Fable, E.

Pitzschke, A.

Sauter, O.

TCV Team

Wagner, D.

Weisen, H.

English

MPG.PuRe

Particle transport in TCV H-modesD. Wágner, E. Fable1, A. Pitzschke, O. Sauter, H. Weisen and the TCV teamEcole Polytechnique Fédérale de Lausanne (EPFL), Centre de Recherches en Physique desPlasmas, Association Euratom-Confédération Suisse, Station 13, CH-1015 Lausanne,Switzerland1Max-Planck-Institut für Plasmaphysik, IPP-EURATOM Association Boltzmanstrasse 2D-85748 Garching bei München, GermanyMotivation and experimental observations24R/Lnea)1.11.31.5n0 e/〈ne〉 b)0.0 0.2 0.4 0.6 0.8 1.0 1.2νGS21.21.4n0.2e/n0.8ec)Figure 1: Peakedness of the density profile as thefunction of the collisionality, measured by the nor-malized inverse gradient length a), and two commondefinition of density peaking b), c).Results from a database analysis ofH-mode density profiles on the Toka-mak à Configuration Variable (TCV)in stationary conditions show that thelogarithmic electron density gradientslightly increases with collisionality.By contrast, earlier observations of H-modes at JET [1] and AUG [2] showedthat the density profiles tend to flat-ten with increasing collisionality. Theaim of this work is to contribute to theunderstanding of this experimental be-haviour of the density profiles.The experimental database is built ona representative set of sufficiently diag-nosed typical H-mode discharges. Thetypical parameters of the plasmas in the database are shown in Tab. 1. Purely ohmic and thirdharmonic electron cyclotron resonance heated (X3 ECH) plasmas are included.The electron density and temperature profiles are measured via Thomson scattering. Densityprofile measurements are cross-calibrated with the Far Infrared Interferometer (FIR). The gra-dient of the profiles are determined by fitting the experimental data with a cubic spline. Thelocal quantities are defined as averages over 0.6 < ρ < 0.8 region where it was found that thelogaritmic gradients are constants and not affected by sawtooth activity. The local quantities areaveraged over a stationary phase of the pulse .37th EPS Conference on Plasma Physics P1.11013.7 < 〈ne〉vol [1019m−3] < 6.10.9 < Te0[keV] < 2.5350 < Ip [kA] < 4201.35 < V [m3] < 1.55150 < POH [kW] < 600250 < PECH [kW] < 1000δedge ≈ 0.45, κedge ≈ 1.7Table 1: Typical parameters of theTCV H-modesFig. 1 shows the peakedness of the density profileas the function of the collisionality. We adopt the col-lisionality definition as it is used by the GS2 code [3].Fig. 1 a) measures the peakedness by the inverse nor-malized gradient length R/Ln|stat, while b), c) showtwo other commonly used measures of the peakingfactor. Points around νGS2 ≈ 1, high density ohmicheated pulses have a R/Ln|stat around 4.5. DecreasingνGS2 down to 0.5, R/Ln|stat stays around 4. The mosttypical ohmic H-mode pulses fall into this collision-ality regime. In the 0.1 < νGS2 < 0.5 range, which isreached by adding 0.5-1.5 MW ECH power, R/Ln|stat decreases down to 2.Theoretical modelWe use the quasi-linear gyrokinetic model presented in [4]. We solve the linear gyrokinetic(GK) equation for electrostatic perturbations with a wavenumber k = (0,ky) using shifted -circles s−α equilibria and obtain ωkR, γk, Γk, the real and imaginary part of the mode frequencyand the particle flux, respectively. ωkR > 0 represents a mode turning in the ion diamagnetic(ITG) direction, while ωkR < 0 corresponds to the electron diamagnetic direction (TEM).The results of the linear simulations cannot be applied directly to the fully developed, satu-rated, turbulent state. ωkR, γk, Γk are evaluated on a range of ky . We then obtain the fluxes andthe mode frequency of the turbulent state by a weighted average over the mode spectrum:ωQLR =∑k wkωkR∑k wk, with wk = A0(γ〈k2⊥〉)ξ∆ky.ΓQL is obtained in the same way from Γk. The wk weights are usually chosen according to aquasi-linear rule. In our case ξ = 2, A0 = 1, ∆ky takes into account the choice of a non-uniformgrid in ky. The GK equation is solved by the initial value flux-tube code GS2 [3].In the absence of core particle sources the stationary state requires that: ΓQL = 0. This condi-tion is used to find R/Ln|stat i. e. the stationary value of the normalized electron density gradientwhich can be compared to the experimentally observed values.Simulation resultsWe perform our simulations with the following parameters (standard case): ε = 0.230, q =1.2, s = 0.7, R/LTe = 9, R/LTi = 6.5, Zeff = 1. The Shafranov-shift parameter α is self consis-tently evaluated with ne = 5×1019 m−3 and Te = 1 keV.37th EPS Conference on Plasma Physics P1.11011.5 2.5 3.5 4.5−0.40.00.4νGS2 = 0.100, Te/Ti = 1.429a)1.5 2.5 3.5 4.5−0.40.00.4νGS2 = 0.100, Te/Ti = 2.000b)1.5 2.5 3.5 4.5−0.40.00.4νGS2 = 0.650, Te/Ti = 1.429c)1.5 2.5 3.5 4.5−0.40.00.4νGS2 = 0.650, Te/Ti = 2.000d)1.5 2.5 3.5 4.5R/Lne−0.40.00.4νGS2 = 1.200, Te/Ti = 1.429e)1.5 2.5 3.5 4.5R/Lne−0.40.00.4νGS2 = 1.200, Te/Ti = 2.000f)Figure 2: Particle flux ΓQL (black circles), and modefrequency ωQLR (red diamonds) as the function of thedensity gradient for different νGS2 (0.1, 0.650, 1.2)and Te/Ti (1.43, 2) values.A series of simulations has been per-formed scanning νGS2 = [0.1 . . .1.2] to-gether with a scan in Te/Ti = [1.5,2].3 ky values used in the range of[0.08,1.2]. The number of ky valuesis small in order to obtain the basictrend while reducing the CPU necessity.The results are summarized in Fig. 2which shows the particle flux ΓQL (mul-tiplied by a factor 5 because of visuali-sation reasons) and the mode frequencyωQLR as a function of the density gradi-ent R/Ln for different νGS2 (rows) andTe/Ti (columns).At lower density gradients the par-ticle flux points inwards (negative val-ues) when the mode frequency is pos-itive (ITG) it crosses the ΓQL = 0(marked with vertical dashed lines) linewhen ωQLR ≈ 0 [4] then going towardslarger R/Ln values it points outwards,the mode frequency becomes negative(TEM). Note that when ITG modes aredominant the slope of the particle fluxhardly changes with the density gradient. On the other hand, since TEM is driven by the densitygradient the particle flux is very sensitive to it. Note that ωQLR ≈ 0 at ΓQL = 0 is consistent withthe results of [4].Increasing the collisionality, ITG modes become dominant (ΓQL flattens), collisions are morestabilizing to TEM. The stationary value of the density gradient corresponding to ΓQL = 0becomes more sensitive to the changes in other parameters for example to the temperature ratio.In this case a finer resolution in ky is necessary. Increasing Te/Ti the shape of the ΓQL curve isconserved, the particle flux increases more at higher collisionality.In ohmic plasmas the neoclassical Ware-pinch can have significant contribution to the den-sity peaking. The strength of this effect depends also on the turbulence regime. In case of the37th EPS Conference on Plasma Physics P1.1101presence of the Ware-pinch one needs to find R/Ln|stat from: ΓQL +neWp = 0. We divide withthe turbulent heat flux qQLΓQLqQL+neWpqQL= 0,then we rewrite the second term assuming: qQL = λQexp, whereQexp =−χPBe ne∇Te = χPBeRLTeneTeR.FinallyΓQLqQL+RWpλ χPBe RLTe= 0, (1)from which one can find the stationary density gradient value with the Ware-pinch effect in-cluded. Note that Wp < 0. The first term is evaluated numerically, while the second term comesfrom the experiments.In Fig. 2 b), c) the Ware-pinch contribution is added to the particle flux according to Eq. 1.Typical TCV ohmic H-mode parameters used: χPBe = 1 m2/s, R/LTe = 9, R = 0.88 m. The λparameter was set to 0.5. It can be seen that the shape of the ΓQL curve strongly influences theposition of the new value of R/Ln|stat.ConclusionsThe ΓQL = 0 stationary condition is set by the subtle balance between ITG and TEM modesas obtained in L-mode simulations [4]. Depending on the turbulence regime the dependenceof R/Ln on the collisionality, temperature ratios can be very different. The neoclassical Ware-pinch also can contribute to the peaking in certain conditions typically when the stationary pointlies in an ITG dominated regime. Note that χPBe is larger in ECH H-modes and therefore theWare-pinch is reduced.AcknowledgementsThe authors thank M. Kotschenreuther and W. Dorland for having made available the GS2code. The GS2 simulations have been run on the PLEIADES2 cluster at EPFL, Lausanne. Thiswork has been supported in part by the Swiss National Science Foundation.References[1] M. Maslov, C. Angioni, H. Weisen and JET-EFDA contributors, Nucl. Fusion 49, 075037 (2009)[2] C. Angioni et al., Phys. of Plasmas 12, 040701 (2005)[3] M. Kotschenreuther et al., Comput. Phys. Commun.49, 075037 (2009)[4] E. Fable, C. Angioni, and O. Sauter, Plasma Phys. and Control. Fusion 52, 015007 (2010)37th EPS Conference on Plasma Physics P1.1101

Particle transport in TCV H-modes

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Particle transport in TCV H-modes

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