundary conditions are dp/dx=0 at x=l; note that b(0)=0 and b(l)=l by definition. This system can numericalle b y solve obtaio t d trajectore nth plasme th f ayo profiln i e (S,a )correspondine th spac d an e g confinement heatin e timeth s ,a g powes i r adiabatically increased from zero to large values.

stabilite Th y boundar f (3.7yo ) bifurcate functioa sheare s sa th f n,o and therminimua s ei m e shearvaluth belo , f eo ,S^ w which ballooning modes ar. Thereforea e l stablal r efo qualitativelt ,i y resemble generie sth c stability boundary that was used in Ref. 23 to represent enhances stability.

Since Ref considere3 2 . case whicr th defo =1.hS thin i 0 s wor wile kw l take m ç^ - ^ (A-ÖL') -Cl.yiH. Strictly speaking, the stability boundary of Eq. (3.7) is valid in the low-beta, small-shear limit of a circular cross-section tokamak. In the present analysis, we transcend this limit for the sake of comparison at finite shear values.

Figur showe1 steady-state sth profila eS- e trajector severar yfo l increasing values of the power parameter A. For values of A greater than approximately 35, the trajectory enters the second stability region without encountering ballooning instability. Therefore, for these large powers, the confinement time, whic beed hha n decreasin functioshows a a s n a , gni A f no Fig wil, 2 . l favorabls reverit o t e INTOR value. Thi sees i sFign ni , 2 . which is a plot of the confinement time as a function of the power. Figure 2

98 2.0

1.5

T/T, 1.0

0.5

Power increasing Power decreasing

3,0 50 1.0 a 2,0 FIG. 1. FIG. 2. shows thaconfinemene tth t time begin degrado st e with auxiliary heating when the normalized power exceeds A=1.9, but reverts to T— at high power (A>35.1) when the plasma enters the second stability regime. We might also expect that if the power were now decreased, the confinement time would exhibit a hysteresis type of behaviour. That is to say, beginning from the high-beta regime and decreasing the power, we find that the confinement time first remains at T_. and then drops to its degraded value, although this transition occur lowea t sa r valuA (viz. r efo , A=5.4) than whepowee nth s ri increased starting from the low-beta regime.

As an example to illustrate how much power would be required in this mode attaio lt nsecond-stabla e plasma profile apple , w resulr e ou th y o t proposed Second Regime Experiment (SEX) tokamak [24], whose large-aspect-ratio configuration would operate with toroidal field BQ=1. mino, 0T r radius Ok =0.17 m, major radius R=1.5 m, and edge safety factor q =4.1. Equation 3 (3.5) can be rewritten as

(3.8)

if we introduce the Murakami density limit TvC-VO ** — and recall thaplasme tth a curren give1 s ti y nb Then, the critical value o=35.f A 1 corresponds to a power of P=11.4 MW.

It should be cautioned that thicrit s is only an estimate; if another confinement scaling were assumed to be operative in the ballooning-stable regime, the power estimate could change.

99 e largTh e power require achievo t d e self-stabilization pointa o st possible are improvemenf ao t withi treatmentr nou . Large heating power (Ae7) tends to depress the safety factor q on axis to a value below unity. Thu shoule sw d perhaps take into accoun effece tth sawtoothinf to g neae rth axis. In Ref. 22 this difficulty was addressed by flattening the p and q profiles within the q=l surface and matching the pressure gradient at q=l to powee th r deposited withi . Includinnit sawtoota g h regio thi n wouly ni swa d be expecte worseo t d confinemente nth .

calculatione Th presene th n si t work indicate that steady-state high-beta self-stabilized equilibria exist, albeit at rather high heating powers. Whether the plasma can actually evolve from a stable low-beta state to suc high-betha a self-stabilized state require solutiioe sth e th f no temporal evolution problem. Work on this problem is reported elsewhere [25].

REFERENCES

1. O.P. Pogutse, E.I. Yurchenko. Reviews of Plasma Physics, Vol. 11, Consultant Bureau (1986)

2. G.A. Navratil, T.C. Marshall. Comm. Plasma Phys. Contr. Fusion, 10. 185 (1986)

3. J. Green, H. Zehrfeld. Nucl. Fusion, 13., 750 (1983)

Rosenbluth. M . . Phys4 Damn al Tsao. ,S Va t .e ,. ,J Rev . Lett. . 196,51 7 (1983)

Coppi. B Crew. ,G . Ramos. ,5 J . Comm. Plasma Phys. Contr. Fusion1 1 , ,8 (1983)

Chance. M 6., S.C. JardiStix. T d .n an Phys. Rev. Lett 196, ,51 3 (1983)

Autonsen. T 7. Basu. ,B Coppi. . ,ProcB al IAEh t .,8t e A Conference, Brussels (IAEA, Vienna, 1981)3 ,8 . Volp , .1

8. A.B. Mikhailovskii, V.D. Shafranov. Sov. Phys. JETP, 39, 88 (1974)

9. A.B. Mikhailovskii, V.V. Demchenko. Proc. 10th Europ. Conf. Contr. Fusion Plasma Phys., Vol. 1, » 11, Moscow, 1981

100 10. A.B. Mikhailovskii, E.I. Yurchenko. Plasma Phys, 24. 977, 1982

11. A.B. Mikhailovskii, V. V. Demchenko, A.Ya. Omelchenko. Sov. J. Plasma Phys, 9, 204 (1983)

12. A. Todd, M. Chance, J. Greene et al. Phys. Rev. Lett, 18, 826 (1977)

Bateman. G Peng. . ,Y 13 . Phys. Rev .9 (1977 Lett82 . ),38

. 14 A.B. Mikhailovskii, E.I. Yurchenko. Preprint IAE-3705, I.V. Kurchatov Institute of Atomic Energy, Moscow, 1982

Demchenko. V . V . , 15 A.Ya. Omel'chenk A.Bd oan . Mikhailovskii. Sov. J . Plasma Phys, 10, 295 (1984)

. 16 A.B. Mikhailovskii. Sov. Phys. JETP, 4 (19733_7.27 , )

. 17 J.W. Connor, R.J. Hasti J.Bd ean . Taylor. Phys. Rev6 . 39 Lett . ,40 (1978)

. 18 A.B. Mikhailovskii. Nucl. Fusion3 (197448 » ),14

. 19 A.B. Mikhailovskii, Kh.D. Aburdzhaniy a. Plasm 9 a(1979 10 Phys . ),21

. 20 A.B. Mikhailovskii. Nucl. Fusion5 (19759 , ,15 )

. 21 L.E. Zakharov Shafranov. D . ,V . Preprint IAE-2789, I.V. Kurchatov Institut Atomif eo c Energy, Moscow, 1977

. 22 J.W. Connor, J.B. Taylor Turner. F . ,M . Nucl. Fusion2 (198464 . ),24

23. G.Y J.W, Dam.n Fu .Va . Preprint IFSR-213, Institut Fusior efo n Studies, Unviersit Texasf yo , Austin, 1987

Navratil. A . G ,. T.C24 . Marshall. Comments Plasma Phys. Contr. Fusion. ,10 184 (1986)

. 25 G.Y J.W, . Fu Dam n Rosenbluth. va N ,. M . Interne Procth f .o . Schoof lo Plasma Physics - Workshop on Theory of Fusion Plasmas (Intern. School of Plasma Physics, Varenna, Italy) 153-160. ,pp , 1987.

Next page(s) left blank STATUPHAEDRUS-E TH F SO T TOKAMAK AND THE PHAEDRUS PROGRAM

H. HERSHKOWITZ, PHAEDRUS GROUP Nuclear Engineering and Engineering Physics Departments, Universit f Wisconsin-Madisonyo , Madison, Wisconsin, United State f Americso a

Abstract

e middlTh e sized Phaedrus-T tokamak w unde,no r construc- Phaedrue th tion d ,an s Progra e describedar m e Phaedrus-Th . T tokamak will employ 3-4 MW of ICRF, Alfven wave power, to study edge effects, ponderomotive effects, mode control and mode conversion. The Phaedrus Program also will continue to employ the Phaedrus-B tandem mirror to study ICRF effects.

Introduction Many in the small tokamak community are probably not very familiar with the Phaedrus Program because until recently we have carried out experiments in a different geometry, i.e. a tandem mirror e missioPhaedrue Th .th f no s r Prografo s mha several years been the study of effects on plasmas associated with rf in the ion cyclotron range of frequencies (ICRF). During the last two years our mission has changed its emphasis from tandem mirro tokamao t r k related issues. At the present time the Phaedrus Program consists of two major devicesPhaedrus-e th ) (1 : B tandee th m ) mirror(2 d ,an Phaedrus-T tokamak whic currentls i h y under construction (with operation expected in the summer of 1989). The devel- r prograopmenou f s showo ti m n schematicall Fign i y .whic1 h give evolutio e B fiel th se th d f coio n l setr s ou use n i d experiments. The original design consisted of a central cell (with B ~ 0.05 T) bounded by quadrupole end cells [1]. By taking advantag radiae th f lo e ponderomotive force associated with ICR were w F e abl operato t e e wit ha full y axisymmetric B-field in 1983 [2]. The original device was modified in 198 y insertiob 5 f (0.o n ) "chok8T e e th ende coils f th o s t a "

103 Evolution of B field Coi! Sets Phaedrus-T (1988)

Original Phaedrus (1980)

Axisyrnmetric (1983) a I' ==^=;^ ? 5 a --======;=5 a ;• --\ j

Phaedrus-8 (198S) s | g — *-' -^'?j^ — —' ^-^vp-^A-ij x 3.4m 11.2m Figure 1

Phaedrus-8 (1983) Evolution of B field coil sets in Phaedrus Program

central cell (raise 0.0~ o . t 8dThiT) s device, Phaedrus-B, s modifieva axisymmetrir fo d c operatio Februarn i n y 1988. During 1988, construction began on the Phaedrus-T tokamak whic s basei h d upovacuue th n m chambe d fluan r x cor f ISX-o e A [3]. The principal difference is the addition of 3-4 MV of ICRF and the construction of new toroidal field coils which matc existine th h g Phaedrus power supply. Phaedrus-B and Phaedrus-T parameters are compared in Table 1. Phaedrus-T parameters are based on those obtained in ISX-A, withou applicatioe th t ICRF f ne o hig Th .h ICRF Table 1

Phaedms-B Tandem Mirror Phaedrus-T Tokamak

Best simultaneous Parameters based on parameters achieved ISX-A so far

R(m) 0.92

a(m) 0.26

B(T8 (chok0. ) e coil) < 1.2 0.08 (cen. cell)

3 12 12 13 np(cm" ) 4 x 10 , 6 x 10 6 x 10

(eV0 16 , 35 ) 500.

T.(0) (eV) 2500 7 , > 500.

130.

t E(msec) -0.2 20.

Prf{MW) < 0.8 < 4.

104 energy density combined witrelativele th h y modest volumf eo Phaedrus-T should resul highese th somn i tf eo t ICRF power density tokamak experiments ever carried out.

Experimental Program Both devices will share the same staff, control room and power supplies. The staff consists of 7 scientists, 7 technicians graduat5 1 , e student 0 undergraduates2 d san e W . pla continuo t n e using both devices (with alternate month operation) to carry out experiments relating to four ICRF issues — Edge Physics, Ponderomotive Effects, Mode Conversion d Mod,an e Control. Combining results from both devices should resuln improvea n i t d understandin f scalino g g and also help in untangling the physics involved.

Edge physics Initial experiment Phaedrus-n o s T will investigate impurity generation at device boundaries. Once ICRF is operable wile ,w l concentrat n impurito e y generatiot a f r y b n the Faraday shield and the device boundaries. We will also attemp directlo t t y determin f sheatr e h effects. Pondero- motive effects on the edge plasma equilibrium and limiter bias effec edgn o t e plasma potential wil evaluatede b l . Ponderomotive Effects on the tandem mirror are most easily studie y observinb d effece th g f ponderomotivo t e force on the stability of interchange modes [4]. Over the last five year e havsw e studied ponderomotive effects associated with a wide range of frequencies both above and below the ion cyclotron frequency co , and with both the left and right hand components of rf electric fields. Effects associated with w unde no B fiel e re d paralle, ar dinvestigation e E th o t l . Z These effect e likele mosar b s o tt yimportan edge th e n o t plasma profil n tokamaksi e e ponderomotivTh . e force associated with E is interesting because it is predicted to £ change sign with w when w is near to . [5]. In addition to edge profile modificatio n tokamaksi n , investigations wile b l carrief predicteo t ou d d ponderomotive force modificationf o s sawtoot hmagnetif o stabilit d an c] islan[6 y d formation [7].

105 Mode Conversio n tandei n m mirrors normally occurs along the B field (in the axial direction) while it occurs in the radial direction in tokamaks. Direct measurements of rf wave fields in Phaedrus-B allow us the option of investigating the details of mode conversion. We believe that experience gaine Phaedrus-Bn i d , operated with witd purD an hH- e H mixtures will aid us in interpreting mode conversion effects in Phaedrus-T where direct measurements of the rf field strengths may not be possible.

Mode Control The present Phaedrus-B design employs two "rotating field antennas" (see Fig. 2) spaced l m apart (which each consist closelo otw f y spaced pai duaf o r l half-turn antennas which have adjustable relative phasing) in the central cell as well duao tw l s half-tura n antenna s eacn i d i scell en ht I . possible to adjust the azirauthal mode from m = +1 to m = -1 by varying the phase of the components of the rotating field antennas or to vary the k spectrum by operating with two of £ the dual half-turn antennas spaced l m apart and adjusting their phase. Phase adjustments to the antenna takes 10 usée carriee b n andurint ca dou d dischargega .

sonn

- 6000

Figure 2

Phaedrus-B d centraan z s lv cel| |B l -200 -100 0 100 200 sketc f rotatinho g field antennas DISTANCE FROM M1DPLANE (cm)

Mode control experiment Phaedrus-n i s T will initially cente Alfven o r n wave current drive. Mode Control experi- ment n Phaedrus-i s B wil lpresene attempth f o tmak o t e t eus antenna phasing capability to study effects such as Alfven resonance associated with radial plasma profile variations.

106 Phaedrus-T Tokamak Hardware A cartooPhaedrus-e th f o n T tokama s showi k Fign i n . .3 We have chosen to operate with a circular plasma but have retained rectangular toroidal field coil alloo t sr futur fo w e modification plasme th n ai s shap d vacuuan e m chamber)p to A . view of the stainless steel vacuum chamber and the 18 toroidal field coil s showi s Fign i n . 4 Nine "pie" sections are separated by stainless steel bellows. The original ISX-A vacuum chamber was modified to include four pairs of large (34 cm diam) vertical access ports and as well as six large horizontal ports. This configuration will allow a variety of ICRF toroidal antenna locations. The vertical ports will allo possibilite th w f insido y s welea s outsidla e antennas.

Figure 3

Phaedrus-T Tokamak

G3rH^^^^^t:%p5^rG? ' ^^^/'.'/^^^^^/j-f

Figure 4

viep f Phaedrus-To wo T Tokamak

Coil design e toroidaTh l field coil eace sar h constructe4 2 f o t ou d copper plates (0. thick)m 4c e coilTh . s were designeo t d provid maximue th e m amoun f coppeo t r consistent wite th h

107 shape of the original ISX-A TF coils to allow us to make contact with the ISX-A data base.

Phaedrus-T ICRF systems A four stage amplifie n loa(o r n froAlamos Lo m s National Laboratory) wil oveW lM frequenca r4 provid o t p eu y rangf eo 2-20 MHz e intermediat.Th e stage broadbane sar onld an dy the final amplifie tuneds i ) .MW r 4 (40Thi - s0W k makee th s amplifier well plannee suiteth o t dd Alfven wave experiments. Addition of a pulse line will extend the amplifier operation to more than 100 msec. Initial experiments will utiliz clase th e sA transforme r coupled 400 kW amplifier with one partial turn loop antenna. Subsequent experiments will employ some form of rotating field antennas (currently under discussion).

Current Relevant Experiments

Model Antenna Experiments 18] W ecentrae havth ef o l mad e celus e l plasm Phaedrus-n i a B t o f near stud e r th vicinite yfield th modea n i sf o y l antenna (locate e mode Th dFign i lnea . antenna4 .A r2) , shown schematicall ° loo60 pa antenn s Fign i i y , 5 .a wita h Faraday shield consisting of a single layer of cylinders.

Probe access Chamber wali (r = 6Ocm)

Backplane Figure 5 Antenna strop Phaedrus-B test antenna sketch

Lateral shields

108 Measurements are made with three orthogonal "B-dot" probes in planes parallel to the plane of the Faraday shield, i.e. the z(toroidal-poloidal9 - wit| B h| ) d planean J . |B Datr fo a G 2 no plasma present, (2 cm from the Faraday shield) are given in Fig. 6. The strap is indicated by the dashed rectangle currene th d tan horizontae flowth n i s l direction e mosTh .t surprising resul s beeha t n thamaximue th t 0 Q fiel4 B m s i d percen B field e s largth a t . importane s b ea Thi y sma t because B... field e oftear s n neglecte n analysei de th f o s D vaves excited by such antennas.

0 5 10 -10 -50 5 10 15 azimuthal position (cm) azimuthal position (cm) Figure 6

B Bd an plana abovm n c e i e2 e th I ZI Faraday modee shielth f o ld antenna

Curren Octobef to Status a r s— 198 8 As of October 1988, new lab space has been created for the Phaedrus-T devic d x-raan e y shieldin s beegha n installed. The re-porting of the vacuum chamber has been completed and it is now under vacuum at 1 x 10 torr (without any bakeout). Toroidal field coils are under construction.

Plans Experiments in the summer of 1989 will begin with ohmic heating measurement establiso t s baseline th h e characteris- mako device t th ticed f contacan eso t witISX-e th h A data base. RF studies vill begin with a 60° outside loop antenna and investigate ion cyclotron and Alfven wave heating. During 199 wile w 0 l begin ICRF edge effect studies with emphasi sheathf r n so d impurit an s y generatioe th s welna s la first attempt t Alfvea s n wave current drive.

109 ACKNOWLEDGEMENT

This work is supported by U.S. Department of Energy Grant DE-FG02-88ER53264.

REFERENCES . 1 al.BREUNt e , , ,"ExperimentR. Tandea n i s m Mirror Sustained and Heated Solely by RF," Phys. Rev. Lett. 47, 1833 (1981). 2. PERRON, J.R., HERSHKOWITZ BREUN, ,N. , R.A., GOLOVATO, d GOULDING S.Nan F Stabilizatio."R , ,R. n a f o n Axasymmetric Tandem Mirror," Phys. Rev. Lett. , 19551 , 5 (1983). 3. ORMAK Group, "Result ORMAKe th f ,o s ISX-A d ISX-,an B Programmes," Nuclear Fusio 113, 25 n 7 (1985). 4. HERSHKOWITZ, N., "Ponderomotive Stability of MHD Modes in Mirrors," Varenna, Italy, September 1-11, 1987, Workshop on Mirror-Base d Field-Reversean d d Approache Magnetio t s c Fusion, Conference Proceeding e Internationath f o s l Schoo Plasmf lo a Physics (1988). 5. CHUN, S-T., "Ponderomotive Force and Rotational Effects e Stabilitth n o Plasma: of yTandea n i s m Mirror," Ph.D. Thesis, Nuclear Engineering and Engineering Physics, Universit Wisconsin-Madisof o y n (1986). 6. LITWIN, C., "Ion Cyclotron-Frequency Stabilization of Internal Kink Mod d Sawtootan e h Oscillationn i s Tokamaks," Phys. Rev. Lett. 60, 2375 (1988). 7. Private communication with J. Tataronis (1988). 8. Data provided by R. Majeski, T. Tanaka, and T. Intrator (1988).

110 PRELIMINARY DESIG SMALA F NO L ASPECT RATIO TOKAMAK

G.O. LUDWIG . MONTEA , S Laboratörio Associad Plasmae od , Institute de Pesquisas Espaciais, Jos o s CampoSà édo s P.M. SAKANAKA Institute de Fisica "Gleb Wataghin", Universidade Estadual de Campinas, Campinas Brazil

Abstract

preliminare Th y conceptual desig smala f o nl aspect ratio tokamak is presented. This tokamak is based upon the spherical torus concept and will be the prototype (PROTO-ETA) of the Brazilian Advanced Tokamak Experiment (ETA). The device parameters are derived from engineering and empirical physical constraints e tentativ.Th e parameter value e aspecsar t

ratio A

toroidad 0.6axi= an Q sB 5T l plasma curren edgn a er I t=0.3 fo safet A 8M y

factor qa=4.5. A simplified zero dimensional model is employed to predict plasma performance and auxiliary heating requirements. RF-assisted startup and noninductive current drive techniques are envisaged. This study results in a device design based on conservative assumptions which, when builded- , shoulup d allo e investigatiowth higf no h beta tokamak operatioe th n i n first stability regime.

1. INTRODUCTION

A new toroidal device (ETA) with a small aspect ratio A=l.5 plasma d A rangM an abees 1 eha currene n th recentl n i t y proposee b o t d constructed at the new Brazilian plasma physics centre [1,2]. Such spherical torus RF driven tokamak can potentially achieve very high values of ß(^20%) s compacanit d t geometr s attractivi y advancer fo e d reactor applications. Sinc efficience th e currenf o y t drivcruciaa s i e l w parametelo a r fo r aspect ratio steady state device s felwa tt ,i necessar preceo t y largee dth r experimen prototypa y tb e (PROTO-ETA) which include solenoisa d with limited inductive capability e inductiv.Th e approac quits i h e reliabl wild ean l allow the testin othef o g r current drive C helicitmethodD d an syF R suc s a h injection.

Ill The main objective of the prototype experiment is to study the physics of small aspect ratio tokamaks, with particular regard for the dependence of MHD and transport on aspect ratio. In this respect it is important to test the validity of ß limits as given by the Troyon scaling. n additionI e devic,th e wil e use lb o tes t d t efficient current drive techniques and to develop diagnostics systems and the technical expertise necessary for the construction of larger experiments such as ETA. It should be mentioned that in fusion experiments the importance of ß is illustrated by the condition to achieve ignition written in the form:

2 ß TEB 2.3> , wich favors high beta configuration sphericase th suc s ha l torus while keeping the good confinement properties of the tokamak. Furthermore, the increase in B due to paramagnetic effects should improve the fusion efficiency. followine th n I g section simplified engineering considerations are presented concerning the design of the central column of the device. Details of the physics basis wich determine the expected plasma behavior are given next. Finally plasme ,th a operating condition discussee sar d within the framework of a zero-dimemsional model.

2. SIMPLIFIED ENGINEERING DESIGN

The central column represent criticasa l design a area n i spherical torus. The reduced space and the large plasma current that must be generate t severpu d e design constraint e inductivth n so e solenoid, which fits onto the central toroidal field conductors. The inner leg of the toroidal field coil s designei s occupo t d minimue th y m possible space consistent with the ampere-turns required to produce the desired magnetic field on axis,

6 Ntlt = 27rR0B0/]j0 = 1.2 x 10 A.

The major radiuequas takee b wa 0.3o o o t nlt sR whic, 6 m h turns out to be about the minimum machine size compatible with the inductive

solenoid requirements inductioe value th .Th f o e s axisn no 0.6wa = 0 , ,5B T chosen to allow the use, at the second harmonic resonance, of the 35 GHz gyrotrons currently being developed in Brazil [3]. The total current will be carrie coil2 1 y sb d forme holloy b d w conductors water coole paralleln i d . The current densitinnee th rtoroidae n i yth leg f o s l field coil limites si d

by the temperature rise ATt = 60 K in copper attained during the flattop

electrical pulse of tt = 2s duration. Neglecting the heat transfer from the

112 watee coppeth ro t rdurin s ha pulse e th g eon

1/2 2 [= t Pmj cpATt/(ptt)] MA/m2 7 = ,

3 where pm=8960 kg/m is the mass density, cp = 386 J/kg K is the specific resistivite th s i m x 10~ fi f copper0 8o y 2. = e externa p Th . hea d an t l radius of the central column is, therefore, given by

1 2 [N= e r t l(7rAt/ tjt)] / 0.0= m 9 e activth s centrae i wher th are TTr A ef ao l column e packin.Th g factor 2 e t was assumed to be Ac=0.65. Instead of hollow conductors it is also possible to use radially cut or laminated bars. This lamination is necessary to provide the desired plasma current risetime determined by the inductive solenoid flux penetration time. The difusion time of magnetic field lines in the toroidal field coil central estimatee columb e eddn th nca y y currendb t time scale 2 TD^y characteristie conductivite th th , wheros s ai L i L a e d an y c lengtf o h the system. With appropriate design the solenoid flux exchange time can be millisecondsw reducefe a o t d , indicating that preionizatio exampler fo , nby , electron cyclotron radiation would stil requiree lb d immediately before current startup.

The thickness s available for the inductive solenoid is determined by geometrical constraints, as illustrated in Fig. 1 which define dimensione th s e deviceth f so . Settin distance th g combinatio, d e n thicknese o th fvacuue th f mso vessel inne e distancrth wal d lan e froe mth

r

Fig. Definition1 . f PROTO-ETo s A dimensions,

113 plasme walth o alt boundary (including space necessar instrumentation)r fo y , at 0.03m the solenoid thickness is

0.04m= d - ,e r - Rs) = 0 e ( l- wher inverse th e e aspect 0.56 = rati e e thicknes s . Th i o innee th rf o swal l of the vacuum vessel is chosen to be the smallest possible, compatible with the requirements of mechanical strength, to increase the wall electrical resistance and reduce the eddy current induced in the vessel.

The magnetic flux available from a cylindrical coil of 3 3 r- ]/(3sinfinits) d + )an g (r e [ wher, lengt= BQ ^ r es ^ Ti h= mTr

B£> = yo j £, A£I s is the induction at a point inside the coil. The current density in the inductive solenoid is stress-limited and given by

2 12 MA/m 0 /s/2)]}+ [U25 e = 0,i (r sf A /

wher peae packine th eth k d tangentiagan factoa MP s 0 i r7 l = stresu c s si X^ = 0.65. The solenoid will be made up of 4 radial layers of water cooled hollow conductors wound with opposite helical pitc n ordei h reduco t r e field errors. The value of the available magnetic flux is

3 3 <{>„= (7Tu0 /3r- )e [(r]s) j+ e nX 0.3n= . 0Wb

Considerable improvemen obtainee b n ca tf dispersio i d n strengthened coppe useds i r nearle whicn b i , n hyca cas. value a th ef o e doubled (^ 140 MPa) and the available flux increases to 0.42 Wb. Furthermore, the outer coils can provide an increase in the total flux linkage of ^ 20% with respect to the flux due to the solenoid alone. It must be pointed out simple th tha n ei t approximatio strese th r s fo nlimi t used s abovwa t i e assumed thasolenoie th t thin-wallea s i d d cylinder with uniform tension. The actual situatio mors i n e peae completh k d tangentiaxan l e stresth n o s e smalth ln o coi radius i l s edge wher maximue th e m amplitud inductioe th f o e n is

B B + T B 8 r T 24 1/8 2 max= £' E> (R° ^ fi0' =V e> 3' =

Assuming a copper temperature increase AT^ = 60 K, the maximum equivalent flattop pulse duration can be estimated by

114 3. PHYSICS MODELS AND CONSTRAINTS

The equilibrium toroidal plasma current depends on the true

MHD safety factor qa (at the plasma edge), the induction BQ, the aspect ratio 1 A=a/Ro=e~ and the plasma shape (elongation K, triangularity 6), according to I = 2-rr a K Bp l + _ 2ir a^ K BQ 1 + f (e, K, <$,), u„ R„ q «

2 where qa = qc f (e, K, o), qc = q* (l + K ) / (2i<) is the equivalent cylindrical kine safetth k s safeti y * factoq yd factoran r e functioTh . n f (e, K, 6) can be fitted by [4] (1.1= 0.99) - 6 2 f(e , eO.lli+ K , 0.476+ ce- 2)1 ( 2 .)/

Fon edga r e safety facto = 4.5 q r, near natural elongation K=1.8 and triangularity 6 = 0.6 (q =2.0) the plasma current is I =0.38 MA.

e densitTh s limitedi y r stablfo , e ohmically heated tokamak operation Murakami-Hugile th y ,b l density limi] [5 t

20 3 nMH=1.5 B0/(qcR0) =1. unitn 10(i 3f so m~ ). r auxiliarFo y heated plasma limie th sgives i t y nb

20 3 nMH(aux)=2.1 Bo/(qcRQ) s 1.9 (in units of 10 m~ ). e criticaTh l volume-averaged valu betf o e reachee ab than ca td within idea D stabilitlMH Troyo e gives th i y y nb ] scalin[6 w la g

6 ßc = 0.035 x 10~ Ip / (a B0) = 0.10. The critical value of ß has a strong dependence with the inverse aspect rati e (foo r^ 0.5e shows )a Fign ni wher., 2 targee th e t operating point for the PROTO-ETA device is indicated.

0.2

O.I I x=l.8 6=0.6 0.0 I in 0 1. 8 0. 6 0. 4 0. 2 0. 0 0. e Fig. Variatio2 . criticae th f no l valu wit3 inverse f th heo e aspect ratio e, according to the Troyon scaling law (the target operating point for PROTO-ET indicated)s i A .

115 The confinement is described globally by combined ohmic and auxiliary heating scalings

where T^ is given by the Neo-Alcator scaling law

T T 2 ß = NA= 0.071 n20 aR0 qc and T. by the Kaye-Goldston L-mode confinement time [7]

T T 6 02x 10 6 2 55 K 28 n 26 0 09 A= KG= ' ~ V" ** V' °* 20°' A±0.5/ (WA0.58 aO.«*9 Bo - ), n atomiio e auxiliare cth th mcis s whers i i s ^ A numbeeA yW powed an r r deposited

plasmae ith n generaln I . H-modr . L ,fo T, e2 = confinemen G K T takn = A ca T e e on t e globaTh l confinement model here considered leade mosth somo t sf to e

pessimistic predictions.

The plasma flux requiremen bots tha n inductiv a h a d an e resistive component

Assumin coiastanga t current sequence requiree ,th d flun ca x be estimatey b d V Vp + p V = V where the plasma resistance R^ was assumed constant during the equivalent flattop pulse duration t . The plasma inductance can be aproximated by

Lp = y0R0{ln[8R0/(a/K)] + 1± / 2 - 2}, where the value of the plasma internal inductance depends on the current profile according to

0.6 - broad profile j = ^0.8 - normal profile 1.0 - peaked profile

Takin orden L =0.3 I s g calculato . t 1.^0ha r 5yH e on .e 8 th e plasma resistance one has to estimate the electron temperature, which is nexe th dont n i sectione .

116 4. PLASMA PERFORMANCE

The physics parameters space of a tokamak experiment can be explore vera n yi d simpl usiny ewa globaa g l (zero-dimensional) mode. ] [8 l The global power balance equation is

9Q / 3t = -Q /

where the total plasma energy is

Q= (3/2) < neTe + n±T± > Vp.

Definin density-averagee th g d temperatur and the average density n= /2, the expression for Q becomes

Q=3n T Vp = 4.81 x 1CT n2Q T V ,

wher densite unitn th ei f s 10so i y 20 m~ temperature 3V ,th (thes ke n i e s i e 2 2 units are used in all pratical expressions in this work) and V = 2-n a K RQ plasme th s ai volume must I .pointee tb t tha n calculatinou di t g volume- averaged quantities the plasma poloidal cross-section is assumed elliptical so thaplasme th t a minor cross-sectiona plasme th d aan K I2 = Tl a ^ A are s i a surface area is A = 4u2 [(1 + ic2) /2]1'2 aR_. The corrections due to ao U triangularity are kept only in the factor f(e, K, <5) relating the MHD and

cylindrical safety factors. The power loss due to transport is Q/TE, where

energe th Ts yEi confinement time describe previoue th n i d s section. The power density loss due to radiation (Bremsstrahlung) is givey nb 2 1/2 2 3/2 3 3 3/2 PR = e6 g Z ne nz Te / [6(3/2) ^ Tr eQ c h me ] 3 20 2 1/2 = 5.35 x 10 Zeff (ne/10 ) Te ,

wher Gaune th e t factor l

=(27r/Ap R rdrP * ,)/*

1 2 minoe th rs wher i (ab)equivalen= e radiu t a f th ea < f / ' so = t circular plasma cross sectio i= r a*)^ (A n. Assuming parabolic profile e forth mf so

n(r )n= 0i ( l-

T(r) = T0(l - i

jp(r J)= 0 r ( l-

117 the average density, density-averaged temperature d averag,an e current densite ar y

n = (2TT/Ap) Si* n(r) rdr = no/2,

T = [2ir/(n Ap)] /** n(r) T(r) rdr = 2 TQ/3,

j2 Q /5= r . rd ) (r (2^/Ap= j j * )/*

Therefore, the average value of PR can be written in the form

3 2 = 5.35 x 10 gRZeff n*0 T^ ,

where the radiation profile factor gR is calculated by

1/2 1/2 2 1/ 0 o po gR = (2n/A)/*[n2(r) T (r)/(nT (8/7= r d )r ] (3/2 1.40= ).

The total powe o radiatiort lose du s s i n

3 i/2 % = <%> Vp = 7.49 x 10 Zeff nf0 T Vp.

= 2 2 The ohmic power densit s i yPj 2 Tl(jj jg+ ) )» whers i n e the Spitzer classical resistivity correcte r trappefo d d particle effects

2 (2i[3 r T/ )3/2A n i 0.5]n= Y 1 ml/ Y 2 e

9 3/2 =1.66 x IG" Yneo Y± In A / Te .

For Te in keV, the Coulomb logarithm is given by

20 In A= 15.2 - (1/2) In (ne/10 ) + In Te = 14 a facto s i anri Y dwhic h accountpresence th r f impuritiefo so e s

Y±= 0.580 Zeff + 0.773 Zeff / (0.840 + Zeff).

The local neoclassical resistivity enhancement factot (a r low collisionality v * < 1) is approximated by

1 1/2 2 ~ (r/R ^net o= 0) r .

Note: the electron collisionality is

3/2 25/2 2 3 2 v= el* e qRv 0/ [ve(r/R0) ]=4.9 Z A 0ef10~x n RfI q Qe ^n (T/ g r / ), whichplasme th t a,a edge, becomes

3 2 3/2 ve*£6.86 x 10~ n2Q Zeff qa RQ / (T e ). The average ohmic power densit calculates i y d neglecting the poloidal current contributio strongna e b (thiconservativ t n ,bu sca e assumption sphericaa r ,fo l torus equilibrium)

2 2 2 = = ,

118 wher average th e e current densit s givei ytotae n termnth i lf so plasm a current by j = I / A and

2 2 3/2 jp(r) = (5/2) (Ip/Ap) (1 -r /a ) .

The current density on axis is

2 2 K+ , )/(1 ] ( ) 2[ K ] ) Q q Q R o n / [5B = Q B ) j2 0(2p(0 [ / K= ) (y )] K 0 R+ 0 q1 c( ) ][

where q = 2 qc/5 is the safety factor on axis for the assumed profiles. Hence, the average ohmic power densit writtee fore b th n m n ca yi n

gfi §neo

where rig (T) is the Spitzer classical resistivity evaluated at the density- weighted average temperature

9 3/2 8 3/2 TIS (T) = 1.66 x 1(T YI In A / T = 2.33 x 10~ Y ± / T > the ohmic power profile factos i r

2 2 3/2 2 1/2 2 1/ gn=(25/3 r- /a1 )(5/3( = , (2/3)r ) * 36 d )/* . r (2/31 = a~ ) and the neoclassical resistivity enhancement factor is

2 2 3 2 2 3 r> d -r /a ) / r d r ] / [/** (1 -r^a ) /- r d r] . A rough approximation parametere th n ,i s rang f interesteo s ,i givey nb

t1 - °'767 (/K e Finally, the total ohmic power is given by

W 2

, where the plasma resistance is defined by

2 2 Rp = 3.17 x 10-8 Y. gneo Vp/(T3/ Ap ).

The plasma parameters operating spac s showi en Fig ni 3 . for the prototype experiment. The ohmic equilibrium contour corresponds to a steady-state solutio globae th f lno power balance equation wheo n

auxiliary power addeds (Wi Aplasme ) =0 .Th a temperatur thin i e s case,

assumin 0.4s T 1 gs keV i Z verifiee e, ^2 On . £= s plasma that r ,fo a density nealowee th r r Murakami-Hugill limit 0.080= ,3 5n T/B2 reachee th s critical value given by the Troyon scaling law.

119 0.2 0.4 0.6 0.8 T(keV)

Fig. 3. Steady-state contours in plasma parameters operating space for the PROTO-ETA device.

Fig shows.3 . , also, auxiliary powed an r 1 contour= A W r fo s . AdditionaMW 2 l heating open possibilite th s operatiof o y lowet na r densities or at g values above the Troyon limit. The most sucessful technique for auxiliary heating of tokamak plasmas has been the injection of high-energy neutral particles [9]. To ensure adequate heating of the plasma interior s necessarii t preferentiallo t y y deposit particle th e e beam e energth n i y plasme centeth f ao r accordin beae e criterioth th m, wher 4 s o i ä t g A A e a/ n trapping length

17 X=l/(n0oeff) =5.5 x 10 Eb/ (Ab nQ Z^ff ) (0 < y< 1), neutrae e energth th f s o yEi lv atomie particleth ^ cA masd n amusan i s .

Since the central density nQ = 2n, one can estimate the minimum energy necessary to heat the center region

' Z0 Ifb 2 A n f1 a 9 Eb> For the small size prototype experiment, a 20 keV beam energy should suffic adequatr fo e e heating. Since this energy valus ei 2 3 abov criticae th e l energy Ec=14.8 AbTe/Ai 'energetie ,th c ions will

preferentially heaplasme th t a electrons f (fo 0.4o = abouV e r% 1T ke 40 t the injected particle energ transferes i y ione th s o [10])t d . Amajor effect in the determination of the loss rate of energetic ions is the toroidal field ripple, which must be kept at a minimum. This effect should be taken accounn desigtoroidae e i th th f n no ti l field coils. In order to improve plasma performance, and possibly operate H-mode th confinementf n o ei ,divertoa beins i r g considere PROTOe th n -i d ETA device. The discharge should operate with a single null magnetic configuration and the divertor plates will be located in a pumping chamber in the lower part of the device. This configuration will permit the production

120 of a broad current profile and the separation of the high impurity level scrapeoff region frocurrene th m t channel. Provision wil made lr b fo e biasin e toroidath g l divertor plates with respece anotheon o t o test r t current driv DC-helicity eb y injection [11]. This scheme demonstratef ,i d for tokamaks, should lead to an efficient and simple current drive system, where the power is derived from a relatively low voltage (200^ 300V) DC source. Furthermore, the current drive efficiency by this method is not limited by the plasma density, a feature which is particularly atractive for tokamak reactor applications. Another current drive scheme that shoul e trieb d d employs

whistler waves wit « f hce f f-r-r,> « als o know lowes na r hybrid current drive (LHCD). One advantage of this scheme is that the whole wave energy can be coupled to the electrons by an adequate choice of wave frequency. Also, high power source readile ar s y availabl verd an ey reliable coupline th d ,an g technology is well known and very efficient. On the other hand, from the theory of RF current drive it is well known that the efficiency is proportional

to l/n^t and it has been observed experimentally to fall off with u>Df/<»).,e« From preliminary ray tracing calculations it was found that the plasma centre

can only be accessed by waves with high nn (^ 4) and typical values of u3 g/o^e are verY high (^2), which would seriously hinder this current drive scheme y tracinra .A g studmora n ei y realistic magnetic field geometry, including paramagnetic effects underwas i , alloo t y wbettea r evaluation. Table 1 summarizes the design parameters of the PROTO-ETA device basie Th . c parameter e initiallsar y specified, allowin calculatioe gth n plasml oal f a equilibrium parameters accordin physicae th o t g l constraints presented in this work. Finally, the plasma performance parameters are

calculated assuming ohmic equilibrium (WA = 0) and operation at the density limi. t ) (n„ n „=

121 TABLE 1. PARAMETERS OF THE PROTO-ETA DEVICE

BASIC PARAMETERS (INPUT)

Invers- e aspect ratio ...... ,e . 0.56 - Elongation, K ...... 1.80 Triangularity- ...... ,8 . j...... 0.60

Majo- r toroidal radius, R.Q(m) ...... 0.36

- On-axis toroidal induction, BQ(T) ...... 0.65 - Edge-plasma safety factor, q ...... 4.5 atomin Io - c mass number ^ ...... ,A 1 . Effectiv- chargen io e...... f f ,Z 0 2. .

PLASMA EQUILIBRIUM

- Toroidal plasma current, I (MA) ...... 0.38

- Cylindrical safety factor, qc ...... 2.0 On-axi- s safety factor ,q ...... 0.80 - Murakami-Hugill density limit, n^ (1020 m~3) ...... 1.3

-Troyon beta limit, ßc ...... 0.10 Plasm- a inductance ,(uHL ) ...... 0.35 - Plasma volume, V (m3) ...... 0.52 - Plasma poloidal cross-sectional area, A (m2) ...... 0.23 - Plasma surface area, A„(m2) ...... 3.6 o

PLASMA PERFORMANCE (OHMIC EQUILIBRIUM, n2Q=nMH) - Density-averaged plasma temperature, T(keV) ...... 0.41

Ohmi- c power, Wfi(MW) ...... 7 2. .

Radiate- d power, WR(kW) ...... 8 8. . - Plasma energy, Q(kJ) ...... 14

- Energy confinement time, TE(ms) ...... 5.0 Plasm- a resistance ,(yŒR ) ...... 8 .1 - Equivalent flattop pulse duration, t (ms) ...... 24 ( =0.30 Wb)

122 REFERENCES

[I] GALVÂO, R.M.O.; GOES, L.C.S.; LUDWIG, G.O.; MONTES, A.; UEDA, M. "Proceedings of the Energy Independence Conference on Fusion Energ d Plasman y a Physics, 17-21 August, Janeiroe 1987d o ,Ri , Brazil, P.H. Sakanaka (Editor) (World Scientific, Singapore, 1988), p. 471.

] ROBINSON[2 , D.C. Nuclea r 1 (1988)Fusio33 , .28 n

[3] BARROSO, J.J.; CASTRO, P.J.; CORREA, R.A.; GALVÂO, G.P.; LUDWIG, G.O.; MONTES ; NONO,A. , M.C.A.; ROSSI, J.O. "Proceeding Energe th f yso Independence Conferenc Fusion o e n Energ Plasmd an y a Physics, 17-21 August, 1987, Rio de Janeiro, Brazil, P.H. Sakanaka (Editor) (World Scientific, Singapore, 1988), p. 226.

] SELCOW[4 , B.C.; PENG, Y-K.M.; UCKAN, N.A.; HOULBERG, W.A. "Proceedingf so the llth Symposiu Fusion mo n Engineering, Austin, Texas, 18-22 November, 1985 . 1111,p .

[5] MURAKAMI, M.; GALLEN, J.D.; BERRY, L.A. Nuclear Fusion 16, 347 (1976).

[6] TROYON, F.; GRUBER, R.; SAURENMANN, H.; SEMENZATO, S.; SUCCI, S. Plasma Phys. Controlled Fusion 26, 209 (1984).

[7] KAYE, S.M.; GOLDSTON, R.J. Nuclear Fusion 25, 65 (1985).

[8] UCKAN, N.A.; SHEFFIELD, J. In "Tokamak Start-Up", H. Knoepfel (Editor) (Plenum Press, 1986) p. 45.

[9] MENON, M.M. Proc. of the IEEE 69^, 1012 (1981).

[10] SWEETMAN, D.R. Nuclear Fusion 13, 157 (1973).

[II] ONO, M.; GREENE, G.J.; DARROW, D.; FOREST, C.; PARK, H.; STIX, T.H. Phys. Rev. Lett. 59, 2165 (1987).

Next page(s3 )12 left blank TOKAMATMA R- K FOR ALFVEN HEATING AND CURRENT DRIVE RESEARCH

A.G. KIROV, V.D. MEDUN, L.F. RUCHKO, G.I. ASTAPENKO, D.A. VOJTENKO, A.V. SUKACHEV, A.Z. RAKHEL'KIN, V.P. SIDOROV, A.G. ELFIMOV, K.G. KOMOSHVILI, M.A. STOTLAND, S.E. IL'INSKIJ, N.I. MALYKH, I.S. LEDNEVA, L.L. KALAYJYAN, L.B. KISLOVA, M.Sh. BURDIASHVILI, V.A. MILOSERDOV, S.N. MORDIK, R.A. TERTERYAN, V.I. KUZNETSOV, V.Sh. GAMGIA, V.H. ZHARIKOV, V.V. ONISHCHENKO, A.G. NAGORNYJ, L.Ya. MALYKH, Yu.N. GUBIN, M.V. LOMTATIDZE, I.S. FURSA, T.P. BOCHIKASHVILI I.N. Vekua Institute of Physics and Technology, USSR State Committe r Utilizatioefo f Atomino c Energy, Sukhumi M.V. DMITRIEVA, G.A. PESTRYAKOVA, I.F. POTAPENKO, S.Yu. MEDVEDEV M.V. Keldysh Institute of Applied Mathematics, Academy of Sciences of the USSR, Moscow V.P. BOYUN, V.F. GUBAREV, Yu.G. KRIVONOS, A.I. NEBOOKIN, I.K. RUBIN, B.K. OSTAPCHENKO, G.F. GUSEV V.M. Glushkov Institut f Cyberneticseo , Ukrainian Academ f Sciencesyo , Kiev Unio f Sovieno t Socialist Republics

Abstract

The conceptual design of a small-scale tokamak TMR is presented. The tentative paramete re aspec valueth e tmajo, sar 5 rati < r oA radiu s 0.5= R toroida, 5m l magnetic fiel 2.5= axin o d toroidad o TsB an l current Ip = 100 kA,. RF heating and current sustainment system techniques are envisaged. Alfven wave heatin choses i gmaia s na metho auxiliarr fo d y heating in TMR tokamak.

I. The Goal and the Problems Alfven heatin choses gi maia s nna metho additionar fo d l heating in the TMR tokamak. The TMR device is meant for study physice th g heatinf so in drivind gan g current generatioy nb J — 14. — "î Alfven wave fairlr sfo y high parameter nt f eso -e1 m 0^c

Physica d technologicalan R TM l e solve e taskth "b y o db st device are:

125 - developin methoa g intW supplyinr M fo do3 2- o poweP t gH p ru a plasma; selectio- optimaf no l modes excited (m»n,t optimizatiod an O) n of antenna spectrum; - studies of toroidal effects and finite ft influence on Alfven wave generation and absorption (toroidal coupling of modes, energy absorptio periphery,etc)e th t na ; _ 2 _- -I/ J - researches on Alfven heating physics for ne^ 10 ^"cm and attaining TQcd 1keV; researche- drivinf so g current generation efficiencier sfo

"plateau" ( ne(0)c^10 ^cnf^) and "banana" regimes; - noninductive sustainment of the tokamak current for - studyin procese th g s controllin energe gth y input positiod nan

the region of local driving current ( j (r) and Te(r) profile variation) durin pulsga d thiean s control D influencMH e th n eo stabilit discharga f o y energd an e y confinement; - researche nonlineaf so r effects accompanyin Alfvee th g n heating.

2. TMR Design and its Principal Parameters Realization of the above program imposes rather rigid re- quirements both on the tokamak design and parameters and its main suppl d controyan l systems principae .Th l plasma parameters

and required Bö ( P and I are calculated in sections below. We have chose followine nth g principal parameter TMHr sfo : 12cm= a , R=55cm

B0max^2,5T, I^ 100kA - Stage 1 =i 5T»I pnu«r 200kA ' Stage 2 4 ' 2 = 3f1 ' 'i? d ^ 10 cm" '

2,OkeV - Stage 2 1%, '"p. =1*5ms, «"c*,,- =10-»20ms c ftp Stag- 1 e W M 2 U = = 2*4 MW - Stage 2 R compleTM e xTh consist followine th f so g components: the tokamak proper, including the vacuum system; the poloidal field power supplies and control systems; HP systems; diagnostical means

126 The electromagnetic system (Fig.1) consists of: longitudinae th - l magnetic field winding comprisin coils6 1 g , each of them made of a monolithic unit in a stainless steel casing; - the inductor represented by a four-yoke iron magnet with field winding; contro- l field winding^comprising equilibriu correctind man g windings (Pig.2).

PCD,

FIG.l. Schematic view of the TMR tokamak and positions of the diagnostical tools.

1. Inductor ferromagnetic core; 2. Toroidal field coil; 3î OH-induetor windings; PFW1. 4 - main vertical field windings; ,B_ PFW2. 5 - additional vertical field windings; ,B_ z 6. PPW3- horizontal field windingsT ,B FIG.2. Cross-sectio f inductoo n d poloidaan r l field windings in the TMR tokamak.

127 A ttoroidae Stagth J M , 1 e9 la fiel y db windingd fe e sar condenser bank .modulatoA specifia f ro c design enableo t s su shape magnetic field pulses with BQs2,5T and'Ti — 0,1s and those

with B^4T and O^ <^> 0,03s (Fig.3). At Stage 2 feeding from the Q electrical network is provided to generate pulses with BQ^ 5T and <"£--/1s. The vacuum discharge chamber is made of stainless steel. The chamber has 14 ports with three branch-pipes (two vertical pipes and a horizontal one). Horizontal branch-pipe e suppliesar introduco t d antennaF eH s while vertical onemeane diagnostir sar fo t c purposes.

FIG.3 R discharg.TM e scenario.

3« Basic Regimes 3. Ohmi1. c Heating Regimes 14 3 Stage 1. For I =100kA, BQ=1,8T, q1=2,4, =1,10 cm" within an assumptio parabolif no c distributiowhe, T nd usinan n gn ni various energe scalinth r y gfo lif e time - re e cas th f o e n i sistive heating e shoul[_1on , ]d expec t=l60*190e> ^ rT d ?an

t^ £ =7-»10ms^the ohmic heating power being POH=:0,2-0,3MW.

Stage 2.For I =200kA, B=5T, q-|=3»3, n =1» 10^cm~^, the estimates Q

yield =250+350eV,Hu 5+11ms, e=5 , PQH=0,3->0,5MW. 1

128 3.2. Additional Heating Regimes The estimations of plasma parameters in L and H regimes for Alfven heatin e givegar n below obtaine basie th t &*&\% Goldf da n so o * stone scaling fl~] f or T^j it should be noted that for H regime, this scaling has been used with the factor of 2. The values of are given for * n;> =5 '101 •'c3 m- 3.

=100kAI Stag . 1 e , P=2MW, BQ=2*2,5T 1 3 L-regime ?<-n]?c> a 5-10 eV- cm" , ^ Te>~j 0,SkeV l6 3 H-regimeî d 9 -10 eV, cm" , ^ Tg> d 1, 4keV o y Q- ——"——Stag ep 2—. I =200 kA, P= 4 MW, B = 4*5 T ———"*—I~regim—e ; ^ nT_e> -± 1.7 3 «• 10 .4'7 cm-', T^T^^ake e V H-regime ; <-nT>cr! 2, 6 * 10 ' eV cm J, ^ T>^ 4 fceV 6 l^™"*™"""""""'^*^™* C ^ Peak values of average densities expected are~ïT „ =(0,7fl,8) or\ T C3O 7 max lO^m"-3 for B =2T and "n^^ad, 8f4,5) TO^m J for B = 5T. Upper and lower values of densities correspond to Murakami limits: M= 0,2 (gettered wall) and M =0,5 (additional cleaning of the chamber by a glow discharge and programmed gas filling) [ 2J .

Drivin3 3. g Current Generation Regime Driving current magnitude estimations for absorbed HP powers obtainee b y ma d froformule th m a taken from Ref.

Temperature evaluation derivee b y sma d froenerge mth y balance equation using Alcator and Goldstone scalings for ^C£ . For the local power input at the half-length of the radius and for PA1MW, M 2 Z 2 X V /V 2 i= * eff. ' = ph Te - °» ' ? U,Zi)^ 4, we obtain the following estimatio drivine th r gnfo current:

wit Goldstone hth e scaling used, and:

Alcatoe th r rfo scaling. It follows from these relations that in order to generate a current of the order of Ohmic one (Inu= 0» 1 MA.) at the plasma den 3 — 9 1 3 — n sito y _ n = lO m J, 2-4 MW of power is required. For n=3»10 3m J , both scaling spowee yiel th e required rf ar do V abouMÏ 1 .t

129 4. HP Heating and Current Sustainment Systems n ordeI fino rt optiman a d l spatial spectru fielde th - f mo sge nerated by antennas (the fields which allow to realize tho regimes with HP power absorption both in the central part of a plasma co- peripherye th t a lum d controo ,nan t drivine lth g current profiles), antenna impedance computations are performed using unidimensional MHD and kinetic codes and by means of a two-dimensional kinetic code wells a , . It has been found that for heating and driving current gene - plasme ratinth t ga column periphery preferabls i t ,i induco t e e modes with small N =1,2, M= 1, However, for heating at the central part, this regime doe appeat neede optimae sno b on o o rst t d lan generate the M=-1, N=-(4~6) modes. dischargen I s witcentrae hth l part heatin fairlga y "high- "pu spatiae th rit f o yl spectrum shoul ensuree db d travellindan P gH waves should be used, otherwise, a significant part of the HP power will be absorbed at the plasma periphery. The choice of the M=-1, U=-4 mode for plasma heating is also due to the fact that (as impedance versus Alfven resonance zone po- sition curves have shown generatinn )o g this mode resula s ,a f o t small variation P fielH e dth frequencyn si efficientln ca e ,on y realiz scenarie discharge th th f o e movin energe th g y input zone location fro axiae mth l regioe plasmth f no a colum-tho t ep n u peri- phery Pig.shoult I • note4e db d that such conditions exist during

significant changes in the discharge parameters: ne, q, BQ.

3 6» I O. 1 0. 0

Impedance versus the Alfven resonance o -a zone location one: B = 2 T, n(o) =3 n10 Jcm , q(a) » 3.7, Hg FIG.4.

130 e firsAth t t stag R f operationdevico eTM e eth modulan so r poloi- dal antennas wil usee lb d which wil introducee lb d intchambee th o r through eight horizontal branch-pipes. Such an arrangement allows us to ensure a fairly convenient spectral. content of the HP fields generated resula s .A phasinf to currente th g antennn si a elements e choicth f o theio et e r du location d an managee sw reduco t d e th e amplitudes of harmonica with M=1, UT= 1-4 to the value which is maie lesth n s f M=-1o tha $ ,1 n N=-4 harmonic amplitude. Each antenna module has four radiating elements made of stain- less steel coate layers) u d anten e (6 wit .Th (100wiN u hC -Ti d )an havs na e slitted screens introducinn .O P^2Me th g W power inte th o plasma currene antenne ,th th n equa- ts i ai in Ic^1,4k o le t th d Aan

put voltage uvrj is nearly 6 kV ( rf = 6MC). The tetraphase HP generator is assembled on GI-26A triodes ac- cordinindependene th o gt t generation circiut drivine th n .I g generator, means for controlling the output signal frequency (ûé/£ -= ± 0,2) and amplitudes are provided, the control being accomp- HP-TMe lisheth a R dvi contro l system durin dischargega . The HF-TMR control system is a microprocessor real-time system to control variation frequenciesn si , phase shiftP fielH d dsan amplitudes durin dischargega HP-TMe .Th R control - systede s i m signated for conducting experiments on: -stabilizatio spatiae th f no l positio Alfvee th f no wave trans- formation zone when nß(r), parameterQ TJB e (rd )an s undergo variat- ions ; - scannin Alfvee gth n wave transformation zone; scannin- drivine gth g current generation zon orden i e o rt shap desirablea e current profile, dàïiv^. r't) ThmodulatorgeneratoP y eH b d fe s ri s consistinC lonf - go gL line step-ud san p transformers. maio Thtw en operation modes are: output = 4°kV ' W= 5°°kj ' ^ =1 0 ms' 2- 17 max. output . 20 kV, Wmax = 5°° kj* * 5° ms'

5. Poloidal Fiel Plasmd dan a Current Control System (CPPT -TMR) CPPT-TM relaa s Ri y adaptive syste controllinr mfo plasme gth a column positio currend nan t plasmavaluee th n si . CPPT-TMR consists of the following subsystems: - power suppl poloidaf yo l fiel ohmid dan c heating windings (capacitor banks or industrial electricity, 30 MVA);

131 fas- t thyristor (12kA ,transistoro 1kVtw d )an s, (1kAkA 5 ,0, 0,3kV) three-position switch poloidae , unitth r sfo l windings; - thyristor (l6kA, 1kV) three-position switch units for trans- former ohmic heating windings; - fast magnetic data acquisition (16 channels and data transmis- sion via the Fiber Optic link) ; - special multiprocessor unit for real time processing of magne- tic and plasma data (<'n>&J, <"T>&)), and to transmit output data via the Fiber Optic link to the thyristor and transis- tors switches« CPPT-TMR allows us to ensure the longitudinal current generation, build-u d sustainmenplasmR pan TM e ath accordinn t i presee th o tgt program for cPp/c(f«2 MA/s, I ^ 200kA, t £ 0,2s, j^ 1,5 and the co- lumn displacement AR= durinm 3m *whole th g e discharge. The basic computational course of the THE discharge is shown in Pig. 3 . Design and function characteristics of CPPT-TMR allow us to perform researches both with the plasma HP heating and the driving current generation. CPPT-TMR is designed and produced in Sukhumi Institute of Physics and Technology and in Institute of Cybernetics of the Ukrainian Academy of Sciences.

Diagnostica. 6 l Syste Experimentad man l Data Processing e followinTh g diagnostical tools wil employee lb expee th -n i d riments: UHF (microfrequency) interferometer and HOT laser n.(r); 0 Thomson scattering, rubin lase r(r)T ; five-channel analyser rfo c* neutral TjXo); second harmonics radiation 2i«JCe^Te(r); soft- X-ray measurement s(o)T ; resonance fluorescence metho pyroelectri; dn. - detectorl ca s Eya^Cr); Langmuir probes, Te,ne, scrap layerf of e ; electrotechnical measuremen t(Rogowsks y , multicoibeltstL • ,J l probes diamagneti,a cm,n, coilj , loo, p winding); spectroscopy in visible light. Diagnostical data acquisitio primard nan y processin accomps gi - lished by the measurement-computation control system of TMR (MCCS- TMR).MCCS-TMR is a three-level control system; it allows us to operate during the discharge real time and the real-time pause between the discharges. MCCS-TMR performs: measurements, data acquisition, data processing; the TMR device control; the discharge real-time control of the plasma current, the plasma column position, the driving cur- rent generation zone location and the HP heating zone position; the data communication between the operating boards of the experimenters throug locae hth l computational network; processing, storagd ean presentation of experimental results.

132 REFERENCES

1. IHTOR, p.28, PhasA I eI , IAEA,Vienna,1986. 2. Mukhovatov V.S. in the book"Itogy Nauki i Tekhniki", Plasma Physics , issueseriesin , 1 d. ,v "b y VINITI, Moscow, 1980,p.6. 3. Belikov V.S.,Kolesnichenko Y.I.,Plotnik I.S., Proc.of the 14-th Europ.Conf«on Plasma Phys.and Contr.Fusion, Madrid, 1987, v.11D, P.III, p.1040.

Next page(s3 13 ) left blank LITHIUM BEAM ACTIVATED EDGE PLASMA SPECTROSCOPY - RECENT RESULT ATOMID SAN C DATABASR EFO QUANTITATIVE STUDIES

F. AUMAYR*, R.K. JANEV**, M. SCHNEIDER*, J. SCHWEINZER*, H. WINTER* Institu* r Allgemeinfü t e Physik, Technische Universität Wien Atomi* * c Data Unit, Nuclear Data Section, International Atomic Energy Agency Vienna, Austria

Abstract

Recent progres e developmenth n i s Li-activatef o t d charge-exchange spectroscopy for diagnostics of tokamak edge plasmas is described. The status of a proof-of-principle study for Li-CVS at the TEXTOR tokamak at KFA (Jülich, FRG s linei ) d out.

Li-CXS/Revie1. w

The scheme in fig. 1 presents the already known applicabilities of lithium beam-activated plasma diagnostics. These methods reln o y either impact excitation or offering of an electron for capture by lithium atoms injected into a. plasma of interest. Considering at first impact excitation of injected Li atoms, such processes permit the measurement of electron density, magnetic field d electroan s n temperatur ei beaL alon e m th gpath . Correspondin e regioth f o prioo nt g r interest e injectioth , n energy can be chosen accordingly. One may apply either slow Li beams from heated ovens, moderately fast (som ) beameU e s produce y laseb d r ablatio r faso n t (above keV) beams generate y chargb d e exchange /1/. Of special interest is electron capture from injected Li atoms into hydrogen or impurity ions residing in the plasma, which in turn form excited species, since the capture takes place exclusively

into excited states. This has been investigated e.g. for protons /2/,

+ He (cf2 . also figs. 2a, b from /3/) and heavier impurity ions (C^+, Oq+, /4/). A general account of electron capture from Li by impurities in view to their density measurement by means of Li-CXS (Li-activated charge exchange spectroscopy) has recently been presented /5/.

135 plasma parameter signal excitation process

electron density l 670. Li m 8n electron impact excitation

magnetic field distrib. l splittinLi g electron impact excitation

electron temperature +HeI LC U+ I injectio othef no r specieF LI s+

densit impuritf yvisiblo d an v eu y ions electron capture into excited states ,...) line radiation

hydroge densitn nio y Ha 656.3 nm electron capture into H(n=3)

temperaturn io e line profiles electron capture

drifn io t velocity Doppler shift electron capture

local electric field Lil (forbidden electron impact excitation + LIF transitions)

A schematics : Fig1 . ! lis f Li-activateo t d plasma diagnostic applicabilities

136 He2+ + Li - He+(n) + L,i+ -u - ——f- 9 — *-#^>j 10-- - ON

D,,° ———— - 5- He2+ + Li 10"8- -"A N - Hell 468, émissiom 6n n ' K^k

10*- — i ^* ^^ ~~~ ""\ ' J^ Experlmenl Theory expenmenî: ; ^-'^. P S Ht-(nTE ) S AO» O Birret Lcventlud tan l 1981 - / n.l A £ this woifc •s. / *• „.3 • C} ' 1 —— theory: =H= Fntsch and Un 1983 (cf lexrt n«3 4 - — _._ 17 10" - i i i j i i i i 1 5 2 1 0.5 0 20 5 10 15 (a) E(keV/amu) E(keV/amu)

Fig. 2: Cross section r electrofo s n captur n He^i e +-Li collisions, from réf. /3/. ) Compariso(a f measureo n a calculatean d d He+(n) population cross sections. ) Compariso(b f measureo n d calculatean d d HBll(468, ) emissionm 6 n cross sections.

2. Recent measurements at TEXTOR

The feasibilit f electroo y n density measuremen- y meanb in t f o s jected Li beam/impact excitation has been demonstrated since long /6/, However, for application of Li-CXS the requirements on the injected Li beae considerablar m y larger concernin e beath g m equivalent current density /?/. Recently, first attempts have been mado t e demonstrate the feasibility of Li-CXS at the tokamak experiment JülicA TEXTOKF t ha R /8/. Fig 3 show. n examplea s U ,ke wher5 1 a e Li beam has been injected into the TEXTOR plasma, with the equi- valent neutral beam current being of the order of 1 mA only. Nevertheless, a charge exchange signal due to electron capture by E from injecte i atomL d s clearli s y visible. At present, these experiments are carried on with much higher neutral currents of approximately 10 mA, for which a much better signal/noise ratio for the CX line radiation can be expected /?/.

3. Data base for beam attenuation studies

We have used very simple models to calculate the attenuation i grounL f o d state atom intensity alon e injecteth g i beamL d , considering eithe i grounL r d state atom d ionan s s only r Li(2po , ) n intermediata s a e third state /5/. However s becamha t i ,e apparent

137 r/cm 34.0 40.0 43.0

1.89 1.90 TIME/S 1.91 1.92

: a pulseUS3 Fig f o B. i L dbea r measurinmfo g electron density ("Li-I" densit C wels a s ) a yl e {"Cedgth e n "i ) + 5 5+ region of the TEXTUR tokamak, KFA Julien /8/. The edge regio s beenha n scanne y usinb d n oscillatina g g mirror in the observation path from the Li beam within the plasma edge toward the optical spectrometer. Also showmonitoa s i ni beaL r e msignath intensity r fo l . The signals increase rapidl r smallefo y r minor radius because of increasing plasma and impurity ion density, but decrease still further inside because of both Li beam attenuatio vignettind an n e observatioth f go n system.

that suc treatmena h simpleo to s i t sinc must e neglecno on et t f the important role of relatively long-lived intermediate excited Li states, which are relatively easily further excited or ionised by both electron impac electrod an t n capture. Thereforo perfort t ou i m havL beat e w ese em attenuation calculations by considerin states0 1 o . t fig cf ,p , gu wit 4 e followin. th h g goals in mind. Collectio l relevanal f no t dat r crosfo a s section f importanco s e for Li beam attenuation (cf. fig. 4), and calculation of corre- sponding reaction rate coefficients. Use of these data base for attenuation calculations, by assuming particular plasma profiles. Evaluation of the necessary minimum number of Li states for reliable attenuation calculations as obtained by comparison from appropriate measurements. Eventual inclusio f modeno l impurity specie r considerinfo s e th g importanc i f beaL theso e r mfo eattenuation .

138 0 Li(4p) Li(4d) Li(4f) l Li(4s) Li(3p) Li(3d) Li(3s) 2

3 Li(2p)

4

5 Li(2s)

6

10 - state attenuation model

4 < Li(n,n < 02 * e~ - impact excitation/deexcitation * e" - impact ionization * radiative decay * H - impact excitation/deexcitation ionizatio- + H * n captur- + H e*

: FigSchematica4 . i l stateL lis f o t s (top collisionad )an l reactions (bottom) considered for advanced Li beam attenuation calculations.

s Ifinait n l state this attenuation study should provid s witu e h a reliable method to evaluate profiles of plasma parameters as density, temperature and impurity charge state fraction even in e plasmth a region si beaL whers i malreade th e y strongly attenuated.

n conclusionI e alreadth , y acquired experience wit i beam-activateL h d plasma diagnostics show e greath s t promis f theso e e novel diagnostic methods for measuring a rather complete set of data for magnetically confined fusion plasmas, which are of great value for a still better understanding of such experiments.

139 ACKNOWLEDGEMENTS These studies haue been supported by Kommission zur Koordination der Kernfusionsforschung at the Austrian Academy of Sciences, and by International Atomic Energy Agency under Research Contract No. RC 4549/R1/RB.

REFERENCES

/1/ A. Pospieszczyk, F. Aumayr, H.L. Bay, E. Hintz, P. Leismann, Y.T. Lie, G.G. ROSS, D. Rusbüldt, R.P. Schorn, P. Schueer and H. Winter, J.Nucl.Nat. (1989, in print) . AumayrF / Fehringe. M /2 ,Winter. H d an r, J.Phys. At.Mol.PhysB: . 17(1984)4201 . AumayrF / . Schueinze/3 J , . WinterH d an r , J.Phys. BAt.Mol: . Opt.Phys. 2_2(1989, in print) . BrazukA / . Winter/4 H , . Dijkkamp0 , Boellard. A , , F.J .e Heed r and A.G. Drentje, Phys.Lett. 101A(1984)139 /5/ H. Winter and F. Aumayr, Invited Papers 18. Int. Conf. on Phenomena in Ionized Gases, Suansea/UK, July 1987, ed. . TerrW y Williams4 32 . p , /B/ J. Fujita and K. McCormick, Proc. 6. Europ. Conf. on Controlled Fusion and Plasma Physics, Moscou 1973, p. 121 111 H. Winter, Comm.At.Mol.Phys. 12(1982)165 / H.L/8 . Bay . HintzE , . LeismannP , . RusbüldtD , . AumayF ,d an r . WinterH , Report Jül-2139 A JülichKF , , July 1987

140 DESIG TESTIME-OF-FLIGHD A F NAN TO T ANALYZER

. STÖCKELJ . VETESNÎKP , . JAKUBBAK , . ZÂCEF , K Institute of Plasma Physics, Czechoslovak Academ f Sciencesyo , Prague, Czechoslovakia E.L. BEREZOVSKIJ I.V. Kurchatov Institut f Atomieo c Energy, Moscow, Union of Soviet Socialist Republics A.B. IZVOZCHIKOV A.F. loffe Physico-Technical Institute, Leningrad, Unio f Sovieno t Socialist Republics

Abstract

A diagnostic technique for the measurement of the energy of fast charge-exchange atoms from magnetically confined plasma is presented. The constructive details and its preliminary test on the stand of the time-of-flight analyzer (TOFAN) are described. The analyzer is proposed for the determinatio temperaturn io e CASTOe th th e f o n th eRo r tokamafo d an k ions energy specturm resolutio e scrape-ofth t na f T-1 e 5laye th f tokamako r .

INTRODUCTION

The energy analysis of fast charge exchange atoms from plasma represent a widespreas d metho r determinatiofo d e distribith f o n - tion function of plasma ions in tokamaks /!/. However, a commonly used method (i.e. a conversion of the neutral flux to the ion one in a stripping cell and subsequent energy analysis of the ions /2/) is generally suitable for energies of atoms greater than 1 keV. In the lower energy range e sensitivitth , e standarth f o y d analyzers rapidly drops with energy and moreover, a large uncertainity in absolute calibration appears, espectially below 100 eV. Therefore, such analyzer e lesar s s suitabl r smalfo e l devices wite centrath h l ion temperature in the range of hundreds electronvolts, where a direct time-of-flight analysis of neutral fluxes in the energy range from 20 to 1000 eV seems to be more convenient. Basic idea is rather straitforward: a neutral flux from plasma is at first mechanically chopped to short bunches and after a sufficiently long flight path throug a drifh t tub s registerei e d ba secondary-emission-typy e detector e detecto th e for f Th .o m r output e simplsignab n ca yl e energlinketh o t yd spectruf o m neutrals. The shutter opening time (microseconds) should be suffi-

141 ciently shorter than the flight time of the particles through the drift tube (ten f microsecondso s t reasonablge o )t e energy resolu- e analyzerth tio f o n .

The described time-of-flight analyzer (TOFAN) is proposed for determination of the central ion temperature on the CASTOR tokamak /3/ and for the monitoring of energy resolved particle fluxes froe plasmth m a edg n T-1i e 5 tokamak similae Th . r analyzers have already been installed on PIT /4/, ASDEX /5/ and TORTUR /6/ to- e samth kamak er reasonsfo s . We report here some construction details of the TOFAN (described also in /7/) and its preliminary test on the stand n auxiliarba y n gunio y.

CONSTRUCTION DETAILS OF TOFAN o basiThtw e ce time-of-flighpartth f o s t analyzer, i.e. the chopper system and detector, are seen in Fig. 1, showing an experimental arrangemen r preliminarfo t y tes s wella t .

TO SCOPE

HUtriPllER «KF

: CYLINDER -3,3 kV J r i 1 V -3,7 kV ilOV CtS IN CHOPPED BEAM

TARGET/

DEI ECTOR G DISCHARGPI E

Fig. 1 Schematic arrangement for the test of the TOFAN by a particle beam. The ion gun is shown in Fig. 5 in more L ; detailsm l = L , DET = 0.3. m 6

+ CHOPPER SYSTE+ M The energetic particle n sourcs io fror tokaman (o a em k plasma) pass at first to a rotating chopper disc. The chopper (the stainless steel disc of thickness 0.3 mm) has 60 equally m widthspacem 4 m lengt,0. m d mechanicalld 2 slit2 an h f o s y

142 cutted at a 80 mm radius. The chopper disc is driven by an asynchronous motor of a gyroscope, modified for operation under high vacuum conditions. Its short-circuited rotor turns inside the vacuum chamber on the two standard bearings, coated by a mo- lybdenum power before installation e statoTh . r windint a s i g e atmospherith c pressure, separated froe rotatinth m g a par y b t thin (0.3 mm) stainless steel wall. The stator winding is supp- lied by a three phase generator, which frequency can be control- led in the range of 300 - 400 Hz. There is another slit 0.25x20 mm directly behin e discth d , which a vacuuact s a s m break between the source of analyzed particles and drift tube. Moreover, the width of the fixed slit defines the form of the instrumental (shutter) function of the copper system. The vacuum chamber of e choppeth r e differentiallsysteb n ca m y pumped f necessaryi , .

Such arrangement, however, doesn t allow a continuous opera- tion of the motor due to the overheating of the stator winding. Therefore, a cyclic operating scenario is proposed for operation under tokamak discharge conditions e choppe e FigTh se ,. 2 .r disc can reach the operation speed (20 000 rpm) in about 3 min. The temperature of the stator winding starts to increase at that time up to 60 ° due to the power losses in the stator winding. After a tokamak shot e poweth , r supple speeth f s switcheo d i dy an f of d the disc starts to decrease with the rate of about 1000 rpm

20000-

10 000

Fig. 2 The cyclic scenario of the chopper system operation

143 per minute. Under high vacuum conditions, the rate of decrease f rotationo s determinei s d e qualitnamelth y f b bearingyo y d an s a measure useb s a dn io controlca t e l them. However, another e switchinpoweth f ro suppln o g y leada rapi o t sd increasf o e e speeth f rotationso d n principleI . e timth , e interval between e subsequenth t powe n regimer o e coolinshortenerb ai n n a ca s g y b d of the stator windings.

+ DETECTOR+ The particle detector arrangement is similar to that used in /4/ e particl.Th e flux impact n aluminiua s m disc, approx. 90 mm o.d., emitting secondary electrons (or may be negative ions /5/, whic e acceleratear h d throug n extractioa h e nshie th hol n -i e ldin e secondarg Th cylinde . o energeV t y0 p u rparticle40 y e ar s registered by an off-axis electron multiplier. The local electric field shaping near the target surface, which is necessary for an efficient collection of secondary particles is reached by tit- e Al-targeth lin ° witf o g5 h mule (1 t respecth e axi -f th o s o t t tiplier y possibilitb d )an w o applvoltagt ylo a y e betweee th n targe d shieldinan t g cylinder e typicaTh . l - potentialva e th f o s rious detector element e indicatear s n Figi d . 1

Preliminary test of the TOFAN The TOFAN assembly was tested by the ion beam from PIG-dis- charge /8/. The ion beam with an energy E travels at first through e choppeth r system e Figse , . Tha1 n afte e flighth r e t th pat , L h ions are accelerated by the potential of the detector cylinder eLI + E and hit the target. The typical mass-compositio n beamio e , th usin e f o nth g air as a working gas, is presented in Fig. 3. Some characteristic mass-number PIG-discharge th e b f o sn , OH ca Ojt, H| +? s N^ ,'C0 a e simply identified. The similar mass spectrum is shown in Fig. 4 for another discharge condition d hydroge e an fillins th s a ng gas. n resolvN ca ionsd e an on ,e BesidH threO f o e hydrogen compo-

nents H, , H? , H-,. However, thre are at least two peaks (at t = 3,5 and 16 us), e simplb t no ywhic n identifiedca h e flighTh . t time d amplian s - tude f thio so peak tw s s remain unchanged after applicatioe th f o n potentia e deflectioth n o l n plates (also show d n Figi nan ) .1 their position is independent on the extraction voltage of the

144 AIR E»« 230 «Y

«0 TIME [ft]

\ 7 1 23 6 9 173« 28 3Î «450 MASS-NUMBER

Fig. 3 The mass spectrum of the beam from PIG-discharge, using air as a working gas.

HYDROGE N; E,'1SV O»

WITHOUT DEFLECTION

Fig. 4 The mass spectrum of the beam from PIG-discharge, using hydrogen as a working gas, a) without the deflection voltage e deflectioth ) b n voltag s appliedi e .

ion source. Consequently, this peak e identifiear s s neutraa d l particles created just inside the ion gun. Taking into account the total flight path L , . + L, the E/M ratio of the first peak give r energfo s f neutralo y n unreasonabla s e high value with respect to the anode-cathode voltage of the ion source, when s assumedi 2 = M . Therefore e firsth , t pea s supposei k e b o t d the atomic hydrogen. Assumin w thae neutralno gth t - sse froe th m cond peak have the same energy, we can estimate their mass-number . However20 - 6 1 , = more rangM ith ne f o eprecis e identification of the neutral peaks needs the longer flight path.

145 Note than e individuawidta th tf o h n peaio lk well corres- e shutte th e for pondf th o m r o t sfunctio n (show y dotteb n d line in Fig. 5), whereas the width of the neutral peaks is noticeably broader t indicateI . n componensio e assumethab e th n t s ca ta d monoenergetic, while the neutrals should have substantially broa- der energy distribution.

S INLEGA T

b)

Fig. 5 a) Schematic arrangement of the PIG-discharge. Formation of the neutral beam with energy e.U. is indicated. ) Distributiob e potentiath f o n l e alon th e axi f th go s PIG-discharge (schematically).

e proposeTh d mechanis e fasth tf o mneutra l generation inside the PIG-discharg s schematicalli e y show e n positivFigi nTh . 5 e ions from the anode plasma column strike the gas-covered cathode surface. Some secondary negative ione producear s d acceleratean d d back towards the anode up to the energy eU.. There, due to colli- sions then lose electroca yth s d travean n l throug e extractith h - on hole out from the discharge region as fast neutrals. Such me- chanism requires for neutrals to be particles with an affinity to electron, i.e. they should exis s negativa t e ions. Earlier /8/, we have identified the negative ions H7, 07 and OH~ in the beam extracted from PIG-discharge, which were produce y thib d s mechanism.

146 SUMMARY e describeTh d preliminary test demonstrates thae develoth t - ped time-of-flight analyzer works approprietly. From the construc- tion poin f viewo t e opeth , n questio s stili ne life-timth l f o e the copper system bearings. Up to now, the bearings were in opera- tion more than one hunderd hours without any noticeable drop of their quality. Such time interva s sufficieni l r managinfo t f o g the preliminary measurement f energo s y resolved neutral flux from the CASTOR tokamak plasma, which are planned to start in the near future. However, before the instalation of TOFAN on the tokamak, the absolute calibration of the detector should be performed. Namely, the secondary emission coefficient for the Al-target has to be determined for correct evaluation of the energy spectrum. Such calibration procedur w underwayno s i e .

ACKNOWLEDGEMENT

e author Th n Dvoféks respon Ja wa e indebte . ar o s Mr wh ,- o t d sible for the technical construction of the device.

REFERENCES

/!/ Izvozchinov A., Petrov M. P.: Fizika plazmy, 14, 1988, No. 1. . 19 - 0 p1 . /2/ Afrosimov V. V.: Berezovskij E. L., Gladkovskij A. I. et al.: Soviet Phys. Techn. Phys , 19615 . . 1378p , . / /3 Djabili d CASTOan . RK n team: Czech , . Phys1987J .37 B ., p. 713 - 724. : Rev / , CoheA. /4 E. Vos.. SeiS n. 0 s . Instr. 53/11/, 1982, p. 1696. / /5 Verbeen ProcI : . H. k12t h Eur. Conf n Contro . . Fusiod an n Plasma Phys. Budapest 1985, Vol. II., p. 583. /6/ Brocken H. J. B. M., de Kluiver H.: Plasma Physics, 25, - 319 7 .31 . p , . 3 . 1983No , /7/ Stb'ckel J., Vetesnïk P.: In Proc. of Seminar on plasma diag- nosti r T-15fo c . Neugrandenburg, sept. 1987. / /8 Jakubk , Stb'cken ProcI K. a : . 3. l 11th I.C.P.I.G. . 482p , , Prague 1972

Next page(s7 ) lef14 t blank TOKAMAK EDGE PLASMA INVESTIGATION BY LASER BLOW-OFF

J.S. BAKOS*, G. BÜRGER*, I.B. FÖLDES*, P.E. GIESE*, D. HILDEBRANDT**, L.N. KHIMCHENKO***, P.N. IGNACZ*, . KOLTAI*L . PASZTI*F , . PETRAVICH*G , , . SZIGETIJ * * Central Research Institute for Physics, Budapest, Hungary Zentralinstitu* * r Elektronenphysikfü t , Akademie der Wissenschafter der DDR, Berlin, German Democratic Republic *** I.V. Kurchatov Institute of Atomic Energy, Moscow, Union of Soviet Socialist Republics

Abstract

e edgTh e plasma density versus plasma radius functio MT-e th 1f ntokamao k plasma is measured by a new laser blow-off method. Thin film of sodium evaporated on glass substrate is blowed off by a Q-switched ruby laser pulse. The enhanced shortening of the pulse of neutrals was observed along the beam propagation toward the plasma center by measuring the resonance light intensit atomf yo s exciteplasme th y adb electrons.

The density of the plasma is calculated from the measured exponential time decay of the blow-off light pulse without any further calibrating measurement. The measured density distribution of the edge plasma can be fairly well describe parabolicay b d l functio plasme th f ano radius innerside neath o rt limiter radiu consonancn i s e wit microwavresule e hth th f to e interferometer measurement.

The transport of sodium atoms injected into the plasma using laser blow-off methoe intrinsi thath d an df to c impurities using deposition probes are investigated. e investigationresule th Th f to s show slighsa t toroidal asymmetre th f yo fluxesimilaa d san r exponential decay lengt fluxer hfo everf so y kinf o d particles. The transport process for the intrinsic and nonintrinsic impurities similaseeme b plasme o s t thath o rt f ato ions.

Measurement of the intensity of the impurity atomic line in the instrumented limited chamber is used for the determination of the impurity containment time. Using the scaling law for the impurity containment time the can be determined.

149 1. INTRODUCTION

The importance of the edge plasma parameters is emphasized several e recenth time n i t s literatur s thesa e e parameters determine the bulk plasma behaviour decisively. Therefore the edge plasm s investigatei a d extensively nowadays.

The edge plasma physical processes can be investigated even e cas th f smalio en l size tokamak. Therefor e decidew e o t d make measurements in the edge plasma on the MT-1 tokamak using nonintrinsic impurity injection by laser blow-off method, instrumented rail limiter, visible multichannel spectroscopy, deposition probes and nuclear analitical methods.

e Mt-Th 1 tokamaa smal s i lk size research tokamak, with restricted numbe f accesseso r e maiTh n . characteristicf o s

1135 Tne the tokamak as follows: Ro = 40cm a = 9cm Bt=1 T 'max ** discharge duration r=9msec.

. EDG2 E PLASMA DENSITY DISTRIBUTION MEASUREMENT e mosth t f o importan e On t edge plasma parametere th s i s density versus plasma radius distribution which is measured besides Langmuir probes by laser blow-off methods.

e LangmuiTh r probe measurements have usuath e l interpretation difficulties and they disturb the plasma state appreciably.

150 e previouth All s laser blow-off experiment shar e samth e e complication. Namely the blow-off particle density decreases with decreasing plasma radius e becausionizatioth f o e y b n plasma electrons. The plasma density can be determined if the intensite resonancth f o y e ligh measures e i th t d an d decreas e blow-ofth f o e f particle s takei s n into accounr o t it is measured in a separate measurement [1.2].

In our measurements the decrease of the number of blow- f neutraof l particle s directli s y useo t determind e th e electron densite edgth en i e tokamayregio th f o nk plasma.

2.1. PRINCIPLE OF THE MEASUREMENT

e laseIth n r blow-off process burst f differeno s t particles are produced with given velocity distributions and centre of mass velocities of the different particle bursts. Among these

particles only the neutrals penetrate into the plasma in radial direction through the magnetic field of the tokamak. e neutralTh e excitee tokamaar sth y b dk plasma electrond an s

they emit - for instance - resonance light. The intensity of the resonance light is

l(r,t)=ne(r).n(r,t)..V.Q/(4iT)

where ne(r), n(r,t) and are the density of plasma electrons, that of the blow-off neutrals and the electron

velocity (v) averaged excitation cross-section (a). r is e e the plasma radius. V and ft are the volume and the solid angle of the observation respectively.

151 The fast time dependence of the resonance light pulse is used e determinatioth r e fo densite methoth th f n o nt d y usen i d our measurement.

The space and time dependence of the number of atoms per volume elemen d velocitan t y interval (<3vj i.e e .densitth y (f(x,t;vj) of the atoms of velocity (v) of the burst created e laseith n r f bloprocesof w s describei s e followinth y b d g equa: n o ti

[a/ô v.d/ôx]f(x,t+ t ; v)=-«7j.ve>.ne(x).f(x,t;v)) (2 ,

the solution of which is given as x +K

f (x,t; v)=t°.B(v) ,exp(-1/v. j.ne(x) .dx) ]expm i [t-x/vI . 1 i { l ]}d O ) (3 -K

where the x coordinate is counted from the laser blow-off

atom source in the radial direction. is the velocity averaged ionization cross-sect i on . As is well known the independenc e cross-sectioth f o ee temperaturth n e o n th f o e plasma can be supposed in the temperature range (10-10O eV) e edgth f eo plasm a constan a s e i [3]d B(vth an s t° ,i t ) velocity distributio e blow-ofth f o n f atoms e densitTh . f o y atoms can be got after integration on the velocity (v) i.e.

a n(x, tj =t°.B(x/t) . x/t .exp(-t/x. <0j . ve>.ne(x) .dx} . (4) 0 e velocitTh y distribution functio e expresseb e n th ca n y b d

temporal function of the n(xo,t) density of atoms at the xo position as

e B(x0/t)=n(x0, t) .t /{t°.x0} (5)

152 where

*o

) (6 expl -t/x,n> e v e1 .d, 0}=

(x,t)=n(x) .gix) .n(Xo,t) .x/Xo.expL-t/x .v, >.ne(x),dx.

e o

e alsW o suppose thae functioth t n g(x)= t doeno s e electrodepenth n o d n temperature [3]( Sobelma198. al 1. ) et n

If the measurement is performed by multichannel device observing the light intensity at (x,,x,+j) intervals, the ratio of the signal of two consecutive channels can be given as

(8)

where

x. +1 x,

Mj i=<0, vj. > . (1/x, |n. (x )dx-l/x. ,jn. (x) .dx] 1 e +1 e e

+ o o

M,+}(| can be got as the the result of fitting procedure

i.e. «t is the result of the measurement. Namely C(x^,x, ) l+ t doedepenno sn o timd e e thereforb n ca e M,+ j i determined from the measured time dependence of the function

r smallefa s i rj x = l4 -x thax ., D ix nf I . ) t , , x ( 1 / ) t , i . 4 , x ( I then the mean density of the plasma in the Xj+j ,Xj interval can be given as

ne(x,)=1/Dx. j ne(x) .dx=M, +1 t , ve>.x,/Dx

153 e meaTh ne ionizatioth valu f o e n cross-sectioe b n ca n calculated using the Sobe Iman- Va i nste i n-Lotz ' s semi emp i r i ca I form e [4Jul ( 198Sobelma. al 1) wit . het n reliabl a II sm erroe r e densitth d an y distributio e determineb n nn ee (xca on )n i d tokamak shot without any calibration.

2. a. EXPERIMENTAL SET-UP

e e experimentaschemTh th f o e l set-u1 - MT p e mounteth n o d tokamak (R = 4O cm, a = 9 cm, 8-^ =1,O T and Imax -^5 kA) can be seen in F i g . 1 .

RAIL LIMITER

APERTURE LIMITER BLOW OFF 'OBSERVATION PORT Fig.l. Schematics! view of the MTt tokamak horizontal cros- section.

e laseTh r blow-off assembly (CH mountes e i lowe)th n ro d port e tokamakth f o . a vacuuThi s i s m vessel pumped separateld an y it is separated from the tokamak by the valve (V). This chamber contain e blow-ofth s f target.

A circular glass e plat th s fastenee i axi th ef o so t d stepping motor (SM). This motor rotates the glass plate by a small angle between tokamak shots under computer controle Th . sodiur e glasn th filn so mplat e e frotokamath m k sids i e evaporated in situ from the Na source. The tight of the O- switched ruby laser is focused on the film by the lens (Li).

154 Trie propertie f thio s s blow-off plasma were describei c n i d recent paper [5](Bakos et.al. 1987), The blow-off particles procèd e directioth e tokaman i th e f o nk centre e distancTh . e of the blow-off target to the plasma edge is 65 cm. The Na D resonance light excited by the tokamaK plasma electrons are observed in about 2 cm range along the path of the blow-off neutral n a optica y b s l arrangement throug e sidth h e porf o t the tokamak using a seven channel photomu11 ipli er array. The observed e e flighparticleregioth th f f o o t ns imagei s y b d the lens (L2) to the entrance slit of the monochromator (M) which selects the Na D line. Multichannel fiber optics (F) is placed on the exit slit of the monochromator which guides the light originating from different e entrancplaceth f o s e slit to different photomul t i p l i ers (PMS) .

PMS

Fig.2. Experimental set-up. CH : Chamber for in-situ evaporatioe blow-ofth f o f n target containing evaporation source (NS) , substrate disK , stepping motor (SM) and valve (V). L1 : laser beam focusing lens: ligh 2 L ,t collectin gmonochromator: lenM , s , : multichanne F l fiberoptic S photomul11pPM , s l iers observing different spatial sections of the blow- f beamof .

155 e e th Th photomusignal e ieri ar f p o digitize i s l t s d every 4 psec. The results are stored in the memory of the Camac data acquisition system using intelligent crate e tokamath f o k e dat d e controllerpulsth en ar al e al e th t A . A 114TP transferre e 8th computeo t dr furthefo r r data handlin d storagean g .

The tokamak plasma was limited to the radius a=7,5 cm n a adjustabl y b e rail limiter e geometr e Th apertur.th f o y e limiter (a=9 cm) and the rail limiter can be seen in Fig.1.

3. 3. RESULT OF THE MEASUREMENT

e resulTh a measuremen f o t e e tsignal seveth th i.e .n f o s channels which are registered in one laser blow-off shot can be seen in Fig.3. The laser is fired 3 msec after the

Haul

6.

3.1 3.2 t [msec]

Fi. 3 gPhotomu111pt r ie signals taken simultaneousle on n i y toKamak shote spatiaTh . l distance between adjacent channels is O.3 cm.

156 beginning. of the tokamak shot. (The pulse of the third channel is digitized with the speed of 1 MHz as an exception. e toroidaTh )n thi i sT l e case fiel1 Th s .i d maxima of the pulses of the different channels are about 25 psec after the time of the ruby laser firing. This correspond e velocitth o t ys 2,86 10 . cm/sec taking into account the distance of the blow-off target from the volume e observationth f o o N differenc. e arrivath n i el timf o e particles can be observed at the different channels because of the high speed of propagation of particles and the small distances (about Dx=0.3 cm) between the channels. The duratio e puls th e channes abou i th f 0 e2 o npse 15 t to a N lc which is the furthest from the tokamak centre. The shortening of the pulses of the photomu 1 1 i pi i ers in the consecutive channels is clearly seen in Fig. 3. We suppose that this shortenin s i simplg y because slower particles hav a shortee r mean free path in the plasma. The time axis in fact correspon n atoa o mt velocitd y axis. e Froth e ratith mf o o channel e e derivedensitb th sn ca dy withou y furthean t r supposition on the velocity distribution of the blow-off particles. Thi s jusi s t explaine n Sectioi d , 2 n Usine th g procedure formulated in Section I the electron density versus plasma radius functio e b calculated n ca n e e resulth Th .f o t calculation can be seen in Fig. 4. The dots with the error e meath n e bare densitvaluear th s f o s y wite calculateth h d experimental errors using the data of many shots. The curve visualize e commonlth s y supposed density distributiof o n tokamak plasmas

(r)=nf 0. [1-(r/a)] (11)

157 n T 10 ne[cm| x

10 rlcm]

Fig.4. Electron density versus plasma radius . Points

t werdo ed measurean denotee X th presen y y b b d t

y b Langmuimetho d an d r probes respectivelye Th .

continuous curve represents a parabolic density

distribution correspondin e linth e o t g averaged

density s whicwa measureh y b dmicrowav e

interferometer .

taking into accoun e linth te averaged density whics i h

measure y microwavb d e interferometer.

The oscillatory behavioe densitth f o ry distributios i n

remarkable. Further measurements are needed to clear up the

cause of this oscillation, The highest density observed may

be erroneous because the ionization cross-section can be

change t thia d s radius because increasinth f o e g temperature e plasma th e regioe validit th f e suppositioTh o f th .o n f o y n

on the temperature independence of the cross-sections

needs further investigations.

158 3. IMPURITY TRANSPORT INVESTIGATIONS

Properties of particle transport in tokamak plasmas can be investigated under clear circumstances using nonintrinsic impurities [6]. A commonly used method of injecting impurity atoms inte e plasmlaseth o th s ri a blow-off process e injecteTh [7]. d impurity atoms, whic e transportear h y b d the plasma, can be collected by deposition probes, by which the radial distribution of these atoms can be determined [8] .

Usine laseth g r blow-off method, alkali metal atome ar s injected into the MT-1 tokamak plasma.

The transport of these nonintrinsic impurity atoms is investigate y b dusin g deposition probes, whic e placear h t a d poloidally different location measuring the radial distribution of the atomflux . SimuItaneosIy the radial distribution of intrinsic impurities and the plasma ion flux e determinedb n ca .

Usin a bidirectionag l floating collecto Fign i .r prob1 D ( e e toroidath ) 5 l e fluxeinjecteth f o s d sodiue th d tha an f mo t intrinsic impurities were detecte dependencn i d e minoth n ro e e radiuplasmth t a as edgee impuritieTh . s accumulater fo d abou 0 dicharge2 t s were detected post-morted SIMSan S . RB y b m The discharges were reproducible and without disruption according to the other diagnostics (current, loop-voltage measurements, magnetic and electric probes, X-ray pinhole camer d densitan a y measurement) n additioI . e plasmth n n io a flow to both sides of the probe which were isolated from

159 each other was temporally monitored at different radial positions of the probe by biasing the probe up to -60 V with respece linerth o t .t e locatioTh e prob th s e toruchose p wa f eth sido to nt sa ne poloidally opposite to the entry of the Na-beam into the plasm d toroidallan a y opposit e actinth o t ge sector limiter, whics positione wa m (sem h 5 a minoe7 t a r do r radiu5 6 f o s Fig.5 and [9]).

MWI MT-1

RBEROPTICS PM1 ,PM2

MONOCHROMATOR

Tig.5 Experimental arrangement. PM1-PM8 are photomuItipiiers. LI, L2 are lenses. CH, SM, D, and ES, are vacuum chamber of the blow-off assembly, stepping motor, glass disk substrat d evaporatioan e n source of Na. FL, and SB are the ruby laser beam and e sodiuth m atomic beam e respectivelyth s i V . observatio e doublar 2 e nLP , LP1 volume02 d an , , 01 . depositio d erosioan n n probe d singlan s e Langmuir e th s i e raith l I s i limiteMW probes l d R an r. microwave interferometer.

160 This implies thae probth t e coul t measurno d e directional floweffect caused by the influx of sodium into the plasma or by particle acceleration toward the limiter. The connection length of the probe to the limiter depends on the safety e limiteth t factoa r radiusj q r . Usuall e q|-valuth y s wa s between 5 and 6. For these cases the probe had a connection length to the limiter greater than 12 m.

Fig.6 shows an example of the radial dependence of impurity d plasman fluxen io a s collecte n boto d h probe sides. Among the collected impurities are the injected impurity Na, the major metallic intrinsic impurities Fe (wall and limiter material o (limiteM d an ) r material e tracth d e an )impurit i L y whic s injectewa h earlien i d r experiments.

Generally, the radial and directional dependences of the impurit d plasm an n fluxey io a s were similar e distincTh . t feature n exponentiaa e ar s l radial deca f theso y e fluxen o s both probe sides with an e-folding length of about 12 mm and weaK asymétrie toroidal flow to the probe. In the majority of e experimentth e e electrofluxeth th s o t s n side were slightly larger than those to the ion side of the probe at all minor radii. Howeve e e fluxe e electroratith th th ro f t o so n side of the probe divided by that to the ion 8id« ehowed fluctuations from one exposure to the next but which was always les e plasms th t thaleasa r a factona£ fo t f iono r s and the injected impurity. Reversal of the direction of the plasma current did not influence the flux ratio of the plasma e injecteth iond an sd impurity significantly.

161 s _"e oc .05-

recycled A .02

1Ô2 80 85 90 95 100 r[mml Fig.Sa Plasma ion e injecte,th de recyclesodiuth d an md lithium impurity fluxes collecte n boto d h probe sides in dependence of the minor radius. (A) ion side and (o) electron side. The solid lines with the e-folding e plottee figurar th m n m i de 1 1 d an 2 1 lengt= e dL h only for comparison.

10 5

2 iow E o "3

2 lo17 5

2

id6 0 9 5 8 80 95 100 r [mm] Fig,6 e nonintrinstTh b c impuritiee distributionF d an o M s s versus the minor radius. (A) ion side and (o) electron side. The solid lines with the e-folding

e lengt plottee figurar th m hn m i ddt_e1 1 onl r e= fo y compari son.

162 Other collection features were particularly observed for fluxe f o tracs e impuritiei L (se e e MK Fige s Th . 6.}. different behavior of Li can probably be explained by the fact thae singlth t e ionized, recycled lithiuw m lo ato f o m velocity liver lonfo se gSOLth . tim n i Therefore e th e distribution shows the position of the source of the atoms beeing at the wall . But the fluxes of the major intrinsic impurities behaves differently froe generath m l behavior fo r some exposures. These variation e explaineb n ca s y impuritb d y influxes from local e sourcewalth l t inta e s collectioth o n e proberegioth f .o n More detailed result n thio s s effece ar t describe a separat n i d e paper [10].

In the case of the plasma ions and the injected impurity it e cab assumen d thae dominanth t te collectesourcth f o e d

particles is outward radial transport from the main piasma. In fact the collection features are similar to those expected r particlfo e effluxes froe maith m n plasma e radiaTh . l decay

length (oLe ) of such effluxes can be related to the radial

transport coefficien t D [11,12,13,14t ]

Dt=dLe where

D and R are the connection length and the major radius. vp is the parallel ton velocity. The factor 6 results from the fact that the used sector limiter spanned a poloidal angle of about 6O°.The scrape off action of the collector probe with a poloidal exten s neglecte wa f abou o d° 1O t d here.

163 For plasma tons the ion sound speed, given by

2 vp=iakTe/m,)*/ , can be used, where Te is the electron

temperature prototh , nm massd an e . Taking Te-value f abouo s t V derivee 0 d2 from probe measurement plasme th t a s edge, e experimentath l data yiel e diffusio a valudth f o e n constant f o protons which agrees wite Bohth hm value.

The application of the above formalism to impurtty fluxes need e sparalle th dat f o a l impurit n velocit e io ySOL th n i -y plasma which may be considerably higher than the impurity ion thermal speed [15). However from the same radial decay of plasma ion and impurity fluxes we conclude that the ratio 0^

divided by vp is same for both plasma ions and for all the impurity species. This sugges - togethet r wite similath h r directional behavior of the collected fluxes - that the impurity transpor strongls i t y couplee dynamicth e o th t d f o s background plasma.

We can not explain the observed weak directional asymmetry of e Na-fluxeth d e an s th s plasma wela sn theilto a r fIuctuation.

Possible explanations for the existence of the directional asymmetries would be either the flow induced by a variation of plasma parameters along the magnetic field lines or plasma drift processes with significan e impuritiestth draf o g . Furthermore spatial variatio f o perpendiculan r particle transpor n causca t a poloidalle y asymmetric edge plasma [16], which may generate toroidal plasma flow [16J.

164 One might suggest that a préffered particle transport to the probe electron side coul e facth dt o occurt e thae th du et collecting flux tube on this side intersects outer regions of e toruth s wher e perpendiculath e r transpor expectes i t o t d be higher [16,17]. However data obtained with Langmuir probes (LP1 and LPE in Fig. 1 ) in front of the sector limiter (18] are in contrast to this hypothesis. These results showed a

preferred plasma transport to the ion drift side of the limite r botfo rh direction e plasmth f ao s current durine th g same discharges.

This may indicate a dependence of the direction of the parallel plasma flow on the toroidal position. Thus the result e explaineb n alst ca sn unifor no a o y b d e m th drif f o t edge plasma. The observed asymmetry needs further i nvestigat i ons.

4. NON INTRINSIC IMPURITY CONFINEMENT MEASUREMENTS

The nonintrinsic impurity transport are investigated using laser blow off impurity injection and instrumented limiter. a movabl y e b plasm Th m em s limitee radiui a5 th 7 o f t o sd rail limiter of pumped limiter construction [19],

The radiation of the different atoms can be observed before the neutralising plate (Fig. 7) projecting this volume to the entrance slit of a monochromator and using photomu11ipiier.

165 .VESSEL

Fig 7 . Schemati ce instrumente th wie f o v d (imiter with optical observation NP1 and NP2 are the neutralizing e th e electronsidth ion d plate an f o - s e e monochromsteth e ar respectivelyL d MP an r d an n Mo . e photomu111plth . ier

Laser blow-off burst of atoms of soctium 10 injected into the plasm n aa angl edgt a ee 18O° toroidall a poloidallan y y relative to the position of the limiter. The place of the deposition of the nonintrinsic impurity ions can be calculated using the electron density distribution measured e blow-ofth als y b o f burs f atomo t s [20e centrth ] , f maso e s e thermath d lan e burstvelocitth .f o y

If the nonintrinsic ions are deposited inside the limiter radiue ionth ss penetrate e intcorth o e plasmd an a consecutively ionised. Afterwards the multiple charged ions effuse into the edge plasma where they are accelerated to the limiter chamber. If the ions are deposited mainly in the SOL they diffuse along the field line strait to the limiter.

r case Iou nimpuritth e y ione deposite ar e sblow-of th y b d f burst inside the limiter radius.

166 e e increasintensitTh th f o ( e lighy e t th signaf o ) l resonanc e sodiue th linf o m e e atomlimiteth n i s r chamber indicate the arrival of the injected ions.

The light signal (V) in the limiter chamber delays about one msec relative to the time of the injection (t,) and decreases exponentially (see Fig. 8). The e-foldmg time varies in the msec region depending on the plasma condition. Using the

scaling law for the impurity confinement time [21]. the Zeff e b e calculatefoun1.8-2.s b i o n t t i dca 5d an dwhic e ar h e Iir able values.

logV

3

2

1

0

-1

-2

-3

_J———I———I———I———I———L_ 2 1 1 1 0 1 9 8 7 6 5 4 3 2 1 0 t [msec)

Fig. 8 Intensity of the optical atomic line of the injected impurity atom versu e sth instrumente timn i e d limiter chamber before the neutralizing plate.

5. SUMMARY

e densitTh y distributio e edg th e e MT- f th o plasmn f 1o a tokamak is measured using laser blow-off method. Differently from previous blow-off methods the measured temporal decrease

167 e blow-ofth f o f light pulse which cause y lonizatiob d s i n e calculatioth use r e densityfo dth e f advantago Th n . f o e this method is its simplicity and absolute character without requirin y calibrationan g e e resuledgTh th .f e o tplasm a density measurement agrees e witresulth hf microwav o t e measurement of the bulk plasma density supposing the parabolic density distribution e Th observe, d density oscillation and the range of the applicability of the method needs further investigations,

Fluxes of the injected Na collected at the plasma edge showed similar radial and directional dependence as the plasma ion fluxes monitored usin e samth g e probe e radiaTh . l decaf o y e plasm n accordancth i n fluxeto as wa s e with Bohm diffusion. There is no plausible explanation for tire observed weaK directional asymmetry of the particle flow in the edge piasma.

Observing the increase and consecutive fall of the intensity e resonancth f o e einjecte th Iin f o e d nonintrinsic impurity sodium atoms in the chamber of the instrumented limiter of pumped limiter construction the impurity containment time is

determined. Usin e welth gl knowe n b e Zscalin en th f fca w la g determined and it is found between the value of 1.8-2.5,

168 REFERENCES

) [1 Kadot , MatsuokK. a , RamoH. a s H.J., Miyak, S. é a T.(1984Od Tsuchid d , an FujtK. ), a Usu J. a. T i J.Nuclear Materials 138 & 129, 960

[2J Pospieszczy Ros, A. . kG.,(1987)G s , Europhysics Conference Abstracts Vol. 11 D, 14 th European Conference on Controlled Fusion and Plasma Physics, Madrid, eds. F. Engelmann, J. L. Alvarez Rivas, p.1280.

[3] Kadota K.,Poszpieszczyk A., Bogen P., Hintz E.: (1984),IEEE Trans. Plasma Sei., PS-12, 264

[4] Sobelman I. I., Vainstein L.A.,Yukov E.A. (1981) Excitation of Atoms and Broadening of Spectral lines, Springer Verlag, Berlin Heidelberg New York

[5] Bakos J.S., Ignâcz P.N., Szigeti J.,Kovacs J.(1987) Appl.Phys.Lett.51, 734

[6] R. C. Isler :Nuclear Fusion, 24, (1984) 1599.

. MarmarS . Cecchi. L E . CocheA . J ,. S ] , n[7 :Rev. Sei. Instr.,46, (1975) 1149.

[8] R. A. Zuhr, J. B. Roberte, B. R. Appleton :Nucl. Sei.

Appl.,1, (1983) 617.

169 [9] D. Hi Idebrandt, J. S. BaKos, G. Bürger, F.. Pâszti, 6. Petravich : preprint of the Central Research Institute r Physicfo s Budapest, KFKI -1987-51/D

. [10HildebrandD ] . al.e publisheet b t o ,t n Plasmi d a Physic d Controllean s d Fusion

[11] A. S. Wan et al., J. Nucl. Mater., 145-147, (1987) 191.

. Nucl. McCormicJ [12K . ]. al Mater.. et k , 145-147, (1987) 215,

[13] U. Samm et al., J. Nucl. Mater., 145-147, (1987) 206.

. StangebyC . [14P ] . NuclJ , . Mater., 121, (1984. )36

J P.C.Stangeby[15 : Phys.Fluids , 326230 , , (1987).

[16] A.S.Wane J.Nucl.Mater: al t . 145-147, 191, (1987).

[17] B. LaBombard, B,L ipschu1tz: MIT Plasma Fusion Center preprint, PFC/JA-85-42.

[18] J.BaKos: e Centrareporth f o tl Research Institutr fo e Physics, Budapest , KFKI - 1988-O2/D

[19] Bakos J. S. et. al. to be published in the Rev. Sei. Instr.

[20] Bakos J. S. et. al. to be published in the Plasma physics and Controlled Fusion

[21] Blackwell B. et. al., IAEA-CN-41/I-3

170 ATOMIC IRON CONCENTRATION MEASUREMENTS BY LASER INDUCED FLUORESCENC TO-N EI 2

K.Yu. VUKOLOV, N.N. SHVINDT I.V. Kurchatov Institute of Atomic Energy, Moscow, Unio f Sovieno t Socialist Republics G. LIDER, U. VENZEL Zentralinstitu r Elektronenphysikfü t , Akademie der Wissenschaften der DDR, Berlin, German Democratic Republic

Abstract

The paper is devoted to a promising diagnostics of impu- rit yplasme atom th laser-induce e meany n ath b i s f o s d fluores- cence. The experiments on the measurement of Fe-atom concentra- TO-e th tio 2n ni tokama e describedkar .

The Laser-Induced Fluorescence (LIF a promisins )i g diagnostics for the study of impurity atoms in the plasma within large fu- sion devices. The LIF instrumentation for the T-15 tokamak is being developed now^an LIF-detectore th d s were e testeth n i d experiments on the measurement of Fe-atom concentration in the TO-2 tokamak. The TO-2 facility is a small racetrack tokamak with two toroidal divertors. The scheme of the TO-2 are shown on Fig.1.

1 - magnetic core; 2 - main divertor coils; 3 - divertor plates stainles- ;4 s steel chamber - inle ;5 t valve; 6 - separatrix; 7 - divertor chambers; 8 - diagnostic ports; HF-antenna- 9 additiona- 0 ;1 l divertor coils.

Fig. 1 . The scheme of the TO-2 tokamak.

Two toroidal divertors are placed in straightforward sections of the tokamak. The plasma equilibrium is provoded by a system of feedback automatic control. There is an ICRH system centrae placeth n i dl cross-section withi ntoroidaa l o part antenns .It poloidae ath occupien i l 0 n angl15 sa f o e

171 direction and serves as a limiter, when the separatrix is located in front of it.

The measurements of atomic iron concentration by LIF were performe divertoe th n i d r experimentao regimtw n i e l runs. The differenc experimentae th n i e l condition gives si n ni Table I. Table I.

* * Parameters : Experimental runs * I I *1 I Materia antennf o l a sheath stainless steel carbon Antenna radius,r 13,5 cm 14,5 cm cl Separatrix radius,r m 12,c 5 m 13,c 5 Toroidal magnetic field, Bo 1 T T 2 1, Electron temperature 300 eV 300 eV

The LIF-experimental arrangement showe s ar Fig n ni .2 d consis an pulsea f o t d laser system hollo,a w cathode tube wavelengte th r fo h calibration, movable test limiter, optical detection system and instrumentation for registration. IS 9 10 13

— excime1 r e laserlaserdy - boxca— ;3 ;2 r integrator; 4 - 19 - 20 - multipliers; 5 - monochromator; 6 - 7 - oscilloscope; 8 - photo- diode; 9-12 - lens; 11 - mirror; 13 - prism; 1 4- ligh t- hollo pip5 1 e; w cathode tube; 16 - glass plate; 17 - vacuum vessel; 18 - test limiter. Fig. 2. The scheme of LIF experimental arrangements,

172 The laser system include n excimesa r a lasetunabl d e ran dy e laser. The main specifications of this system are: sample rate - , outpuHz 0 t10 puls lasee resonanca dy e t e renerga th f o ey line of Fe-atoms ( ^ = 302,06 mm) - 0,4 m^ , pulse length - , spectra1ns 5 l widt h- 0,01 . 5nm Radiation of the laser tuned to a selected transition of iron atoms excites thes ee observatioatomth n i s n volume, they emie fluorescencth t e radiation whic s collectei h leny b d s and focused at the detection system, The three level system used for iron atoms is: excitation fro grouna m d stat detectiod 302,0t a ean m 6m 382,0t a n m 4n (transition to a metastable level). The numbe f fluorescencro e photonunit-volumee th n i s ,

NF, is:

+ branchine th Th es i facto gJ 3 nratio^ 2/f A( 2i>r£ ,/ ) , which take accoune th s f transitiono t l otheal n ri s metastable e th e s numbei th 7 / s f atomi o r level d L n statN i san , . sm 1 e function of the laser data and atomic transition probabilities. Takin e accounth g f concreto t e detection conditionsn ca e on , reduce Eq.(i) to the dependence of atomic iron density, /fc T , on a fluorescence signal, UM , in the observation volume:

) m 2 A +

Here IL is the factor taking the account of geometrical and op- tical parameters of the detection system, K^ is the gain of registration. The optical system is calibrated with band lamp, and the gains of registration system elements are measured separately maxima.e th Facto s i l measuree r2 erro th n ri d den- sities of Fel. The separately- resolved neutral Pe-density is measured as a function of radial position for the test limiter relative totokamae ,th k wall e observatio.Th n volum s situatei e d close in front of the test limiter surface. The movahle test limiter istainlessa s steel cylinder s witit diameteha , cm 2 3, r o angln wit, a n axia5 t a h2 ea f l of apertur t cu s uppei e d ren lasefoe rth r beam.

173 In the first experimental j>un the observation volume 3 e seconth n di rund an ,, whem c n interferenc na 1 0, s wa e fitter was used instead of a monochromator, it was about 0,5 cm3.

e typicaTh l experimental oscillogram e showar s Pign ni , .3 I,**

I_____ t .___!l _ Fig. 3. The typical . «••*• experimental oscillo- grams : - aplasm a current; - belectro n density; LL - c

it to so » so ft to to 9» u» no no

A temporal dependence of fluorescence signal is shown in Fig.3c. The first peak is associated with the discharge ignition. In the steady-state levee plasme 100tth th l s o hm t a p frou e 40t mth s hm of fluorescence signal slightly increases that correlates witha correspondin e plasmg th ris n ai e density e finao .Th t le du pea s i k a poor confinement in the end of discharge. The measurements in the first experimental run were performed at three test limiter positions at a radius, /£ , equal to 12cm, 13 cm and 14 cm. One can see (Pig. 4a) that the measured atomic q T iron density in a steady-state is 1Cr cm J at r» =12 cm, when the test limiter was placed outside the separatrix surface at the plasma boundary. When the test limiter was moved on 1 cm within the divertor cm)3 1 averagee = ,layeth ^ r r( d iron densit abous wa y factoa t r lowe0 1 f ro than that measure, r t a d e thase t n n^-sca se On . 1cm 2 Q. T cnT0 1 =t a J =13 cm. Such a fast drop of iron density indicates

174 »I CM 3-

cm 1 Pig. 4. Temporal O t dependence of Fei densit n froni y t e tesoth ft limi- 1 - ' 3 ter. to it ta te ne i-, uo na ttt la so 20in

higa h efficienc divertoe th f o y r layer. Actually maie th ,n erosion mechanis r thesfo m e test limiter position s sputterini s y ionb g s and a drop in the measured iron density means a reduction in the n fluio x loadine testh to t glimiter . Wite testh ht limiter with- drawa e iroth n P antennl , H densit inte cm th o4 a =1 y shado, r t wa is reduce. m abouo c t d 0 1 t 7-3 e spatiaTh l distributio Pel-densitf o n y alon lasee th g r beam path was measred with the test limiter at 12 cm. An exponential decay length, A , was deduced from the signal reduction (see Pig.5),

20 -

= 5 mm g - , 6 Pig. 5. The spatial distributiol Pe f o n density along the laser beam path with • 2 the test limiter positione= y i t a d = 12 cm ^ 8 to (2 mm

The X-axis represent e distancth s e frotese th mt limiter surface to the centre of observation volume, giving a good approximation radiaa r fo l distance. Thu have sw e . founmm 5 d = tha I / t In the second experimental run the neutral Pe-density depen- dencradiaa n o e l positio tese th t f limiterno , whe e lattenth s rwa placed in the HP-antenna shadow, was measured. The measurements

175 were performed at r? =15 cm, 16 cm and 18 cm. Note that the sensitivity of instruments permits to measure the Pel-density up to the wall radius 18 cm in this experimental run. The experi- menta thae le tempora se th resultt n ca e showle sar On n Pign i . .4b dependence of Pel-density does not change significantly in com- parison with that measure firse th tn i dexperimenta l run. In Pig. 6. the Pel-density near the surface of the test limite functioa s ra radiaf no l positio showns ni .

to'- Pig. 6. The Pel density I04 e n fronth i f o t test limites ra iff a function of it position ni 10* d thexperi2n e - .i.i. . . ! mental run. g r n 6 1 s i t i a / 12

The averaged iron density near the wall, n .- 5 105 cm— 3 , is 3ess than e ordeth f y o rthab t tesm a tc t6 1 limite = r , rcm positio 5 =1 a ny magnitude, meant i.e I =51 £ . s.n^ tham 0c t ions 6hav influn a -e 3 - e testh enc tn o elimite r sputterin n depto g o leshn sm c tha5 , n1 antenne th n i a shadow.

176 A 40 keV NEUTRAL LITHIUM BEAM SOURCE FOR TOKAMAK CASTOR

. ZÄCEKF . STÖCKELJ , . JAKUBBAK , . BADALECJ , , M. VALOVIC, K. KOLÄCEK Institute of Plasma Physics, Czechoslovak Academy of Sciences, Prague, Czechoslovakia

Abstract The paper deals with the results of two years'development of energetic lithium atoPraguP e mIP Th e source. th n ei developmen mads twa e under Research Contrac 4551/Ro tN B entit- led "Lithium beam diagnostics" concluded between the IAEA and P PragueIP submittee .Th d paper summarize resulte sth s obtai- ned in the frame of this Contract. The source will be used for measurement of the plasma pa- rameter poloidad san l magneti csmale fielth ln o dtokama k CASTOR.

INTRODUCTIO. 1 N The active corpuscular diagnostics of the tokamak plasma usin lithiue elemene probine gth th th s f a mto g vera bea s yi m prospective method wit wide hth e rang possiblf eo e applicati- s /4»5/on . Amon moae gth t atractiv belonge on e space sth e resolved measurements of the electron plasma density, local measurements of the various types of impurities ions densities measuremend an currene th f o tt density distributio tokaman ni k plasmas maie th n s .physicaA l task tokamae solveth n o dk CASTOR /6/ is the lower hybrid current drive, first of all the measu- rement of the radial current distribution should extend the diagnostic possibilitie thin so s device substantially.

The described source of energetic Li atom beam consists of £ solid ion emitter, extracting electrode system, accelera- ting syste neutralizerd man conceptuae th r .Fo l desigf o n this device the concept of well-tried neutral lithium beam proposen gu McCormicy b d ASDEr kfo X tokama employes kwa , d/7 8,9/.

177 2. EMITTER OP THE Li IONS

Por the reasons of the simplicity we decided to use a solid type of the lithium ion source (/3-eucryptite). It is known from literature that such typ emittef o e s beerha n used for many purposes including the active corpuscular diagnostics (e.g. /9,10,11/ d tha )provet an i t abilits it d provido t y a e sufficient densit particlef o y s flu smaller xfo r plasma devices, As a model for the construction of auch emitter we took the Spectra-Mat Corp Watsonvillf .o sourcn eio e describen i d /12/ with a certain heater modification, see in more detail /!/. The results concerning the emissivity of the developed emitte givee rPigar d Pign n i an Pig . .2 .1 show.1 lonsa g

time dependenc currene th f o et Icol measure plana y b de collec- e n fronth i placed f m voltage r biaseto m an th to 0 V 6 dk n o d5 e emitter temperature heateth o t d e 1150°C possibls i t .I o et conclude, thacapacite totae th t th lf o yextracte d electrical (abou0 0 1 chargto t p u e 3 mAh achievables )i . Pig. 2 shows the dependen-

ce of Icol on the collec- tor voltage. The parameter of the curves is tempera- ture of the emitter. Prom this measurements we can conclude that currenf o t the Li ions 1 mA will be obtainable at temperatures 10 12 time [h] emittee oth f r about 1300- 1350°C and extracting vol- Fig . .1 Currene th f o t tag. kV e w abovfe a e ion* Li s ICOT extra- cted, from emitter by a plane collector.

3. THE ION EXTRACTING AND POCUSSING SYSTEM

e ion e extracteTh sar d froemittee electricae th mth y rb l field of the extracting electrode and they are successively accelerated and focussed by an electrostatic optical system

178 Pig. 2. Dependence of the current Icol on the collector volta- ge for different temperature of the emitter.

consistin cylindricao tw f o g l tubes schematicaa e ,se l set-up of the lithium ion gun given in Pig. 3 together with neu-trali- d testinan r ze g devices firse , lengt.Th mm t0 7 h tub 6 75mm(j e ) forms one part with extractor. The distance between this tube secone an th de (grounde on d d accelerating electrod, mm 0 3 £ e distanc, mm 0 10 e s betweei lengt) e emittee mm th nth 0 h7 d ran thesl Al eextracto. vermm 3 y2 importans ri t dimensione th f so optical system wer McCormic e basie th taketh f so n n o k opti- mized desig /9,12/n ni .

grid plastic extractor neutraliser suppressor Faraday sciatilator emitter accelerating deflecting with 2 pm electrode plates folia

Udef "60V +50V ' +I5kv

l 200 400 600 800 1000 mm Pig. 3. Schematical set-up of the lithium ion gun together with neutralizer and testing devices.

179 maie Th n results concernin propertiee n th gio e th f so distance th bea n mi e m froabou 4 m t0. emitte givee rar n ni measuremente Th . 5 Pigsd an s,4 were carrie usint ou d Faraga - day cup pictured in Fig. 3 (but located in corresponding posi- tion 400 mm), working in the regime with suppressed secondary emission, i.e. detected current I^= I-r^ (switch of the Faraday housin position gi Fig. nb) , show4 lithiue sth m ions beam current IT . in dependence on the accelerating voltage U^ (beam threr fo eV k temperature0 energy3 o t emittee p )u th f d so r an fixed rati extractinf o bead gan m voltage s^ ^/U^ s 0.14t »I e seeb ny ma thabeae th tm curren severaa f to l hundredA ju f so will be achievable. Fig, 5 shows the measurement of the ion beam profile carriethin i st dou geometr y usin movablga e screen. The profiles given in this figure were obtained as a space derivative of Irj dependence measured by Faraday cup on the screen position /2/ Fige . Th show a ,5 s profiles obtained perpendiculao intw beae th m r r voltag directionfo y d e an sx 10 kV, Fig, 5b shows comparison of the profiles in the same e th r fo d an directiobeao V k tw m 0 r 2 voltage fo d ny an 0 s1 U U same ratio exi/ b= 0.14. It may be said that FWHM of the beam profile is about 15-20 mm without any attempt to optimize it d thaan maketL profile increasIJ sth e th ef eo sharper .

200 -, °'14

1320°C

100 - . 4 Fig. Lithium ion beam current dependencn i accelee th n o e- 1170°C rating voltage Ufe for fixed ratio d Uextan /U H b«O. three different temperatu- 0 3 0 2 0 1 0 res of the emitter.

180 10 kV 1.0

a. u.

Pig. 5 . y/mm/ Bea) a m profiles mea- 0 4 0 2 0 0 4 0 2 0 sured in both perpen- a) dicular x and y dire- 1.0 n Ub=10kV - Ub=20kV ctions for Ub= 10 kV and UQ3ct/Ub= 0.14; a.u. Compariso) b beaf no m 0.5 profile in y directi- on for two different d an 0 (1 value ^ U f o s y/nsn/ 20 kV); Uext/Ub=0.14 0 20 40 0 20 40 b) botn i h cases.

4. NEUTRALIZER OF THE ION BEAM

neutralizatioe Th * bea provideLi s i me th chargef y ndo b - -exchange collision beae th m f ionso s with neutral sodium atoms inside a neutralizing tube heated to the temperature about 300° neutralisee G th /3/ r .Fo r desig adoptee nw concepe th d t

proposed by McCormick /8/e The neutralizer consists of a reser- voir of Na, neutralizing tube and pneumatic valve openning the reservoir for short time period needed for measurement only» Th« temperature of the neutralizing tube is kept about 50 C higher as reservoir one to prevent the condensation of Wa. Test of the neutralizer efficiency in dependence on the reservoir temperatur mads geometrn ewa i e y schematically shown in Fig. 3. For measurement of the neutral atoms the detector (Faraday cup) must be laid out to register the secondary elec- tron current produced by impinging ions and neutrals (switch Faradae oth f y housin deflectina position gi s A . na) g element removar fo non-neutralizef lo d ion usee sw d deflection plates (lengtmutua, mm 0 lh9 distanc show) mm Fig n wells ni 0 a e 3 . 3 . Measuring two quantities - detector current produced by pure neutral bea 9 (thml e deflecting plates activate voltagy b d e 2kV)

181 and current 1^ arising from the total beam, we obtain apparent neutraliser efficiency 8 = I^/I^» The results of such measure- ment in dependence on the reservoir temperature are given in Pig. 6 for three values of beam energy. This figure demonstra- tes that value of efficiency ££»0.9 can be achieved at tempe- ratur wholee th 250° er rangCfo usef eo d beam energy.

1.0 00 Li beam energy 0 (D •H Ü •H a o Pig. 6. •H •P to 0.5 Apparent neutraliser effi- M ciency £ in dependence on the reservoir tempéra- -P

150 200 250 reservoir temperature /°G/

5. MEASUREMENT OP THE NEUTRAL BEAM PROFILE

Measuremen beae th m f profilto s carrievisuy ewa b t -ou d alizatio beae th m f tracno e usin groundega d grid wit plasha - tic scintilator covere thia y ndb aluminium folie e biaseth n o d positive voltag Pige se /3/3 « e , measuremene abou.kV Th 0 1 t t was made in the distance about l m from the emitter, which corresponds to the relevant geometry of tokamak GASTOR (during these measurements Faraday cup was removed, of course).

The image of the beam cross-section is produced in the scintilato y acceleraterb d secondary electrons arisin boty gb h ions and neutrals striking the grid. Behind the scintilator is the vacuum chamber sealed by a window which makes possible to tak photograpa e f thiho s image immediately greae .Th t advanta- ge of this method consists in the instant picture of the beam

182 profile, which enables us to observe the changes of the profile during the optimization of the beam changing the ratio U t/U-. Moreover, using a small deflection of the ions it is possible to separat profilee th ee se ion f o so neutrald t san o s d san directly their incidental departures. No observable departures, however, were discovered. It is possible to say, that profiles neutrad an bot e n o th flsamee hio th beam .e ar sEvidenc f eo this fact is given in Pig, 7, where comparison of pure ion beam (Pig. ?a - cool neutralizer) and pure neutral beam (Pig. 7b - hot neutralizer 0.8 wit« activated ' £ 6an h d deflection plates) u U is give bear nfo m energ keV5 1 y . Paramete ratis ri o ex-t/ b' circulae scalth n eo r scree 5mm/divs ni basi e th thif so n . O s results it may be said that diameter of the optimized neutral distance th bea n i m froemitte e et greatel th mno s s ri a r 10-15 mm.

Uext/Ub ions neutrals

22 0.05 28.5

28.5 0.075 37

20 0.1 28

(a) Pig. 7. Comparison of the beam profile for case pur f th n beamo e ) eio a ;

pure th e ) neutrab l bea €.kV) 2 ( m0.86'= = f j , ,U Ub= 15 keV, parameter Uext/Ub= 0.05, 0.075 and 0.1

183 REFERENCES

al./ t Zacee /! . :kF Rep. 7/8 PragueP 7IP , July 1987 /2/ 2âcek P. et al.: Rep. 17/87 IPP Prague, October 1987 /3/ 2âcek P. et al.: Rep. 15/88 IPP Prague, August 1988 Winte/ /4 RepP Aumaye, rIA H. .: 2/87rP. , Wien 1987 /5/ Tereshin V.l.: IAEA Rep. 1709 P, Wien 1986 /6/ CASTOR Tokamak Group: Rep. IPPCZ-256, Prague 1986 111 McCormick K.: Rep. IPP 111/40, Garching 1980 McCormic/ /8 : Rep kK. 111/82P .IP , Garching 1983 /9/ McOormock K., Kick M.: Rep. IPP 111/85, Garohing 1983 /10/ McCormick K., Kick M., Olivain J.: 8th Europ, Conf. on Contr. Pus. and Plasma Phys., Prague 1977, 140; McCormic Bartirom, kK. Bosc, oK. h M.S.: 12th fîurop. Conf, on Contr. Pus. and Plasma Phys., Budapest 1985, I 199 /11/ Kadota K. et al.: Jap. J. of Appl. Phys. 21(1982), 1260 /12/ Kick M. et al.: Rep. IPP 2/265, Garching 1983

184 RECENT RESULTS FROM SK/CG-1 MACHINE

A. SINMAN Nuclear Fusion Laboratory, Nuclear Researc Trainind han g Centre, Turîdsh Atomic Energy Authority S. SINMAN Plasma Engineering Laboratory, Electrica Electronicd an l s Engineering Department, Middle East Technical University Ankara, Turkey

Abstract

Detailed measurement spheromaa f so k plasma formatio SK/CG-t na 1 device was performed. The plasma configuration has been produced by the C-gun - a novel version of a magnetically driven shock tube. The comparison between the drift wave and the usual spheromak schemes has shown that the compact torus, in different configurations, can be formed depending upon the operational, modes of the C-gun. By means of the analysis of density profiles, the magnetic field configuration, etc., the formation conditions were determined, taking into accoun helicite tth y injectio currend nan t drive mechanisms.

INTRODUCTION

The machine o-f SK/CG-1 (World Survey of Activities in Controlled Fusion Research, 1986 Edition, IAEA, Vienna, p.197) is designed to produce the compact toroids such as Spherical Torus, Spherical Pinch Tokama d Spheromakan k e conceptuaTh . l desigf o- n this machine had been carried out between 1984-1986. Then, up to date, the experimental investigations /1-4/ based 'on the basic principles o-f this design have continued. In summary, the studies n o this machine wite speth h c i-distinctlf f o- icat. s ion y developed magnetica y drive l1 n plasm n (C-gungu a ) have bee e nvie th donw y b e poin validitf o- t Taylor'f o- y s criterion /5/. In SK/CG-1 machine, at low back ground gas pressures between 3O to 7O mTorr, the dri-ft wave scheme has been very interesting, e continuouth o t e du s dri-ft wave instability lasting d 5-2an 0s m bacous f wavo e e instability peculiarity looks a denslik o d t ean e t beam-plasmho a systea close s a md plasm e fluath xloon i p conserver. On the other hand, at higher back ground gas pressures between 7O and 3OO mTorr, it has also been possible to produce a typical spheromak plasma e experimentaTh . l results obtained have been evaluated unde e lighth rf las o t t studiesy b carrie t ou d Coppy /6/ and Peng /7/ then it has easily been understood that

in SK/CG-1 e seconth , d stabilitys e possibleregimb y ma e n thesI . e circumstances, it can also be mentioned -from the plasma -formation e shapeith n Spherica f o- s l Pinch Tokarna d Sphericaan k l Torus.

185 2. SK/CG-1 MACHINE

2.1. System and C-gun

The experimental arrangement has a 4O L octagonal floating -flux conserver whic s alsi e vacuuh th o m chamber either e bacTh k. pressure in the -flux conserver is 5X10''-6 Torr. Four C-guns in 90 degrees angular aparts are arranged around the flux conserver. e systeTh m consistJ capacitok 2 f o- s r bank -for each C-gun e spark-gaanth d p switches controlle y sel-b d f generate V ringU d . The C-gun is a noval and alternative version of the conventional magnetically driven plasma gun. The vertical two electrode e toroidath t a s l plan fluf o- ex conserve e maith e n ar r structur e C-gunth f o e. Sinc e profilth e thif o- es structure looks e C-letterth lik o t e e wil w ,a C-gun ls a cal t .i l The electrical characteristics of the gun con-form with the Critical Damping and Under Damping Modes (CDM and UDM) o-f operation depending upon the back ground gas pressure ranges o-f 40-7O mTor d 75-25an r O mTorr respectively e operatinTh . g period e CDM th s abou i ,t a M thite C-gut UD s th 1O-1bu i o-st fa n , 2us only 2-3 us. Without using crowbaring technique, the operational e transformeb n regimca thi f n o- gu sed froM schemUD m e into CDM. For this purpose, it has been sufficient only to be changed the back groun s pressure,ga d e workinTh , g voltage e C-gurangth nf o e is 1O-15 kv1 and maximum operating loop current is ISO kA. The logaritmic decremen s aboui t UDMe t th 0.5 .t 8a

2.2. Diagnostics

The main diagnostic techniques used are: the Langmuir electrical probes; the magnetic probes and loops; L-R fast operational integrators; the paramagnetic loop including a fast integrator; the resistivity probe; the charge-exchange cell and the visible light spectrum analyzer. Besides e fasth t, storage oscilloscop f HP-1744/o e e th d an A other conventional fast o«»c i 1 1 oscopes of HP-130/C and Tektronix 454/A have been used during data recording.

2.3. Flux Conserver

The walls of the conserver is made of Brass in 7 mm thickness e aspacTh . t conserve e ratith f o o s approximateli r . 2 y At the centre, there exist four axial passive rods. A part of the electrons in the plasma belt produced by C-gun itself, flowing through the mentioned passive rods, toroidal fields of d havro 400-80 e r beepe OG n generated. On the other hand, the back strap and the octagonal surfaces n inductivi e ar e coupling. e eddth ,y o t currentThu e e th du s n i s operational phas f C-guno e e conserveth , r becomes active. After the calculations, using data taken froe measurementsth m , some typical results obtained are as folows: minimum energy storage j characteristins 8 28 tims i e c impedanc 6 ohms 1O C L tims ;i e e constan 2.1s i ts 2(47 n 1 MHz); storage energ 23.s i y 4 Joulr fo e ISO kA C-gun current; time constant

186 . MODE3 F OPERATIOSO D THEIAN N R RESULTS

3.1. Generatio f Drifo n t Waves

Due to the distance between the vertical electrodes is not changed accordin e bacth k o t groung s pressur ga e dcritica th n i e l range o-f 4O-7O mTorr, the discharge through the vertical electrode e C-guth f no- s occurf inneo- d r se ai wallth wit e f th ho- s -flux conserver. This result is very natural, since the distance betwee e verticath n l electrode s largei s r thae distancth n e -from these electrode e wall th n thiI o .t s condition e currentth , s passing through the inner wall and the back strap are in opposite directions. Becouse o-f the mutual inductance between the wall d bacan k strap e seriath , l leakage inductanc e capacitoth f o- e r bank circuit becomes smaller. Thue dischargth s e b n e ca end s a s expected in the CDM. e CDM th e Ishocn, th k heated electron e plasmth n i sa belt with energies around 2O-5 , interactineV O g wite toroidath h l magnetic -field produce e currenth y b dt throug e closeth h d loof o p the plasma belt and back strap, a helical plasma current channel is -formed. Thus, dal-toroi withouo l po l flua ti da x translationa , toroidal -field together with a current channel (E-layer produced by the energetic helical electrons) at the -flux conserver may be generated. This procedure fits to the principle o-f helicity injection. On the other hand, by means of the self toroidal magnetic field of the C-gun directly, it has been generated the ion cyclotron waves in CDM scheme. So, due to the effects of the ion cyclotron waves and the density profile of E-layer at the beginning e reasonablth n i , e back groun s pressurga d e betweeO 4 n 0 mTorr7 d an , drift wave instabilitie e frequencth n i s y rangf o e 4-25 kHz have been distinguished.

3.2. Diagnostics for Drift Scheme

Taking into accoun e specificationth t e problee th b f o o st m investigated, the main diagnostic techniques such as Langmuir and electrical surface probes, magnetic loops and charge-exchange cell have been used n ordeI .o measur t r e plasmth e a resistivity for a unit length and then to determine the flow in the current channel w impedancelo a , , floating electrical surface probs ha e been empl oyed. This prob s v/eri e y simila a simpl o t r e double probe s operatinit d e spacan th g et poin a potentias i te plasmath f o l. Besides o t reduc, e surfacth e e impedance e terminalth e , th f o s probe have shunted wit5 mOhms 6. he primer Th . y w windinglo a f o s impedance transforme e secondee dat th e probth a th d o t an eo r t r processing channel afte n operationaa r l integrator have been connected. e charge-exchangTh e cell withou y magnetian t c analyzea s i r simple ionizatio t essentialli n d celan l y behaves lika e cylindrical n Langmuii m c 6 r1 probd an en cr wit 4 a radiuh 5. f o s length. In this cylinder the back ground gas at the pressures of 4O-7O mTorr is ionized by the run away electrons. The cell takes part on the way of vacuum connection of the flux conserver and by mean f somo s e interface s unitsbeeha nt i ,electricall y insolated from either flux conserve r vacuuo r me systemth s t placa It s .i e angular distances of 45 and ISO degrees from the C-gun and the electrical surface probe respectively.

187 When the Langmuir and the electrical surface probe signals are correlated by the plasma space potential variations of the charge-exchange cell with respec s bee ha o time t tnt i see, n that e drifth t wave alternance e densitth d yan s -fluctuationt a e ar s e samth e phases. Thus durin e on-seth g d afte an e to- th fr f-se f o- t the C-gun, it has been possible to determine the fluctuation phases of the C-gun.

3.3. Experimental Observations from Drift Scheme

By means of a passive conducting rod, located near the centre of the flux conserver and parallel to the vertical nail of e e loweC-gunth th e uppe rd th ,an wallr f fluo s x conservee ar r short circuited. Then the current passing through the wall too is transformed to a closed-loop current. So, the discharge on the capacitor bank circuit is suddenly cut-off and between the electrodes of the C-gun, a potential difference up to 7O t

Fig. 1. Variation of plasma potential in time when C-gun is open c i rcui ted. X0 ns/divaxi20 = s O Y axikWdiv2 , = s .

While the drift wave' is going on, the floating potentials e charge-exchangth of e e e cel35O-4OrespectivTh ar l . V O e Langmuir probe potentials are 1OO-150 V, the cell currents are probe th S5O-40 d e an curren A Ou e 100-15ar t . uA O e variationTh e plasmth n o as space potentia e chargth f o le exchange cell generated probabl e transversy meanb th y f o s e shock e densitth -fron f o yt fluctuation e changear s d dan betweez kH O 1 n 25 UHz. On the other hand, the drift wave frequencies on the electrical surface probe are in the frequency range of 4-e kHz (Fig.2).

188 Fig. 2. A typical result -from electrical sur-face probe -for dri-ft scheme. X axi2 ms/div = s Y axi, = relativs e units Lower trace indicate e variatioth s f o nelectro n density in time taken by Langmuir probe. Here the maximum electron density is about 5X10"14 cm-3.

Calculating the experimental data on Spitzer's resistivity •formula, the average electron temperatures in the range o-f 30-45 V have e been -found. The maximum electron density is about 5X10^14 e l i cm-3 h W . the C-gun on-set e volumth , e averaged bet s aboui a t 0.12 e lifetimTh . e o-f the CT have been lasted 5 ms or even up to s dependinm O 2 n o g the back ground gas pressure between 40 and 7O mTorr.

3.4. Spheromak Formation

At the mentioned C-gun, the shock heated hot electrons <4O- 6O ev1) in the plasma belt, interacting with the toroidal magnetic •field produced by the current passing through the plasma belt and back-strap closed loop, a helical plasma current channel is created. Thus without a toroi dal-poloidal -flux conversion, a toroidal field together wit a currenh t channel Œ-layere th t a ) flux conserver may be generated. This procedure fits to the principl f minimuo e m energy equilibrium e othe(5)th .rn O hand, the helicity existence rate is (dK/dt) = 2Vg F where Vg is the voltage applied to the C-gun, F is the net flux on the area framed by the plasma belt and the wall of the flux conserver. When the experimental data obtained from the CT produced by th e eabov th C-gued an considerationn e comparear s d an d evaluated, then they have been understood that as in the other magnetized co-axial plasma guns, in the C-gun too, the helicity injection and current drive mechanisms can be come into existence. Below the thermal energies of 15 eV for the shock heated electrons in the C-gun, the reconnection probability is lower than 7O %. To produce the helical electron ring far 15 eV, s necessarii t e microseconon y d duration n I .thi s duratione th , toroidal field generate t sufficiente C-guno th s i y nb d .

189 At a distance of 7 cm -from the wall of the flux conserver, e toroidae th poloidath d an ll magnetic -flux densitie e verar s y close being about 60O-3OO G. The decay times o-f the fields have changed between 2.2-3. s whicm 5 h have been calculatee th y b d expression o-f tv = .085) has been obtained.

3.5. Second Stability Regime

Preliminary experiments have been done using a back ground Heliuf -fillino- s m ga g wit a pressurh e rang 4O-25f o- e O roTora n i r single C-gun. In this content the main plasma parameters have been determined as follows: the electron densities between J.O'~15 and 5X10^16 cm-3, the electron temperature in the range of 25-5O ev" depending on the gas pressure, the life time o-f dense toroid generated -for 5-6 ms with the sawteeth perturbation but in stable e range volum 2.5-3.th f th casn o- ei e, 0ms average d total beta 15-18% e forth ,m facto f ellipticao r l shaped plasm= 1.37a b/ a , the safety factor q = O.6, poloidal current density 2OO-30O A/cm2 and lastly Troyon - Gruber constant o-f about 3. e resultth If s obtaine e evaluatear d d withD respecMH a o t t theory /8/ developed recently and an other study /9/, then this system realized takes e catagorieplacth n i e f 'Higo- s h Beta Sperical Torus r 'Sphericao ' l Pinch Tokamak*.

. HEATIN4 CONFINEMEND AN G T MECHANISMS

4.1. The Findings Obtained From Magnetic Devices

e presenth y tB e statuSK/CG-th f so- i machinee driveth y b n C-gun, which is presented here, it has not yet been applied the additional heatin d confinemenan g t technique. it n o s e operatinTh g e C-guperio th abous i e nf o dTh t 40-5 . us 0 maximum toroidal magnetic -flux density generate e poloidath y b d l loop current o-f 15O kA o-f the C-gun is approximately 15-2O kG and the internal electric -field is 9OO V/cm. The optimum Helium gas pressures are 2OO-25O mTorr. It has been determined that, in the initial phase o-f the e dischargfrequencth t a d ye an regiolastins u f 1O-14 o n 2- gz 5MH the intense ion cyclotron waves are generated and as being in the magnetic beach e plasmth , a electron e rethermalizear s e th y b d damping o-f these waves in a -few microseconds. The ion cyclotron waves have been detected directl a magneti y b y c pick-up coit a l an angular distance o-f 135 degrees from the C-gun. It has been understood that the mentioned ion cyclotron waves have a propagation vector and according to the guiding center approximation principle s conservini t i , e characteristicth g f o- s a closed wave e flumotioth xn i conservern . On the total -flux measurements, it has been observed that the diamagnetism is begining again at the initial phase o-f the discharge. After the off-set state of the C-gun, the diamagnetism

190 is translated into paramagnetism. Depending on the total flux decay timee paramagnetisth , m duratio s i nabou t 2.5-3.s m 5 (Fig.3).

Fig . Tota3 . l magnetic flux decayin n timei g . 5 ms/divX axiO. = s Y axi, = relativs e units

e otheth r n handO e shocth ,k heate t electrone ho dth n i s plasm e energiea th bel y b tf 45-6so , eitheOeV r ioniz e bacth ke ground gas at the pressures of 2OO-25O mTorr, or thermal ize this plasma collectively. According to the measurements carried out by the Langmuir probe and paramagnetic loop, after reconnect ion, in 0.5-1.5 us the electron temperatures of the spheromak plasma have been found around 15-3. eV 5

4.2. Optical Radiation Study

In orde o t understanr e heatinth d g mechanis f o SK/CG-m 1 machine more clearly, the optical radiations during the discharge have been investigated. The radiation losses of the spheromak plasma have been searched throughoutly at the gas pressure of 25O mTorr. During measurements, interferenc 25On i -m en filter O e step5 th f o sy b s d continuouslan 1OO m n O y adjustable visible monochrometee th n i r range of 35O-7OO nm have been used. By means of solid state photo sensitive detectors having four definite spectral responses, the plasma radiations begining from UV up to IR regions have been determined. According to the operational data of the C-gun (15O kA, 95O Wem and 25O mTorr), the expected average electron temperatures are about 40-75 eV. The spectral analysis of plasma radiations have also given similar results to these values. It s consequentlha y been understood e thaspheromath t k plasma consists of the He II (54.4O eV) and the other high level ionized I (47.4II N 3 d Cu.II I (54.8eV>an II ) ,O I9eV ) ions(36.t eV 8Bu . meanwhile the VUV and soft X-ray analysis have not unfortunately been possible also t presenA . e constructioth t e softh t f o X-ran y spectroscopy is continuing. The total radiative power losses at above conditions for He II in the range of 250-1OOO nm have been calculated as 3.57X1O"-13 W/electrons.

191 s beeIha t n determined thae opticath t l plasma radiationn i s the band width between 75O and 95O nm, continue about 4OO and 450 us a-fter the o-f-f-set position of the C-gun. In return, on the band widt e 50O-7Omentionef th o- h , nm O d optical plasma radiations last only 2OO-25O us (Fig.4). Whereas on the band width o-f 25O- 70O nm, this duration r x ses up to 5OO us by the contribution of UV radiations (Fig.5). Thus, as the C-gun in operation and in e firsth t perio f o 15O-2Od s u followinO e off-setth g e th , optical radiation band of 2OO-35O nm is more effective and in this duration, there also exist some contributionR I f o s components on total radiative power losses.

Fig. 4. Signal of optical radiation in the detection range of 5OO-70. nm O X1 ims/divaxi0. = sO mWdiv Y axi1O , = s .

Fig. 5. Signal of optical radiation in the detection range of 250-70O nm. i ms/divX axiO. = O smWdiv Y axi1O , = s .

192 Accordin e totath o lt g-flu x signal e toroidath , l -fielf o d the spheromak plasm . e Whems aspac th n las 5 t mosea 3. tt potentiae Langmuith f o- rl prob s evaluatei e d with respeco t t time, a drop on the space potential level down to the -floating level in 1.5 ms after the off-set of C-gun and then a rising o ut plas t space potential valus m hav e5 e agai1. been i n n observed (Fig.6). Succesively, the space potential has remained constant -for 6 ms and -finally, an after-glow region is appeared -for 12 ms. Due to the gas pressure is not changed, this drop and succesively rising in the electron density can attribute to the increas ionizatiof o- e nn othe i rat r ro e e contributiowordth o t s n o-f new hot electrons. The total period of this occurence is about 3 ms and this result is very close to the total flux period. The flat space potential region of 6 ms which probably characterize e E-layerth s n definca , quiscen» = e d waran t m plasma clouda matte s A f fact.o r , during this perio e toroidath d d an l the poloidal field * zeroar s .

A resul Fig. 6 .t froe Langmuith m r probe measurements. X axis = 2 ms/div, Y axis = relative units.

. CONCLUSION5 S

The main results obtained in this study are:

- The compact toroid having drift wave instability is not an unstable O a behavioutoroistat MH f o n ei d r havin e microth g - instabilities, but it is a closed wave-electron ring which is the current channel modulate e drifth y t b dwav e itself.

- Taking into consideration the guiding center approximation for the electrons in this character, one can mention from the closed loop formation in the flux conserver. The mutual inductance between E-layer and the flux conserver can confine this system.

193 - Due to the current channel o-f the CT modulated, the azimuthal and toroidal -field distributions may not be in clasical meanings. Nevertheless in the period o-f 5-20 ms passing up to the di-f-fusion depending on the back ground gas pressure, it is a hot and dense plasma ring conservin propertiess it g .

- It has been seen that a CT which is not a conventional spheromak can be realized. The density pro-file o-f E-layer and its variations versus time are now investigating.

T modeC s A expecte-i l d whic occures i h a close s a d e d th loo n i p E-layers consistin temperaturf o- g d densitan e y fluctuationd an s serial plasma spheres like a string beads.

e initiath n I - l e dischargeth phas f o ee shocth , k heated electron e plasmth f ao- s belt, either ioniz e bacth ek grouns ga d (He, 40-250 mTorr r thermalizo ) e electronth e thin i s s plasma urni .d me

e influencth e toroida y th B f - o el fiel f o dabou t 15-2, kG O produce y b plasmd a belt insid e fluth e x conserve e bacth kd an r strap a close, d helical current channee fluth xn i conservel s i r coming into existance.

- The energetic helical electrons in the current channel are formed the E-layer and as in the beam-plasma interactions, under the influence of toroidal field, the ion cyclotron waves in the frequency range generated ar f 1O-1o ez MH 5 . Damping these waves in 3-4 us, the electrons in the plasma are rethermalized.

e paramagnetisTh - s probabl i e selT th C e evenf th f yt o a tm toroidal magneti ce helica fielth f o dl current channel.

- In the heating mechanism, there exist the phases of shock heating, rethermalizatio n cyclotroio y b n n wavee dampinth d an g ohmic heatin y paramagnetismb g .

- For the confinement of CT, the mutual inductance between the flux conserver and the E-layer is fairly effective. In addition, it is supposed that the electrons with closed helical orbits e toroidabehavth s a e l electron field coils. e mutuath lo t inductanc e Du - e betwee e bace th nth k strad an p wall o-f flux conserver, the energy transfer from capacitor bank to the conserver is possible. Thus, becouse of the eddy currents, the flux conserver contains the self paloidal fields.

ACKNOWLEDGEMENTS

This work was performed under a cooperative agreement betwee e Turkisth n h Atomic Energy Authorit e Internationath d an y l Atomic Energy Agency, Contrac . 3823/R3/RBNo t .

194 REFERENCES

/!/ SINMANjS., SINMANjA., in Plasma Physics and Controlled Nuclear Fusion Research (Proc. lith Int. Con-f . Kyoto, 1986) Vol.2,IAEA Vienna (1987) 731.

/ SINMAN,S./2 , SINMAN.A. n Controllei , d Fusio d an Plasmn a Physics (Proc. 14th Europ. Con fMadrid. , 1987), , VolD 1 .1 ParEuropea, II t n Physical Society (1987) 465.

/3/ SINMAN,S., SINMAN,A., in Controlled Fusion and Plasma Physics (Proc. 15th Europ. Coni . Dubrovnic, 1988), Vol. 12B, Part II, European Physical Society (1988) 617.

/ SINMAN,A./4 , SIMMAN,S., ibid. . 621p , .

/5/ TAYLOR,J.B., Phys. Rev. Lett 3 (19743 . ) 1139.

/ COPPI,B./6 Fusio . t 1 al. e ,e 9 (1979,Nu 1 n ) 715.

171 PENG,Y-K.M., STRICKER,D.J. Fusio. 1 e 6 Nu ,(19862 n ) 769.

/S/ COPPI,B., et al., in Re-f . 6., p. 721.

/ PENS,Y-K.M./9 , 'Feature f Sphericao s l Torus Plasma f Ultro s a w AspecLo t Rati d Largan o e Elongation d 'Smalan ' l Tokamaks -for Future Fusion Energy Research' by Gross,R.A., et al., oral presentatio e IAEth A t a Technican l Committee Meetinn o g Research Using Small Tokamaks, September 9-12, 1985 Budapest, Hungary.

Next page(s5 )19 left blank PRELIMINARY RESULTS OF THE INVESTIGATION OF SLOW MINOR RADIUS COMPRESSIO HT-6N NO B TOKAMAK

Yexi HE, Cheng ZHANG, Jikang XIE, Linzhong LI, Pinjian QIN, Dequan GUO, Zhixuan PAN, Chuanbao DENG, Guoxiang LI, Hengyu FAN, Junyu ZHAO, Kong HUANG Institute of Plasma Physics, Academia Sinica, Hefei, Anhui, China

Abstract

The slow compression along plasma minor radius on HT-6B Tokamak bees ha n studied theoreticall d experimentallan y a tim n ei y scale several times longer thaenerge nth y confinement tim plasmaf eo . gooThera s d ewa agreemen t between experimen theoryd tan e result.Th s showed that during slow compressio plasma-wale nth l interectio- re s nwa duced state th ,f plasm eo n edgi a e regio s beenha n changed o thas , t plasma confinemen s improvetwa d efficientl plasme th d a an yparameter s were increased apparetly.

I. Introduction

e researcTh f adiabatio h c compressio f plasmo n Tokaman o a k have been carrie largelt ou d y both experimentall d theoretian y - cally^ since 1968. Tuman-Id Firsan t resultIC AT n so consisted with adiabatic compression law and demonstrated the seperatio t plasmho f o na frolimitere th m . However implee th , - ment of adiabatic compression along plasma minor radius in large tokamak meets some essential technological difficulties because of its requirement of very complicate power supply and magnet system to provide fast rise of a toroidal field. So that we are interested in slow compression (The toroidal field rise time is longer thaenerge th n y confinement tim plasmaf knows o ei t nI ). compressioe th o t thae du tn time longer than plasma energy con- finement highls timei t i ,y importan r plasmfo t a heating thaf i t plasma confinemen s improve i tcompressioe th n i d n phaser Ou . initial numerica experimentad an l lB show 6 studie T nH than so n i t compression phase the level of partical recycling reduced, the

197 stat plasmf o e a nealimitee th r r change o thas d t natur f plasmeo a confinemen s improvei t d efficiently d favourabl,an plasmo et a heating.

2. Theoretical mode numericad an l l simulation

D A transporsyste1- f o m t equations (including neutral parti- cle process) coupling with toroidal and poloidal field equations and MHD equilibrium equation has been developed and the process of slow compressio s studiei n d numerically.

9"e .! ! / n9IS _ }i£ ÎJË. JL_ "e 3ur = U ; b ax n u r~ "a^x" 3x~ ^x~ a 3x e r a 9x

, 3 3"e e .2 T Te^_ 2 r e 3T r u S 3TTe e n z e a 3x 3 nea x 3x^3x ' 3 ax

. 2Te 9^£ + _L 1_ /-- - 3Te^ '— Te-T-

-7. 2x10"^^ Zef£ n _ 9 . _ e 3 .._ 1 / , 3 2T 9T-j , 1 N ! 9T- = ——— T~(xn pX-iT~^e-v 3 —— —— ) T~C+ xD "5)+47— - 0n e n„e x 3x i3x ^2 p 3x 3x 3nea^x £ 9j_Ü _ i 3u a 2Ti li lZ ur p lazl T i r _n 3/2 i^ï n a 3x 3ax 3a 3x le ep

_ _L __ _|VK 1 3 K 11 3t'"-?~ 3x^c, "" " " "

_ \ B 3 3B_ Y , 620 _ -_ 0j> 1 C X ~x a I^x " x - "3 3/ x 3 2 '

e. 3x;

198 compressioe th s i r u ndensite velocityth s f neutrai o y, IL . l ratparticlee ionizationf th eo s i ,I nvjln anomalous i ,S= Y ^ s facto f Spitzeo r r resistance rate f chargth o e s i e,F exchange,D is anomalous diffusion coefficient. Xe» X- is the heat conductivity of electron and ion respectively. The transport coefficients are consided as follow: The resistivity is the Spitzer resistance multiplied by ano- malous factor Y:

conductivitn io e Th neoclassicals i i yX , electron conductivity diffusiod an e X n coefficien anomlouse ar determines tD i e ,x y b d psudoclassica ltimen te modneoclassicaf so r eo l value e definW . e

D as minimum of DA and Dg, D^ is Alcator scaling law, Dg is Bohm diffusion coefficient. The neutral particle distribution function f(v,x) is determined by:

(v|~ + SNf)- | NF(o(v-vi) + o(v4-v±))

decrease th s S,. i neutraf eo l particl y ionizatioeb d chargnan e exchange righe th tn I side. value th ,velocitf o en thermaio s i y l velocity before charge exchange, probability of each opposite direc- tion is 0.5 respectively. The boundary condition is: f(+a,v)=

N0<5(v+ v 0e flu) ,limitet th e neutra a x tha , th Nis s s t0i i rvl 0 ,v particle thermal velocity at boundary. We assume the temperature

of influx neutral particle is 10 eV. N0 is determined by recycling condition. The calculation was carried out using typical parameters for the HT-6B experiment, which are listed below. MajoR r radius 45cm Minor radius a 12cm

Before compressio 0 B n 4.2KG After compression Bmax 7.2KG

Raise time of toroidal field TC 3ms x 12 3 Line average electron density rTe 5.4 10 cm~

199 Figure 1 shows the plasma density profiles before and after compression thae se t n plasmca e a.On particles concentrato t e t thcor ho ey compressio eb d centranan l plasma density increased.

—— after compression —— before compression

eo

0 1. 8 0. 6 0. 4 0.0. 2 r/a

Fig. computee Th l e profiln d e before and after compression e effecth f particlo o t t e Budu t e diffusion, there remainw lo a s density plasme edgeth t , a aplasm a separated from wal n certaii l n extent. Figur 2 (a,be ) show e timth s e evolutio f electroo n d nan ion energy loss. One can find out that during compression the energy loss due to particle diffusion, electron thermal conduc-

VJ

- 45 . • 8 "" . : , " B O3 5C m 6 - u

4 1 / I 25 • /^*~^ 1 "Tf-jf' v• ^-~— . _^._—_ __ __ . _ ^ 2 - X'' — /1^// 15 • ^«__-»...... ^...... „.....~ ------^^^" ~ —_ -- - /'" i j i i j j _ 0 j ij i 5 1 ) t 1 __1 1 I vt^" 1 1 C) 2 0 41 6 8 8 6 1 04 2 (3 T(ms) T (ras)

'-!> ion temperature after conductivity ionization. - —The loss by increase of The loss by charge exchange electron temperature The loss by diffusion of ion after ionization The loss by ion conductivity —— The loss by radiation lose diffusioy Th b s . . . n of electron

Fig.time Th e2 d evolutioan e compute) th (a f no n io d electro ) energ(b n y loss

200 tivity, ionizatio d chargnan e exchange decreases efficientlyt I . is shown that because the interection of plasma with wall re- duces, the level of particle recycling is suppressed in compres- sion phase,that results in decrease of ionization and charge ex- change loss, on the other side the change of plasma profile causes e plasmchangth f a o e e edge statth t ,a e which e increasleadth o t s e of plasma confinement time as shown in Fig.3. From Fig.3 one can e thae shortese th t conpressioe th r . is £ bettee T n th e tim, th r is e

T(eV) 160 T (after)

120 : Te(before) 80 T^aftert ;____) 40 ! T-r (before)* "'""•-•"A. 0 r i i i i i l i i 0 0.2 O.A 0.6 0.8 1.0 r/a Fig.3 The computed profiles of electron temperature and ion temperature befor d aftean e r compression

n conclusionI ^ increase,T s graduall value th eo t yT nea o t r c durin a slog w compression, resultin efficiencn a n i g y comparablo t e

adiabatic compressions. Fig.k gives the simulation results with T, e 13 3 TI, Teo reaches up to 165eV, Iio - 63eV and neo «= l .3X10 cm~ 12 from their initial values Teo = 118eV, TIO = AOeV and neo = 9xl0 cm~3 respectively.

2.0

1.5

1.0

0.5 0 10 12 1A T(ms) Fig. e timTh 4e evolutio computee th f o n d energy confinement time with dif- ferent time of compression (TC=(!) ) ms 7 ) (A , ms 5 ) (3 , ms 3 ) (2 , 1.5ms

201 3. Slow compression experiment on HT-6B tokamak 3.1 The description of HT-6B HT-6B is a small tokamak with- following parameters R = 45cm, a = 12.5cm,

Ip = 10 - 50 KA, BT = 0.4 - LOT 13 3 "ne = (0.4 - 3.0)xl0 cm~ meetinr Fo compressioe th g n requirement e connecte,w e th d toroidal field paralle o coiltw n si l serie scoil8 eacs n si hha series to decrease the system inductance. Fig.5 shows the cir- cui f toroidato l field power supply e capacitoTh . r s bani 6 k for the background toroidal field up to 5.0KG with a flat-top time of 7ms. The toroidal field will raise to LOT within 3ms using bank 4,5 and keep a plateau of 10ms by the network C\, r verticafo s i . l Cj , 1>2»fiel L\ , ^3 d an wav o C eC"2 » head, then the vertical field will hold at a stationary value by the branch current of toroidal field circuit.

-i- C *3 « H»

Fig. e circuiTh 5 f toroidato l field power supply

202 3.2 Experimental results The background plasma parameters are:

BT = 4.2KG, 16KA, n = 7.0xl012cm~3, 0.5 ms.

At the 7th ms, BT jumps to 7.4 KG within 3 ms, Fig. 6 shows thT waveformB e . Fig.7-Fig.12 shoe oscillagrairth w . curvef so plasma parameters. One can see that, during compression, the 5 * 1 " — "

p havI o apparend n e an , V t changes e increasen , s from 7.8x10

3 to 9.0xl0cm~12 and kee a flat-topp e signaTh . Langmuif o l r

probe located at r=12.1 cm shows Iisat decreases and the amplitude of fluctuation falls greatly during compression. The plasma hori- zontal displacement increase up to 1.5cm outward because the feed- back system was not applied. After B-j max, the A// decrease

gradually and turns to inward. The Ip has a tendency of gradual in- crease. In Fig. 10, soft x-ray at the plasma centre has a considera- ble increase during compression 5.5cmt ,a keept ,i s constan- ap t proximatly, in the exrernal region, the SX intensity decrease.

BT(kG)

6 3 0 0 5 0 4 0 3 0 2 0 1 0 T(ms)

Fig.6 The waveform of toroidal field

A, .(cm)

2

0

-2 W 4 1 2 1 0 1 8 6 4 2 T (ms) Fig. wavefore Th 7 plasmf mo a horisontal displacement (with compression at 7 ms)

203 in oo X K

O. I > M

6 1 4 1 2 1 0 1 8 6 4 2 T (ms)

Fig.8 Waveform of loop voltage V., plasma current I >L p

U

O X X vO *^ • u u~i ^ n (with compression) t«o ••-X^ e •H Q) Hie e (withoun t compression) 6 1 4 1 2 1 0 1 8 6 4 02

Fig. 9 Waveform of the ion satuation current I. and line average electron density n£

ar.u 3.0'

2.0 •f before compression

A after compression 1.0

0 0.2 0.4 0.6 0.8

r/a

Fig.10 X-ray intensity profile

204 > oo m oo

> M 1

0 8 1 6 1 4 1 2 1 0 1 8 6 4 2 T(ms)

Fig.11 Waveform of horizontal displacement A.^,loop voltag , plasmeV a curren I t without compression 0 J6 p

13 3 ne(xl0 cm )

1.12

0.56 0 0 2 6 8 10 12 14 16 18

Fig.12 Waveform of line average electron density without compression

4. Discussion There are two significant characteristics in our compression experimentcompressioe th s i e vers .On ni y slow compressioe ,th n * 3ms/0.5ms)« £ /T tim T s abou( ei x time£ .T si t Anothe f e so th s ri toroidal field holds at a constant above 10ms after compression. Tabl eshowI variatione sth plasmf so a parameters compared with computation results.

s a 107eW V before compression 21e ~ d AT s Van ,e wa obot h using the SX emission analysis. The line average elctron den- OH sity increase a facto y b df 1.15o r coule W . d obtai0.5ms= g nT , c Tg = 0.72ms. From these results one can see compression improves the confinement of energy and particle significantly.

205 TABL . EVARIATIONI PLASMF SO A PARAMETERS COMPARE COMPUTATIOO DT N RESULTS

Parameters Experimental value Computation value

Teo /Teo 1-20 1.40

n I ~nH 1.15 1.17

/ TH 1.44 i.70

During compression positioe ,th plasmf no a moved outward,

showed the increase of ß value when compression. The Ha line intensity at r = 7cm had a little decrease, comparing with the variatio Langmuif o n r probe signaln concludca e ,plasmae w th e - wall interactio weakeneds nwa , maybe plasma colum s contractednwa , From the curve of SX emission intensity as radius, one can notice corresponding electron density profile sharpened after compression consistene th d ,an t positio 6cm~ r )( n consist with computation very much. conclusionn I , slow minor radius compression wittime th he scale much longe rimprovn thaca g nT e plasma confinement then increase plasma parameters apparently, especially to the plasma hot core. That provides a useful way to us to study the plasma confinement.

REFERENCES

Artsimovich. A . [1L ] , Nucl. Fusion 12(1972)5 ,21 ] Bol[2 al.t ,e , Phys. Rev. Lett 9 (1972).2 , 1495 [31 Berezovsk al.t e ,. L Proc . yE Europ.7 . Conf Contrn .o . Fusio Plasmd nan a Phys. Lausanne (1975)5 4 , Daughney. C. . C Bol. , K ] ,[4 Nucl. Fusion 17(1977)7 ,36 al.t Guir. e Me ,. e K Plasm ] [5 a Phys Contrd .an . Nucl. Fusion Research, 1978. V.I (1979), 335 ] V.E[6 . Golant, Plasma Phys Contrd A .an 1 . . No Fusio 6 2 . nV (1984), 77

206 LIST OF PARTICIPANTS

Dr. Xie Ji -kang Professor G.A. Wavratil Institute of Plasma Physics Chairman and Professor of Applied Physics Academia Sinica,6 2 P.O x Bo . Columbia University in the City of Wew York Hefei Anhui Mew York, M.Y. 10027 People's Republic of China USA Dr. Yuanxi Wan Or. StöckeJ , l Institut f Plasmo e a Physics Institut f Plasmo e a Physics Academia Siriica Czechoslovak Academy of Sciences 6 2 P.Ox Bo . Pod vodarenskou veri 4 Hefei, Anhui Province Praha 8, Czechoslovakia People's Republi f Chino c a Dr. Gerson Otto Ludwig . GüntheK . Dr r Institute de Pesquisas Espaciais Akademie der Wissenschaften der DDR Laboratorio Associad e Plasmd o a Zeritralinstitut für Elektronenphysik 5 C.P51 . 1086 Berlin 1220 o Doss CamposSa 1 do e P R , Hausvogteiplatz 5/7

Dr. L. Jankowicz Dr. Vian Shangjie Deputy Director Deputy Director Soltan Institut r Nucleafo e r Studies Southwestern Institut f Physico e s Otwock Swierk 05400, Poland Leshan, Sichuan People's Republic of China Dr. K.K. Jain Institute for Plasma Research o YupinHu . gDr Bhat, Gandhinagar 382 424 Director India Institut f Plasmo e a Physics Hefei, Anhui Dr. ZaceF . k People's Republi f Chino c a Institute of Plasma Physics Czechoslovak Academ f Scienceo y s Dr. J.S. Bakos Pod uodareskou vezi 4 Departmen f Plasmto a Physics CS-18 1 Prah1 2 Czechoslovaki, 8 a a Central Research Institut r Physicfo e s Hungarian Academy of Sciences . BenkadM . Dr a Budapest XII Labo Fusion COTA H- 1525 Budapest P.O.B. 49 N.C.R. B.P. 1017 Hungary Alger Gare, Algeria . H.HDr . Brevnov Dr. A. Sinman I.V. Kurchatov Institut f Atomio e c Energy Turkish Atomic Energy Authority 46 Ulitsa Kurchatova Ankara Nuclear Researcd han D-182 Moscow Training Center USSR Besevler Ankara, Turkey . A.GDr . Kirov Dr. S. Sinman I.ftl. Vekua Institute of Physics Middle East Technical University and Technology Electrical and Electronic Department USSR State Committee for the Utilization Plasma» Engineering Laboratory f Atomio c Energy Ankara, Turkey Sukhumi USSR Dr. J, Fujita Institute of Plasma Physics Dr, K.P. Vukolov Nagoya University I.V. Kurchatov Institut f Atomio e c Energy Nagoya 464 6 Ulits4 a Kurchatova Japan D--182 Moscow USSR

207 . OfoysoW . Dr v Dr. Jiao Boliang USSR State Committe Utilizatioe th r fo e n Southwestern Institut f Physico e s of Atomic Energy Leshan, Sichuan Staromonotny Per. 26 People's Republic of China Moscow USSR o DrGinGa .i D g Southwestern Institut f Physico e s . WinteH . Or r Leshari, Sichuan Institut für Allgemeine Physik People's Republic of China Technische Universität Wien Wiedner Haupstrasse 8-10/134 Dru BiaG . o 0 -1040 Wien Southwestern Institut f Physico e s Austria Leshan, Sichuan People's Republi f Chino c a Dr. I-". Aumayer Institut für Allgemeine Physik Dr. McKnight Technische Universität Wien US Departmen f Energo t y Wiednor Maupstrasse 8- 10/134 Washingto C 20'j4D n 5 A 1040 Wien USA Austria Dr. IM. Hershkowitz Ogaw. Y . aDr Departmen f Physico t s Technologie University of Wisconsin Max-Planck--Institu r Plasmaphysifü t k 1150 University Avenue Bolt^mannstrasse 2 Madison, Wisconsin 53706 1390 D--8046 Garchin i Münchebe g n USA I--RG . LuckhardS . Dr t Dr. D.C. Robinson Plasma Fusion Center Culham Laboratory Massachusetts Institut Technologf o e y UKAEA Cambridge, Massachusetts 02139 Abingdon, Oxfordshire 0X14 3DB USA UK Dr. GrossG . o . J.DMr . Fletcher Istituto Fisica del Plasma Atomic Energy Corporatio f Souto n h Africa CI\IR (Via Basini), 15 P.O. Box 582 20133 Milano Pretoria 0001, South Africa Italy

. P.Kw Dr .Ka Dr. David Thayer Institut r Plasmfo e a Research Science Applications International Corp. Bhat, Gandhinagar 382 424 USA India . AntoniDr o Guccillo . NascimentI o ENEA - Dipartimento FUSION Universidade de Sao Paulo Via Enrico Fermi, 27 Institut e Fisiced a 00044 Frascati Rua de Matao Italy Travessa R, 187 Cid. Universitciria 0550p o PaulCe Sa 8P S o Dr. A. Sen Caixa Postal 20516 Institute for Plasma Research Brazil Bhat, Gandhinaga4 42 2 38 r India i BingreDrSh , n Southwestern Institute of Physics Leshan, Sichuan People's Republic of China

o om

208