A. Banon Navarro

Free Energy Cascade in Gyrokinetic Turbulence

In gyrokinetic theory, the quadratic nonlinearity is known to play an important role in the dynamics by redistributing (in a conservative fashion) the free energy between the various active scales. In the present study, the free energy transfer is analyzed for the case of ion temperature gradient driven turbulence. It is shown that it shares many properties with the energy transfer in fluid turbulence. In particular, one finds a (strongly) local, forward (from large to small scales) cascade of free energy in the plane perpendicular to the background magnetic field. These findings shed light on some fundamental properties of plasma turbulence, and encourage the development of large-eddy-simulation techniques for gyrokinetics.

Core turbulence behavior moving from ion-temperature-gradient regime towards trapped-electron-mode regime in the ASDEX Upgrade tokamak and comparison with gyrokinetic simulation

Additional electron cyclotron resonance heating (ECRH) is used in an ion-temperature-gradient instability dominated regime to increase R/LTe in order to approach the trapped-electron-mode instability regime. The radial ECRH deposition location determines to a large degree the effect on R/LTe. Accompanying scale-selective turbulence measurements at perpendicular wavenumbers between k⊥ = 4–18 cm−1 (k⊥ρs = 0.7–4.2) show a pronounced increase of large-scale density fluctuations close to the ECRH radial deposition location at mid-radius, along with a reduction in phase velocity of large-scale density fluctuations. Measurements are compared with results from linear and non-linear flux-matched gyrokinetic (GK) simulations with the gyrokinetic code GENE. Linear GK simulations show a reduction of phase velocity, indicating a pronounced change in the character of the dominant instability. Comparing measurement and non-linear GK simulation, as a central result, agreement is obtained in the shape of radial turbulence...

Modulation of Core Turbulent Density Fluctuations by Large-Scale Neoclassical Tearing Mode Islands in the DIII-D Tokamak

We report the first observation of localized modulation of turbulent density fluctuations n[over ˜] (via beam emission spectroscopy) by neoclassical tearing modes (NTMs) in the core of the DIII-D tokamak. NTMs are important as they often lead to severe degradation of plasma confinement and disruptions in high-confinement fusion experiments. Magnetic islands associated with NTMs significantly modify the profiles and turbulence drives. In this experiment n[over ˜] was found to be modulated by 14% across the island. Gyrokinetic simulations suggest that n[over ˜] could be dominantly driven by the ion temperature gradient instability.

Phase space scales of free energy dissipation in gradient-driven gyrokinetic turbulence

A reduced four-dimensional (integrated over perpendicular velocity) gyrokinetic model of slab ion temperature gradient-driven turbulence is used to study the phasespace scales of free energy dissipation in a turbulent kinetic system over a broad range of background gradients and collision frequencies. Parallel velocity is expressed in terms of Hermite polynomials, allowing for a detailed study of the scales of free energy dynamics over the four-dimensional phase space. A fully spectral code – the DNA code – that solves this system is described. Hermite free energy spectra are significantly steeper than would be expected linearly, causing collisional dissipation to peak at large scales in velocity space even for arbitrarily small collisionality. A key cause of the steep Hermite spectra is a critical balance – an equilibration of the parallel streaming time and the nonlinear correlation time – that extends to high Hermite number n. Although dissipation always peaks at large scales in all phase space dimensions, small-scale dissipation becomes important in an integrated sense when collisionality is low enough and/or nonlinear energy transfer is strong enough. Toroidal full-gyrokinetic simulations using the Gene code are used to verify results from the reduced model. Collision frequencies typically found in present-day experiments correspond to turbulence regimes slightly favoring large-scale dissipation, while turbulence in low-collisionality systems like ITER and space and astrophysical plasmas is expected to rely increasingly on small-scale dissipation mechanisms. This work is expected to inform gyrokinetic reduced modeling efforts like Large Eddy Simulation and gyrofluid techniques.

Gyrokinetic large eddy simulations

The large eddy simulation approach is adapted to the study of plasma microturbulence in a fully three-dimensional gyrokinetic system. Ion temperature gradient driven turbulence is studied with the GENE code for both a standard resolution and a reduced resolution with a model for the sub-grid scale turbulence. A simple dissipative model for representing the effect of the sub-grid scales on the resolved scales is proposed and tested. Once calibrated, the model appears to be able to reproduce most of the features of the free energy spectra for various values of the ion temperature gradient.

Free energy balance in gyrokinetic turbulence

Free energy plays an important role in gyrokinetic theory, since it is known to be a nonlinear invariant. Its evolution equations are derived and analyzed for the case of ion temperature gradient driven turbulence, using the formalism adopted in the Gene code. In particular, the ion temperature gradient drive, the collisional dissipation as well as entropy/electrostatic energy transfer channels represented by linear curvature and parallel terms are analyzed in detail.

Gyrokinetic studies of core turbulence features in ASDEX Upgrade H-mode plasmas

Gyrokinetic validation studies are crucial for developing confidence in the model incorporated in numerical simulations and thus improving their predictive capabilities. As one step in this direction, we simulate an ASDEX Upgrade discharge with the GENE code, and analyze various fluctuating quantities and compare them to experimental measurements. The approach taken is the following. First, linear simulations are performed in order to determine the turbulence regime. Second, the heat fluxes in nonlinear simulations are matched to experimental fluxes by varying the logarithmic ion temperature gradient within the expected experimental error bars. Finally, the dependence of various quantities with respect to the ion temperature gradient is analyzed in detail. It is found that density and temperature fluctuations can vary significantly with small changes in this parameter, thus making comparisons with experiments very sensitive to uncertainties in the experimental profiles. However, cross-phases are more robust, indicating that they are better observables for comparisons between gyrokinetic simulations and experimental measurements.

Global and local gyrokinetic simulations of high-performance discharges in view of ITER

One of the key challenges for plasma theory and simulation in view of ITER is to enhance the understanding and predictive capability concerning high-performance discharges. This involves, in particular, questions about high-beta operation, ion temperature profile stiffness, and the physics of transport barriers. The goal of this contribution is to shed light on these issues by means of physically comprehensive ab initio simulations with the global gyrokinetic code GENE, applied to discharges in TCV, ASDEX Upgrade, and JET-with direct relevance to ITER.

Experimental turbulence studies for gyro-kinetic code validation using advanced microwave diagnostics

For a comprehensive comparison with theoretical models and advanced numerical turbulence simulations, a large spectrum of fluctuation parameters was measured on the devices ASDEX Upgrade, TCV, and Tore-Supra. Radial profiles of scale-resolved turbulence levels in H-mode discharges are measured and compared with GENE simulations in the transition range from ion-temperature-gradient to trapped-electron-mode turbulence. Correlation reflectometry is used to study the microscopic structure of turbulence and GAMs in discharges where poloidal flow damping was varied by means of variations of the shape of the poloidal plasma cross-section and collisionality. Full-wave codes and synthetic diagnostics are applied for the interpretation of the data.

Applications of large eddy simulation methods to gyrokinetic turbulence

The large eddy simulation (LES) approach—solving numerically the large scales of a turbulent system and accounting for the small-scale influence through a model—is applied to nonlinear gyrokinetic systems that are driven by a number of different microinstabilities. Comparisons between modeled, lower resolution, and higher resolution simulations are performed for an experimental measurable quantity, the electron density fluctuation spectrum. Moreover, the validation and applicability of LES is demonstrated through a series of diagnostics based on the free energetics of the system.