Giroud, C.

Maslov, M.

Weisen, H.

Zabolotsky, A.

Infoscience - École polytechnique fédérale de Lausanne

Scaling of density peaking in JET H-modesH. Weisen1, A. Zabolotsky1, M. Maslov1, C. Giroud2, and JET EFDA contributors*email: henri.weisen@epfl.ch1)Centre de Recherches en Physique des Plasmas, Association EURATOM - Confédération Suisse, EPFL, 1015 Lausanne, Switzerland  2)UKAEA, Abingdon, UK Abstract: Results from an extensive profile database analysis of JET density profilesin H-mode, show that the density peaking factor ne0/<ne> in JET H-modes increases as theeffective collisionality νeff≈10−14RZeffne/Te2drops from ~1 to the low values expected forITER (~0.06 for the inductive reference scenario). Density peaking is also correlated withGreenwald number NG, particle outward flux Γ from the neutral beam source and Ti/Te. Theinfluence of parameters related to magnetic shear, such as li and q95 is weak and ambiguous.There is no significant correlation with βN, ρ*, LTe and LTi. Scaling expressions developedusing many combinations  of parameters show that νeff is the most important scalingparameter. H-modes heated only by ICRH are on average only slightly less peaked than H-modes dominated by NBI, demonstrating that neutral beam fuelling can only explain a modestpart (~20%) of the peaking. Scaling expressions involving νeff, NG, RG/(neχ) and Ti/Te suggestthat ne0/<ne> may exceed 1.5 in ITER, providing a boost of fusion power of more than 30% forfixed β and NG with respect to the usual assumption of a flat density profile.1. IntroductionThe very existence of anomalous pinches leading to peaked density profiles has been estab-lished unambigously in fully radiofrequency-current driven L-mode discharges in Tore Supra[1] and TCV [2]. The view that density peaking in H-modes may also be a consequence ofanomalous inward pinches has however regularly been questioned, on the basis that H-modeplasmas in the existing experimental database have a finite inductive field and are neutral beamfuelled[3][4][5]. Even the penetration of edge neutrals has been considered as a possible con-tributor to density peaking [5]. In this paper we show that neither of these mechanisms is suffi-cient to explain the existence of peaked density profiles in JET H-modes, making the conclusionof the anomalous nature of density peaking in H-modes unescapable. We then proceed to searchfor scalings of the peakedness of the density profiles suitable for extrapolations to ITER. Theinstrument of this investigation is a profile database of a wide variety of H-modes in JET, whichIAEA Tech. Workshop, St.Petersburg, 27-31.9.2005, draft 20.9.2005, to be submitted for special PPCFconference issue contains equilibrium profiles from EFIT reconstructions, particle and power deposition profilesallowing steady state heat and particle balances to be computed for each of the 300 time-slicesamples in the database. Table 1 shows the range of variation of the most important number ofdimensional and dimensionless parameters. Both conventional H-modes and ‘hybrid’, charac-terised by a wide core region with flat shear are represented in the database.2. Conventional terms in the particle balanceThe effect of edge neutrals has been shownto be too weak to contribute to sustainingdensity gradients, based on neutral penetra-tion calculations and on experimental evi-dence from a comparison of deuterium andHe discharges [6]. Since the cross section fordouble CX in He is one order of magnitudesmaller than that for CX in deuterium, theCX chains, which provide the mechanismfor inward neutral transport, are effectivelyquenched in He++ plasmas. Despite such afundamental difference, density profiles in He plasmas are no less peaked than their identicalD+ counterparts (fig.1), produced in two dedicated experimental campaigns, ruling out anyinfluence of edge neutral on core density gradients. The majority of H-mode plasmas in JET are dominated by NBI heating and therefore have acore source of particles, which may be expected to contribute to sustaining density gradients.The contribution of beam fuelling to the density gradients in steady state may be estimated as∇ne/ne)NBI=ΓNBI/(Dne) . For a typical JET plasma with ne∼5×1019m-3 and 10 MW of NBIheating, the fuelling rate is some 1021s-1, of which some 40% are deposited inside r/a=0.5,corresponding to ΓNBI∼5×1018m-2s-1. Hence, in order to sustain a typical gradient Table1: Range of parametersIP MA BTT ne19PNBIMWPICMWPLHMWν*ei νeff ρ* βT βN Ti/Te q95 li NGmin 0.9 0.8 1.7 0 0 0 0.01 0.05 0.02 0.44 0.5 1.8 2.25 0.68 0.2max 3.7 3.7 10 18 12 3 0.4 2 0.01 3.9 3.3 0.5 6.4 1.1 11.2 1.4 1.6 1.8 21.21.41.61.82ne(0)/<ne> for Dne(0)/<n e> for He1<ne(0)⋅10−19<2.52.5<ne(0)⋅10−19<33<ne(0)⋅10−19<3.53.5<ne(0)⋅10−19<4Fig. 1 Comparison of peaking factors in deuteriumplasmas and in helium plasmas.∇ne⁄ ne∼1m-1, D would have to be of order 0.1m2/s, a low value when compared to heat dif-fusivity. Unlike heat diffusivities, particle diffusivities cannot be obtained on a routine basis.We therefore relate the beam fuelling contribution to the effective heat diffusivity χ=Q/(ne∇Te+ni∇Ti)≈Q/(2ne∇Te), where Q is the total heat flux, as follows: eq.(2)For entirely beam heated plasmas Eb=Q/ΓBNI is the average beam energy (~90keV at JET). Fortypical ∇Te/Te~2m-1 and Te~3keV at mid radius, D would have to be ~10 times smaller thanχ in order to explain a density gradient ∇ne/ne∼1m-1. For purely radio-frequency heated H-modes, as present in the dataset, only the Ware pinch or an anomalous pinch can contribute todensity peaking. The contribution of the former can also be related to χ: On fig.2, we plot the experi-mental ∇ne⁄ ne versusΓNBI⁄ (χne)+VW/χ, evaluated atr⁄ a=0.5. The figure presents thedata presented in ref [7], sup-plemented by  H-modes domi-nated by radio-frequency (RF)heating. The symbols refer toclasses of fnb=QNBI⁄ QTOT. Thecontribution of the Ware pinchis comparable to, or larger than,the NBI contribution only forPNBI<2MW corresponding typ-ically to fnb<0.2. The variation of  ΓNBI⁄ (χne) for NBI dominated plasmas (red dots) stems notfrom changes in ΓNBI (becauseQNBI/ΓBNI=Eb≈const), but from the range of ∇Te in the dataset.Considering only NBI dominated discharges, one could be misled to misinterpreteting the datane∇ne-------- NBIΓNBIDne----------χD---TeQ ΓNBI⁄-------------------2 Te∇Te------------⋅ ⋅≈=ne∇ne-------- WareVWD------χD---VWχ------⋅= =0 0.05 0.1 0.15 0.200.511.52ΓNBI/(χne)+VWare/χ at r/a=0.51/L n at r/a=0.5 0.6<fnb<1   0.2<fnb<0.6 0.01<fnb<0.20<fnb<0.01  Fig. 2 Inverse density gradient length ∇ne⁄ neversusΓNBI⁄ (χne)+VW/χ. Symbols refer to fraction of NBI heating.as a proof that NBI fuelling is the cause of density peaking. Considering also RF dominateddischarges and Rf-only discharges (stars in fig.1), it becomes plain that there is no obviouscorrelation between ∇ne/ne and ΓNBI⁄ (χne)+VW⁄ χ. In addition, the magnitude of D/χrequired would have to be implausibly low, ~10-2 for RF-only H-modes! We conclude that thecombined beam fuelling and Ware pinch are unable to account for the observed density gradi-ents, however beam fuelling may still be a significant contributor, depending on the real valueof D/χ.3. Dimensionless parameter interdependenciesWe wish to constructdimensionless scalingexpressions for R∇ne/neand ne0/<ne>, using bothempirical scaling parame-ters and parametersinspired by theory. The lat-ter, R∇Te/Te R∇Ti/Ti andR∇q/q correspond to thethermodiffusive and curva-ture pinches respectively[8]. The effective collision-ality νeff≈10−14RZeffne/Te2 governs drift wave stabilityand is predicted to influence the ratio of anomalous convection to particle diffusivity V/D [10].βN and ρe* are other key scaling parameters for drift wave driven transport and MHD stability.Instead of distinguishing between parameters for electrons and ions, we introduce Ti/Te, whichis theoretically expected to be related to the nature of the drift instability (ITG or TEM) andhave a strong influence on particle convection [8]. We also include RΓNBI/(χne), RVW/χ andtheir sum in an attempt to account for the source and Ware pinch in the particle balance. TheR/LnR/L n96−65−57−636157−35−332928−22−21ne0/<ne>n e0/<n e>96−71−65−705350−33−212625−30νeffν eff−65−71948552−373421ν*ν*−57−6594804032NGN G−63−708580−224836−3042−21Γ/neχΓ/n eχ6153−2299−473144−45Γ/neχ+VW/χΓ/n eχ+V W/χ575099−433038−41VW/χV W/χ−35−3352404829−20−4631−21−22R/LqR/L q−33−2136−47−4329−30−2990−27−34−35Ti/TeT i/Te29263130−20−30−30−383425−32q95q 952825−37−304438−46−29−3039−362657lil i−22−45−413190−30−30−58−54−22−28R/LTelidR/L Telid−21−3839−25−363348βNβ N−30343242−21−2734−58−2585−30ρ*ρ*21−3425−36−54−368520−26R/LTiR/L Ti−3226−22332052R/LTeeceR/L Teece−21−22−3557−2848−30−2652Table 2: Correlation coefficients Greenwald fraction NG=1014πa2neIp  is not a ‘canonical’ dimensionless parameter, but hasbeen included because it is a reference parameter for the ITER operation scenarios and dis-plays a high degree of correlation with density peaking in H-mode.Table 2 displays the cross correlation  coefficients for R∇ne⁄ ne, ne0⁄ <ne> and the above namedparameters. All local quantities are evaluated at or around (for gradients) r/a=0.5. The parame-ters with the highest cross correlation with R∇ne/ne are νeff, NG and ΓNBI/(χne), followed byTi/Te and R∇q/q. There is no indication for thermodiffusion, nor for dependencies on βN andρe*. Figs 3 and 4 show the peaking factor versus νeff and NG respectively. Fig.2 confirms an earlierobservation of a dependence of density peaking on collisionality on AUG [10]. On fig.2 we seethat H-modes with no or little NBI heating are on average somewhat less peaked that domi-nantly NBI heated discharges.4. Scaling with dimensionless parametersIn table 3 we construct a series of scaling expressions of the form R∇ne⁄ ne=c0+Σcjpj, byincluding successively more parameters pj, starting with those most strongly correlated withR∇ne/ne, until the corresponding coefficients cj are too poorly defined for consideration andthe standard deviation σ ceases to decrease. The intervals in he table correspond to 90% confi-dence. The last column provides the extrapolation to the ITER inductive scenario, assumingνeff=0.06, NG=0.85, Γ=0, Ti/Te=0.9. As above, local parameters are taken at mid-radius. Used10−1 10011.21.41.61.82νeff at r/a=0.5ne0/<n e> ITER0.6<fnb<1   0.2<fnb<0.6 0.01<fnb<0.20<fnb<0.01  10−1 10011.21.41.61.82νeff at r/a=0.5ne0/<n e> ITER0.6<fnb<1   0.2<fnb<0.6 0.01<fnb<0.20<fnb<0.01  Fig. 3 Density peaking versus effective collision-ality νeff. Symbols: fraction of NBI heating.Fig. 4 Density peaking versus Greenwald numberNG. Symbols refer to νeffon their own, the three main parameters would provide conflicting predictions for ITER (fitsno 1-3). However all combinations including νeff lead to the expectation of fairly peaked den-sity profiles in ITER, with R/Ln typically in the range 2.4-3. The coefficient for the Ware pinchparameter RVWare/χ is too poorly defined for this parameter to be included in the scalings.Lumping RVWare/χ  together with RΓ/neχ is practically equivalent to using RΓ/neχ alone.When NG is included in a fit involving νeff, the corresponding coefficients become ill deter-mined, suggesting that this parameter may not be an appropriate scaling parameter for densitypeaking. When local or global measures of magnetic shear (such as li in fits 7 & 8) areincluded, results depend on the presence of the particle flux term, their contribution becominginsignificant when the latter is included, as a result of correlations between these parameters. The values of the coefficient for the particle flux parameter, RΓ/neχ, can be interpreted as χ/D.We note that, when Ti/Te is introduced as a fitting parameter, the value obtained for χ/D dropsTable 3: Scaling expressions for R/LnTable 4: Scalings for ne0⁄ <ne> and fusion power enhancementnfit, ne diagnosticc0 logνeff NG RΓ/neχ Ti/Te li σfit ITER1) SVDI 1.67±0.1 -1.35±0.2 0.52 3.32) SVDI 3.61±0.2 -2.58±0.4 0.53 1.423) SVDI 1.64±0.12 2.73±0.43 0.54 1.644) SVDI 2.48±0.5 -0.86±.34 -1.14±.66 0.51 2.565) SVDI 1.21±0.1 -1.18±.14 2.32±0.31 0.38 2.655) SVDI 2.86±0.2 2.12±0.3 2.22±0.34 0.42 1.066) SVDI 1.53±0.41 -0.99±.27 -0.43±.54 2.28±.31 0.38 2.377) SVDI 2.23±0.95 -1.27±.36 -0.39±.72 0.77±.33 -1.14±.72 0.31 3.18) SVDI 1.59±0.93 -1.03±.35 -0.59±0.68 1.21±0.54 0.60±0.32 -0.34±.76 0.29 2.579) SVDI 0.78±0.26 -1.28±.19 1.28±0.48 0.70±.31 0.29 2.9710) SVDI 1.27±0.59 -1.01±.35 -0.62±.67 1.32±0.48 0.62±0.31 0.29 2.539’) Lidar TS -0.14±.54 -1.36±.39 0.79±0.98 0.83±0.62 0.60 2.2710’)Lidar TS 0.84±1.2 -0.82±.71 -1.23±1.36 0.86±0.97 0.68±0.64 0.59 1.4c0 logνeff NG RΓ/neχ Ti/Te σfitITERne0/<ne>ITERne95/<ne>PDT/PDT flatfixed β and NGPDT/PDT flatfixed β and ne951.22±0.15 -0.27±.09 -0.16±0.17 0.21±0.17 0.15±0.08 0.07    1.54    0.76     1.33    1.231.09±0.07 -0.34±.05 0.20±0.12 0.17±0.08 0.07    1.65    0.71     1.38    1.19from near 2.3 to 1.3. This can be understood from the twofold effect of NBI, which is to fuel,contributing to increasing the density gradients, and to increase the Ti/Te ratio. An increase ofTi/Te is expected to shift the balance of the unstable drift modes away from TEM’s towardsITG’s. According to drift wave turbulence theory [8], ITG’s are characterised, in addition to adominant inward anomalous curvature pinch, by inward thermodiffusion, whereas for TEM’s,thermodiffusion is outward, leading to less peaking. The sign for the coefficient of Ti/Te is con-sistent with this prediction, as is the value obtained for χ/D≈1.3, which is close to the theoreti-cal value, 3/2 [8]. A value of χ/D≈1.3 is also within the range of χ/DT obtained fromexperiments using trace amounts of tritium puffed into a large variety of JET discharges [12]We offer scalings 9 and 10, which have the smallest σ, as the ones most probaby representativeof the density peaking behaviour. Fits 1-10 are obtained from density profiles produced byinverting JET interferometer data by the SVD-I method [11], cross checked with a simple finiteelement method [13]. Profiles obtained from the JET LIDAR Thomson scattering system aremore scattered due to statistical noise, but  importantly, they are on average less peaked thanthose from interferometry, as seen in fits 9’ and 10’ in itallic in table 3. The discrepancy shouldbe treated as a systematic uncertainty until resolved. Table 4 provides fits for the peaking factorusing the parameters of the most succesful fits , 9 &10, in table 3.5. Possible benefits and drawbacks for ITERBefore attempting to quantify the benefit ofpeaked density profiles for ITER fusionperformance, we ascertain with the help ofthe correlation matrix (table 2) that temper-ature profile peaking is not correlated withdensity peaking, nor with any of the abovescaling parameters for density scaling.Electron temperature profiles from LIDARTS in JET have a large degree of variability,with no obvious correlation with operatingconditions. For assessing the benefit in fusion performance, we therefore chose to select theelectron temperature profile most similar to the ITER simulation in ref.[9], i.e.1 1.2 1.4 1.6 1.8 211.11.21.31.41.5ne0/<ne> relative DT fusion power0.6<fnb<1   0.2<fnb<0.6 0.01<fnb<0.20<fnb<0.01  Fig. 5. Relative increase of fusion power with peak-ing factor for fixed NG and β.T(0.95a)≈0.17T(0), scaled up to T(0)=18keV. The D-T fusion power is then calculated as assuming first a flat density profile (as in [9]) for referenceand then the whole range of density profiles observed experimentally normalised such as tohave the same NG. As the stored energy varies somewhat when the density profile is changed,the temperature profile is renormalised such as to conserve β and hence to remain within therestrictions of the operating scenario. In fig.5 we see that the ratio of PDT from plasmas withpeaked density profiles to that with the flat reference profile is almost entirely determined bythe peaking factor. Projections for ITER (table 4) suggest an increase in fusion power of morethan 30%. For the inductive scenario [9], which is heated by 80MW of alpha particle heatingand 40MW of auxiliary heating, this means that most of the auxiliary heating  can be replacedby the increased alpha power, leading to Qfusion>30.On the downside we have to consider that for fixed NG and β, density peaking unavoidable-leads to a reduction of the pedestal density below the average density, by some 20-30% for theabove ITER projections. This may affect divertor performance by making detachment moredifficult. If however the density limit is linked to the pedestal density, rather than the line aver-age density, a simple remedy is to raise the edge density to the target value with a correspond-ing temperature reduction to conserve β. In this case the effect of peaking is still beneficial,although somewhat less than at fixed average density (table 4).Density peaking might provide a means to salvage fusion performance if the edge density limitdrops to half of the expected value [14]. At constant β, fusion power with peaking expected forITER in table 4, would still exceed the flat reference case by some 30%. However divertoroperation at such a low density is questionable.References[1]  G.T. HOANG et al, Phys. Rev. Lett. 90 (2003) 155002[2]A. ZABOLOTSKY et al, Plasma Phys. Contr. Fusion 45 (2003) 735[3]J. STOBER et al., Nuclear Fusion 41 (2001) 1535 [4]L. GARZOTTI et al, Nuclear Fusion 43 (2003) 1829[5]M.VALOVIC et al, Plasma Phys. Contr.Fusion 46 (2004) 1877[6]A. ZABOLOTSKY et al, submitted to Nuclear Fusion (2005)[7]  WEISEN H. et al, Nuclear Fusion 45 (2005) L1-L4[8] X. GARBET et al (2004), Plasma Phys. Controll. Fusion 46 (2004) B577[9]V. MUKHOVATOV et al, Plasma Phys. Contr. Fusion 45 (2003) A235PDT 17.6 106× e σv〈 〉nDnT Vd∫=[10] C. ANGIONI et al, Phys. Rev. Lett. 90 (2003) 205003[11] I. FURNO et al, Plasma Phys. Contr. Fusion 46 (2004) [12] K.-D. ZASTROW et al, Plasma Phys. Controll. Fusion 46 (2004) B255[13]A. ZABOLOTSKY, ‘Particle transport in tokamak plasmas’, PhD thesis, EcolePolytechnique Fédérale de Lausanne EPFL, 2005[14] K. BORRASS et al., Nuclear Fusion 44 (2004) 752

Scaling of density peaking in JET H-modes

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Scaling of density peaking in JET H-modes

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