Session NI2: Gyrokinetic Modeling

Flux-driven global gyrokinetic simulation of tokamak turbulence

The Eulerian gyrokinetic turbulence code GENE (www.ipp.mpg.de/\textasciitilde fsj/gene) has recently been extended to include full radial temperature, density, and geometry variations. Moreover, collisions between any pair of particle species and electromagnetic effects are considered, and the turbulence can be either gradient- or flux-driven. In the former case, Krook-type sources are employed across the radial domain to keep the profiles almost constant, while in the latter case, localized sources and sinks are used, and the central temperatures and densities may float. Careful benchmark tests are performed successfully. In addition to running GENE in a stand-alone fashion, the code is also coupled to the TRINITY transport solver in order to facilitate extremely long time scale simulations. This setup is applied to address three related transport issues concerning nonlocal effects. First, it is confirmed that in gradient-driven simulations, the local limit can be reproduced - provided that finite aspect ratio effects in the geometry are treated carefully. In this context, it also becomes clear that it is useful to define a modified $\rho$* value, reflecting the width of the profiles (not of the device). Thereafter, extensions to flux-driven cases are presented. Second, the nature and role of heat flux avalanches are discussed in the framework of both local and global, flux- and gradient-driven simulations. Third, important aspects of transport barrier physics are studied in the context of electron internal barriers in TCV as well as edge barriers in ASDEX Upgrade.   

Particle Pinch in Gyrokinetic Simulations of Closed Field-line Systems

Gyrokinetic GS2 simulations of plasma turbulence and particle and heat transport in a dipole magnetic field geometry created by a ring current are presented. This study is relevant to the MIT/Columbia University Levitated Dipole Experiment (LDX) [Kesner et al, Plasma Phys. Reports, 1997], a fusion experiment designed to explore hot plasma confinement in a dipolar magnetic field. The work also has potential applications to planetary magnetospheres. In addition to magnetohydrodynamic (MHD) ideal interchange and ballooning modes, a non-MHD mode known as the entropy mode is present in this system. The entropy mode has a scale length smaller than ideal modes ($k_\perp \rho_i \sim 1$) but comparable growth rates. Considering parameter regimes that are ideally stable, we explore the physics of turbulent transport generated by entropy modes, finding enormous variation in the nonlinear dynamics as a function of the density and temperature gradients. In particular, we report here the existence a new particle pinch regime, in which the particles are transported up the density gradient. We show that this discovery is consistent with gyrokinetic and two-fluid quasi-linear theory. The presence of a particle pinch appears to be consistent with recent observations in LDX [Boxer et al, Nature Physics, 2010].   

Magnetic stochasticity in gyrokinetic simulations of plasma microturbulence

One of the fundamental components of a steady state tokamak or stellerator fusion reactor is the structural integrity of nested magnetic surfaces. The consequences of losing this integrity can have very serious implications, ranging from sawtooth crashes to disruptions. In the present work, we use GYRO to examine the perturbed magnetic field structure generated by electromagnetic gyrokinetic simulations of the CYCLONE base case as $\beta$ is varied from .1\% to .7\%, as first investigated in [J. Candy, Phys. Plasmas {\bf 12}, 072307 (2005)]. By integrating the self-consistent magnetic field lines to produce Poincare surface of section plots, we demonstrate destruction of magnetic surfaces for all nonzero values of $\beta$. Despite widespread stochasticity of the perturbed magnetic fields, no significant increase in electron transport is observed. We can quantify the stochastic electron heat transport by using test particles to estimate the magnetic diffusion coefficient $D_{st}$ [A.B. Rechester and M.N. Rosenbluth, PRL {\bf 40}, 38 (1978)] for hundreds of time slices in each simulation and find the time-history of $D_{st}$ to be highly correlated with the electron heat transport due to ``magnetic-flutter'' computed in the simulations. The mechanism that couples electromagnetic turbulence to the linearly damped high-n tearing modes that are responsible for reconnection will be discussed.   

Natural Fueling of the Core and Edge in a Tokamak Fusion Reactor

A natural fueling mechanism\footnote{W. Wan, S. E. Parker, Y. Chen and F. W. Perkins, Phys. Plasmas {\bf 17}, 040701 (2010).} that helps to maintain the main core deuterium and tritium (DT) density profiles in a tokamak fusion reactor is presented. In H-mode plasmas dominated by ion-temperature gradient (ITG) driven turbulence, cold DT ions near the edge will naturally pinch radially inward towards the core. This mechanism is due to the quasi-neutral heat flux dominated nature of ITG turbulence and still applies when trapped and passing kinetic electron effects are included. Fueling using shallow pellet injection or supersonic gas jets is augmented by an inward pinch of could DT fuel. The natural fueling mechanism is investigated using the gyrokinetic turbulence code GEM and is analyzed using quasilinear theory. Profiles similar to those used for conservative ITER transport modeling that have a completely flat density profile are examined and it is found that natural fueling actually reduces the linear growth rates and energy transport. Additionally, it is shown that the Helium ash diffuses radially outward as the cold fuel moves radially inward. The natural fueling effect may also apply to the edge pedestal density buildup. Recent DEGAS 2 calculations indicate the neutrals in the pedestal are colder than the background ions.\footnote{D. Stotler, International Transport Task Force Meeting, Annapolis, MD (2010).} We intend to do further work to determine what cold fuel profiles are needed to fuel the pedestal and if they are consistent with edge neutral source models. Natural fueling (either in the core or edge) requires a two component (hot bulk and cold fuel) plasma and charge exchange collisions tend to equilibrate the ion and neutral source temperature reducing the effect. We will further investigate the relevant collisional time scales and further demonstrate the viability of the natural fueling mechanism for ITER parameters.   

Advances in Validating Gyrokinetic Turbulence Models in L and H mode Plasmas

Robust validation of predictive turbulent transport models requires quantitative comparisons to experimental measurements at multiple levels, over a range of physically relevant conditions. Towards this end, a series of carefully designed validation experiments has been performed on the DIII-D tokamak to obtain comprehensive multi-field, multi-point, multi-wavenumber fluctuation measurements and their scalings with key dimensionless parameters. In this talk we present the results of two representative validation studies: an elongation scaling study performed in beam heated L-mode discharges, and a $T_e/T_i$ scaling study performed in quiescent H-mode discharges. Key experimental observations to be tested include a 50\% increase in energy confinement time $\tau_E$ when the elongation kappa was increased by 50\% in the L-mode discharges, with accompanying decrease in fluctuation levels, and measured QH-mode fluctuation scalings and 30\% decrease in $\tau_E$ when on-axis $T_e/T_i$ is varied from 0.55 to 1.2 via application of ECH heating, all of which are consistent with initial linear growth rate calculations with TGLF. Transport predictions from both the quasilinear TGLF model and nonlinear GYRO simulations are presented and compared to power balance analysis, as well as direct comparisons of GYRO-predicted and measured fluctuation levels. A set of simple metrics is presented and used to quantify the absolute and relative agreement between TGLF, GYRO, and experiment.   

Turbulence and transport reduction with innovative plasma shapes in TCV -- correlation ECE measurement and gyrokinetic simulations

Due to turbulence, core energy transport in tokamaks generally exceeds collisional transport by at least an order of magnitude. It is therefore crucial to understand the instabilities driving the turbulent state and to find ways to control them. Shaping the plasma is one of these fundamental tools. In low collisionality plasmas, such as in a reactor, changing triangularity from positive (delta=+0.4) to negative triangularity (delta=-0.4) is shown on TCV to reduce the energy transport by a factor two. This opens the possibility of having H-mode-like confinement time within an L-mode edge, or reduced ELMs. An optimum triangularity can be sought between steep edge barriers (delta$>$0), plagued by large ELMs, and improved core confinement (delta$<$0). Recent correlation ECE measurements show that the reduction of transport at negative delta is reflected in a reduction by a factor of two of both the amplitude of temperature fluctuations in the broadband frequency range 30-150 kHz, and the fluctuation correlation length, measured at mid-radius. In addition, the fluctuations amplitude is reduced with increasing collisionality, consistent with a reduction of the Trapped Electron Modes (TEM) drive. The effect of negative triangularity on turbulence and transport is compared to gyrokinetic code results: First, global linear simulations predict shorter radial TEM wavelength, consistent with the shorter radial turbulence correlation length observed. Second, at least close to the strongly shaped plasma boundary, local nonlinear simulations predict lower TEM induced transport with decreased triangularity. Calculations are now being extended to global nonlinear simulations.