Session NI3: MFE Transport and Turbulence

The Role of ITG/TEM/ETG Cross-Scale Coupling in Explaining Experimental Electron Heat Flux and Profile Stiffness

Anomalous electron thermal transport in tokamak plasmas is the ``great unsolved problem of tokamak transport physics'' [Batchelor Plasma Sci. Tec. 2007]. For years it has been speculated that short wavelength ETG turbulence plays a key role, but simulation capturing both ion and electron-scale turbulence simultaneously had never been tested quantitatively against experiment due to extreme computational requirements. Only recently have gyrokinetic codes and supercomputing resources together been able to capture the physics of cross-scale coupling between long wavelength ITG/TEM and short wavelength ETG turbulence. In C-Mod, long wavelength simulations often under-predict electron heat flux. As a result, dedicated experiments have been performed in L-mode plasmas to validate multi-scale nonlinear gyrokinetic simulations. In this talk, the first set of full-physics, multi-scale simulations of a tokamak plasma performed with the GYRO code are compared to experiment. The simulations include coupled ITG/TEM/ETG turbulence (k$_\theta \rho_s < 48.0$) at realistic mass ratio (m$_i$/m$_e$ $=$ 3600), with experimental inputs for impurities, geometry, ExB shear, and collisions. 100M CPU hours were required for six simulations to scan the ITG and ETG drive terms (a/L$_{\mathrm{Ti}}$ and a/L$_{\mathrm{Te}})$ within experimental error bars. The multi-scale simulations show for the first time that ETG streamers coexist and nonlinearly couple with ITG and zonal flows. This nonlinear cross-scale coupling enhances both ion and electron heat fluxes by up to a factor of 10 above standard, long wavelength simulation, resulting in simulations that simultaneously match experimental ion and electron heat fluxes and electron profile stiffness. The new physics of ITG/ETG/zonal flow coupling has important implications for predictions of ITER performance and may be linked to phenomena such as confinement transitions and rotation reversals.   

Gyrokinetic studies of core turbulence features in ASDEX Upgrade: Can gyrokinetic simulations match the fluctuation measurements?

Worldwide, gyrokinetic codes are used to predict the dominant micro-instabilities as well as the resulting anomalous transport in fusion experiments. A careful verification and validation of these codes is crucial to develop confidence in the model and improving the predictive capabilities of the numerical simulations. To date, the validation of gyrokinetic simulations versus experiments is mainly done at a macroscopic level, namely, by comparing turbulent heat fluxes. This is usually achieved by varying the profile gradients within the experimental error bars until a match with the experimental heat fluxes is obtained. However, since the turbulent fluxes are caused by plasma fluctuations on microscopic scales, it is also necessary to validate gyrokinetic codes on a microscopic level. We will describe a recent step in this direction by presenting simulation results with the gyrokinetic code GENE for an ASDEX Upgrade discharge. In particular, after flux-matched simulations are achieved, density fluctuations measured by means of Doppler reflectometry are compared with results of gyrokinetic simulations. We will also show that density and temperature fluctuation amplitudes and even the fluctuation spectra can be very sensitive to small changes in the profile gradients. This implies that a match of gyrokinetic simulations with experiment measurements for these quantities can be very difficult to achieve. However, it is observed that cross-phases between different quantities are robust to changes in this parameter, indicating that cross-phases could be a better observable for comparisons with experimental measurements.   

Role of Density Gradient Driven Trapped Electron Modes in the H-Mode Inner Core with Electron Heating

We present new experiments and nonlinear gyrokinetic simulations showing that density gradient driven TEM (DGTEM) turbulence dominates the inner core of H-Mode plasmas during strong electron heating. Thus $\alpha$-heating may degrade inner core confinement in H-Mode plasmas with moderate density peaking. These DIII-D low torque quiescent H-mode experiments were designed to study DGTEM turbulence.\footnote{D. R. Ernst et al., 2014 IAEA Fusion Energy Conference, St. Petersburg, Russia, paper CN221-EX/2-3.} Gyrokinetic simulations using GYRO (and GENE) closely match not only particle, energy, and momentum fluxes, but also density fluctuation spectra, with and without ECH. Adding 3.4 MW ECH doubles $T_e/T_i$ from 0.5 to 1.0, which halves the linear TEM critical density gradient, locally flattening the density profile. Density fluctuations from Doppler backscattering (DBS) intensify near $\rho=$0.3 during ECH, displaying a band of coherent fluctuations with adjacent toroidal mode numbers. GYRO closely reproduces the DBS spectrum and its change in shape and intensity with ECH, identifying these as coherent TEMs. Prior to ECH, parallel flow shear lowers the effective nonlinear DGTEM critical density gradient 50\%, but is negligible during ECH, when transport displays extreme stiffness in the density gradient. GS2 predictions show the DGTEM can be suppressed, to avoid degradation with electron heating, by broadening the current density profile to attain $q_{0}>q_{\mathrm{min}}>1$. A related experiment in the same regime varied the electron temperature gradient in the outer half-radius ($\rho\sim 0.65$) using ECH, revealing spatially coherent 2D mode structures in the $T_e$ fluctuations measured by ECE imaging. Fourier analysis with modulated ECH finds a threshold in $T_e$ profile stiffness.   

Turbulence Decorrelation via Controlled $E$x$B$ Shear in High-Performance Plasmas

Multi-scale spatiotemporal turbulence properties are significantly altered as toroidal rotation and resulting ExB shearing rate profile are systematically varied in advanced-inductive H-mode plasmas on DIII-D ($\beta_N\approx$2.7, $q_{95}$=5.1). Density, electron and ion temperature profiles and dimensionless parameters ($\beta_N$, $q_{95}$, $\nu^*$, $\rho^*$, and $T_e$/$T_i$) are maintained nearly fixed during the rotation scan. Low-wavenumber turbulence ($k_\bot\rho_S < 1$), measured with Beam Emission Spectroscopy, exhibits increased decorrelation rates (reduced eddy lifetime) as the ExB shear rises across the radial zone of maximum shearing rate (0.55$ < \rho < 0.75$), while the fluctuation amplitude undergoes little change. The poloidal wavenumber is reduced at higher shear, indicating a change in the wavenumber spectrum: eddies elongate in the direction orthogonal to shear and field. At both low and high shear, the 2D turbulence correlation function exhibits a tilted structure, consistent with flow shear. At mid-radius ($\rho\sim$0.5), low-k density fluctuations show localized amplitude reduction, consistent with linear GYRO growth rates and $\omega _{ExB}$ shearing rates. Intermediate and high wavenumber fluctuations measured with Doppler Back-Scattering ($k_\bot\rho_S\sim$2.5-3.5) at $\rho$=0.7 and Phase Contrast Imaging ($k_\bot\rho_S > 5$) exhibit decreasing amplitude at higher rotation. The energy confinement time increases from 105 ms to 150 ms as the toroidal Mach number (M=$v_{TOR/vth,i}$) increases to ${M_o} \approx$ 0.5, while transport decreases. TGLF calculations match the $T_i$ profile with modest discrepancies in the $T_e$ and $n_e$ profiles. These results clarify the complex mechanisms by which ExB shear affects turbulence.   

The Impact of Nitrogen Seeding on Turbulent Transport in Ohmic Plasmas in Alcator C-Mod and Gyrokinetic Simulations

Nitrogen seeding experiments performed on the Alcator C-Mod tokamak demonstrated that main ion dilution can decrease turbulence driven transport in both the low-density linear (LOC) and high-density saturated (SOC) ohmic confinement regimes. The seeding was observed to reduce the density fluctuations in the region of $r/a > 0.75$, and increase the inverse ion temperature gradient scale length ($a/L_{Ti}$) without increasing the gyrobohm-normalized energy flux ($Q_i/Q_{\mathrm{GB}}$), which indicates either an increase in the critical ion temperature gradient or a decrease in the stiffness of the ion transport. The nitrogen seeding also caused the intrinsic core toroidal rotation to reverse direction in SOC plasmas, causing the rotation profiles to become LOC-like. Simulations with the nonlinear gyrokinetic code GYRO (with $k_\theta\rho_s \leq 1$) showed that main ion dilution reduced the ion transport both by decreasing the stiffness and by increasing critical gradient. In LOC plasmas main-ion dilution primarily increased the critical gradient, while in SOC plasmas it primarily decreased the stiffness. A quantitative comparison between the local GYRO energy flux and the experimental energy flux showed agreement at $r/a = 0.8$ (where the turbulence is strongly unstable) in both the ion flux and the electron flux in the LOC regime. In the SOC regime the GYRO ion flux shows an underprediction relative to experimental flux measurements while the electron flux shows agreement between experiment and GYRO. At $r/a = 0.6$ (where the turbulence is marginally stable) local GYRO over predicts both the ion and the electron energy fluxes relative to experiment. When global effects are taken into account at $r/a = 0.6$, the GYRO and experimental ion energy fluxes agree, but the electron energy fluxes are under-predicted. This may indicate the importance of high-k (with $k_\theta\rho_s \geq 1$) electron modes that were not included in the simulations.   

Phase space effects on fast ion transport modeling in tokamaks

Simulations of burning plasmas require a consistent treatment of energetic particles (EP), possibly including the effects of instabilities. Reduced EP transport models are emerging as an effective tool to account for those effects in long time-scale simulations. Available models essentially differ for the main transport drive, which is associated to gradients in real or phase space. It is crucial to assess to what extent those different assumptions affect computed quantities such as EP profile, Neutral Beam (NB) driven current and energy/momentum transfer to the thermal populations. These issues are investigated through a kick model, which includes modifications of the EP distribution by instabilities in real and velocity space [M. Podest\`{a} et al., Plasma Phys. Control. Fusion 56 055003 (2014)]. TRANSP simulations including the kick model are applied to NB-heated NSTX discharges featuring unstable toroidal Alfv\'{e}n eigenmodes (TAEs). Results show that TAEs mainly affect fast ions with large parallel velocity, i.e. the most effective for NB current drive. Other portions of the EP distribution are nearly unperturbed. Core NB driven current decreases by 10-30{\%}, with even larger relative changes toward the plasma edge. When TAEs evolve in so-called avalanches, the model reproduces measured drops of $\sim$ 10{\%} in the neutron rate. Consistently with previous results, the drop is caused by both EP energy loss and EP redistribution. These results are compared to those from a simple diffusive model and a ``critical gradient'' model [N. Gorelenkov et al., Proc. 25$^{\mathrm{th}}$ IAEA-FEC, St. Petersburgh (Russia), CD-ROM file TH/P1-2, (2014)], which postulates radial EP gradient as the only transport drive. The importance of EP velocity space modifications is discussed in terms of accuracy of the predictions, with emphasis on Neutral Beam driven current.