Andris M. Dimits

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 comparative study of the turbulent Rayleigh–Taylor instability using high-resolution three-dimensional numerical simulations: The Alpha-Group collaboration

The turbulent Rayleigh–Taylor instability is investigated in the limit of strong mode-coupling using a variety of high-resolution, multimode, three dimensional numerical simulations (NS). The perturbations are initialized with only short wavelength modes so that the self-similar evolution (i.e., bubble diameter Db∝amplitude hb) occurs solely by the nonlinear coupling (merger) of saturated modes. After an initial transient, it is found that hb∼αbAgt2, where A=Atwood number, g=acceleration, and t=time. The NS yield Db∼hb/3 in agreement with experiment but the simulation value αb∼0.025±0.003 is smaller than the experimental value αb∼0.057±0.008. By analyzing the dominant bubbles, it is found that the small value of αb can be attributed to a density dilution due to fine-scale mixing in our NS without interface reconstruction (IR) or an equivalent entrainment in our NS with IR. This may be characteristic of the mode coupling limit studied here and the associated αb may represent a lower bound that is insensiti...

Three-dimensional simulation of a Richtmyer-Meshkov instability with a two-scale initial perturbation

Three-dimensional high-resolution simulations (up to 8 billion zones) have been performed for a Richtmyer–Meshkov instability produced by passing a shock through a contact discontinuity with a two-scale initial perturbation. The setup approximates shock-tube experiments with a membrane pushed through a wire mesh. The simulation produces mixing-layer widths similar to those observed experimentally. Comparison of runs at various resolutions suggests a mixing transition from unstable to turbulent flow as the numerical Reynolds number is increased. At the highest resolutions, the spectrum exhibits a region of power-law decay, in which the spectral flux is approximately constant, suggestive of an inertial range, but with weaker wave number dependence than Kolmogorov scaling, about k−6/5. Analysis of structure functions at the end of the simulation indicates the persistence of structures with velocities largest in the stream-wise direction. Comparison of three-dimensional and two-dimensional runs illustrates th...

Discrete Particle Noise in Particle-in-Cell Simulations of Plasma Microturbulence

Recent gyrokinetic simulations of electron temperature gradient (ETG) turbulence with flux-tube continuum codes vs. the global particle-in-cell (PIC) code GTC yielded different results despite similar plasma parameters. Differences between the simulations results were attributed to insufficient phase-space resolution and novel physics associated with toroidicity and/or global simulations. We have reproduced the results of the global PIC code using the flux-tube PIC code PG3EQ, thereby eliminating global effects as the cause of the discrepancy. We show that the late-time decay of ETG turbulence and the steady-state heat transport observed in these PIC simulations results from discrete particle noise. Discrete particle noise is a numerical artifact, so both these PG3EQ simulations and the previous GTC simulations have nothing to say about steady-state ETG turbulence and the associated anomalous heat transport. In the course of this work we develop three diagnostics which can help to determine if a particular PIC simulation has become dominated by discrete particle noise.

Progress in understanding turbulent mixing induced by Rayleigh–Taylor and Richtmyer–Meshkov instabilities

Turbulent hydrodynamic mixing induced by the Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities occurs in settings as varied as exploding stars (supernovae), inertial confinement fusion (ICF) capsule implosions, and macroscopic flows in fluid dynamics facilities such as shock tubes. Turbulence theory and modeling have been applied to RT and RM induced flows and developed into a quantitative description of turbulence from the onset to the asymptotic end-state. The treatment, based on a combined approach of theory, direct numerical simulation (DNS), and experimental data analysis, has broad generality. Three areas of progress will be reported. First, a robust, easy to apply criteria will be reported for the mixing transition in a time-dependent flow. This allows an assessment of whether flows, be they from supernova explosions or ICF experiments, should be mixed down to the molecular scale or not. Second, through DNS, the structure, scaling, and spectral evolution of the RT instability induced fl...

Particle simulation of Coulomb collisions

The interactions of charged particles in a plasma are governed by long-range Coulomb collision. We compare two widely used Monte Carlo models for Coulomb collisions. One was developed by Takizuka and Abe in 1977, the other was developed by Nanbu in 1997. We perform deterministic and statistical error analysis with respect to particle number and time step. The two models produce similar stochastic errors, but Nanbus model gives smaller time step errors. Error comparisons between these two methods are presented.

Gyrokinetic simulations of E×B velocity‐shear effects on ion‐temperature‐gradient modes

Data from several current tokamak experiments indicate that the equilibrium perpendicular velocity field can become strongly sheared accompanying the transition from the L mode to the H mode, i.e. improved, confinement, and that fluctuation levels are reduced. Linear theory suggests that velocity shear can stabilize ion‐temperature‐gradient (ITG) modes when the frequency shift experienced by the mode due to the radial dependence of the Doppler shift is comparable to the growth rate. To confirm the predictions of linear theory and to explore nonlinear issues, e.g., self‐generated shear flows, saturation amplitudes, and the concomitant energy transport levels, two‐ and three‐dimensional gyrokinetic simulations of ITG modes have been performed. The simulations were done with and without magnetic shear in a slab configuration using the partially linearized (δf) algorithm to reduce statistical noise. The simulations confirm theoretical analyses of the stabilizing and destabilizing effects of imposed perpendicu...

Gyroaveraged equations for both the gyrokinetic and drift‐kinetic regimes

The regime of validity of nonlinear gyrokinetic equations is extended to cover uniformly both the usual drift‐kinetic and gyrokinetic regimes through the use of an expansion in the parameter e∼(ρ/λ⊥)e(φ−v∥ Az/c)/T. Here, ρ is the gyroradius, λ⊥ is the scale length of the electrostatic and parallel magnetic potentials φ and Az, c is the speed of light, and T is the temperature. This is made possible by a preparatory split of the potentials into gyrophase‐dependent and independent parts. For nonlinear fluctuations saturated at mixing‐length levels (e.g., with eφ/T∼λ⊥ /L, where L is the equilibrium scale length), e is of order ρ/L for all scales λ⊥ ranging from ρ to L, and is therefore small in plasmas of fusion interest.

Simulation of ion temperature gradient turbulence in tokamaks

Results are presented from non-linear gyrokinetic simulations of toroidal ion temperature gradient turbulence and transport. The ion thermal fluxes are found to have an offset linear dependence on the temperature gradient and are significantly lower than gyrofluid or IFS-PPPL model predictions. A new phenomenon of non-linear effective critical gradients larger than the linear instability threshold gradients is observed and is associated with undamped flux surface averaged shear flows. The non-linear gyrokinetic codes have passed extensive tests, including comparison against independent linear calculations, a series of non-linear convergence tests and a comparison between two independent non-linear gyrokinetic codes. The most realistic simulations to date used actual reconstructed equilibria from experiments and a model for dilution by impurity and beam ions. These simulations highlight the importance of both self-generated and external E × B flow shear as well as the need for still more physics to be included.

Time-Step Considerations in Particle Simulation Algorithms for Coulomb Collisions in Plasmas

The accuracy of first-order Euler and higher-order time-integration algorithms for grid-based Langevin equations collision models in a specific relaxation test problem is assessed. We show that statistical noise errors can overshadow time-step errors and argue that statistical noise errors can be conflated with time-step effects. Using a higher-order integration scheme may not achieve any benefit in accuracy for examples of practical interest. We also investigate the collisional relaxation of an initial electron-ion relative drift and the collisional relaxation to a resistive steady-state in which a quasi-steady current is driven by a constant applied electric field, as functions of the time step used to resolve the collision processes using binary and grid-based, test-particle Langevin equations models. We compare results from two grid-based Langevin equations collision algorithms to results from a binary collision algorithm for modeling electron-ion collisions. Some guidance is provided on how large a time step can be used compared to the inverse of the characteristic collision frequency for specific relaxation processes.