UW - CPTC 06 - 4 Final Report on the OFES ELM Milestone for FY 2006

Executive Summary This document reports the successful completion of the OFES Theory Milestone for FY2006: Increase resolution in simulations of macroscopic plasma edge phenomena. Optimizing confinement and predicting the behavior of burning plasmas require improved simulations of edge and core plasma phenomena, as the characteristics of the edge can strongly affect core confinement. For this quarterly milestone, we will simulate nonlinear plasma edge phenomena using extended MHD codes with a resolution of 40 toroidal modes. An important issue for fusion plasma theory is the occurrence of Edge Localized Modes (ELMs) in tokamak plasmas. We apply large-scale numerical computation with fluid-based plasma models to ELM-unstable equilibrium profiles that have been fit to data from the DIII-D device at General Atomics (http://fusion.gat.com/diii-d/). Building upon the successful completion of the milestone for FY2005, we include the number density profile created from laboratory observations and electron-fluid dynamics, in addition to increased spatial resolution for the toroidal coordinate and the poloidal plane. The effects of toroidal ion flow are considered through computations with resistive magnetohydrodynamics (MHD). The linear and nonlinear ELM computations are performed with the NIMROD code (http://nimrodteam.org) that allows users to select from MHD and two-fluid models. The Hall and electron pressure terms distinguish the two-fluid electric field, as appropriate for low-frequency dynamics. The present two-fluid model also includes the Braginskii gyroviscous stress in the ion evolution. A single temperature is used for the ion and electron fluids—two-temperature modeling being left for future work. However, many of the computations use anisotropic thermal conduction, and the ratio of parallel and perpendicular thermal conductivities is 10 7 in the 40-mode nonlinear two-fluid computation. This computation also has temperature-dependent electrical resistivity computed locally from the evolving three-dimensional temperature profile. Linear calculations for an equilibrium that is fit to measurements of DIII-D discharge 113317 test the numerical convergence properties of the present NIMROD algorithm on ELMs. Substantial poloidal resolution is required to reproduce eigenfunctions with large toroidal wavenumbers (n), but the radial resolution can be economized provided that the computational mesh is packed near the separatrix of the equilibrium. Convergence is then established with finite element basis functions of polynomial degree as large as 7 for MHD modeling and 8 for two-fluid modeling. The resistive MHD calculations find growth-rates that increase with n, but the two-fluid model shows a cutoff for n≥30. The radial profile of the diamagnetic drift is narrower than the width of the intermediate-n …