r'lasmo Thqaics on2 Cormol l e i ?mion Vo1.28, 3 0 . I A pp.179-190, 1986 P r i n t e d i n Great B r i t a i n

07L1-3335/86$3.00+ .OO 0 1 9 8 6 I n s t i t u t e of Phys ics and Pergamon Dress Ltd.

ENERGY CONFINEMENT AND PLASMA HEATINti DURING LOWER HYBRID EXPERIMENTS IN FT

F'. A l l a d i o , E. Barbato, G . B a r d o t t i , R. Bart i romo, G . Bracco, F. Bombarda, G. Buce t i , P. B u r a t t i , A . C a r d i n a l i , R. Cesar io , F. C r i s a n t i , R. De Angel i s , F. De Marco, M. de P r e t i s , D. F r i g i o n e , R . G i a M e l l a , M. G r o l l i , S. Mancuso, M. Marinucci , G . H a z z i t e l l i , F. O r s i t t o , V . P e r i c o l i - R i d o l f i n i , L . P i e r o n i , S. Podda, G . B . R i g h e t t i , F .Romanel l i , D . S a n t i , F . S a n t i n i , G . Tonin i , A.A. T u c c i l l o , O.Tudisco,

G. Vlad and V. Zanza

Associazione EURATOM-ENEA s u l l a Fus ione , Centro Ricerche Energia F r a s c a t i C.P. 65 - 00044 F r a s c a t i , Rome, I t a l y

ABSTRACT

power up t o 450 kW has been i n j e c t e d i n t o t h e plasma of FT i n t h e e l e c t r o n h e a t i n g regime (n 5 5X1Ox3 ~ m - ~ ) producing e l e c t r o n and i o n tempera ture i n c r e a s e s of about I keV and . 5 kef r e s p e c t i v e l y wi thout s i g n i f i c a n t enhancement of Z e f f . A d e n s i t y i n c r e a s e i s observed due t o an improvement of p a r t i c l e confinement time. An energy ba lance a t i n t e r m e d i a t e power l e v -

= 300 kW) i s c a r r i e d o u t f o r two d i f f e r e n t t y p e s of d i s c h a r g e s , one wi thout sawtee th E;e?%er wi th cawtee th . The ba lance shows t h a t i n o r d e r t o account f o r t h e t o t a l i n j e c t e d power one has t o assume e q u a l e l e c t r o n thermal c o n d u c t i v i t y f o r t h e OH and t h e OH+RF phase. The energy confinement- t ime does n o t v a r y from i t s ohmic va lue f o r b o t h d i s c h a r g e s . F i n a l l y a n i n v e s t i g a t i o n , a t n above t h e d e n s i t y l i m i t , of t h e r a d i a l source of t h e f a s t i o n t a i l s and of t h e c h a r a c t e r i e s t i c s of t h e Paramet r ic Decay I n s t a b i l i t y i s p r e s e n t e d .

KEYWORDS

Tokamak; plasma h e a t i n g ; waves i n plasma; lower hybr id h e a t i n g ; confinement.

INTRODUCTION

E l e c t r o n h e a t i n g by Lower Hybrid (LH) waves can become an impor tan t method f o r plasma h e a t - i n g f o r t h e r e a c t o r because of t h e a v a i l a b i l i t y of sources ( f - 4-8 GHz) and t h e advanta- geous coupl ing s t r u c t u r e by waveguides.

Bas ic phys ics i s r e l a t i v e l y simple. As i n CD experiments t h e LH wave c r e a t e s an e l e c t r o n t a i l by Landau i n t e r a c t i o n . This t a i l r e l a x e s on t h e bulk e l e c t r o n s v i a Coulomb c o l l i s i o n s . I n t u r n t h e bulk e l e c t r o n s g i v e energy t o t h e i o n s i n t h e same way.

E l e c t r o n h e a t i n g was observed and s t u d i e d i n a number'of experiments a s JFT-2 ( Imai and o t h e r s , 1980), VEGA (Gowezano and o t h e r s , 1962), A l c a t o r C (Porkolab and o t h e r s , 1984) , ET ( A l l a d i o and o t h e r s , 1984a; A l l a d i o and o t h e r s , 1985). 02 Alcator C approximately 1.0 MI4 of n e t RF power was i n j e c t e d i n t o a deuter ium plasma a t n - l X l O I 4 wi th tempera ture rises of about 1 keV. A s t r o n g i n c r e a s e of 2 > 500 kW. On FT t h e maximum n e t power i n j e c t e d was P with an i o n tempera ture i n c r e a s e of about .5 keV (Fig . 1). 8 i m p o r t a n r i n c r g a s e of i m p u r i t i e s was observed; a com- mon f e a t u r e of t h e FT h e a t i n g experiments i s an i n c r e a s e of p a r t i c l e confinement time. During t h e RF p u l s e t h e r e i s a d e n s i t y rise accompanied by t h e decrease of i o n i z a t i o n r a t e s measured by t h e D > 5x10'' cm-3 (r~/%52) t h e i n t e r a c t i o n os t h e wave wi th t h e e l e c t r o n ? d i s a p p e a r s (Al lad i%, 1964b). Energy 1s ab- sorbed f i r s t by i o n s i n t h e range 5 X 1 0 l 3 < n < l.2x1014 ~ m - ~ whi le a t higher d e n s i t i e s Paramet r ic Decay I n s t a b i l i t i e s (PDI) near t h e &?ace of t h e plasma prevent any p e n e t r a t i o n o f t h e wave (Al lad io and o t h e r s , 1 9 8 4 ~ ) .

waq a l soeobserved f o r P W . - 450 % p a t n I

emiss ion a t d i f f e r e n t t o r o i d a l l o c a t i o n s . For n

F. Alladio e t al.

I 0.6 -

0.4 - ,

0.2 c I I

n 1 I 1 I I I I 1 " 200 400 EO0 800 1000

TIME (ms)

Fig. 1. Time evolution of ion temperature measured by CX (B = 80 kG, I 3 300 U, n = 4+5x1013 ~ m - ~ , PE - 450 kW) P

In this paper we first report the results of an extensive study of the power balance per- formed in discharges with and without sawteeth. These studies were done with a net power of 280 kW corresponding to .5 f . 7 5 POH. ,The main results are that the power deposition profile is rather peaked and the energy confinement time does not decrease even assuming 100% ab- sorption. Thereafter we show the main results of the experiments performed at higher densi- ties, namely the spatial and energy distribution of the ions and the characteristics of the PDI.

In the first chapter we give a short description of the heating apparatus and of the way the principal measurements are carried out. Subsequently the particle balance is addressed and we show the improvement of the particle confinement time. In the third chapter the heating experimental results are shown and the results of the analysis of the energy bJlance are presented and discussed. Finally the main results on ion distribution and PDI are exposed.

APPARATUS AND DIAGNOSTICS DESCRIPTION

The LH heating system on FT consists of two launchers, 90° and 180° away from the poloidal limiter in the plasma current direction. Each launcher is a 2x2 Waveguide grill, the single waveguide being 7.1 cm high and 1.5 cm wide. Each array is fed by a 2.45 GHz Varian kly- stron. During heating adjacent waveguides are phased at n relative to each other. A sym- metric n,, spectrum is generated with n,, ranging from 1 . 2 to 3 (Alladio and others, 1984~). Up to now about 450 kW of FS power have been injected into the plasma with good heating rates (Alladio and others, 1985):

A -Ii ni 'fi r l = - 20 ~ m - ~ , eV, kW]

pRF

where i is the species index

Energy Confinement and Plasma Heating in FT 18i

The electron temperature profile and Zef was measured with a soft X-ray PHA system collect- ing spectra in the range 2-15 keV. The5-ray measured temperatures were in good agreement with those measured by Thomson scattering when this system was operating prior to the in- stallation of the second grill, both for OH and OH+RF regimes. Ion temperature profile was reconstructed with a code fitting the radial spectra and fluxes of neutrals measured by a movable CX analyzer. The analyzer looks at the plasma with a small angle around the direc- tion perpendicular to B and detects neutrals coming from ions that are trapped in the rip- ple when they are acce1:rated by the wave. Radiation profiles were obtained by a bolometer looking through the same chord of the neutral particle analyzer. Line emission is monitored by an W monochromator and by several D measurements at different toroidal locations (one of them at the limiter).

PARTICLE CONFINEMENT

An increase in electron density is regularly observed-during RF pulses for discharges in the electron heating regime. In this range of densities (n < 5 ~ 1 0 ' ~ ~ m - ~ ) most of the recycling occurs at the limiter. Figure 2 shows that the D atethe limiter decreases substantially; other D monitors around the torus having only &or variations. The brigthness of Fe XVI line (A'= 335 8) increases approximately by 20 + 30% for Pw c 450 kW. We can compute the particle confinement time T from the particle balance

P

where S, n and n are the volume average of particle sources, density, and density time deri- vative. Even with the pessimistic assumption that the whole intensity increase of iron and oxygen lines is caused by increased influx, the 't improvement is about 1.5 f 2. This pheno- menon observed since the first experiments of glectron heating on JFT-2 (Imai and others, 1980) has been found to be present also in Versator (Porkolab and others, 1985).

RESULTS ON HEATING AND ENERGY CONFINEMENT

The main characteristics of the discharges without (type A ) and with (type B) sawteeth are reported in Table 1 (note that B discharges are at 60 kG). The time evolution of the princi- pal parameters are shown in Fig. 3 and 4 for A and B discharges. The major difference is the

TABLE 1 Parameters of type A and type B discharges

TYPE A TYPE B

OH RF OH RF

80 80

280 300

6.8 6

3.3 4

2.0 3.0

-.75 -1.2

-2.2 -2.2

0 280

440 380

150 240

0 0

60 60

. 310 330

4.6 4.4

3.4 5.2

1.75 2.4

. 9 7 1.4

-2 -2

0 280

570 500

210 350

1.9 3.8

182 F. Alladio e t a l .

8 1 1

I i- a ’ i

I 1

I I * 4 \ I

- 0 U 1

2 c ~

I t

01 I I I I I I I I I

4 .

m i 3 E

U I

0

I = 2

n

3:\ 2 -

b )

1 - -- I

- 1 -

1 I

0 ~ ! R I 1 I

200 400 600 800 1000

TIME i m s ) F i g . 2 . Fe XVI emiss ion , Do emiss ion a t t h e l imiter , l l n e average d e n s i t y ,

f o r a t y p i c a l d i s c h a r g e (I1 = 80 kC, I = 300 U, PW = 280 kW). P

h i g h e r v a l u e reached by t h e e l e c t r o n d e n s i t y i n t y p e B d u r i n g t h e RF p u l s e , t h e d e n s i t y re- maining h i g h e r a l s o i n t h e p o s t h e a t e d phase . F i g u r e s 5 and 6 show t h e e l e c t r o n and i o n temp p e r a t u r e p r o f i l e s b e f o r e and d u r i n g LH i n j e c t i o n f o r type A and B. I n t y p e A t h e e l e c t r o n tempera ture p r o f i l e i s a l r e a d y peaked i n t h e ohmic phase and t h e T i n c r e a s e (- 1 keV) i s well l o c a l i z e d i n t h e c e n t r a l p a r t of t h e plasma i n c r e a s e i s s m a l l e r b u t t h e p r o f i l e i s q u i t e broader . I n type B t h e p e r i o d of t h e sawteetf; i n c r e a s e s when t h e RF power i s a p p l i e d . F i g u r e 7 shows t h e e v o l u t i o n of t h e sawtee th as recorded by a s o f t X-ray d e t e c t o r looking through a c e n t r a l chord. The m o d i f i c a t i o n of the sawtee th o c c u r s i n a v e r y s h o r t time a f t e r t h e RF swi tch on; t h i s can be a s c r i b e d t o a modi-

whi le i n type B $ ischarge t h e c e n t r a l T

Energy Confinement and Plasma Heating in FT

0 I I I I I I I I

I - - I I I I 1 I I I 1 0

2.5

2.0 - 1

5 1.5 - - 1 +

T 7

1 1

T

-

200 400 600 800 1000

T I M E i m s i

Fig. 3. Time evolution of current (a), line average density (b), electron (points) and ion (line) temperature (c), for type A discharges.

184 F. A l l a d i o e t aZ.

2 -

1 -

I I I I I I I I 0

1 - I

2.0 - I

- +

1.5 -

T

i

l-

I I

1.0

0.5

2 00 400 600 800 1000

TIME i m s )

Fig. 4 . As Fig. 3 for t y p e B discharges

Energy Confinement and Plasma Heating i n FT I85

I

T l teV 1 ~ i I

3r

T \ keV 1

3 T

2

1

0 -20 -10 0 10 20

r i c m

Fig. 5. Electron and ion temperature profile 'before (a) and during (b) RF for type A discharges

fication of plasma resistivity due to electron tails rather than to an increase of electron temperature, which occur s on a longer time scale.

To perform the energy balance we have to solve the following equations along the radius as- suming steady state conditions:

aEe E 0 0 = Pin - Pei - Prad - Pxe

aEi - at P O = P . - P c x - a P . e l X I

i? 2s::.+u

186 F. A l l a d i o et al.

T ( l teV

2

a )

-20 -10 0 10 20 r i c m )

F i g . 6 . As F i g . 5 f o r type B d i s c h a r g e s .

where P and P . a r e t h e e l e c t r o n and i o n thermal l o s s te rms , t h e meaning of t h e o t h e r terms b&g the’hsual. P . i s assumed of t h e Chang Hinton (Chang and o t h e r s , 1982) t y p e w i t h a a m u l t i p l i c a t i v e c 6 k t a n t .

During t h e OH phase , b e f o r e t h e FS, s t e a d y s t a t e c o n d i t i o n s a r e well v e r i f i e d and one can s o l v e t h e ba lance e q u a t i o n f o r P wi th t h e u s u a l hypothes is (Z = c o n s t a l o n g t h e r a d i u s , 3 - T 3’2). The t o t a l i n p u t poder Jd3r Pin matches t h e measures ohmic power wi th a v a l u e of Ze c?f about 2 i n agreement wi th t h e X-ray measurements. Moreover it t u r n s o u t t h a t t h e i o n bafance e q u a t i o n y i e l d s f o r t h e anomaly f a c t o r a , a v a l u e between 1 and 1.5.

Problems a r e more s e v e r e dur ing t h e E. In t h i s c a s e we have two unknowns P . n and P . As a m a t t e r of f a c t d u r i n g t h e hea ted phase of t h e d i s c h a r g e , it i s not p o s s i b f e t o rerzte t h e e l e c t r o n tempera ture w i t h t h e c u r r e n t d e n s i t y and i n a d d i t i o n t h e LH power d e p o s i t i o n i s n o t known. Moreover s t e a d y s t a t e c o n d i t i o n s a r e n o t well v e r i f i e d f o r plasma d e n s i t y and c u r r e n t which i n c r e a s e d u r i n g t h e FS p u l s e . To s o l v e t h e ba lance e q u a t i o n we make t h e assumption t h a t t h e e l e c t r o n thermal c o n d u c t i v i t y x does n o t change from t h e OH t o t h e RF phase ena- b l i n g us t o s o l v e f o r Pin. In t h i s c a l c u f a t i o n we have taken i n t o account a term due t o ne,

f f .

Energy Confinemert and Plasma Heating in FT

6 /

187

I I ' I 3 ' 394 396 398 400 402 404 406 408

TIME ( m s i Fig. 7. Evolution of central sawteeth recorded by a soft X-ray detector.

the inductive term Li and we have assumed iI negligible. The validity of these assumptions is tested comparing sd3r P. with the total power injected into the plasma as derived by electrical and W measuremenis. The results of this analysis are shown in Table 2 . Again the ion balance gives a value of - 1 for U indicating that ions behave neoclassically also in presence of the LH waves. The agreement between the calculated and measured power with xe time is given by the expression -. - xeOB makes us confident that our hypothesis are close to reality. The energy confineme!!

4n2 R 3 / 2 J: (neTe + niTi) r'dr' rE(r) =

Pin(r) r'dr'

Table 2 Results of the power balance for type A and type B discharges

TYPE A TYPE B

Before During Before During R€ RF RF RF

(kW) 440 330 570 45 0 'OH P (W 0 280 0 280

E(e 1 (kJ) 3.5 4.6 2.9 5 . 0

E(i+) (kJ) 1.5 2 . 7 2 .1 4 .0

5 7 .3 5 .0 9 . 0

RF-

E~~~ rE (ms) 11.5 12 9 12

n 3.3 4 3 .4 5 .2

I aa F. A l l a d i o e t oz.

where the energy stored in the plasma is computed using a parabolic profile to the power 1.5 for the density, as usual for FT in this regime. Previous measurements with Thomson scatter- ing did not show any variation of density profile with RF power up to 200 KW. In any case a sensitivity analysis of the energy balance varying the exponent of the density profile from 1 to 2 exhibits variations of the results within the error.

Given the agreement between calculated and measured power, the results on confinement are rather model independent. It must be noted that if the absorbed RF power was less than the coupled one, this would imply a decrease of x and an improvement of the confinement. The increase of rE for the discharges of type Beis roughly proportional to the increase of plasma density as it occurs in OH discharges.

OPERATION AT HIGH DENSITY

Increasing the density above the density limit, RF power is absorbed by ions. Also in deute- rium discharges, the LH waves interacts with the minority of H ions present in D plasmas (Alladio and others, 1984b). In order to get information about the wave propagation into the plasma and the wave ion interaction the ion tail radial profile should be known. Unfortuna- tely the interpretation of space resolved CX measurements is difficult because the ripple trapped perpendicular tails are affected by the vertical drift. This makes the energetic ions having long free path to be observed in regions different from the one where they are born. In order to analyze the radial CX measurements a code (Barbato and others, 1985) has been developed which computes the neutral emission including the ripple trapped ions.

Measurements were performed at n = lX1014 ~ m - ~ and n = 1.4X1C14 Unfortunately no measurement just above the densify limit has been don: yet. The main rssults are: a) the ions source is outside r = 15 cm for n = lX10'4 c w 3 and r = 17 cm for n = 1.4X10l4 ~ m - ~ ; b) for the lower density case, shown i% Fig. 8, the minimum resonant enzrgy E is - 6 keV and - 2.5 keV for D and H ions respectively. This implies an U,, of about 6 in agyeement with the value needed to explain the electron heating results; c) most of the tail energy is found in the H tail thus confirming its relevance in the occurrence of the density limit.

At higher densities PDI occur (Cesario and others, 1985) Fig. 9 shows the frequency spectra of the ion cyclotron sidebands in deuterium plasmas at n - 330 kA where up to 15 harmonics are distinguishable. When the processeis so strong no effgcts on the

1.5X1Ol4 c ~ I - ~ , I

, 10s L . --

0 10 20 30 40 50 ENERGY \ k e V )

I L U l o $ , 1

0 10 20 30 40 50 ENERGY : ke l '

Fig. 8. Code simulation of the measured H (a) and D (b) fluxes at 3 different radii. Full lines are obtained with a broad deposi- tion profile 0 < r < 20, dashed lines with a peripherical one r > 15 cm.

Energy Confinement and Plasma Heat ing i n FT i 89

plasma a r e observed. When t h e e x c i t a t i o n of PDI is mi lder (no harmonics beyond t h e minimum o f t h e peak convolu t ion curve of F i g . 9 ) i o n p a r t i c l e i n t e r a c t i o n and neut ron emission a r e s t i l l observed (Cesar io and o t h e r s , 1985). The d e n s i t y t h r e s h o l d f o r t h e occurrence of PDI i s observed t o i n c r e a s e wi th plasma c u r r e n t (Al lad io and o t h e r s , 1984c; Cesar io and o t h e r s , 1985) (F ig . 1 0 ) . This i s b e l i e v e d t o be connected wi th a m o d i f i c a t i o n of t h e plasma border ( P e r i c o l i - R i d o l f i n i , 1985).

0 , 1

I I 1 , I \ , !

600 800 2000 2200 2400 2600

FRERUENCY ( MHz 1

F i x . 9 . The f r e w e n c v s u e c t r a of t h e i o n - c v c l o t r o n s idebands i n deute- - - ._ - rim plasma (n = 1.5x10'4 ~ m - ~ , I = 330 U, B = 80 kG, PRF= = 100 kW). e P

1.5

1.0

0.5

200 300 400 500 6 00 700 10 I k A l

F i g . 10. Threshold d e n s i t y nth f o r t h e ion c y c l o t r o n harmonics v s c u r r e n t I .

P

CONCLUSIONS

R€' power up t o 450 kW has been i n j e c t e d i n t o t h e plasma o f F? producing ion tempera ture i n c r e a s e s of about .5 keV. No s i g n i f i c a n t enhancement of 2 was observed. A doubling of t h e sawtooth per iod was observed a t n - 4X10'3 and PRF - % kW. A r a d i a l energy ba lance was c a r r i e d o u t measuring t h e e l e c t & and ion temperature p r o f i l e s i n d i f f e r e n t sets of t a r g e t plasmas. The main conclus ions a r e : 1) t h e d e n s i t y i n c r e a s e i s due t o an i n c r e a s e of t h e p a r t i c l e confinement t ime; 2) i o n l o s s e s do not c o n t r a d i c t n e o c l a s s i c a l theory ; 3) we can account f o r a l l t h e power i n j e c t e d i n t o t h e plasma s imply assuming t h a t t h e e l e c t r o n thermal c o n d u c t i v i t y i s t h e same i n t h e OH and OH+- phase: less a b s o r p t i o n would imply an improvement of confinement; 4 ) t h e energy confinement time does not vary from t h e OH t o t h e OH+RF regime t a k i n g i n t o account t h e d e n s i t y v a r i a t i o n and a l l t h e power i n j e c t e d i n t o t h e t o r u s . The l e v e l of RF power i s only moderate (Pw - 300 kW) but it i s of t h e same o r d e r a t t h e ohmic power.

190 F. A l l a d i o cZ al.

At densities somewhat above the density limit (i 2 1014 ~m-~), it was deduced that the ion tails originate in the outer part (r > 15 cm) of the plasma column. When strong PDI (- 15 harmonics) are present, no wave particle interaction is observed, even if ion tails are ob- served when PDI are milder (- 5 harmonics). The density threshold for PDI increases with plasma current.

REFERENCES

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