Transport control by coherent zonal flows in the core/edge transitional regime

3D Braginskii turbulence simulations show that the energy flux in the core/edge transition region of a tokamak is strongly modulated - locally and on average - by radially propagating, nearly coherent sinusoidal or solitary zonal flows. The flows are geodesic acoustic modes (GAM), which are primarily driven by the Stringer-Winsor term. The flow amplitude together with the average anomalous transport sensitively depend on the GAM frequency and on the magnetic curvature acting on the flows, which could be influenced in a real tokamak, e.g., by shaping the plasma cross section. The local modulation of the turbulence by the flows and the excitation of the flows are due to wave-kinetic effects, which have been studied for the first time in a turbulence simulation.Comment: 5 pages, 5 figures, submitted to PR

Status of Continuum Edge Gyrokinetic Code Physics Development *

We are developing an edge gyro-kinetic continuum simulation code to study the boundary plasma over a region extending from inside the H-mode pedestal across the separatrix to the divertor plates. A 4-D (ψ, θ, , µ) version of this code is presently being implemented, en route to a full 5-D version. A set of gyrokinetic equations[1] are discretized on computational grid which incorporates X-point divertor geometry. The present implementation is a Method of Lines approach where the phase-space derivatives are discretized with finite differences and implicit backwards differencing formulas are used to advance the system in time. A fourth order upwinding algorithm is used for particle cross-field drifts, parallel streaming, and acceleration. Boundary conditions at conducting material surfaces are implemented on the plasma side of the sheath. The Poisson-like equation is solved using GMRES with multi-grid preconditioner from HYPRE. A nonlinear Fokker-Planck collision operator from STELLA[2] in (v , v ⊥ ) has been streamlined and integrated into the gyro-kinetic package using the same implicit Newton-Krylov solver and interpolating F and dF/dt| coll to/from ( , µ) space. With our 4D code we compute the ion thermal flux, ion parallel velocity, self-consistent electric field, and geo-acoustic oscillations, which we compare with standard neoclassical theory for core plasma parameters; and we study the transition from collisional to collisionless end-loss. In the real X-point geometry, we find that the particles are trapped near outside midplane and in the X-point regions due to the magnetic configurations. The sizes of banana orbits are comparable to the pedestal width and/or the SOL width for energetic trapped particles. The effect of the real X-point geometry and edge plasma conditions on standard neoclassical theory will be evaluated, including a comparison of our 4D code with other kinetic neoclassical codes (such as NCLAS

Reduction of Turbulence by Zonal Flows

Three-dimensional gyrokinetic simulations of ion temperature gradient driven turbulence in magnetically confined toroidal plasmas support the view that turbulence-driven fluctuating E x B zonal flows can significantly reduce turbulent transport. Random shearing of turbulent eddies by zonal flows is analytically studied. It is shown that the fast time varying components of E x B flows, while they typically contribute significantly to the instantaneous E x B shearing rate, are less effective in suppressing turbulence. This is because the shear flow pattern changes before the eddies get distorted enough. We analytically derive the effective E x B shearing rate capturing this important physics, thereby extending the theory of E x B shear suppression of turbulence in toroidal geometry [Phys. Plasmas 2, 1648 (1995)

Composite Skyrme Model with Vector Mesons

We study the composite Skyrme model, proposed by Cheung and G\"{u}rsey, introducing vector mesons in a chiral Lagrangian. We calculate the static properties of baryons and compare with results obtained from models without vector mesons.Comment: LaTeX, 9 pages, 3 figures, to be published in Phys. Rev.

Turbulent Transport Reduction by Zonal Flows: Massively Parallel Simulations

The dynamics of turbulence-driven E x B zonal flows has been systematically studied in fully 3-dimensional gyrokinetic simulations of microturbulence in magnetically confined toroidal plasmas using recently available massively parallel computers. Linear flow damping simulations exhibit an asymptotic residual flow in agreement with recent analytic calculations. Nonlinear global simulations of instabilities driven by temperature gradients in the ion component of the plasma provide key first principles results supporting the physics picture that turbulence-driven fluctuating E x B zonal flows can significantly reduce turbulent transport

ELM triggering conditions for the integrated modeling of H-mode plasmas

Recent advances in the integrated modeling of ELMy H-mode plasmas are presented. A model for the H-mode pedestal and for the triggering of ELMs predicts the height, width, and shape of the H-mode pedestal and the frequency and width of ELMs. Formation of the pedestal and the L-H transition is the direct result of ExB flow shear suppression of anomalous transport. The periodic ELM crashes are triggered by either the ballooning or peeling MHD instabilities. The BALOO, DCON, and ELITE ideal MHD stability codes are used to derive a new parametric expression for the peeling-ballooning threshold. The new dependence for the peeling-ballooning threshold is implemented in the ASTRA transport code. Results of integrated modeling of DIII-D like discharges are presented and compared with experimental observations. The results from the ideal MHD stability codes are compared with results from the resistive MHD stability code NIMROD.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France

Two-dimensional turbulence in magnetised plasmas

In an inhomogeneous magnetised plasma the transport of energy and particles perpendicular to the magnetic field is in general mainly caused by quasi two-dimensional turbulent fluid mixing. The physics of turbulence and structure formation is of ubiquitous importance to every magnetically confined laboratory plasma for experimental or industrial application. Specifically, high temperature plasmas for fusion energy research are also dominated by the properties of this turbulent transport. Self-organisation of turbulent vortices to mesoscopic structures like zonal flows is related to the formation of transport barriers that can significantly enhance the confinement of a fusion plasma. This subject of great importance in research is rarely touched on in introductory plasma physics or continuum dynamics courses. Here a brief tutorial on 2D fluid and plasma turbulence is presented as an introduction to the field, appropriate for inclusion in undergraduate and graduate courses.Comment: This is an author-created, un-copyedited version of an article published in European Journal of Physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at doi: 10.1088/0143-0807/29/5/00

Size Scaling of Turbulent Transport in Magnetically Confined Plasmas

Transport scaling with respect to device size in magnetically confined plasmas is critically examined for electrostatic ion temperature gradient turbulence using global gyrokinetic particle simulations. It is found, by varying device size normalized by ion gyroradius while keeping other dimensionless plasma parameters fixed, that fluctuation scale length is microscopic in the presence of zonal flows. The local transport coefficient exhibits a gradual transition from a Bohm-like scaling for device sizes corresponding to present-day experiments to a gyro-Bohm scaling for future larger devices

Gyrokinetic Simulation of Global Turbulent Transport Properties in Tokamak Experiments

A general geometry gyro-kinetic model for particle simulation of plasma turbulence in tokamak experiments is described. It incorporates the comprehensive influence of noncircular cross section, realistic plasma profiles, plasma rotation, neoclassical (equilibrium) electric fields, and Coulomb collisions. An interesting result of global turbulence development in a shaped tokamak plasma is presented with regard to nonlinear turbulence spreading into the linearly stable region. The mutual interaction between turbulence and zonal flows in collisionless plasmas is studied with a focus on identifying possible nonlinear saturation mechanisms for zonal flows. A bursting temporal behavior with a period longer than the geodesic acoustic oscillation period is observed even in a collisionless system. Our simulation results suggest that the zonal flows can drive turbulence. However, this process is too weak to be an effective zonal flow saturation mechanism