Scott E. Parker

Comparisons and physics basis of tokamak transport models and turbulence simulations

The predictions of gyrokinetic and gyrofluid simulations of ion-temperature-gradient (ITG) instability and turbulence in tokamak plasmas as well as some tokamak plasma thermal transport models, which have been widely used for predicting the performance of the proposed International Thermonuclear Experimental Reactor (ITER) tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1996 (International Atomic Energy Agency, Vienna, 1997), Vol. 1, p. 3], are compared. These comparisons provide information on effects of differences in the physics content of the various models and on the fusion-relevant figures of merit of plasma performance predicted by the models. Many of the comparisons are undertaken for a simplified plasma model and geometry which is an idealization of the plasma conditions and geometry in a Doublet III-D [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159] high confinement (H-mode) experiment. Most of the mo...

A fully nonlinear characteristic method for gyrokinetic simulation

A new scheme that evolves the perturbed part of the distribution function along a set of characteristics that solves the fully nonlinear gyrokinetic equations is presented. This low‐noise nonlinear characteristic method for particle simulation is an extension of the partially linear weighting scheme, and may be considered an improvement over existing δf methods. Some of the features of this new method include the ability to keep all nonlinearities, particularly those associated with the velocity space, the use of conventional particle loading techniques, and also the retention of the conservation properties of the original gyrokinetic system in the numerically converged limit. The new method is used to study a one‐dimensional drift wave model that isolates the parallel velocity nonlinearity. A mode coupling calculation for the saturation amplitude is given, which is in good agreement with the simulation results. Finally, the method is extended to the electromagnetic gyrokinetic equations in general geometry.

A δ f particle method for gyrokinetic simulations with kinetic electrons and electromagnetic perturbations

A δf particle simulation method is developed for solving the gyrokinetic-Maxwell system of equations that describes turbulence and anomalous transport in toroidally confined plasmas. A generalized split-weight scheme is used to overcome the constraint on the time step due to fast parallel motion of the electrons. The inaccuracy problem at high plasma β is solved by using the same marker particle distribution as is used for δf to evaluate the βmi/meA|| term in Amperes equation, which is solved iteratively. The algorithm is implemented in three-dimensional toroidal geometry using field-line-following coordinates. Also discussed is the implementation of electron-ion collisional effects which are important when kinetic electron physics is included. Linear benchmarks in toroidal geometry are presented for moderate β, that is, β ≪ 1, but βmi/mc ≫ 1. Nonlinear simulation results with moderate β are also presented.

L-mode validation studies of gyrokinetic turbulence simulations via multiscale and multifield turbulence measurements on the DIII-D tokamak

A series of carefully designed experiments on DIII-D have taken advantage of a broad set of turbulence and profile diagnostics to rigorously test gyrokinetic turbulence simulations. In this paper the goals, tools and experiments performed in these validation studies are reviewed and specific examples presented. It is found that predictions of transport and fluctuation levels in the mid-core region (0.4 < ρ < 0.75) are in better agreement with experiment than those in the outer region (ρ ≥ 0.75) where edge coupling effects may become increasingly important and multiscale simulations may also be necessary. Validation studies such as these are crucial in developing confidence in a first-principles based predictive capability for ITER.

Three-dimensional hybrid gyrokinetic-magnetohydrodynamics simulation

A three‐dimensional (3‐D) hybrid gyrokinetic‐MHD (magnetohydrodynamic) simulation scheme is presented. To the 3‐D toroidal MHD code, MH3D‐K the energetic particle component is added as gyrokinetic particles. The resulting code, mh3d‐k, is used to study the nonlinear behavior of energetic particle effects in tokamaks, such as the energetic particle stabilization of sawteeth, fishbone oscillations, and alpha‐particle‐driven toroidal Alfven eigenmode (TAE) modes.

Compressed ion temperature gradient turbulence in diverted tokamak edge

It is found from a heat-flux-driven full-f gyrokinetic particle simulation that there is ion temperature gradient (ITG) turbulence across an entire L-mode-like edge density pedestal in a diverted tokamak plasma in which the ion temperature gradient is mild without a pedestal structure, hence the normalized ion temperature gradient parameter ηi=(d log Ti/dr)/(d log n/dr) varies strongly from high (>4 at density pedestal top/shoulder) to low (<2 in the density slope) values. Variation of density and ηi is in the same scale as the turbulence correlation length, compressing the turbulence in the density slope region. The resulting ion thermal flux is on the order of experimentally inferred values. The present study strongly suggests that a localized estimate of the ITG-driven χi will not be valid due to the nonlocal dynamics of the compressed turbulence in an L-mode-type density slope. While the thermal transport and the temperature profile saturate quickly, the E×B rotation shows a longer time damping during...

Electromagnetic gyrokinetic δf particle-in-cell turbulence simulation with realistic equilibrium profiles and geometry

The @df particle-in-cell method for gyrokinetic simulations with kinetic electrons and electromagnetic perturbations [Y. Chen, S. Parker, J. Comput. Phys. 189 (2003) 463] is extended to include arbitrary toroidal equilibrium profiles and flux-surface shapes. The domain is an arbitrarily sized toroidal slice with periodicity assumed in toroidal direction. It is global radially and poloidally along the magnetic field. The differential operators and Jacobians are represented numerically which is a quite general approach with wide applicability. Discretization of the field equations is described. The issue of domain decomposition and particle load balancing is addressed. A derivation of the split-weight scheme is given, and numerical observations are given as to what algorithmic change leads to stable algorithm. It is shown that in the final split-weight algorithm the equation for the rate of change of the electric potential is solved in a way that is incompatible with the quasi-neutrality condition on the grid scale. This incompatibility, while negligible on the scale of interest, leads to better numerical stability on the grid scale. Some examples of linear simulations are presented to show the effects of flux-surface shaping on the linear mode growth rates. The issue of long-term weight growth in @df simulation and the effect of discrete particle noise are briefly discussed.

Modeling of field‐aligned electron bursts by dispersive Alfvén waves in the dayside auroral region

electron resonance. We show that an increased mass density (significant O + density) in the acceleration region is an essential prerequisite to generate an electron burst. The primary effect of the O + is to decrease the phase speed of the Alfven wave. Furthermore, the full gyrokinetic effects of the O + act to produce a region in which the Alfven speed profile is gradually slowing, which allows electrons remaining within the wave to lower altitudes. In these electron bursts, the energy gain experienced by the majority of electrons ranges from tens to hundreds of eV. The trapping occurs if the parallel electric field is substantial enough (� 0.2 mV/m) in the acceleration region to accelerate the background electrons. An integrated energy flux of accelerated electrons is estimated to be 3 erg s � 1 cm � 2 , about 20% of the Alfven wave Poynting flux. INDEX TERMS: 2431 Ionosphere: Ionosphere/ magnetosphere interactions (2736); 2451 Ionosphere: Particle acceleration; 2487 Ionosphere: Wave propagation (6934); 2483 Ionosphere: Wave/particle interactions; KEYWORDS: electron acceleration, Alfven wave propagation, magnetosphere-ionosphere coupling, particle acceleration

Gyrokinetic turbulence simulations with kinetic electrons

Gyrokinetic turbulence simulations are presented with full drift-kinetic electron dynamics including both trapped and passing particle effects. This is made possible by using a generalization of the split-weight scheme [I. Manuilskiy and W. W. Lee, Phys. Plasmas 7, 1381 (2000)] that allows for a variable adiabatic part, as well as use of the parallel canonical momentum formulation. Linear simulations in shearless slab geometry and nonlinear simulations using representative tokamak parameters demonstrate the applicability of this generalized split-weight scheme to the turbulence transport problem in the low β regime [β(mi/me)⩽1]. The issues relating to difficulties at higher β, and initial three-dimensional toroidal simulations results will be discussed.

Electromagnetic Gyrokinetic Simulations

A new electromagnetic kinetic electron δf particle simulation model has been demonstrated to work well at large values of plasma β times the ion-to-electron mass ratio [Y. Chen and S. E. Parker, J. Comput. Phys. 198, 463 (2003)]. The simulation is three-dimensional using toroidal flux-tube geometry and includes electron-ion collisions. The model shows accurate shear Alfven wave damping and microtearing physics. Zonal flows with kinetic electrons are found to be turbulent with the spectrum peaking at zero and having a width in the frequency range of the driving turbulence. This is in contrast with adiabatic electron cases where the zonal flows are near stationary, even though the linear behavior of the zonal flow is not significantly affected by kinetic electrons. Zonal fields are found to be very weak, consistent with theoretical predictions for β below the kinetic ballooning limit. Detailed spectral analysis of the turbulence data is presented in the various limits.