Angioni, C.

Bottino, A.

Brunner, S.

Dannert, T.

Fable, E.

Jenko, F.

Sauter, O.

English

MPG.PuRe

The role of electron-driven microinstabilities in particle transport duringelectron Internal Transport BarriersE. Fable1, C. Angioni2, A. Bottino2, S. Brunner1, T. Dannert2, F. Jenko2, O. Sauter11Ecole Polytechnique Fédérale de Lausanne (EPFL)Centre de Recherches en Physique des Plasmas (CRPP)Association EURATOM - Confédération Suisse CH - 1015 Lausanne, Switzerland2Max-Planck-Institut für Plasmaphysik, EURATOM Association, 85748 Garching, GermanyAbstractExperimental results obtained in TCV electron Internal Transport Barriers (eITBs) showa strong coupling between the plasma density and the electron temperature logarithmicgradients [1]. The plasma density is sustained by an inward thermodiffusive pinch whosetheoretical understanding has not been achieved yet. The level of particle diffusivity, as es-timated in transient transport experiments, indicates anomalous transport as the main mech-anism to create this pinch. On the other hand, a clear improved heat and particle transportconfinement is observed. Gyrokinetic calculations of the pinch coefficients are performed inthe framework of quasi-linear theory neglecting core particle sources and impurities. Therole of non-adiabatic passing electrons is taken into account and shown to be negligible,as well as the so called turbulent equipartition pinch. The coupling between density andtemperature is provided via trapped electrons driven thermodiffusion which is maximizednear the transition between ITG-dominated to TEM-dominated turbulence. This regime isobtained in a plasma characterized by large temperature and density logarithmic gradientsthrough different stabilizing mechanisms discussed here.IntroductionPeaked density profiles are usually observed during the steady-state operation of eITBs inTCV [1]. The density logarithmic gradient is found to be correlated with the electron tempera-ture logarithmic gradient with a robust, in the sense of experimental reproduction, ratio of about0.4-0.5 , i.e.R/Ln ∼ 0.45R/LTe. Neoclassical transport is still negligible in these eITB scenarios[2] and thus we will resort to turbulence codes to elucidate the background physics. The gyroki-netic code GS2 [3] is employed to understand how steady-state density profiles are sustained bythe anomalous pinch for typical eITB parameters. The eITB scenario discussed here involvesthe reversal of the magnetic shear and very strong electron heating, assessing the role of theTrapped Electron Mode (TEM) that is usually associated with flattened density profiles [4].Theoretical backgroundThe steady-state density profile, in the framework of quasi-linear turbulence theory, is givenby the general formula:RLn= −RVD= −CTRLTe−CP ⇒ σe =1ηe=LTeLn= −CT −CPLTeR(1)whereV andD are the pinch velocity and diffusion coefficient respectively. The term−CT RLTe iscalled turbulent thermodiffusion (THD), while the other off-diagonal term has been historicallycalled ’turbulent equipartition’ (TEP) [5]; in this context the latter contains all the off-diagonalcontributions to particle transport which are not linearly proportional toR/LTe. The two coeffi-cients are evaluated with GS2 via a trace-particle method solving a linear system to findCT a34th EPS Conference on Plasma Phys. Warsaw, 2 - 6 July 2007 ECA Vol.31F, P-1.100  (2007)CP. Note that for a single ballooning mode (identified by the value of the poloidal wavenumberkyρi) the two coefficients areindependentof the mixing length rule for|Φ|2 (i.e. the turbu-lence level determines fluxes but not source-less steady-state profiles), allowing a more strin-gent comparison with the experiment without assumptions on non-linear saturation phenomena.The sign convention, as seen from Eq.(1), is such that negative values of the coefficients giveinward pinch contribution, while positive values contribute outward. Without trapping it is pos-sible to evaluate analytically the thermodiffusion coefficient for electrons to be−CT ≈ 0.5 , inagreement with the experimental observations. However, the trapped fraction isft ∼ 0.4 at mid-radius where the maxima of the logarithmic gradients are usually located. Trapped electronscontribute with a strong outward pinch for a mode rotating in the electronic direction, almostreversing the sign ofCT for a strong TEM. We therefore expect the TEM to be marginally stablefor the particle barrier to exist. As will be shown later:CP ≪CT RLTe, allowing us to concentrateon the behavior ofCT only.Understanding the density barrierThe GS2 simulations are done with input parameters from #29859, a typical eITB obtainedin TCV: R/LTe = 16, Te/Ti = 2.5, ŝ= −0.7, q = 2.7, ε = 0.11, αMHD ≈ 1.5. R/Ln is scannedto find the self-consistent steady-state point of zero particle flux.R/LTi andαMHD are varied to−2 −1 0 1 2−0.5−0.4−0.3−0.2−0.100.10.20.3ωRCTαMHD0.30.71.11.5TEMITG (a) 0 0.2 0.4 0.600.10.20.30.40.5σeINPUTσ eOUTPUTαMHD Steady   state(b)0.30.71.11.5Figure 1: a) Thermodiffusion coefficientCT versus the mode frequencyωR for different values ofαMHD obtained with GS2, circles representLTe/LTi = 0.5 and squaresLTe/LTi = 0.8; b) Steady-statediagram forσe = LTe/Ln: σOUTPUTGS2e > σ INPUTGS2e implies an inward flux and subsequent increase ofσe,σOUTPUTe < σ INPUTe implies an outward flux,σOUTPUTe = σ INPUTe (black dashed) provides the steady-statevalue when intersecting the different curves (the intersections aret blesteady-state points)test the response of TEMs and their stabilization. The normalized poloidal wavenumber is fixedat kyρi = 0.3 where the spectrum ofγ/ < k2⊥ > peaks for these parameters (quasi-linear rule,see [6]). We neglect impurity physics assumingZeff = 1, reminding that in the experimentaldischarges analyzed we observe a globalZeff ∼ 3. The calculations are made in the electrostatic(βT ∼ 10−3) and collisionless limit, without core particle sources. The simulations indicate thatCT is maximized, in the inward direction, around the ITG-TEM transition, i.e. whenωR .0, figure 1(a). The maximum value of−CT increases withαMHD , which is thus a favorableparameter. We note also that a higherαMHD gives a sharper transition in the behavior ofCT.Figure 1(b) shows how to identify the self-consistent steady-state point:σ INPUTe represents thevalue ofR/Ln (R/LTe is fixed) given as input to the code.σOUTPUTe is calculated from Eq.(1)34th EPS 2007; E.Fable et al. : The role of electron-driven microinstabilities in particle transport during el... 2 of 4usingCT andCP as obtained by the code. IfσOUTPUTe 6= σ INPUTe it means that the particle flux isdifferent from zero and it is directed inward ifσOUTPUTe > σ INPUTe and outward ifσOUTPUTe <σ INPUTe . The steady-state points, stables if[dσOUTPUTe /dσ INPUTe < 1]σe=σSteady−statee, are locatedat the intersection of the calculated curves and theσOUTPUTe = σ INPUTe line. At high values ofαMHD the steady-state point moves towards higher values ofσe, but it appears as a ’threshold’phenomena rather than a continuous process.R/LTi seems to be fundamental in providing amore efficient effect ofα . Figure 2(a) shows the real frequencyωR for the most unstable mode0.1 0.2 0.3 0.4 0.5−1.5−1−0.500.511.52σeωRαMHD0.30.71.11.5(a) TEM ITG 0 2 4 6 8 10 12−4−20246810R/LnR/LTe=20 ; αMHD=1.5 ; LTe/LTi=0.8−CTt  R/LTe−CTp R/LTe−CPt−CPp(b) Figure 2:a) Most unstable modeωR versusσe. Solid-squares forLTe/LTi = 0.5 and dashed-circles forLTe/LTi = 0.8; b) Pinch coefficientsCT andCP divided into trapped (CtT andCtP) and passing (CpT andCpP)electrons contributions versusR/Ln for one specific case.versusσe. The transition from ITG to TEM occurs nearωR = 0. This point shifts towards higherσe with an increase of the value ofαMHD andLTe/LTi (squares vs circles). Figure 2(b) showsthe two pinch terms−CT RLTe andCP divided into trapped and passing particles contribution. TheTEP coefficientCP is found to be negligible, as well as the contribution of passing electrons.The dominant part of the pinch comes from trapped particles driven thermodiffusion.Combined s-αMHD effectThe barrier existence is provided by the stabilizing effect of both reversal of magnetic shearsand increased plasma pressure via theαMHD parameter [7]. The magnetic curvature drift in theballooning formalism is expressed as:ωD ≈ cosθ +(sθ −α sinθ)sinθ , which for θ ∼ 0 be-comesωD ≈ 1+(s−α −1/2)θ2. Stabilization becomes stronger as the parabola becomes more’peaked’, i.e. as|s−α −1/2| ⇒ ∞. However, the efficiency ofs−α in changing the mode realfrequencyωR depends on the value ofLTe/LTi, while the growth rate seems to decrease sim-ilarly in the two cases. In figure 3 we see that, at fixed gradients, the mode is more and morestable combining magnetic shear reversal and increasing Shafranov shift. The mode being aTEM at small absolute values ofs−αMHD , it switches to ITG whens−αMHD stabilization issufficiently strong. It requires either a large negative shear or a large Shafranov shift. The transi-tion from ITG-dominated to TEM-dominated turbulence is provided bys−αMHD stabilizationof TEM and a value ofLTe/LTi . 1. It is interesting to note that, contrary to the temperaturebarrier which is due to a decrease in the heat flux at constant input power, linked to the decreaseof the mode growth rateγ, the density barrier sustainment is strongly related to the behavior ofthe mode frequencyωR and much less on the value ofγ.34th EPS 2007; E.Fable et al. : The role of electron-driven microinstabilities in particle transport during el... 3 of 4−3 −2.5 −2 −1.5 −1−0.500.511.52s−αR/LTe=20 ; R/Ln=8solid: ωRdashed: γ(a) TEM ITG −2.5 −2 −1.5 −1−0.4−0.200.20.40.60.81s−αR/LTe=12 ; R/Ln=4.8solid: ωRdashed: γ(b) Figure 3:Growth rateγ (dashed) and frequencyωR (solid) versus(s−αMHD) for two cases:LTe/LTi =0.5 (blue) andLTe/LTi = 0.8 (red). Shear is fixed ats= −0.7.The role of impurities, collisionality and ionsPreliminary results show that TEMs are more unstable due to the impurity driver for valuesof Zeff > 2, and thus the density logarithmic gradient is diminished. Collisionality seems toplay a similar role in decreasing the efficiency of trapped particles in carrying the thermodiffu-sive inward pinch. Ions experimental parameters are presently unknown; to make a quantitativecomparison with theory, a future experimental TCV campaign will be devoted to this issue.Discussion of the resultsThe gyrokinetic simulations of particle transport in this eITB scenario are consistent with theobserved density if conditions are met such that turbulence is near the ITG-TEM transition. Theexperimental results show thatR/Ln is sustained by a dominant anomalous thermodiffusiveinward pinch [1]. This inward pinch is maximized at the ITG-TEM transition, i.e. when themode real frequencyωR approaches zero, and the pinch coefficientCT is found to be consistentwith the experimental values. We have shown thatCT is only due to trapped particles. The TEPand the passing particles contributions are negligible. The combination of negative magneticshear and high values ofαMHD stabilize the TEM and can shift the ITG-TEM transition point tohigher values ofR/Ln near the experimental values. The ion to electron temperature logarithmicgradients ratio is also important since it affects directly the ITG contribution. Values of orderLTe/LTi . 1 are required.AcknowledgementsThis work was supported in part by the Swiss National Science Foundation.References[1] E. Fableet al., Plasma Phys. Contr. Fus.48, 1-13 (2006)[2] E. Fableet al., Theory of Fusion Plasmas, AIP Conference Proceedings871, 318-323 (2006)[3] M. Kotschenreutheret al., Comput. Phys. Commun.88, 128 (1995)[4] C. Angioniet al., Nucl. Fusion44, 827 (2004)[5] D. R. Baker and M. N. Rosenbluth,Phys. Plasmas5, 2936 (1998)[6] F. Jenkoet al., Plasma Phys. Contr. Fus.47, B195 (2005)[7] A. Bottino et al., Plasma Phys. Contr. Fus.48(2), 215 (2006)34th EPS 2007; E.Fable et al. : The role of electron-driven microinstabilities in particle transport during el... 4 of 4

The role of electron-driven microinstabilities in particle transport during electron Internal Transport Barriers

http://hdl.handle.net/21.11116/0000-000A-3AD8-2

The role of electron-driven microinstabilities in particle transport during electron Internal Transport Barriers

Abstract

Similar works

Full text

Available Versions

MPG.PuRe