Charlson C. Kim

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...

Large-scale gyrokinetic turbulence simulations: Effects of profile variation

Two common computational domains used in gyrokinetic turbulence simulations are a local flux-tube and a global whole plasma volume. The effect of a radially varying pressure gradient is found to explain some of the qualitative differences between these two models. It is shown that a coherent purely radial mode is the result of profile variation. In addition, as profile variation is increased, there is a fairly sudden transition to much lower levels of heat flux. This may explain lower values found in past global simulations. The self-generated purely radial electrostatic potential is found to be 180° out of phase with the flux-surface-averaged ion temperature. A theoretical relation between these two quantities is derived by relating the E×B nonlinearities for ion density and temperature for purely radial modes. This relation is used to explain the various radial mode shapes. Extending these results, a possible scheme is explored to reduce the heat flux by adding a ripple to the ion temperature profile. I...

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.

Hybrid kinetic-MHD simulations in general geometry

Abstract We present a hybrid kinetic-MHD model consisting of 3 species, the bulk fluid ions and electrons, and a kinetic minority hot particle species. The 3 species equations are derived from moments of the Vlasov Equation and then reduced using the usual hot particle assumption of n h ⪡ n 0 , β h ∼ β 0 to formulate the hybrid kinetic MHD model. The 3 species equations reproduce the usual MHD equations with the addition of a hot particle pressure in the momentum equation. In the limit n h →0, the MHD equations are recovered. These model equations are implemented and examined in the NIMROD code [C.R. Sovinec, et al., Nonline magnetohydrodynamic simulations using higher-order finite elements, JCP submitted for publication] which solves three dimensional magnetohydrodynamic initial-value problems using the finite element method (FEM). The finite elements allow the representation of highly shaped geometries, but the particle-in-cell (PIC) method is complicated by the irregular grid. The associated complications are a nontrivial shape function, a more complex search algorithm, parallelization. We present our implementation of PIC in a FEM simulation and some preliminary results and performance measurements.

The particle-continuum method: an algorithmic unification of particle-in-cell and continuum methods ✩

A new numerical algorithm that encompasses both the δf particle-in-cell (PIC) method and a continuum method has been developed, which is an extension to Denavit’s [J. Comput. Phys. 9 (1972) 75] original “hybrid” method. In this article we describe this new Particle-Continuum algorithm in general, and we note our methods of interpolation. The issue of phase space convergence of this algorithm is discussed. We analyze the induced numerical diffusion of such an algorithm and compare theory with results. We also created a simple problem that demonstrates this algorithm solves the “growing weight” problem.

Low-cost high-performance scientific visualization

The authors discuss the development of a low-cost stereoscopic visualization system using commonly available components. The system is used to improve understanding about the field-line structure and associated dynamics, confinement, and geometry of spheromak plasma. Such a system might interest research groups doing remote large-scale computing.

Electromagnetic gyrokinetic-ion drift-fluid-electron hybrid simulation

Progress on gyrokinetic-ion drift-fluid-electron hybrid simulation is reported. Simulation results are shown from a threedimensional toroidal electromagnetic simulation using field-line-following coordinates. It is found that for & 1:5% there is strong destabilization of Alfvenic ion-temperature-gradient (ITG) driven instabilities. Nonlinear results show a corresponding increase in the the ion heat flux. Secondly, we report very good parallel performance and near perfect scalability was shown on the Cray T3E and SGI O2K using a one-dimensional domain decomposition and digital filtering to handle the shift at the boundary along the magnetic field-line due to toroidal boundary conditions. Finally, we report recent results in the electrostatic limit, which explore a scheme to reduce the heat flux by adding a ripple to the ion temperature profile. Both self-generated and equilibriumEr shear flows are included for the first time. It may be possible to achieve similar results experimentally using ion cyclotron resonance heating.

Validation of single-fluid and two-fluid magnetohydrodynamic models of the helicity injected torus spheromak experiment with the NIMROD code

We present a comparison study of 3-D pressureless resistive MHD (rMHD) and 3-D presureless two-fluid MHD models of the Helicity Injected Torus with Steady Inductive helicity injection (HIT-SI). HIT-SI is a current drive experiment that uses two geometrically asymmetric helicity injectors to generate and sustain toroidal plasmas. The comparable size of the collisionless ion skin depth di to the resistive skin depth predicates the importance of the Hall term for HIT-SI. The simulations are run with NIMROD, an initial-value, 3-D extended MHD code. The modeled plasma density and temperature are assumed uniform and constant. The helicity injectors are modeled as oscillating normal magnetic and parallel electric field boundary conditions. The simulations use parameters that closely match those of the experiment. The simulation output is compared to the formation time, plasma current, and internal and surface magnetic fields. Results of the study indicate 2fl-MHD shows quantitative agreement with the experiment ...

Recent Computational Code Development for Compact Toroids and Suitability for Space Propulsion Applications

Numerical models play a vital role in the development of plasma propulsion concepts. Compact Toroids have been studied for many years as a potential magnetic confinement concept for thermonuclear fusion applications. A sophisticated numerical modeling capability has been developed as part of this study. As compact toroids are now being considered for propulsion applications, it is natural that these codes be adapted for propulsion geometry and plasma parameters. This paper will discuss progress and plans for using the NIMROD code for space propulsion applications.