Borrass, K.

Sandmann, W.

Schweinzer, J.

English

MPG.PuRe

26th EPS Conf. on Contr. Fusion and Plasma Physics, Maastricht, 14 - 18 June 1999      ECA Vol.23J (1999) 1525 - 15281525Separatrix to Pedestal Density Ratio in ASDEX UpgradeH-modes Comparing DIV-I and DIV-II OperationJ. Schweinzer, K. Borrass, W. Sandmann, ASDEX Upgrade- and NBI-TeamsMax-Planck-Institut für Plasmaphysik, EURATOM Association,Boltzmannstaße 2, D-85748 Garching1. IntroductionRecently, there has been increased interest in the ratio of separatrix density nS to the pedestaldensity nC, because for next step devices nS a d nC are subject to distinct constrains which mightbe in conflict. Therefore a reliable basis for extrapolation is necessary. A semi-empirical relationfor the ratio of the separatrix density nS to the pedestal density nC was derived by combiningexperimental findings on characteristic density profile shapes with SOL physics provided by aso-called two-point model of the SOL with the assumption of Bohm-type transverse transport.[1]. This relation has been successfully applied to experimental density profiles obtained inASDEX Upgrade (AUG) H-Mode discharges with the so called Lyra Divertor (DIV-II) [1].Operation with the Lyradivertor, which is moreclosed than the formerDivertor I (DIV-I)configuration had startedin summer 1997. Ingeneral the global plasmaperformance and the coreconfinement were notsignificantly altered by themodification.However, there arecharacteristic changes inthe Scrape-Off-Layer(SOL) [2]. The closure ofthe divertor geometry leadto significantly increasedneutral gas flux density inthe private flux region.However, the relationbetween SOL density andneutral gas flux density inthe divertor is not alteredby the change from DIV-Ito DIV-II [3]. Thus underall conditions thethickness of the DIV-IISOL is increased or at least the same as for DIV-I. In fig.1 density profiles obtained bycombining lithium beam edge profiles with interferometer measurements of the plasma core [4]are presented, showing the typical difference in the gradient region. One consequence of thisbehaviour is a difference in the ratio nS/nC between DIV-I and DIV-II. In this paper we study theimpact of divertor geometries on the ratio nS/nC by extending our previous study [1] to DIV-Idata.00,10,20,30,40,50,60,70,80,5 0,6 0,7 0,8 0,9 1,0 1,1 1,2DIV-I #8087Li-BeamDIV-II #10584Li-Beamne [1020  m-3 ]ρp o lncns800 kA, -1.5T, 7.5MW, ne= 7 . 5.1 019m-3Fig. 1: Typical AUG density profiles for DIV-I and DIV-IIin Type-I ELMy H-mode discharges (averaged over theELM cycle). The line averaged densities are the same forboth discharges as all global parameters too. The gradient isconstant in the pedestal and near the separatrix parts of theSOL. Radial positions of separatrix and pedestal region areindicated by the broken lines. Density of symbolscorresponds to spatial resolution of measurement.26th EPS CCFPP 1999 ; J.Schweinzer et al.: Separatrix to pedestal density ratio in ASDEX Upgrade H-mode...15262. Description of modelThe discussion is guided by a model which relies largely on empirical characteristics of AUGdensity profiles (cf. fig. 1):(I) The density gradient is radially constant in the pedestal and near separatrix region, andin particular, does not jump at the separatrix.(II) The pedestal  width δ (distance between separatrix and the innermost end of the steepgradient region) is constant.Both features lead to a simple relation between nS and nC, where λn is the density fall-off lengthnear the separatrix position.n nCnnS=+δ λλ(1)Assuming δ ≈ λn (cf. fig. 1) and making use of the approximation (1+z)/z ≈ 2(1/z)1/2, with z =λn / δ one getsn nCnS=21 2δλ/(2)which will permit to derive relations in power law form. All other elements of the modeloriginate from two-point models of the SOL [1 and ref. therein]. In particular estimates of themidplane temperature TS and the temperature fall-off length λT are given by:Tq LST∝⊥2 2 7λ/(3)λT S Stn Tq B∝⊥2(4)where L is the connection length and q⊥ the mean power flux across the separatrix. All otherquantities have already been defined or have their usual meaning. Bohm-type transversetransport was adopted in equ. 4. Finally a proportionality between λn and λT is assumed [1].This assumption is supported by experimental findings, although no dedicated study exists sofar which investigates the connection between both fall-off lengths in detail. With thisassumption and with equs. 2, 3 and 4 we get after some simple algebrannn q Rq BSCCt∝⊥7 15958 153 15 7 15/ // /( )(5)Equ. 5 has the desired form and is the basis of the subsequent comparisons with experimentaldata. The size scaling with R8/15 cannot be tested here, because reliable data from othermachines are not available.3. Application to DIV-I and DIV-II dataA database for Type-I ELMy H-mode discharges in DIV-I has been compiled from 24discharges, where timeslices of stationary phases (D2 puffed discharges with Ip=0.6-1.2MA,Bt=-2.5T,-1.5T, NBI: D0->D+, 2.5-10MW) were included, building up a set of 250 datapoints. The dataset for DIV-II consists of 8 discharges with combined density a d power ramp-up scenarios which sum up to a total of 280 data points (D2 puffed discharges with Ip=0.6-26th EPS CCFPP 1999 ; J.Schweinzer et al.: Separatrix to pedestal density ratio in ASDEX Upgrade H-mode...15271.0MA, Bt=-3.0T,-1.5T, NBI: D0->D+, 2.5-7.5MW) [1]. All density profiles are smoothedover ELMs and the plasma shape is the same for all discharges.Assuming that the relevant parameters aregiven by equ. 5 a standard regression analysis leadstonn qq BS fitDIV I Ct,. . . .. . . ..− −± ±⊥− ± ±= ⋅4 35 10121 51 0 09950 96 0 10 08 0 04 0 35 0 07 (6)where nS and nC in m-3, q⊥ in W/m2, Bt in T and all exponents are given with their 95%confidence intervals (R2 = 0.85).The prediction of the model is given by equ. 7 where now only the coefficient of proportionalityin equ. 5 is determined by a regression fit. This coefficient of proportionality Cx is different forboth divertor geometries (DIV-I: C1 = 1.6 x 10-9; DIV-II: C 2 = 2.57 x 10-9).n Cn qq Bx I IIS modDIV xxCt,. .. .          ,  −⊥= =1 47950 530 2 0 47 (7)01234560 1 2 3 4 5 6nS, fit nS, mod n S [1019  m-3]nS, exp  [1019 m-3]DIV-IFig. 2: Quality of both fit approaches for the DIV-Idataset. Comparison between the regression fit(equ. 6, full symbols) and the model result (equ. 7with x=I, open symbols).02468100 2 4 6 8 10DIV-IDIV-IIn S, modDIV-II   [1019  m-3]nS, exp  [1019 m-3]Fig. 3 Application of Equ. 7 with x=II to bothdatasets in comparison to the experimental datapoints demonstrating the differences found forboth divertor geometries.In fig. 2 we compare results from the fit (equ. 6) and the model (equ. 7) respectively for theDIV-I database. A better ordering of the data points by the fit can be noticed. Comparing theexponents in equ. 6 and 8 the more pronounced q95 dependence of the fit is the majordifference. This may at least be partly due to the small variation of Bt and q95 in the DIV-Idataset. For the DIV-II dataset the exponents of the model have been closely reproduced by thefitting procedure and both scalings were practically indistinguishable when compared in thesame way as in fig. 2 [1]. The difference in the operational window for nS by changing thedivertor geometry is also illustrated in fig. 2.26th EPS CCFPP 1999 ; J.Schweinzer et al.: Separatrix to pedestal density ratio in ASDEX Upgrade H-mode...15284. DiscussionThere are various possible reasons for the observed differences between DIV-I and DIV-II. Onewould expect a too strong q95 dependence if nS is determined radially outside the true separatrixposition. The effect of shifting the separatrix position is illustrated in fig. 4 where the scalingfound for DIV-II (equ. 7, x=II) is compared to the experimental DIV-I densities taken 1 cminside the nominal separatrix position. Doing this one single relation would desribe bothdatasets and no differences would occur.Such a big systematic error in the separatrix position between the DIV-I and DIV-II phase is,however, very unlikely as has been checkedby analysing high resolution Te profiles[3,5] and comparing them to various SOLmodels. From this study one wouldestimate an error of the separatrix positionof only a few mm. Therefore, such errorsare unlikely to be the main cause for theobserved differences.Another possible reason might be asystematically smaller pedestal width δ inDIV-I than in DIV-II. Because of equ. 2this would give an effect in the rightdirection. The example profiles given infig. 1 are at least consistent with this view,but much more analysis is needed to clarifythis point.5. Summary and ConclusionsOn the basis of AUG edge data for bothdivertor geometries, the scaling of the rationS/nC with respect to machine and dischargeparameters was investigated with a view to the impact of the divertor configuration. Thediscussion was guided by a semi-empirical model which emphasises the impact of SOLphysics. We have looked for scalings in terms of the parameters uggested by the model. Withthis approach fits for DIV-I and DIV-II data are of similar type and in good agreement with themodel predictions.The main difference between the scalings for DIV-I and DIV-II is the coefficient ofproportionality which differs by a factor of 1.6. At present we are unable to discriminatebetween the different possible causes for this phenomenon.References[1]   K. Borrass, J. Schweinzer, J. Lingertat, Scaling of the Separatrix to pedestal Density Ratio in ASDEXUpgrade H-Modes, to be published. in Nucl. Fus.[2] H.-S. Bosch et al., Plas. Phys. & Contr. Fus. 41 (1999) A401-A408[3] J. Schweinzer et al. J. Nucl. Mat. 266-269 (1999) 934-939[4] J. Schweinzer et al., in Controlled Fusion and Plasma Physics (Proc. 22nd Eur. Conf. Bournemouth 1995),19C, III, European Physical Society, Geneva (1995) 253[5]    J. Neuhauser et al., “Analysis of high-resolution ASDEX Upgrade edge plasma profiles”, EPS99, thisconference0123456780 1 2 3 4 5 6 7 8n S, mod DIV-II   [1019  m-3]ne (R-RS=-1 cm) [1019 m-3]DIV-IFig. 4: nS, mod of equ. 7 with x=II versusexperimental density data points taken1 cm inside the magnetically definedseparatrix position of the DIV-I dataset(reduced number of points).

Separatrix to Pedestal Density Ratio in ASDEX Upgrade H-modes Comparing DIV-I and DIV-II Operation

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Separatrix to Pedestal Density Ratio in ASDEX Upgrade H-modes Comparing DIV-I and DIV-II Operation

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