Session PO08: Magnetic Confinement: Turbulence & Transport

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The Eulerian variational formulation of gyrokinetic systems with electrostatic turbulence is presented in general spatial coordinates by extending our previous work [H. Sugama, {\it et al}., Phys.\ Plasmas {\bf 25}, 102506 (2018)]. The invariance of the action integral under an arbitrary spatial coordinate transformation is used to derive the local momentum balance equation satisfied by the governing equations for the gyrocenter distribution functions and the turbulent potential. This derivation is in contrast with the conventional method using the spatial translation in which the asymmetric canonical pressure tensor generally enters the momentum balance equation. In the present study, the variation of the Lagrangian density with respect to the metric tensor is taken to directly obtain the symmetric pressure tensor which includes the effect of turbulence on the momentum transport. In addition, it is shown in this work how the momentum balance is modified when the collision and/or external source terms are added to the gyrokinetic equation. The results obtained here are considered useful for global gyrokinetic simulations investigating both neoclassical and turbulent transport processes even in general non-axisymmetric toroidal systems.   

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Radial correlation Doppler reflectometry (RCDR) is routinely used to extract the radial correlation length of the turbulence in magnetic confinement devices, but open questions remain in the interpretation of the measured values. Measurements [1] have shown radial correlation lengths exceeding the ion gyro-radius, however DBS is routinely sensitive to intermediate to high-k e- scale fluctuations. This offers several interpretations from the measurement and the underlying turbulence. We present a conceptual study of RCDR using nonlinear gyrokinetic simulations from GYRO and GS2 based on NSTX H-mode and JET L-mode discharges. The turbulence radial correlation length is compared to correlation lengths computed using a synthetic RCDR. The width of the probe beam and the measured wavenumber are shown to be critical parameters determining the RCDR correlation length. The tilt angle of turbulent eddies in the poloidal plane [2] is strongly influenced by Doppler shift and ExB shear. The ultimate goal is to characterize the presence of ITG vs. ETG-driven turbulence through RCDR. [1] Schirmer PPCF 2007, [2] Pinzon NF 2019.   

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First-principles-based calculation of plasma transport in given stochastic magnetic fields has been developed for a global gyrokinetic simulation code GTS to confront specific challenges of thermal quench transport issues in tokamak disruption modeling. A novel delta-f particle approach and a new field solver for the 3-dimensional gyrokinetic Poisson equation enable an effective and accurate simulation of nonlinear evolution of the global plasma profiles in the stochastic magnetic fields. We emphasize the consistent coupling of electron and ion dynamics through transport ambipolarity induced electric field which plays a critical role in determining plasma transport in such systems. The electric fields slow down and enhance the parallel transports of the electrons and ions, respectively, so the ambipolar rarefaction waves propagate from the edge to the core. At the same time, the established potential in the stochastic layer produces strong ExB vortices that mix the plasma across the stochastic field lines resulting in faster radial transports. As a result, we observed a rapid degradation of the global plasma profile within several milliseconds that agrees with the typical time scale of the thermal quench.   

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Gyrokinetic simulations are routinely performed to understand and predict magnetic confinement. Previous works have used model collision operators (e.g., Lorentz, Abel, Sugama models) with approximate field-particle terms of unknown accuracy and/or have neglected collisional finite Larmor radius (FLR) effects. This work moves beyond models to implement a gyrokinetic exact linearized Fokker--Planck collision operator for the first time in a gyrokinetic code (the GENE code)\footnote{Q. Pan, D. R. Ernst, P. Crandall, Phys. Plasmas \textbf{27} (2020).}. The conservative and symmetric Landau form\footnote{Q. Pan, D. R. Ernst, Phy. Rev. E \textbf{99} (2019).} preserves the conservation laws and H-theorem. The new exact operator allows the accuracy of collision models to be assessed. Comparison with the recent Sugama model implemented in the same code\footnote{P. Crandall et al., Comput. Phys. Commun. \textbf{255} (2020).} shows significant differences for temperature-gradient-driven trapped electron mode (TEM) turbulence (up to 68\% in fluxes) and zonal flow damping, also for microtearing modes in a JET-ILW pedestal. The difference is parameter-dependent; the two operators closely agree for density-gradient-driven TEM turbulence and some drift-type modes in the JET pedestal.   

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Turbulent transport in fusion plasmas causes limited performance in present-day experiments. While turbulent fluctuations can possibly be suppressed by exploiting the freedom of stellarator magnetic fields, this task requires robust transport models to enable fast predictions, preferably based only on magnetic geometry. The current state-of-the-art models are built using extrapolations from linear physics. However, the nonlinear character of turbulence calls for the inclusion of the mechanisms responsible of turbulence saturation. With aims to develop a transport model that includes zonal flows as saturation mechanisms of ion-temperature-gradient (ITG) turbulence, we will present the characteristics of zonal flow levels in various geometries of Wendelstein 7-X, simulated using the gyrokinetic code GENE. The exponential decay of the linear response is found to be highly affected by the characteristic geodesic curvature lengthscale, opposite to what is seen in nonlinear simulations. Nonlinearly, the shape of the turbulent mode is increasingly modulated by the drift well, where we define a characteristic lengthscale. We then propose that both lengthscales can be directly related to zonal flow generation and decay, to set the basis for improved transport prediction   

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Strong anomalous transport outside the core of the the Helically Symmetric eXperiment (HSX) is likely due to the Trapped Electron Mode (TEM). This study compares linear and nonlinear gyrokinetic simulations from the GENE code to experimental heat flux and density fluctuation measurements for two configurations: Quasi-Helical Symmetry (QHS) and broken symmetry (Mirror). The Mirror configuration reduces the overlap of the magnetic trapping and bad curvature regions, and reduces the peak TEM linear growth rates. While this suggests the heat flux would be smaller in the Mirror configuration, neither the experimental or nonlinear simulation heat flux matches this expectation. At zero temperature gradient, the electron heat flux is reduced in the QHS configuration, but the difference is negated when including finite temperature gradient and non-unity electron/ion temperature ratio. Matched to experimental parameters, the magnitude of the heat flux from nonlinear simulation shows good agreement with experimental measurements. Simulated density fluctuations are larger when the density gradient exceeds the electron temperature gradient, and reflectometer measurements of turbulence amplitudes localized to the peak driving gradient will be compared to simulation results.   

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A phase contrast imaging (PCI) diagnostic has been implemented on the Wendelstein 7-X (W7-X) stellarator to measure line-integrated, ion-scale density fluctuations with the aim of studying plasma turbulence, which is expected to be the major loss channel of particles and energy compared to the reduced neoclassical transport. In the recent operational campaign, a limit of core ion temperature has been observed under a wide range of plasma parameters. In contrast to pellet fuelled and ECH heated discharges, pure neutral beam injection (NBI) shows no significant rise of the ion temperature, in spite of a strongly peaked density profile that develops in the core plasma with increasing density. The PCI measurements show that the absolute density fluctuation amplitude remains nearly unchanged during NBI. Introducing additional low power ECH can lead to a transient increase of the ion temperature. A low frequency mode can be observed by PCI in this transient phase.   

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Global gyrokinetic particle simulations of electrostatic ion temperature gradient (ITG) instability show that self-generated zonal flows are the dominant saturation mechanism for the ITG instabilities in both LHD and W7-X. Nonlinear spectra in the W7-X are dominated by low-n harmonics, which can be generated both by nonlinear toroidal coupling of high-n harmonics and by linear toroidal coupling with large amplitude zonal flows due to the 3D equilibrium magnetic fields. Simulations of linear collisionless damping of zonal flows show both damped geodesic acoustic mode (GAM) in LHD and low frequency oscillations (LFO) in both LHD and W7-X. The impact of a radial electric field (self-consistently generated by neoclassical theory) has been also analyzed showing a transport reduction due the associated ExB flow. Kinetic electrons enhance ITG growth rate and ion heat transport. First trapped electron mode (TEM) simulations are observed. The mode structure in W7-X seems to be localized in the toroidal region where the magnetic field is weaker.   

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Alternative divertor configurations represent a possible solution to the power exhaust problem in tokamaks. Most of these configurations act on the poloidal length of the divertor legs, the strike point radius, and the flux expansion at the target, aiming to facilitate the access to a highly dissipative, detached divertor regime. The largest uncertainties in the prediction of the optimal geometry are related to the effect of geometry on Scrape-Off Layer (SOL) turbulence. The dependence of turbulence on divertor geometric parameters was experimentally investigated on TCV, exploiting the extensive diagnostic coverage of the edge plasma, including a Reciprocating Divertor Probe Array. This analysis identifies the poloidal divertor leg length as the parameter leading to the largest variation in the SOL heat flux width. These experiments were run at lowered toroidal field, allowing for quantitative comparison with full-size, 3D fluid turbulence simulations performed with GBS [Ricci et al., Plasma Phys. Control. Fusion 2012] in realistic magnetic geometries. A validation of these simulations against experiments through a rigorous procedure will be presented.   

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Multiple gas puff of H$_{\mathrm{2}}$ and D$_{\mathrm{2}}$ of appropriate magnitude are applied during current flat-top in ADITYA-U tokamak to study the cold-pulse propagation and effect of these puffs on plasma confinement. The results indicate the simultaneous occurrence of plasma detachment along with propagation of a cold pulse, i.e., a decrease in the edge temperature ($\rho $ \textasciitilde 0.9-1.0) and an increase in the core temperature on a time-scale less than the energy confinement time, after each gas puff. Initial increase in the radiated power, H$_{\mathrm{\alpha }}$ and CIII signals and subsequent improvement in confinement indicate plasma detachment from the limiter. The increase in energy confinement time by a factor of 2-3 is due to the density peaking along with the suppression of edge density fluctuations due to flattening of density profile in the edge due to gas puff. Both the cold-pulse and the detachment phenomena have a density threshold, i.e., above n$_{\mathrm{e}}$ \textasciitilde 2.7 x 10$^{\mathrm{19}}$ m$^{\mathrm{-3}}$, no detachment and propagation have been observed.   

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Recent and growing evidence points toward the micro-tearing mode (MTM) as an important fluctuation for the heat transport in the H-mode pedestal. An extensive study of the instabilities in the pedestal region has been carried out using local and global linear gyrokinetic simulations using the GENE code and successfully reproduced the magnetic spectrogram for an ELMy H-mode DIII-D discharge (USN configuration, 1.4 MA plasma current, and 3 MW heating power). The simulations of the main instabilities show many properties that can clearly be identified as MTM, including predominantly electromagnetic heat flux, small particle flux, and a substantial degree of tearing parity. The magnetic spectrogram from Mirnov coils exhibits three distinct frequency bands —two narrow bands at lower frequency (~50-100 kHz) and a broader band at higher frequency (~325-425 kHz) with all peaks at r/a=0.975. Global GENE simulations reproduce these bands quantitatively, and many features of these bands can be understood from the basic physical mechanisms underlying these instabilities. For example the MTM instabilities in the lower bands of fluctuations have a slab-like nature, whereas the higher band involves toroidal effects.