Ammar Hakim

A high resolution wave propagation scheme for ideal Two-Fluid plasma equations

Algorithms for the solution of the five-moment ideal Two-Fluid equations are presented. The ideal Two-Fluid model is more general than the often used magnetohydrodynamic (MHD) model. The model takes into account electron inertia effects, charge separation and the full electromagnetic field equations and allows for separate electron and ion motion. The algorithm presented is the high resolution wave propagation method. The wave propagation method is based on solutions to the Riemann problem at cell interfaces. Operator splitting is used to incorporate the Lorentz and electromagnetic source terms. To preserve the divergence constraints on the electric and magnetic fields two different approaches are used. In the first approach Maxwell equations are rewritten in their mixed-potential form. In the second approach the so-called perfectly hyperbolic form of Maxwell equations are used which explicitly incorporate the divergence equations into the time stepping scheme. The algorithm is applied to a one-dimensional Riemann problem, ion-acoustic soliton propagation and magnetic reconnection. In each case Two-Fluid physics described by the ideal Two-Fluid model is highlighted.

A Discontinuous Galerkin Method for Ideal Two-Fluid Plasma Equations

A discontinuous Galerkin method for the ideal 5 moment two-fluid plasma system is presented. The method uses a second or third order discontinuous Galerkin spatial discretization and a third order TVD Runge-Kutta time stepping scheme. The method is benchmarked against an analytic solution of a dispersive electron acoustic square pulse as well as the two-fluid electromagnetic shock (1) and existing numerical solutions to the GEM challenge magnetic reconnection problem (2). The algorithm can be generalized to arbitrary geometries and three dimensions. An approach to main- taining small gauge errors based on error propagation is suggested.

Time-domain simulation of nonlinear radiofrequency phenomena

Nonlinear effects associated with the physics of radiofrequency wave propagation through a plasma are investigated numerically in the time domain, using both fluid and particle-in-cell (PIC) methods. We find favorable comparisons between parametric decay instability scenarios observed on the Alcator C-MOD experiment [J. C. Rost, M. Porkolab, and R. L. Boivin, Phys. Plasmas 9, 1262 (2002)] and PIC models. The capability of fluid models to capture important nonlinear effects characteristic of wave-plasma interaction (frequency doubling, cyclotron resonant absorption) is also demonstrated.

FACETS A Framework for Parallel Coupling of Fusion Components

Coupling separately developed codes offers an attractive method for increasing the accuracy and fidelity of the computational models. Examples include the earth sciences and fusion integrated modeling. This paper describes the Framework Application for Core-Edge Transport Simulations (FACETS).

Ocean optics estimation for absorption, backscattering, and phase function parameters

We propose and test an inverse ocean optics procedure with numerically simulated data for the determination of inherent optical properties using in-water radiance measurements. If data are available at only one depth within a deep homogeneous water layer, then the single-scattering albedo and the single parameter that characterizes the Henyey-Greenstein phase function can be estimated. If data are available at two depths, then these two parameters can be determined along with the optical thickness so that the absorption and scattering coefficients, and also the backscattering coefficient, can be estimated. With a knowledge of these parameters, the albedo and Lambertian fraction of reflected radiance of the bottom can be determined if measurements are made close to the bottom. A simplified method for determining the optical properties of the water also is developed for only three irradiance-type measurements if the radiance is approximately in the asymptotic regime.

Role of Ion Kinetic Physics in the Interaction of Magnetic Flux Ropes.

To explain many natural magnetized plasma phenomena, it is crucial to understand how rates of collisionless magnetic reconnection scale in large magnetohydrodynamic (MHD) scale systems. Simulations of isolated current sheets conclude such rates are independent of system size and can be reproduced by the Hall-MHD model, but neglect sheet formation and coupling to MHD scales. Here, it is shown for the problem of flux-rope merging, which includes this formation and coupling, that the Hall-MHD model fails to reproduce the kinetic results. The minimum sufficient model must retain ion kinetic effects, which set the ion diffusion region geometry and give time-averaged rates that reduce significantly with system size, leading to different global evolution in large systems.

Introducing FACETS, the Framework Application for Core-Edge Transport Simulations

The FACETS (Framework Application for Core-Edge Transport Simulations) project began in January 2007 with the goal of providing core to wall transport modeling of a tokamak fusion reactor. This involves coupling previously separate computations for the core, edge, and wall regions. Such a coupling is primarily through connection regions of lower dimensionality. The project has started developing a component-based coupling framework to bring together models for each of these regions. In the first year, the core model will be a 1 ½ dimensional model (1D transport across flux surfaces coupled to a 2D equilibrium) with fixed equilibrium. The initial edge model will be the fluid model, UEDGE, but inclusion of kinetic models is planned for the out years. The project also has an embedded Scientific Application Partnership that is examining embedding a full-scale turbulence model for obtaining the crosssurface fluxes into a core transport code.

Nautilus: A Tool For Modeling Fluid Plasmas

Plasmas are important in many situations including space and solar physics, lightning, re-entry heating and nuclear fusion. It’s most often the case that the plasma is generated from a cold neutral fluid so there is a transition regime where the plasma is neither fully ionized nor neutral. Furthermore in most high temperature devices a significant amount of neutral fluid may exist (particularly near the wall). As such, is is important that even for high temperature plasmas the transition regime between fully ionized and non-ionized plasmas be modeled. In addition, given the wide variety of temperature and densities that can exist in plasmas, there are many, many different plasma models that are relevant in the different situation. Nautilus is a code that is a collection of these various plasma fluid models encompassing the regimes of neutral flow (important in aeronautics) to high temperature plasmas important in nuclear fusion. The fluid models can use either ideal gas laws or general equation of state. Radiation transport can also be modeled. This paper outlines the physics modeled in Nautilus along with the algorithms and various applications including plasma jet merging, FRC formation and collisionless reconnection.

Validation of transport models using additive flux minimization technique

A new additive flux minimization technique is proposed for carrying out the verification and validation (V&V) of anomalous transport models. In this approach, the plasma profiles are computed in time dependent predictive simulations in which an additional effective diffusivity is varied. The goal is to obtain an optimal match between the computed and experimental profile. This new technique has several advantages over traditional V&V methods for transport models in tokamaks and takes advantage of uncertainty quantification methods developed by the applied math community. As a demonstration of its efficiency, the technique is applied to the hypothesis that the paleoclassical density transport dominates in the plasma edge region in DIII-D tokamak discharges. A simplified version of the paleoclassical model that utilizes the Spitzer resistivity for the parallel neoclassical resistivity and neglects the trapped particle effects is tested in this paper. It is shown that a contribution to density transport, in ...

Coupled core-edge simulations of H-mode buildup using the Fusion Application for Core-Edge Transport Simulations (FACETS) code

Coupled simulations of core and edge transport in the DIII-D shot number 118897, after the L-H transition but before the first edge localized mode (ELM), are presented. For the plasma core transport, a set of one dimensional transport equations are solved using the FACETS:Core solver. The fluxes in this region are calculated using the GLF23 anomalous transport model and Chang-Hinton neoclassical model. For the plasma edge transport, two-dimensional transport equations are solved using the UEDGE code. Fluxes in the edge region use static diffusivity profiles based on an interpretive analysis of the experimental profiles. Simulations are used to study the range of validity of the selected models and sensitivity to neutral fueling. It has been demonstrated that the increase of neutral influx to the level that exceeds the level of neutral influx obtained from analysis simulations with the UEDGE code by a factor of two results in increased plasma density pedestal heights and plasma density levels in the scrape...