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Simulating Photons and Plasmons in a Three-dimensional Lattice

Description: Three-dimensional metallic photonic structures are studied using a newly developed mixed finite element-finite difference (FE-FD) code, Curly3d. The code solves the vector Helmholtz equation as an eigenvalue problem in the unit cell of a triply periodic lattice composed of conductors and/or dielectrics. The mixed FE-FD discretization scheme ensures rapid numerical convergence of the eigenvalue and allows the code to run at low resolution. Plasmon and photonic band structure calculations are presented.
Date: September 3, 2002
Creator: Pletzer, A. & Shvets, G.
Partner: UNT Libraries Government Documents Department

Theory of Perturbed Equilibria for Solving the Grad-Shafranov Equation

Description: The theory of perturbed magnetohydrodynamic equilibria is presented for different formulations of the tokamak equilibrium problem. For numerical codes, it gives an explicit Newton scheme for solving the Grad-Shafranov equation subject to different constraints. The problem of stability of axisymmetric modes is shown to be a particular case of the equilibrium perturbation theory.
Date: July 1, 1999
Creator: Pletzer, A. & Zakharov, L.E.
Partner: UNT Libraries Government Documents Department

ELLIPT2D: A Flexible Finite Element Code Written Python

Description: The use of the Python scripting language for scientific applications and in particular to solve partial differential equations is explored. It is shown that Python's rich data structure and object-oriented features can be exploited to write programs that are not only significantly more concise than their counter parts written in Fortran, C or C++, but are also numerically efficient. To illustrate this, a two-dimensional finite element code (ELLIPT2D) has been written. ELLIPT2D provides a flexible and easy-to-use framework for solving a large class of second-order elliptic problems. The program allows for structured or unstructured meshes. All functions defining the elliptic operator are user supplied and so are the boundary conditions, which can be of Dirichlet, Neumann or Robbins type. ELLIPT2D makes extensive use of dictionaries (hash tables) as a way to represent sparse matrices.Other key features of the Python language that have been widely used include: operator over loading, error handling, array slicing, and the Tkinter module for building graphical use interfaces. As an example of the utility of ELLIPT2D, a nonlinear solution of the Grad-Shafranov equation is computed using a Newton iterative scheme. A second application focuses on a solution of the toroidal Laplace equation coupled to a magnetohydrodynamic stability code, a problem arising in the context of magnetic fusion research.
Date: March 22, 2001
Creator: Pletzer, A. & Mollis, J.C.
Partner: UNT Libraries Government Documents Department

Gabor Wave Packet Method to Solve Plasma Wave Equations

Description: A numerical method for solving plasma wave equations arising in the context of mode conversion between the fast magnetosonic and the slow (e.g ion Bernstein) wave is presented. The numerical algorithm relies on the expansion of the solution in Gaussian wave packets known as Gabor functions, which have good resolution properties in both real and Fourier space. The wave packets are ideally suited to capture both the large and small wavelength features that characterize mode conversion problems. The accuracy of the scheme is compared with a standard finite element approach.
Date: June 18, 2003
Creator: Pletzer, A.; Phillips, C.K. & Smithe, D.N.
Partner: UNT Libraries Government Documents Department

Kinetic Damping of Toroidal Alfven Eigenmodes

Description: The damping of Toroidal Alfven Eigenmodes in JET plasmas is investigated by using a reduced kinetic model. Typically no significant damping is found to occur near the center of the plasma due to mode conversion to kinetic Alfven waves. In contrast, continuum damping from resonance near the plasma edge may be significant, and when it is, it gives rise to damping rates that are compatible with the experimental observations.
Date: May 3, 2005
Creator: Fu, G.Y.; Berk, H.L. & Pletzer, A.
Partner: UNT Libraries Government Documents Department

Plasma Dielectric Tensor for Non-Maxwellian Distributions in the FLR Limit

Description: Previous analytical and numerical studies have noted that the presence of fully non-Maxwellian plasma species can significantly alter the dynamics of electromagnetic waves in magnetized plasmas. In this paper, a general form for the hot plasma dielectric tensor for non-Maxwellian distributions is derived that is valid in the finite Larmor radius approximation. This model provides some insight into understanding the limitations on representing non-Maxwellian plasma species with equivalent Maxwellian components in modeling radio-frequency wave propagation and absorption.
Date: July 8, 2003
Creator: Phillips, C.K.; Pletzer, A.; Dumont, R.J. & Smithe, D.N.
Partner: UNT Libraries Government Documents Department

Modeling of Neoclassical Tearing Mode Stability for Generalized Toroidal Geometry

Description: Neoclassical tearing modes (NTMs) can lead to disruption and loss of confinement. Previous analysis of these modes used large aspect ratio, low beta (plasma pressure/magnetic pressure) approximations to determine the effect of NTMs on tokamak plasmas. A more accurate tool is needed to predict the onset of these instabilities. As a follow-up to recent theoretical work, a code has been written which computes the tearing mode island growth rate for arbitrary tokamak geometry. It calls PEST-3 [A. Pletzer et al., J. Comput. Phys. 115, 530 (1994)] to compute delta prime, the resistive magnetohydrodynamic (MHD) matching parameter. The code also calls the FLUXGRID routines in NIMROD [A.H. Glasser et al., Plasma Phys. Controlled Fusion 41, A747 (1999)] for Dnc, DI and DR [C.C. Hegna, Phys. Plasmas 6, 3980 (1999); A.H. Glasser et al., Phys. Fluids 18, 875 (1975)], which are the bootstrap current driven term and the ideal and resistive interchange mode criterion, respectively. In addition to these components, the NIMROD routines calculate alphas-H, a new correction to the Pfirsch-Schlter term. Finite parallel transport effects were added and a National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)] equilibrium was analyzed. Another program takes the output of PEST-3 and allows the user to specify the rational surface, island width, and amount of detail near the perturbed surface to visualize the total helical flux. The results of this work will determine the stability of NTMs in an spherical torus (ST) [Y.-K.M. Peng et al., Nucl. Fusion 26, 769 (1986)] plasma with greater accuracy than previously achieved.
Date: August 21, 2002
Creator: Rosenberg, A.L.; Gates, D.A.; Pletzer, A.; Menard, J.E.; Kruger, S.E.; Hegna, C.C. et al.
Partner: UNT Libraries Government Documents Department

Nonlinear Simulation Studies of Tokamaks and STs

Description: The multilevel physics, massively parallel plasma simulation code, M3D, has been used to study spherical tori (STs) and tokamaks. The magnitude of outboard shift of density profiles relative to electron temperature profiles seen in NSTX [National Spherical Torus Experiment] under strong toroidal flow is explained. Internal reconnection events in ST discharges can be classified depending on the crash mechanism, just as in tokamak discharges; a sawtooth crash, disruption due to stochasticity, or high-beta disruption. Toroidal shear flow can reduce linear growth of internal kink. It has a strong stabilizing effect nonlinearly and causes mode saturation if its profile is maintained, e.g., through a fast momentum source. Normally, however, the flow profile itself flattens during the reconnection process, allowing a complete reconnection to occur. In some cases, the maximum density and pressure spontaneously occur inside the island and cause mode saturation. Gyrokinetic hot particle/MHD hybrid studies of NSTX show the effects of fluid compression on a fast-ion-driven n = 1 mode. MHD studies of recent tokamak experiments with a central current hole indicate that the current clamping is due to sawtooth-like crashes, but with n = 0.
Date: July 7, 2003
Creator: Park, W.; Breslau, J.; Chen, J.; Fu, G.Y.; Jardin, S.C.; Klasky, S. et al.
Partner: UNT Libraries Government Documents Department