Bartiromo, R.

et al.

Igithkanov, Y.

Janeschitz, G.

Kerner, W.

Pogutse, O.

Schittenhelm, M.

Wagner, F.

Cordey, J.

MPG.PuRe

1041THE ALFVEN DRIFT-WAVE INSTABILITY AND THE SCALING OF THEEDGE TEMPERATURE AT THE L-H TRANSITION0. Pogutse, Yu. Igitkhanov“, W. Kemer, G. Ianeschitz“ and 1G. Cordey.JET Joint Undertaking, Abingdon, Oxon., OX14 3EA1 UK.*ITER Joint Central Team, Ioint Work~Site, D—85748 Garching, Germany.ABSTRACTThe stability analysis of Alfven drifi type modes leads to a threshold condition for the L—H transition.This condition yields the scaling for the edge temperature, which is in agreement with theexperimental results.1. INTRODUCTION, The measurement of the electron edge temperature To and density no on JET and other tokamakssuggest that there is an ideal @[2 beta threshold for the onset of Giant ELM’s. Furthermore, thedata reveal also the existence of a second beta threshold (below the ideal ballooning limit) for the L—Htransition and a. third threshold for the onset of type III ELMs. These findings suggest that the Alfvendrift—Wave instability (ADW) plays an essential role in the edge plasma dynamics. There is strongexperimental evidence that the main plasma instabilities change from ion temperature gradient modesin the plasma core to electron drift modes near the plasma edge. The stability theory gives the resultthat with increasing piasma pressure, the Alfven waves mix with electron drift waves and suppress theunstable long wavelength perturbations, which are dominant in the transport,2. DISPERSION RELATION AND DIMENSIONLESS PARAMETERSThe expression for the ion density perturbation follows from the kinetic equation:. ew‘ ra—aB.- _ 2) » eqo' m—m_, 1n»: —1+~,q_.__'ex ("II (2] (v J 'n =_[_1+____,___. j”’ TOi <[ w .. kllvll P ) 0 ) fa; H I To, a) l + z DThe perturbed electron density follows from the electron hydrodynamic equations:a) the linearised electron density equation is:"'e 9W‘_ _ l 'n “Mir—“invall'0 02h) the parallel component of the electron motion equation yields:. .Tl +"_‘a.= ei”'_fi_'_h2_"nl+g vll';TI. "0 To. kllc Tu. VT-a) +iv,where R are the dissipative terms R = -————-— ;k u" r:e) Ampere’s law gives:1042“1'” _ ”'cT0: v%£d) The temperature perturbation follows from the energy equation:.2 2I‘HVTE T' 6133' 2 F—--— rwvrTOE=—ku"ug'(r0- w+fV¢ 70¢ 3From these equations the expression for the perturbed electron density is derived:on (kn'vr'.k:5'} .1+2_(‘”"‘3’2W -T)‘5n _" [w—m.P+:ii-ki52] 3 maiwkflzvg. ep‘4— 0 2 2 Tm (klvA-ir ) -1+2_ m .E o.[w«m.p+6-kf52] 3wéi-kfv},Here a). = “(055,113,3 I’eBo)~€ln(nD)/o‘ir is the electron drift frequency for the density, lq is the)1/2longitudinal wave number, VTe = (T09 /me is the thermal electron velocity; v, is the electroncollision frequency and 5 = claim is the collisionless skin length, (T)=a1+ive. We define thedimensionless fi‘equenc and transverse wave number as Q = a) - x f c k = k 'Y 0 p 5, J. p s ,where as = (Te /M ) ”1 is the sound speed; p s = es la) Bi is the ion Lannor radius andTc the electron temperature. The relevant dimensionless parameters in the problem are:mammal/831mm), v: hire/ctp = which, lc‘, q. = d lung/d inn“), I=TgelTOI-,The quasineutrality condition n}: )1} yields the dispersion relation for the Alfven drift wave instability.It is an algebraic equation of fifth order with complex coefficients containing five independentparameters: [3 U , V , ,u , n . , r , A more detailed analysis shows that after additionalrenormalization:o” =Q/‘fiI—-, kflzk/fi., fln=fio/,u, V" = v/JI.the ADW instability can be characterised by only two dimensionless parameters the normalisedplasma beta and the normalised collision fiequencyHa HA ”Ifl~=flu=[M,] 4“.e 1 ’ V“: v = [214,] My.”lit in B, kw?” :iy m 1,1rHHere x0 characterises the pressure scale length, l is the mean free path and k” is the parallel wavea anumber. All quantities are taken near the separatn‘x.3. TRANSPORT COEFFICIENTSThe difi'usion and thermalconduction coefiicients for the ADW instability are evaluated as:to, _— 3 z =D = - =__ a: .s F)“ xi<flntvnl)’ K” Znofixiffi..V.,)10431/2m 1+(Va/V<r)zx:VLi’—-[—-——]——v[livir + (vn lvn)‘”]mwherev” = t /(l + fin”: (SeeFig.l-Fig.2).4. L-H THRESHOLD CRITERIONThe analysis of the turbulent coefficients shows that the transport decreases for5,, > 1 + v.3“.This condition yields the scaling for the edge temperature at the L «H transition, The estimate of X4;(inside the separatrix) is derived fiom the assumption that the turbulent transport coefficients arecontinuous across the separatrix and that the convection (collisionless) or conduction (collisional)model in the SOL applies. ’5. COMPARISON WITH THE EXPERMENTSThe temperature inside the separatrix is approximated by: T(a — Ax) = To .04. Ax ”a ) 4 Thenwe obtain for v,‘ > I:T”, (a e Ax) = 32‘6-A“”5J’Sng,’g”°B,,’;5Ij/jaA7” -Axm (theory)1T‘“”(a _ 2 cm) : l4 Sugwilh B ,°-'=3i-‘1;-5=31% [e V ] (ASDEXUP)andforvn<lzTEV (a “ Ax) = 23-3‘A ‘1’25’101-9‘Bor1smai42‘AxmThe general expression for T.v reads:' -osfl . _ f“T” (a _ Ax) = c, L£MJ .Axm,/3 2"me amwhere f1=(i+2/5.v1)/(i+vi), f2=(l+3fIO-Vl)/(l+vl), f3=(1+vt)/(1+7/1o.v1),.f4=(1+3/5-v1)/(l+vl) and “=0.” /n‘,)“”°, ,1" :(Bw-IW x31)”,31 = cuA ”ls-"’agnyl This formula contains two parameters CT, (:31. The theory gives c1=23.3,ca;='1.4. The fitting with the ASDEX experiment gives 01:10, cm=0.7. The same values are used forall the other tokamaks too. The comparison theoretical prediction with the experimental data [ITERInternal Memo, Yu.Igitchanov at. al, No 117MD82970423F1 (1997)] is given on Figs. 3 - 6.6. CONCLUSIONSThe main conclusions are. 1) the Alfven drifi model predicts that the turbulent transport is suppressedwhen the conditionzfin > 1 + v,“ is satisfied; 2) the transport coefficients change their dependence onplasma parameters from x ~ Tum/no“5 (for B“ < vi“) to x ~ now/Tom”3 (for B“ > VI”); 3) the Alfvendrifi model predicts the edge temperature scaling in agreement with experimental findings.Furthermore, the qualitative character of the scaling depends only weakly on the SOL transport.Ta(8V)T.(W)1044flntA)3_.10 E-10 0 10-8n (on)F79. 1 Fig. 2Fig. 1. The dimensionless transport coefficient 3 . Fig. 2 The asymptotic properties of :5.ASIDE! UP: Edge oparah‘onal Space DIII—Dr L—H transitlan. wu" H-mode \\\ v Early H-rnodzG lypa | ELMS‘); —— Dn‘h-Aflven inst.5 0 ELM—fraa 3% 0vods - °\' \490— -, H-moda 06;) g 400 ‘.E III ELM’-'. 8WD“ 0 s 53 \\ v v V13 \\ v v v Vt; \ vo w ",_ x250 " v“ \\ v v v y ,.‘:"~:1_—. 17:1: 1‘ 'Y '1'' 30 l l t L aD 2 4 B E 10 1 2 3 4 5n mum-a low5=0.1 n 10‘9"“:( ) high a = 0.1 pmasm { )'3 LwH A ball. at TD 0 'T‘ypc-l ~v hall. at law 5 I Compound I: Tl-H Fig. 4A ball.at high 6 ‘2 Densityllmtt --- -..—H DriflrAJvan. name! .39): 0 Type HtFig, 3 1000 JEF: L—H transman ' L _ H (2TJT—GO: L—H translfion 7 . )—— Theory: arm-Amen inst. ‘" L‘H Dr'fl'm’fl" (Z a 1)EDG— 0 Experimental data 800400:““‘ N J S? 600n \ E.-5 _‘ 1:200" 400g én t | 5 arm Q0.? 0.5 0.9 1.0 0.5 3.0Denslty(1019 m—a) n (1oIs urn)Fig. 5 5‘9- 5Fig. 3 -6. The theoretical (dashed lines) and experimental (points) scalings of thc edge temperature over edge densityfor difl'erent tokamaks.

English

The Alfven Drift-Wave Instability and the Scaling of the Edge Temperature at the L-H Transition

The Alfven Drift-Wave Instability and the Scaling of the Edge Temperature at the L-H Transition

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