Alexander, M.

Buttery, R.

Gruber, O.

Kass, T.

Maraschek, M.

Pena Hempel, S.

Sandmann, W.

Sesnic, S.

Sokoll, M.

Stäbler, A.

Zehrfeld, H.

Zohm, H.

English

MPG.PuRe

0001[3-Limiting Phenomena in ASDEX Upgrade1‘1, Zohm. M.Alexander. ‘R,. Buttery, S. de Pena Hempel, O. Gruber, ‘T.(_3. Hondor.T. Kass, M. Maraschek. W. Sandmann. S. Sesnic. M. Sokoll, A. Stablcr.'H.R. Wilson. IIP. Zehrfeld, ASDEX Upgrade Team. NBI—GroupMP1 {fir Plasmaphysik. EURATOM Association, 17785748 Garching. Germany' UKAEA Government Divison. Fusion. Culliam, Abingdon OXMSDB, UK1.) IntroductionFor future fusion reactors with magnetic confinement it is necessary to maximize the fusionpower output for a given magnetic field, both for economic as well as for technical reasons(cg critical holds ofsuperconductors). This directly translates to a high stored energy andthus to a necessary high value of d = 2,10 < p > /B2 [1).1n toroidal magnetic fusion devices such as the toltoinak or the stellarator. different factorsmay limit the achievable ,5. Two main distinct reasons are the equilibrium limit (when theShafranov shift approaches the minor plasma radius) and the .13-limit due to MHD activity.The equilibrium limit results in Jpn“. x 1/6 and can thus be avoided by chosiug a properequilibrium configuration. In a tokamalt, the second limit has been shown to roughly scalelike 3”.“ m Ip/(uB) ~ (/q [‘2] This so-called Troyon-limit led to the definition of 5N =3/(Ip/(uB)). The paper focuses on the MHD phenomena giving rise to the 13»limit in ASDRXUpgrade. a medium size tokamak with ITER relevant geometry [3].2.) Operational AspectsThe heating power necessary to reach a certain VB depends on plasma geometry and pa-rameters. For an energy confinement scaling TE ~ 0.05 x Hl'pRan/Pl” (derived from theJET-DULD scaling [4] with H—inode multiplier H), we obtain for ASDEX Upgrade (If. :1.05 m. a = 0.5 m. I: : 1.6) P(fiN) : 2.15(BN/H)213,2. With an available heating power of10 MW, using tin-m,” z 3 and H r: 2, D-limit studies can only be conducted at B, S 1.3 ’1'unless improved confinement occurs. Thus. our database is acquired at B! s 1.9 T.For the discussion of neoclassical tearing modes, the collisionality u“ = q/(au) is animportant parameter. It scales like u" ~ (n/T2)(qa/(2) whereas 53 ~ nT/BZ. Thus. atconstant ti. we find 11' ~ (ana/B‘Hq/e’) and we have to use a scaling u N Bd/fl/nl/3 tomatch [TIER in the dimensionless numbers if. 11”.: and (1. For I'I‘ER parameters Bt : 5.7 T.n = 1.25 X1020 m’3 and a = 2.8 m, we find that an ASDEX Upgradc shot at 1.5 "I‘ shouldbe run at. n : 0.38 X1070 rn'a. The lowest possible density in ELMy Hemode is proportionalto 17,, which itself is fixed by the requirement q : 3. For the example above (correspondingto I}, = 0.8 MA) the minimum density is about 0.5 x 1020 m‘3. Therefore. we cannot run atexactly the ITER dimensionless parameters: at the right (1, the collisionality is higher by afactor of (0.5/0.38)3 : ‘24. Increasing the density will increase this factor ~ n3.The B-liuiit may either occur as a saturation (W does not follow a rise in P), as. a fl-drop(W decreases with increasing P) or as a [i—limit disruption. It has been shown before that inASDEX Upgrade. below q = 3, the fl—limit is disruptive whereas above q = 3, a saturationor drop occurs [5]. In [5]. only the energy from magnetic reconstruction was considered: wehave now found good agreement between these values and the. total kinetic energy. Fromthe Troyon-scaling, we would expect fiNmuz 95 f(q) In ASDEX Upgrade. we usually findfiNVMI z 3 for q 2 3, but for q s 3, lily-1m, drops with q to values around ‘2 for q —> ‘2[5]. The highest values of 5N were achieved with the highest triangularity (6 z 0.4). In thisconfiguration. we transiently achieve HA! z 3.3 without I,7 ramp.Another extension of the Troyon—scaling has been proposed in DIII-D by including (5 into43a0014445 ' 4:5.1; B: yérip/(ae)3.6“ ‘ 44 3.5—.’ it,05 37* B au/(B) {3;}? 24— iB‘ « {3‘5” ‘1_ c .v._ _31.11 i} 21:33 1.113 r n0.9— {If (f 0.1“,'. ‘5 .or .. "1‘ W] h”; l“ on lb. WI .0.0 0.3 0.5 0.9 1.2 1.5 0.0 0.3 0.5 151/ma) AIHamFigure 1: Plot off} against the normalization [p/(aB) (left) or [JP/(LIB) (right). Including1. can acruuut for (lie high if cases obtained in 1;, ramp~down experiments.the scaling [L1]. in ASDBX Upgrade. we have varied (l; by 1;» ramp-down and thus achievedthe highest values of p‘,, z 3 and 5,1; m 4.5. As shown in Fig. 1. including [. into the smiingalso provides a reasonable lit to the ASDEX Upgrade data. Note that, due to a slightlydifferent definition. our l'; is about 10 Ur. smaller than that of Dlle.3.) MHD Mode Behaviour at the (El-limit.\n analysis of ti1( ideal kink stability of LVpil a1 ASDEX lI pgradr high 5 equililiria 1151111.,(in ERAlO code [7] reveals stabilitv for 3N < 3.5 even without a conducting wall with thelimit given by the (21) mode. Including the ASDEX Upgrade vacuum vessel stabilizes thismode up to fly 4.1. The (3.2) mode appears at 13N z 3.7 without wall. but can alsohe wall-stabilized here. However, for [3N : 4.1. it cannot be stabilized and now dominatesthe mode pattern. The pressure gradient is usually below the critical gradient for idealballooning except at the plasma edge, where it 1:5 linked to the. occurrence of type 1 13t inthese discharges. Thus, ideal MHD cannot explain the usual limit of [JN S 3.3.In the experiment. we can distinguish two types of mode activity giving rise to n i'l-limit:q 2 1 activity: fl—saturation is mostly connected to activity on the q = 1 surface. This isoften a continuous (1,1) mode which probably is connected to a (1,1) island (as it may lastfor several 100 ms, a time. scale on which 2111 internal kink should form an island). This modeleads to a saturation of liN- 1n discharges with high beam power at nearly perpendicularinjection, we also see I'ishbonl: bursts with a dominant (1,1) structure, but also higher helicitycomponents [8]. OCCurrence of repetitive fishbnnes may lead to a drop of [3N by less than 10‘79. Usually. sawteeth persist. but their repetition rate slow: down. The sawtooth losses donot play a significant role in the li—liinit.q > 1 activity: in addition to the (1.1} activity, we often see tearing modes on surfaceswith q > 1. An example for :1 time sequence is given in Fig.2.lle1e initially a. (1 1] modeexists At 1:13-15 4(4 3) mode develops and. 40 ms later, a (3 ‘2) develops. From theplot of the amplitudes dof ti18 different modes it can be seen that the q > 1 islands drivethe initial (1.1) mode and produce higher harmonics with equal toroidal mode. number ‘viutoroidal mode coupling. During this sequence. {3N can drop significantly (by up to 30 (Yr).These tearing modes at high ,3 are usually attributed to the neoclassical tearing modewhere the island is driven nonlinearly by the loss of bootstrap current due to a. flatteningof the pressure inside the island [9]. In a more recent theory [10], it is found that, due lo(liamagnctic stabilization, a threshold island width Wm. exists below which no neoclassical(100]it» ..i1-i‘rl .l= .8325 i=1 .8455 t:1.8875o (3.3)Frequency[kHz]SXR-Ernissivity[an]O1.8 1.85 1.9Time [s]Figure 2: Typical sequence ol‘resistive modes at the delimit. The left plot shows SXR-signalfrequencies as a function of time, the right plots Show the amplitudes of various modes froma deconvolution ol'SXR line integrals.island will occur and thus one needs a ”seed island' of W > W”,r to start neoclassical tearing.For ug/(iwrw) < 1, this width is greatly reduced. To check this theory in ASDEX Upgrade,we performed a ii—limit experiment where, at fixed I? and Bi, the density was increased bya factor of ‘2. Following the scaling above, this corresponds to a change in u‘ by a factorof 8. Although there was no pronounced effect on Batman the MHD behaviour changed: atthe lowest collisionality, the rise in [3 was limited by (1,1) activity whereas at the highestcollisiouality, the. sequence shown in Fig. 2 involving neoclassical tearing modes occured. Forthe whole collisionality scan, we are in the regime i/i/(cwtpc) < l, but due to Wm, ~ pp“the threshold island size decreases at constant 5 but lower temperature. it turns out that acomparison of local parameters at the (3,2) surface yields good agreement with this theory.assuming a seed island width of 2: ‘2 cm [11]. The onset of such tearing modes usuallycoincides with ELMs or sawteeth. therefore it is likely that a seed island of thc right. helicityis produced by these events.To independently prove that the observer] islands are of neoclassical origin, we calculatedthe dill'urence in bootstrap current 13l for a typical pressure profile at the ,‘iilimit when thepressure is flattened at the (3,2) surface in a region of 5 cm (corresponding to the saturatedisland width estimated from Mirnov analysis). Then, we calculate the width of the magneticisland produced by a helical current of magnitude Alb, (for an 800 ltA discharge at the,3-limit. All, 3 3.5 kA). The island width (calculated in this manner is close to the 5 cmwe started with, indicating that this would be a saturated neoclassical island. Also, theseislands often grow linearly in B for 2: 10 ms, which is another feature of the neoclassicaltearing mode [9]. Finally, for reasonable current profiles, one would always expect A’ < (J forthe (4.3) mode. so we have to rely on the neoclassical driVe.An interesting difference between the q : l and the q > 1 activity is their influence on thetoroidal plasma rotation. Fig. 3 shows an example where a q 2 1 limit occurs (1 = 1.3 :3). Anincrease in beam power leads to another rise in B followed by a drop due to the occurence ofa (3.2) tearing mode. Only the (3,2) mode leads to a significant drop of toroidal rotation ofThe core (inside the (3/2) surface). This may be explained by an increase in the viscosity dueto the MHD activity, and also by the interaction of the rotating (3,2) mode with the resistivewall and the static error field. Both clfects would be much more pronounced for the (3,?)mode than for the (Li) mode Note that, as stated above, the (3.2) has a bigger effect on45«001HgafiliugPog/flmfll)” W TauE “3l lo [TEE—ESP~—:-- M S .‘l 1 w” 4-.v _. . : 3.0 l ; 1 13~— A 1 r6.0 . lxww«,,.,:l .1 1.57 4,0 ‘ 14#18040 7. 2:0 12- m A » ~ 0.0 . ’- .1. . .. ~ :0~ giiyjiy EVE.“ (5&2) Moog : . . Tavoidaflglalwn 1171.77 m (r/iazv 0.07) ms10050_ . OMifnov Achyity Oddfi (A- .1) Mode Tu(pldal Flptalxon 9312.12 m (r/zi = 0,9) km/s. W I . .‘ ' an3020m. . ., , . , .. 0E913 flomawd .._. . . ,. . lon lampelawe. a1 ‘77.“!e = 0&1) M.A-‘--\,_,._.._-‘ fi~._.,fi.,,‘,\1_, (3.0 3032.0 '21}x V 1-0 I a7 7 0.0 » » » 1 o1.25 1.5 1.75 2 2.25 145 1.5 1.75 2 2.25Time [s] Tlmo [s]Figure 3: {Himil by {1.1) activity (1.3 5) and than by a (3.2) tearing mod? (1.78 s). The(3.2) mode has a significant. influence on toroidal rotation of the core.nonliim'uent then the (1,1). as indirutrrd by thc decreased ll—nmch': multiplier (for thtA ~samc‘1"; and «'lousiljr, one needs more beam power).Thus “9 cuurlndc that tlm :3 limit wilh q > 1 inorll. actiV‘iLv in ASDEX Upgrade: is mainly“1W [1 hV' 1ll('fi[flbll11y 011.t neoclasnilal ILELF111'LI 1110(l1. Lhis 1%LSpl‘Cli1llV 1illpUl’1iUl1 as tlnAA59modes winetimi-s an ciduntnlly ocrur at fly-valuer'. “all belou the values 5| uled ztlx'Aww, um.)- biline to a Chung" in A’ or due to an eSpcciully large ser‘tl island (lllt'l‘tf arc exampls‘s down toiv = 2.4). The [l-Lh‘op lnll'uc‘luccd can be restored by incrunsing the healing power. but atthrA expense of n rerluwd confinement due 10 the mode as Shown in Fig. :1.Finally. 11 should 1m noted that fi—limil. disruptions in ASDEX Upgrade happen only several100 111:;aflf'rtlieocr'url'eni'e of the. actual Dilimit and seem 10 be due to a. loss 01' conl'incmant(filmed by the (31.2) morle with subsequent l'l—L transition. and the occurrence of a MARFEcausing a ("2.1) lIlOllt'. 'l‘hns. a typical 134111111 disruption. as has been identified ill TPTR(12]. docs not. appear in .-\SD|3X Upgradu. even at the lowest qivaluc 012.3.[1; [TERaK'T and Home Teams, Plasma Phys. Controlled Fusion 37 (11-105) A19.['2] TROYON. 1". 421 £11.. Plasma Phys. Controlled Fusion 26 (1984).[3] KOPPENDORE‘ER w 81 31.. 14th ]A EA Conference. {ABA—(twat; / A224} (1992).(11:: SCHISSEL. D. ct .11.. Nucl. Fusion 31 (1991) 73.[5| ZOHM. H. CI al. Plasma Phys. Controlled Fusion 37 (1995) A3l3.(6] L"_\0. L L at al..14lh lAEA Conference. Wiirzburg. lAEA»CN-56 / A1719 (1992).[7] 1 l TJENS H 91 al. Comput. Phys. Commuu. 69 (1092) 287.[R] I\ ASS 1' el al. 22nd BPS Conference. Bournemouth IV (1995) 41[£1CHAVG 7. el al Phys. Rev. Lett. 74 (1.995) 4663.[10] VV II S().’\ H. (At al. Phys. of Plasmas 3 (1996) 248.[11] WILSON. 11. e1 ah this conference. to appear in Plasma Phys. Controlled Fusion (1996).[1: ] FREDERICKSON. 12.01 3.1.. Phys. of Plasmas 2 (1995) 1216.46

Beta-Limiting Phenomena in ASDEX Upgrade

http://hdl.handle.net/21.11116/0000-000A-E955-0

Beta-Limiting Phenomena in ASDEX Upgrade

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