Angelino, P.

Bottino, A.

Dif-Pradalier, G.

Garbet, X.

Ghendrih, P.

Grandgirard, V.

Jolliet, S.

McMillan, B.

Sarazin, Y.

Tran, T.

Villard, L.

English

MPG.PuRe

Effects of plasma current on drift wave turbulenceP.Angelino1, X. Garbet1, L. Villard2, A. Bottino3, S. Jolliet2, Ph. Ghendrih1,V. Grandgirard1, B. F. McMillan2, Y. Sarazin1, G. Dif-Pradalier1, T. M. Tran21 Association Euratom - CEA, CEA/DSM/IRFM, Cadarache, 13108Saint-Paul-lez-Durance, France2 Centre de Recherches en Physique des Plasmas, EPFL, AssociationEuratom-Confédération Suisse, Lausanne, Switzerland3 Max Plank Institut für Plasmaphysik, Garching, GermanyIntroductionThe operation mode of the future thermonuclear reactors is constrained by the demandof reducing the turbulent transport, which has a major impact on the determination ofthe energy confinement time. The predictions on the turbulent transport level in ITERare based on scaling laws extrapolated from experimental data, rather than a proven andjustified transport model. In these laws the exponent of plasma current is of order unity,hence the importance of this parameter and the necessity to bring theoretical bases tothe scaling laws found in the experiments. Global nonlinear gyrokinetic simulations canprovide more insight to these experimental observations as it has been shown in [1]. Fromthose studies a relationship emerges among the turbulent transport, zonal flow and GAMoscillations through the total plasma current. The amplitude of GAM oscillations in-creases at lower plasma current, resulting in a less effective suppression of ITG turbulenceby zonal flows. Plasma current has an effect not only on GAMs but also on importantquantities such as the orbit widths and linear stability spectrum. As a consequence ofthe combination of these effects, the ion heat flux in the radial direction (the directionrelevant for confinement) is found to scale linearly with the total plasma current. In [1],the analysis has been restricted to a decaying turbulence because of numerical and com-putational limitations. In the following, it will be shown how this analysis can now beextended to stationary turbulence, thanks to recent improvements in numerical techniquesand to the availability of more computational power. In particular, the introduction of anew noise control method and of heat sources [2] make it possible to run simulations ofa steady state turbulence with the global nonlinear gyrokinetic code ORB5 [3][4]. Thesesimulations, compared to the previously available ones, allow us to extend the analysis ofthe mutual interactions of ITG turbulence and large scale flows to a stationary state andto perform a more rigorous statistic analysis of turbulent transport.35th EPS Conference on Plasma Phys. Hersonissos, 9 - 13 June 2008 ECA Vol.32D, P-4.033  (2008)0 0.2 0.4 0.6 0.8 101234567sqs  1X 1.5X2XFigure 1: [left] The three safety factor qs profiles labelled accordingly to the total plasma current case.[right] Logarithmic gradient profiles of temperature (R/LT ) and density (R/Ln). The regions where theheat source/sink is applied are marked with yellow boxes.Model and parametersIn the code ORB5, ion motion is described by means of the nonlinear gyrokinetic Vlasovequation discretized with a Particle In Cell (PIC) scheme. An adiabatic model is used forelectrons, where the flux surface averaged part of the potential has been subtracted inorder to obtain the correct zonal flow amplitude [5]. The system is closed by the Poissonequation that, in the long wavelength approximation, reduces to quasi neutrality equationwhich is solved with a finite element scheme (FEM).Three simulations are presented where the total plasma current has been varied in threesteps: 1, 1.5, 2 (these values are used in the following to label the simulations) times abasic value of IN0 = 0.31, where IN is the normalized current IN = IP/aB. Here, IP is theplasma current [MA], a = 0.48 the minor radius on equatorial plane [m], and B = 1.91the vacuum magnetic field at the center of the discharge [T]. The variation of total plasmacurrent presented here is equivalent to a rescaling of the safety factor (qs) profile as shownin Fig. 1-left, while all the other parameters are kept constant (in particular the magneticshear, which is known to have important effects on the underlying micro-instabilities).The basic configuration is Deuterium plasma with circular magnetic surfaces, normalizedLarmor radius ρ∗ = 1/256 and inverse aspect ratio 0.36. The initial profiles of temperatureand density gradient are shown in Fig. 1-right.A Krook operator modified to conserve energy and preserve zonal flows [2] has beenapplied. Values used in this paper for the Krook noise control coefficient are γs ∼ γITG/20(where γITG is the linear growth rate of the ITG instability), which will be found effective35th EPS 2008; P.Angelino et al. : Effects of plasma current on drift wave turbulence 2 of 40.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9−2.5−2−1.5−1−0.500.511.52x 109sd(K(s))/ds0 0.5 1 1.5 2 2.5x 10501020304050t [Ωi−1]signal/noise  2X1.5X1XFigure 2: [left] Power per unit radius. K(s) is the power deposited in the volume inside the flux surfaces, with the energy in units of miv2Ti, mi and vTi being the ion mass and thermal velocity respectively.[right] Signal to noise ratio.to avoid sampling noise accumulation at late times. In all simulations the noise to signallevel is kept below 10% as shown in Fig. 2-right (the noise definition used here is the oneproposed in [6]). In addition, a heating operator has been chosen to act only in selected’buffer’ regions, one spanning the radial interval 0. < s < 0.3 and the other spanningthe radial interval 0.7 < s < 1 (s is the radial coordinate defined as s = √ψ/ψedge).This choice, combined with the shape of the temperature gradient, effectively couples theplasma with a thermal bath, sustaining the temperature at the center and cooling downthe plasma edge, but leaving a turbulent region where the temperature gradient is leftfree to evolve self-consistently. The effective profile of the energy deposited, integratedover the whole simulation time, is plotted in Fig. 2-left.Results and conclusionsWe compare the time evolutions of the temperature gradient (represented by the tem-perature gradient length R/LT ) and of the heat flux. These two quantities are averagedover the radial interval 0.3 < s < 0.7, where the drive of the turbulence is maximumand the source is switched of. A temporal moving average is also applied with a timewindow of 7 · 104Ω−1ci . Fig. 3 shows that decreasing the total plasma current causes a netincrease in the turbulent heat flux which results in an increased difficulty in sustainingthe temperature gradient with a fixed source level (here represented by the Krook heatingcoefficient γH = 1 · 10−4). Doubling the input power in the 1X case compared to the 2Xcase (Fig. 2) is still not sufficient to maintain a temperature gradient as steep as for the2X case, see Fig. 3-left.35th EPS 2008; P.Angelino et al. : Effects of plasma current on drift wave turbulence 3 of 40.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 105−8−7.8−7.6−7.4−7.2−7−6.8−6.6−6.4−6.2−6t (Ωci)R/LT  1X, γH = 3⋅10−41X, γH = 10−41.5X, γH = 10−42X, γH = 10−40.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 10500.511.522.533.5x 10−4〈Q̂〉t (Ωci)Figure 3: [left] Temporal moving average of the ion temperature gradient length R/LT . [right] Temporalmoving average of the normalized heat flux Q̂ = Q/(nicsTe). ni is the ion density, cs the sound speedand Te the electron temperature.These results show that the dependence on the current of the turbulent transport foundfor decaying turbulence [1] can be extended to a stationary turbulent state, thus thepresence of an extra degree of freedom, represented by the heat source, makes not trivialto recover the linear behavior of transport with the total plasma current (see Fig. 3-right).A statistical analysis of zonal flow and GAM properties will be the subject of future work.AcknowledgmentsThe CRPP authors where partly supported by the Swiss National Science Foundation. TheORB5 simulations have been run on the IBM Blue Gene parallel machine at the EPFL, Switzer-land.References[1] Angelino, P. et al. Plasma Phys. Control. Fusion 48, 557—571 (2006).[2] McMillan, B. et al. Physics of Plasmas 15 (5), 052308 (2008).[3] Jolliet, S. et al. Computer Physics Communications 177 (5), 409—425 (2007).[4] T.M. Tran et al. in Theory of Fusion Plasmas, Int. Workshop. Editrice Compositori,SIF, Bologna, page 45, (1999).[5] Angelino, P. et al. in Theory of Fusion Plasmas, Int. Workshop. Editrice Compositori,SIF, Bologna, page 329, (2004).[6] Bottino, A. et al. Physics of Plasmas 14 (1), 010701 (2007).35th EPS 2008; P.Angelino et al. : Effects of plasma current on drift wave turbulence 4 of 4

Effects of plasma current on drift wave turbulence

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Effects of plasma current on drift wave turbulence

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