Alcuson, J.

Grulke, O.

Warmer, F.

Xanthopoulos, P.

English

MPG.PuRe

Turbulent transport mechanisms in Wendelstein 7-X plasmasJ.A. Alcusón1, F. Warmer1, P. Xanthopoulos1, O. Grulke1,2 and the W7-X Team1.1 Max Planck Institut fuer Plasmaphysik, Greifswald, Germany2 Technical University of Denmark, Copenhagen, DenmarkIntroduction. Radial transport in non-optimized stellarators is dominated by a high neo-classical (NC) contribution. In tokamaks, as this contribution is inherently minimal due to thesymmetry of the device, the radial losses are essentially attributed to turbulence [1]. The op-timized Wendelstein 7-X (W7-X) stellarator is designed to reduce the NC transport down totokamak levels. Results from the first and the second experimental campaigns in W7-X suggestthat NC transport is not sufficient to explain the radial losses in several scenarios (especiallyat the edge re f f > 0.6), opening the door to the turbulent transport contribution as a plausiblecandidate to explain these discrepancies.Figure 1: Profile examples for density (top)and temperatures (bottom) considered inGENE simulations.The present work aims to serve as a guide for fu-ture studies connecting experimental and numeri-cal estimations of turbulence in W7-X. Based ongyrokinetic simulations performed with the GENEcode [2, 3] under W7-X experimental conditions,we will characterize the turbulent transport by iden-tifying the dominant electrostatic instability (basi-cally ion temperature gradient ITG, electron tem-perature gradient ETG and trapped-electron modeTEM) in two different configurations, standard(EIM) and high mirror (KJM), at ion scales (scalesusually measured by the diagnostics). Simulationsused in this analysis are linear, flux-tube and havekinetic ions and electrons. All simulations are setin the same magnetic surface1 (s0 = 0.5). For eachconfiguration two different scenarios are imple-mented: core and edge, both based on typical pro-files measured during the last W7-X OP1.2a cam-paign.1Instability growth rates also depend on the radial position, but in the profiles used for the study such variationis below 10% and the dominant instability is the same.45th EPS Conference on Plasma Physics P2.1088Figure 2: Stability maps in terms of a/LTi and a/LTe for core plasmas in standard (left) and high mirror(right) configurations. Dominant micro-instability regions at ion scale are also marked. The black regionrefers to not accesible conditions during OP1.2a.Instabilities are characterized in terms of their propagation (ion or electron) direction andtheir mode amplitude structure (localized or extended). The dominant instability at ion scales isdetermined using a mixing length model in terms of γ/(kyρ)2, where γ is the maximum growthrate of the instability, and kyρ the associated perpendicular wavenumber. A criteria where theion scales are clearly favored.Stability maps. In the core, W7-X density profiles are usually flat, but have a rather steepelectron temperature (Te) profile (see Fig. 1). Therefore, our core simulations assume zero den-sity gradients ∇n = 0, and strong electron temperature gradients a/LTe ≥ a/LTi where a is theminor radius and a/LT =−a∇ lnT . The electron temperatures are usually higher than ion tem-peratures, so simulations are set for Te/Ti = 3.5. Fig. 2 shows the stability map of the growthrates for both configurations. The ETG and ITG regions are slightly bigger in the high-mirrorconfiguration reducing the "mixed mode" region, where the modes appear with similar growthrates at ion scales. In general both configuration exhibit a very similar map. The dominant insta-bility switches from ITG to ETG (slab-style) as we increase the electron temperature gradient(from bottom to the top).For the outer region of the plasma, our simulations assume coupled species: ni = ne, Ti = Teand ∇Te = ∇Ti (see Fig 1). Fig. 3 shows stability maps in the outer plasma for both config-urations. ITG and TEM regions similar to the standard configuration are also present in highmirror configuration. Nevertheless, strong gradients regions (top-right in the maps) show a dif-45th EPS Conference on Plasma Physics P2.1088Figure 3: Stability maps in terms of a/Ln and a/LT for core plasmas in standard (left) and high mirror(right) configurations. Dominant micro-instability regions at ion scale are also marked.ferent behaviour. In fact, the high mirror configuration has a dominant ITG at ion scales andan ion driven TEM (iTEM) [5] instead of a mixed mode like in standard configuration as wecan see in the left plot of Fig. 4. iTEM are trapped modes as the ordinary TEM, but propa-gate in the ion direction. They draw free energy from ions, rather than from electrons, but theyneed the trapped-electron population to exist and are associated to maximum-J configurations.By "mixed ITG/iTEM" instability we allude to a situation where the instabilities are practicallyindistinguishable regarding growth rates and scales. When both configurations exhibit the lastmixed mode instability they usually have a similar growth rate, but the high mirror configura-tion has the instability displaced to shorter scales as we can see in the second plot of the sameFig. 4.Conclusions and future work. Neoclassical transport estimations seem to have discrepan-cies with real measurements in the last W7-X campaigns and turbulent transport is the bestcandidate to explain these discrepancies. Stability maps are a very useful first step to charac-terize the dominant instability for future comparisons between turbulent transport experimentalresults and numerical simulations. Using general profiles from W7-X measured plasmas we cancreate these maps for different configurations. In particular, we show the stability maps of stan-dard and high mirror configurations at ion scales. With the experimental profiles considered,only ITG and slab-ETG instabilities are possible in the core. These instabilities are not stronglyinfluenced by the configuration, producing very similar stability maps for both cases.In the outer plasma, ITG, TEM and slab-ETG instabilities can drive the turbulence at ion45th EPS Conference on Plasma Physics P2.1088Figure 4: Left: Growth rate spectrum for standard (blue) and high mirror (red) configurations witha/Ln = 6 and a/LT = 8. Right: Same mixed ITG/iTEM instability for standard and high mirror.scales. Stability maps are different in the strong gradient region, where the standard configura-tion exhibits a mixed ITG/iTEM instability whereas the high mirror configuration an ITG. Inparticular, the latter configuration also has a non dominant iTEM. Its higher quasi-isodynamicitythan the standard configuration should reduce the trapped-electron population which probablyis related with a weaker TEM response, allowing the ITG to become dominant. In the regionsof mixed ITG/iTEM and of strong gradients, TEMs are not at the same scale, and usually highmirror TEMs are at smaller scales. The scale displacement implies different energy and fluxesin non-linear simulations even if both configurations have the same dominant instability andsimilar growth rate. Nonlinear simulations are also necessary to estimate the energy and fluxesproduced by these instabilities. The ultimate goal is to quantify the total contribution of theturbulent transport to the power balance and clarify if the neoclassical estimations and turbulentcontribution are enough to explain the heat losses.References[1] P. Helander, C.D. Beidler, T.M. Bird, M. Drevlak, Y. Feng, R. Hatzky, F. Jenko, R. Kleiber, J.H.E. Proll. Y.Turkin and P. Xanthopoulos, Phys. Control. Fusion 54, 124009 (2012).[2] F. Jenko, W. Dorland, M. Kotschenreuther and B.N. Rogers, Phys. Plasmas 7, 1904 (2000).[3] P. Xanthopoulos, H.E. Mynick, P. Helander, Y. Turkin, G.G. Plunk, F. Jenko, T. Goerler, D. Told, T. Bird andJ.H.E. Proll, Phys. Rev. Lett. 113, 155001 (2014).[4] J.H.E. Proll, P. Helander, J.W. Connor and G.G. Plunk, Phys. Rev Lett. 108, 245002 (2012).[5] G.G. Plunk, J.W. Connor and P. Helander, J. Plasma Phys. 83, 715830404 (2017).45th EPS Conference on Plasma Physics P2.1088

Turbulent transport mechanisms in Wendelstein 7-X plasmas

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Turbulent transport mechanisms in Wendelstein 7-X plasmas

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