Alcuson, J.

Beurskens, M.

Bozhenkov, S.

Bähner, J.

Edlund, E.

Ford, O.

Grulke, O.

Hansen, S.

Huang, Z.

Langenberg, A.

Pablant, N.

Porkolab, M.

Smith, H.

Stechow, A.

Vano, L.

Windisch, T.

English

MPG.PuRe

Core plasma density fluctuations in Wendelstein 7-X ECRH plasmasJ.-P. Bähner1, J. A. Alcusón1, S. K. Hansen2, A. v. Stechow1, O. Grulke1,3, T. Windisch1,H. M. Smith1, Z. Huang2, E. M. Edlund4, M. Porkolab2, M. N. A. Beurskens1, S. A. Bozhenkov1,O. P. Ford1, L. Vanó1, A. Langenberg1, N. Pablant5, and The W7-X Team11Max Planck Institute for Plasma Physics, Greifswald, Germany2MIT Plasma Science and Fusion Center, Cambridge, MA, USA3Technical University of Denmark, Kongens Lyngby, Denmark4SUNY Cortland, Cortland, NY, USA5Princeton Plasma Physics Laboratory, Princeton, NJ, USAIntroductionThe Wendelstein 7-X (W7-X) stellarator was optimised for reduced neoclassical transport,which was proven to be successful in the first experiment campaigns [1, 2]. Accordingly, anoma-lous transport becomes more important for the global confinement and the focus of interest shiftstowards turbulence. As part of the efforts to understand the nature of turbulence in W7-X andeventually its role for transport, this work investigates turbulent core density fluctuations in reg-ular discharges of W7-X experimentally via phase contrast imaging (PCI) [3, 4] in combinationwith gyrokinetic simulations with the code GENE [5].Radial localisation of density fluctuations0.0 0.2 0.4 0.6 0.8 1.0reff/a0246 neTeTi0.0 0.2 0.4 0.6 0.8 1.0reff/a0246810a/Lna/LTea/LTiFigure 1: Experimental plasma densityand temperature profiles and correspond-ing normalised gradient length scales ofW7-X XP:20180906.38, 4.5s-6.5sA gas-fuelled hydrogen discharge with 3.2MWof electron cyclotron heating in the standard mag-netic configuration is investigated as a representa-tive reference case for the majority of experimentsin the last operation phase. There is no direct ionheating in this type of discharge and the ion temper-ature remains low and relatively flat throughout theplasma core, while the electron temperature is cen-trally peaked. The plasma density profile is flat overmost of the plasma radius. Fig. 1 shows the exper-imental time averaged profiles and correspondingnormalised gradient length scales.The PCI diagnostic measures line integrated electron density fluctuations through the wholeplasma with a temporal and spatial resolution that allows for the measurement of low frequency47th EPS Conference on Plasma Physics P5.1065ion scale turbulence and a simultaneous wavenumber and frequency (k f ) analysis. The measure-ment direction of the spatial resolution is perpendicular to the line of sight and roughly poloidal.Fig. 2 shows a wavenumber-frequency spectrum of the reference discharge. Opposing propaga-tion directions with respect to the measurement direction are reflected by positive and negativewavenumbers. In both wavenumber branches, it is observed that a large fraction of the spectralpower is carried by fluctuations with the same phase velocity in the measurement direction, vPCIph .5 0 5k [1/cm]100200300400f [kHz]302010psd [dB]Figure 2: Experimental k f -spectrum byPCI with dominant phase velocities andwavenumber spectrum (top panel).It reflects a projection of the fluctuations propaga-tion velocity in the binormal direction onto the mea-surement direction,vPCIph = uy · êm, (1)where the former, uy, is a combination of the mode’sphase velocity in the plasma frame, vITGph , and aDoppler-shift by the E×B rotation of the plasma,uy = vITGph + vE×B ≈ vE×B. (2)The E×B velocity is generally much larger that the phase velocity of the turbulent modes[6, 7, 8]. A single dominant phase velocity in the wavenumber-frequency spectrum thereforeimplies, that most of the fluctuations are localised at a certain radius such that the E×B velocityat that radius determines the observed vPCIph .0.0 0.2 0.4 0.6 0.8 1.0reff/a1050510E rNC [kV/m]i-roote-rootDRFigure 3: Radial electric field measure-ments by Doppler-reflectometry (DR) anda DKES simulation.For a direct comparison to the E×B velocity atthe position of the PCI measurement, neoclassicalsimulations with the code DKES [9] are used to ob-tain the ambipolar radial electric field, which gen-erally agrees well with measurements by Doppler-reflectometry (DR) and other diagnostics [8, 10, 11](see fig. 3). The local E×B velocity is then ob-tained byvE×B = 〈Er〉NC|∇reff|/B, (3)where 〈Er〉NC is the flux-surface averaged value simulation output, B is the magnetic fieldstrength and |∇reff| accounts for the flux compression.A direct comparison is only valid between vE×B and uy. Therefore the projection describedin eq. (1) has to be inverted, which depends on the position along the PCI line of sight and evenslightly varies across it. Fig. 4 shows the comparison of the inferred uy (black) and vE×B (blue).47th EPS Conference on Plasma Physics P5.10651 0.75 0.5 0.25 0 0.25 0.5 0.75 1inboard                 reff/a             outboard642024vdia e    v [km/s]    vdiaielectron   root ionrootvE × BPCI uyvE × B + ITG vphFigure 4: Comparison of binormal velocity correspond-ing to dominant phase velocity in the PCI spectrum andlocal E×B velocity along the PCI line of sight.The faded blue and black lines rep-resent the variation across the PCIlaser beam, colour weighted by therespective laser amplitude. The redmark is the phase velocity of themost dominant mode obtained fromlinear gyrokinetic simulations addedto the E×B velocity in order to il-lustrate the approximation in Eq. 2.The quantities match best at a radialposition of reff/a≈ 0.75, at the wellof the ion root solution. The matchimplies that this is the radial location where the strongest fluctuations arise.Gyrokinetic simulations with GENELinear simulations for several positions along the plasma radius were performed for a detailedanalysis of the radial evolution of microinstabilities. Idealised profiles based on the experimen-tal reference case were used as input to the simulations. It is found that the electron temperaturegradient contribution is dominant for most of the plasma and even for intermediate scales. How-ever, it is worthwhile running simulations without an electron temperature gradient (a/LTe = 0)in order to investigate ITG and TEM only, which generally determine the ion scale fluctuationsnon-linearly. A clear picture arises in these simulations in normalised units: The ITG mode isdominant (over TEM) at all radii and the growth rate increases with increasing effective radius,which strictly follows the evolution of a/LTi, the driving term for ITG modes. The normalisa-tion strongly depends on the ion temperature, which is why the picture changes in real units.0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0reff/a0123456n2[1017m3] inboardoutboard02468Ti[keV/m]Figure 5: Local density fluctuations fromnon-linear GENE flux-tube simulationsand ion temperature gradient.At the very edge, the growth rate is reduced and thedominant mode moves to higher wavenumbers. Ul-timately, the ion-scale growth rate peaks at reff/a≈0.7, which supports the experimentally observed lo-calisation from the perspective of linear microin-stabilities. In order to simulate density fluctuations,non-linear simulations are needed. Flux-tubes thatintersect the PCI line of sight at three different ra-dial locations were chosen and the correspondinggradients of the experimental profiles (fig. 1) used47th EPS Conference on Plasma Physics P5.1065as input. Furthermore, the simulations were electrostatic, collisionless and both ions and elec-trons were treated kinetically. Fig. 5 shows the density fluctuations at the location of the PCI lineof sight on the inboard and outboard side. We find additional support for the radial localisation,because in the flux-tube at reff/a = 0.75 the density fluctuations are the strongest. Additionally,there is a difference between the inboard and outboard side at this radial location, which is ob-served in the experimental k f -spectrum of PCI (fig. 2). The ion temperature gradient is shownalongside the density fluctuations in order to illustrate the close connection to the dominantdrive of turbulence in this radial region.ConclusionDensity fluctuations in regular W7-X discharges are characterised by a dominant ITG-driveand a radial localisation at reff/a ≈ 0.75, which generally is the same radial region as theEr-well. This can be shown experimentally and in gyrokinetic simulations (for more details,see [12]). TEMs play a minor role at all radii and scales. ETG is linearly strong but not ob-served in the outer half of the plasma experimentally or in non-linear simulations.AcknowledgementsThis work is partly sponsored by the US Department of Energy, Office of Fusion Energy Sci-ences under grant number DE-SC0014229. This work has been carried out within the frame-work of the EUROfusion Consortium and has received funding from the Euratom research andtraining programme 2014–2018 and 2019–2020 under grant agreement No 633053. The viewsand opinions expressed herein do not necessarily reflect those of the European Commission. S.K. Hansen acknowledges support by an Internationalisation Fellowship (CF19-0738) from theCarlsberg Foundation.References[1] T. Klinger et al., Nucl. Fusion 59 (11), 112004 (2019)[2] R. C. Wolf et al., Phys. Plasmas 26 (8), 082504 (2019)[3] E. Edlund et al., Rev. Sci. Instrum. 89 (10), 10E105 (2018)[4] Z. Huang et al., J. Instrum. 16 (01), P01014 (2021)[5] F. Jenko et al. Phys. Plasmas 7 (5), 1904–1910 (2000)[6] G. D. Conway et al., Phys. Rev. Lett. 106, 065001 (2011)[7] T. Windisch et al., Rev. Sci. Instrum. 89 (10), 10H115 (2018)[8] D. Carralero et al., Nucl. Fusion 60 (10), 106019 (2020)[9] S. P. Hirshman et al., Phys. Fluids 29 (9), 2951–2959 (1986)[10] N. Pablant et al., Phys. Plasmas 25 (2), 022508 (2018)[11] O. Ford et al., Rev. Sci. Instrum. 91 (2), 023507 (2020)[12] J.-P. Bähner et al., J Plasma Phys. (2021) accepted47th EPS Conference on Plasma Physics P5.1065

Core plasma density fluctuations in Wendelstein 7-X ECRH plasmas

http://hdl.handle.net/21.11116/0000-0009-AD07-D

Core plasma density fluctuations in Wendelstein 7-X ECRH plasmas

Abstract

Similar works

Full text

Available Versions

MPG.PuRe