Scott Kruger

Generalized reduced magnetohydrodynamic equations

A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Ad...

Dynamics of the major disruption of a DIII-D plasma

The dynamics of the major disruption of DIII-D discharge 87009 are investigated with the NIMROD code [Sovinec et al., J. Comput. Phys. 195, 355 (2004)]. To explore the time dynamics in a computationally efficient manner, a fixed-boundary equilibrium is used to model the physics of a plasma being heated through an ideal magnetohydrodynamic (MHD) instability threshold. This simulation shows a faster-than-exponential increase in magnetic energy as predicted by analytic theory [Callen et al., Phys. Plasmas 6, 2963 (1999)]. The dynamics of the heat flux loading on the divertor surfaces is explored with an equilibrium that has the plasma beta raised 8.7% above the best equilibrium reconstruction to start above the ideal MHD threshold. The nonlinear evolution of the ideal mode leads to a stochastic magnetic field and parallel heat transport leads to a localization of the heat flux that is deposited on the wall. The structure of the heat flux deposition is dependent upon the magnetic topology that results from th...

Edge localized linear ideal magnetohydrodynamic instability studies in an extended-magnetohydrodynamic code

A linear benchmark between the linear ideal MHD stability codes ELITE [H. R. Wilson et al., Phys. Plasmas 9, 1277 (2002)], GATO [L. Bernard et al., Comput. Phys. Commun. 24, 377 (1981)], and the extended nonlinear magnetohydrodynamic (MHD) code, NIMROD [C. R. Sovinec et al.., J. Comput. Phys. 195, 355 (2004)] is undertaken for edge-localized (MHD) instabilities. Two ballooning-unstable, shifted-circle tokamak equilibria are compared where the stability characteristics are varied by changing the equilibrium plasma profiles. The equilibria model an H-mode plasma with a pedestal pressure profile and parallel edge currents. For both equilibria, NIMROD accurately reproduces the transition to instability (the marginally unstable mode), as well as the ideal growth spectrum for a large range of toroidal modes (n=1–20). The results use the compressible MHD model and depend on a precise representation of “ideal-like” and “vacuumlike” or “halo” regions within the code. The halo region is modeled by the introduction ...

Analysis of Recurrent Patterns in Toroidal Magnetic Fields

In the development of magnetic confinement fusion which will potentially be a future source for low cost power, physicists must be able to analyze the magnetic field that confines the burning plasma. While the magnetic field can be described as a vector field, traditional techniques for analyzing the fields topology cannot be used because of its Hamiltonian nature. In this paper we describe a technique developed as a collaboration between physicists and computer scientists that determines the topology of a toroidal magnetic field using fieldlines with near minimal lengths. More specifically, we analyze the Poincaré map of the sampled fieldlines in a Poincaré section including identifying critical points and other topological features of interest to physicists. The technique has been deployed into an interactiveparallel visualization tool which physicists are using to gain new insight into simulations of magnetically confined burning plasmas.

Geometrical influences on neoclassical magnetohydrodynamic tearing modes

The influence of geometry on the pressure drives of nonideal magnetohydrodynamic tearing modes is presented. In order to study the effects of elongation, triangularity, and aspect ratio, three different machines are considered to provide a range of tokamak configurations: Tokamak Fusion Test Reactor (circular) [Fusion Technol. 21, 1324 (1992)], DIII-D (D-shaped) [Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159], and Pegasus (extremely low aspect ratio) [Fonck et al., Bull. Am. Phys. Soc. 41, 1400 (1996)]. For large aspect ratio tokamaks, shaping does very little to influence the pressure gradient drives, while at low aspect ratios, a very strong sensitivity to the profiles is found. In particular, this sensitivity is connected to the strong dependence on the magnetic shear. This suggests that at low aspect ratio it may be possible to stabilize neoclassical tearing modes by a flattening the q profile near low order rational surfa...

Modelling of ELM dynamics for DIII-D and ITER

A model for integrated modelling studies of edge localized modes (ELMs) in ITER is discussed in this paper. Stability analyses are carried out for ITER and DIII-D equilibria that are generated with the TEQ and TOQ equilibrium codes. The H-mode pedestal pressure and parallel current density are varied in a systematic way in order to span the relevant parameter space for specific ITER plasma parameters. The ideal MHD stability codes, DCON, ELITE and BALOO, are employed to determine whether or not each ITER equilibrium profile is unstable to peeling or ballooning modes in the pedestal region. Several equilibria that are close to the marginal stability boundary for peeling and ballooning modes are tested with the NIMROD non-ideal MHD code. When the effects of finite resistivity are studied in a series of linear NIMROD computations, it is found that the peeling?ballooning stability threshold is very sensitive to the resistivity and viscosity profiles, which vary dramatically over a wide range near the separatrix. When two-fluid gyro-viscous and Hall effects are included in NIMROD computations, it is found that harmonics with high toroidal mode numbers are stabilized while the growth rate of harmonics with low toroidal mode numbers are only moderately reduced. When flow shear across the H-mode pedestal is included, it is found that linear growth rates are increased, particularly for harmonics with high toroidal mode numbers. In nonlinear NIMROD simulations, ELM crashes produce filaments that extend out to the wall in the absence of flow shear. When flow shear is included, the filaments are dragged by the fluid and sheared off before they extend to the wall.

Calculating electron cyclotron current drive stabilization of resistive tearing modes in a nonlinear magnetohydrodynamic model

A model which incorporates the effects of electron cyclotron current drive (ECCD) into the magnetohydrodynamic equations is implemented in the NIMROD code [C. R. Sovinec et al., J. Comput. Phys. 195, 355 (2004)] and used to investigate the effect of ECCD injection on the stability, growth, and dynamical behavior of magnetic islands associated with resistive tearing modes. In addition to qualitatively and quantitatively agreeing with numerical results obtained from the inclusion of localized ECCD deposition in static equilibrium solvers [A. Pletzer and F. W. Perkins, Phys. Plasmas 6, 1589 (1999)], predictions from the model further elaborate the role which rational surface motion plays in these results. The complete suppression of the (2,1) resistive tearing mode by ECCD is demonstrated and the relevant stabilization mechanism is determined. Consequences of the shifting of the mode rational surface in response to the injected current are explored, and the characteristic short-time responses of resistive te...

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).

Global gyrokinetic simulations of the H-mode tokamak edge pedestala)

Global gyrokinetic simulations of DIII-D H-mode edge pedestal show two types of instabilities may exist approaching the onset of edge localized modes: an intermediate-n, high frequency mode which we identify as the “kinetic peeling ballooning mode (KPBM),” and a high-n, low frequency mode. Our previous study [W. Wan et al., Phys. Rev. Lett. 109, 185004 (2012)] has shown that when the safety factor profile is flattened around the steep pressure gradient region, the high-n mode is clearly kinetic ballooning mode and becomes the dominant instability. Otherwise, the KPBM dominates. Here, the properties of the two instabilities are studied by varying the density and temperature profiles. It is found that the KPBM is destabilized by density and ion temperature gradient, and the high-n mode is mostly destabilized by electron temperature gradient. Nonlinear simulations with the KPBM saturate at high levels. The equilibrium radial electric field (Er) reduces the transport. The effect of the parallel equilibrium cu...

Concurrent, parallel, multiphysics coupling in the FACETS project

FACETS (Framework Application for Core-Edge Transport Simulations), is now in its third year. The FACETS team has developed a framework for concurrent coupling of parallel computational physics for use on Leadership Class Facilities (LCFs). In the course of the last year, FACETS has tackled many of the difficult problems of moving to parallel, integrated modeling by developing algorithms for coupled systems, extracting legacy applications as components, modifying them to run on LCFs, and improving the performance of all components. The development of FACETS abides by rigorous engineering standards, including cross platform build and test systems, with the latter covering regression, performance, and visualization. In addition, FACETS has demonstrated the ability to incorporate full turbulence computations for the highest fidelity transport computations. Early indications are that the framework, using such computations, scales to multiple tens of thousands of processors. These accomplishments were a result of an interdisciplinary collaboration among computational physics, computer scientists and applied mathematicians on the team.