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Hydromagnetic Stability of a Diffuse Linear Pinch

Description: Abstract: "The hydromagnetic energy principle is applied to the derivation of necessary and sufficient conditions for the hydromagnetic stability of a linear pinch with distributed plasma current (a diffuse linear pinch). The results are quite general in that the axial and azimuthal components of the magnetic field, which determines the structure of the pinch completely, are treated as arbitrary functions of distance from the axis. For purpose of illustration, the general results are applied to the limiting case of a pinch with the plasma current confined to an infinity thin layer (a sharp pinch)."
Date: August 1959
Creator: Newcomb, William A.
Partner: UNT Libraries Government Documents Department

Preliminary Report on Magnetogasdynamic Aspects

Description: Report describing studies on magnetogasdynamic aspects, presented in three sections: a summary of relevant magnetofluidmechanic fundamentals; a review of relevant literature on flow modification in magnetofluidmechnics; and the results of analytical investigations on highly restricted magnetofluidmechanic flows.
Date: August 1961
Creator: Chenoweth, D. R.
Partner: UNT Libraries Government Documents Department

Note on Possible Stabilization Due to Coupling

Description: Abstract: "By a simple illustration it is pointed out that, conceivably, the real coupled character of the general magnetohydrodynamic equations may lead to much slower instability growth rates, if not stabilization, than predicted from the linearized set of equations."
Date: July 1, 1955
Creator: Greyber, Howard D.
Partner: UNT Libraries Government Documents Department

Ideal Magnetohydrodynamics Stability Spectrum with a Resistive Wall

Description: We show that the eigenvalue equations describing a cylindrical ideal magnetophydrodynamicsw (MHD) plasma interacting with a thin resistive wall can be put into the standard mathematical form: Α⋅χ = λΒ⋅ χ. This is accomplished by using a finite element basis for the plasma, and by adding an extra degree of freedom corresponding to the electrical current in the thin wall. The standard form allows the use of linear eigenvalue solvers, without additional interations, to compute the complete spectrum of plasma modes in the presence of a surrounding restrictive wall at arbitrary separation. We show that our method recovers standard results in the limits of (1) an infinitely resistive wall (no wall), and (2) a zero resistance wall (ideal wall).
Date: May 22, 2008
Creator: Jardin, S.P. Smith and S.C.
Partner: UNT Libraries Government Documents Department

Final Technical Report - SciDAC Cooperative Agreement: Center for Wave Interactions with Magnetohydrodynamics

Description: Final technical report for research performed by Dr. Thomas G. Jenkins in collaboration with Professor Dalton D. Schnack on SciDAC Cooperative Agreement: Center for Wave Interactions with Magnetohydrodyanics, DE-FC02-06ER54899, for the period of 8/15/06 - 8/14/11. This report centers on the Slow MHD physics campaign work performed by Dr. Jenkins while at UW-Madison and then at Tech-X Corporation. To make progress on the problem of RF induced currents affect magnetic island evolution in toroidal plasmas, a set of research approaches are outlined. Three approaches can be addressed in parallel. These are: (1) Analytically prescribed additional term in Ohm's law to model the effect of localized ECCD current drive; (2) Introduce an additional evolution equation for the Ohm's law source term. Establish a RF source 'box' where information from the RF code couples to the fluid evolution; and (3) Carry out a more rigorous analytic calculation treating the additional RF terms in a closure problem. These approaches rely on the necessity of reinvigorating the computation modeling efforts of resistive and neoclassical tearing modes with present day versions of the numerical tools. For the RF community, the relevant action item is - RF ray tracing codes need to be modified so that general three-dimensional spatial information can be obtained. Further, interface efforts between the two codes require work as well as an assessment as to the numerical stability properties of the procedures to be used.
Date: July 1, 2012
Creator: Schnack, Dalton D.
Partner: UNT Libraries Government Documents Department

Computation of Multi-region Relaxed Magnetohydrodynamic Equilibria

Description: We describe the construction of stepped-pressure equilibria as extrema of a multi-region, relaxed magnetohydrodynamic (MHD) energy functional that combines elements of ideal MHD and Taylor relaxation, and which we call MRXMHD. The model is compatible with Hamiltonian chaos theory and allows the three-dimensional MHD equilibrium problem to be formulated in a well-posed manner suitable for computation. The energy-functional is discretized using a mixed finite-element, Fourier representation for the magnetic vector potential and the equilibrium geometry; and numerical solutions are constructed using the stepped-pressure equilibrium code, SPEC. Convergence studies with respect to radial and Fourier resolution are presented.
Date: March 29, 2013
Creator: S.R. Hudson, R.L. Dewar, G. Dennis, M.J. Hole, M. McGann, G. von Nessi and S. Lazerson
Partner: UNT Libraries Government Documents Department

Effects of Magnetic Field on the Turbulent Wake of a Cylinder in MHD Channel Flow

Description: Results from a free-surface MHD flow experiment are presented detailing the modi cation of vortices in the wake of a circular cylinder with its axis parallel to the applied magnetic fi eld. Experiments were performed with a Reynolds number near Re ~ 104 as the interaction parameter, N = |j x#2; B| / |ρ (υ ⋅ ∇), was increased through unity. By concurrently sampling the downstream fluid velocity at sixteen cross-stream locations in the wake, it was possible to extract an ensemble of azimuthal velocity profi les as a function of radius for vortices shed by the cylinder at varying strengths of magnetic field. Results indicate a signi cant change in vortex radius and rotation as N is increased. The lack of deviations from the vortex velocity pro file at high magnetic fi elds suggests the absence of small-scale turbulent features. By sampling the wake at three locations downstream in subsequent experiments, the decay of the vortices was examined and the effective viscosity was found to decrease as N-049±0.4. This reduction in effective viscosity is due to the modi cation of the small-scale eddies by the magnetic fi eld. The slope of the energy spectrum was observed to change from a k-1.8 power-law at low N to a k-3.5 power-law for N > 1. Together, these results suggest the flow smoothly transitioned to a quasi-two-dimensional state in the range 0 < N < 1.
Date: April 17, 2013
Creator: John Rhoads, Eric Edlund and Hantao Ji
Partner: UNT Libraries Government Documents Department

Calculation of Eddy Currents In the CTH Vacuum Vessel and Coil Frame

Description: Knowledge of eddy currents in the vacuum vessel walls and nearby conducting support structures can significantly contribute to the accuracy of Magnetohydrodynamics (MHD) equilibrium reconstruction in toroidal plasmas. Moreover, the magnetic fields produced by the eddy currents could generate error fields that may give rise to islands at rational surfaces or cause field lines to become chaotic. In the Compact Toroidal Hybrid (CTH) device (R0 = 0.75 m, a = 0.29 m, B ≤ 0.7 T), the primary driver of the eddy currents during the plasma discharge is the changing flux of the ohmic heating transformer. Electromagnetic simulations are used to calculate eddy current paths and profile in the vacuum vessel and in the coil frame pieces with known time dependent currents in the ohmic heating coils. MAXWELL and SPARK codes were used for the Electromagnetic modeling and simulation. MAXWELL code was used for detailed 3D finite-element analysis of the eddy currents in the structures. SPARK code was used to calculate the eddy currents in the structures as modeled with shell/surface elements, with each element representing a current loop. In both cases current filaments representing the eddy currents were prepared for input into VMEC code for MHD equilibrium reconstruction of the plasma discharge. __________________________________________________
Date: September 25, 2012
Creator: Zolfaghari, A.; Brooks, A; Michaels, A.; Hanson, J. & Hartwell, G.
Partner: UNT Libraries Government Documents Department

Performance Characteristics of a Liquid Metal MHD Generator

Description: Report issued by the Argonne National Laboratory discussing the performance of magnetohydrodynamic generators. As stated in the abstract, "an experimental study was made of the performance characteristics of a liquid metal MHD generator utilizing single-phase sodium-potassium and two-phase sodium-potassium-nitrogen fluids. The purpose of this study was to compare the generator performance with theory for single-phase flow and to determine the effects of the introduction of the gaseous phase on the generator output and efficiency" (p. 9). This report includes tables, illustrations, and photographs.
Date: July 1964
Creator: Petrick, Michael & Lee, Kung-You
Partner: UNT Libraries Government Documents Department

Final Report for "Implimentation and Evaluation of Multigrid Linear Solvers into Extended Magnetohydrodynamic Codes for Petascale Computing"

Description: Extended magnetohydrodynamic (MHD) codes are used to model the large, slow-growing instabilities that are projected to limit the performance of International Thermonuclear Experimental Reactor (ITER). The multiscale nature of the extended MHD equations requires an implicit approach. The current linear solvers needed for the implicit algorithm scale poorly because the resultant matrices are so ill-conditioned. A new solver is needed, especially one that scales to the petascale. The most successful scalable parallel processor solvers to date are multigrid solvers. Applying multigrid techniques to a set of equations whose fundamental modes are dispersive waves is a promising solution to CEMM problems. For the Phase 1, we implemented multigrid preconditioners from the HYPRE project of the Center for Applied Scientific Computing at LLNL via PETSc of the DOE SciDAC TOPS for the real matrix systems of the extended MHD code NIMROD which is a one of the primary modeling codes of the OFES-funded Center for Extended Magnetohydrodynamic Modeling (CEMM) SciDAC. We implemented the multigrid solvers on the fusion test problem that allows for real matrix systems with success, and in the process learned about the details of NIMROD data structures and the difficulties of inverting NIMROD operators. The further success of this project will allow for efficient usage of future petascale computers at the National Leadership Facilities: Oak Ridge National Laboratory, Argonne National Laboratory, and National Energy Research Scientific Computing Center. The project will be a collaborative effort between computational plasma physicists and applied mathematicians at Tech-X Corporation, applied mathematicians Front Range Scientific Computations, Inc. (who are collaborators on the HYPRE project), and other computational plasma physicists involved with the CEMM project.
Date: June 19, 2008
Creator: Vadlamani, Srinath; Kruger, Scott & Austin, Travis
Partner: UNT Libraries Government Documents Department

A Regularized Approach for Solving Magnetic Differential Equations and a Revised Iterative Equilibrium Algorithm

Description: A method for approximately solving magnetic differential equations is described. The approach is to include a small diffusion term to the equation, which regularizes the linear operator to be inverted. The extra term allows a "source-correction" term to be defned, which is generally required in order to satisfy the solvability conditions. The approach is described in the context of computing the pressure and parallel currents in the iterative approach for computing magnetohydrodynamic equilibria. __________________________________________________
Date: October 13, 2010
Creator: Hudson, S. R.
Partner: UNT Libraries Government Documents Department

Numerical Studies of Magnetohydrodynamic Activity Resulting from Inductive Transients Final Report

Description: This report describes results from numerical studies of transients in magnetically confined plasmas. The work has been performed by University of Wisconsin graduate students James Reynolds and Giovanni Cone and by the Principal Investigator through support from contract DE-FG02-02ER54687, a Junior Faculty in Plasma Science award from the DOE Office of Science. Results from the computations have added significantly to our knowledge of magnetized plasma relaxation in the reversed-field pinch (RFP) and spheromak. In particular, they have distinguished relaxation activity expected in sustained configurations from transient effects that can persist over a significant fraction of the plasma discharge. We have also developed the numerical capability for studying electrostatic current injection in the spherical torus (ST). These configurations are being investigated as plasma confinement schemes in the international effort to achieve controlled thermonuclear fusion for environmentally benign energy production. Our numerical computations have been performed with the NIMROD code (http://nimrodteam.org) using local computing resources and massively parallel computing hardware at the National Energy Research Scientific Computing Center. Direct comparisons of simulation results for the spheromak with laboratory measurements verify the effectiveness of our numerical approach. The comparisons have been published in refereed journal articles by this group and by collaborators at Lawrence Livermore National Laboratory (see Section 4). In addition to the technical products, this grant has supported the graduate education of the two participating students for three years.
Date: August 29, 2005
Creator: Sovinec, Carl R.
Partner: UNT Libraries Government Documents Department

Hall MHD Modeling of Two-dimensional Reconnection: Application to MRX Experiment

Description: Two-dimensional resistive Hall magnetohydrodynamics (MHD) code is used to investigate the dynamical evolution of driven reconnection in the Magnetic Reconnection Experiment (MRX). The initial conditions and dimensionless parameters of the simulation are set to be similar to the experimental values. We successfully reproduce many features of the time evolution of magnetic configurations for both co- and counter-helicity reconnection in MRX. The Hall effect is shown to be important during the early dynamic X-phase of MRX reconnection, while effectively negligible during the late ''steady-state'' Y-phase, when plasma heating takes place. Based on simple symmetry considerations, an experiment to directly measure the Hall effect in MRX configuration is proposed and numerical evidence for the expected outcome is given.
Date: January 9, 2003
Creator: Lukin, V.S. & Jardin, S.C.
Partner: UNT Libraries Government Documents Department

Three-Dimensional Magnetohydrodynamic Simulation of Slapper Initiation Systems

Description: Although useful information can be gleaned from 2D and even 1D simulations of slapper type initiation systems, these systems are inherently three-dimensional and therefore require full 3D representation to model all relevant details. Further, such representation provides additional insight into optimizing the design of such devices from a first-principles perspective and can thereby reduce experimental costs. We discuss in this paper several ongoing efforts in modeling these systems, our pursuit of validation, and extension of these methods to other systems. Our results show the substantial dependence upon highly accurate global equations of state and resistivity models in these analyses.
Date: March 9, 2010
Creator: Christensen, J S & Hrousis, C A
Partner: UNT Libraries Government Documents Department

Modeling and analysis of the high energy liner experiment, HEL-1

Description: A high energy, massive liner experiment, driven by an explosive flux compressor generator, was conducted at VNIIEF firing point, Sarov, on August 22, 1996. We report results of numerical modeling and analysis we have performed on the solid liner dynamics of this 4.0 millimeter thick aluminum liner as it was imploded from an initial inner radius of 236 mm onto a Central Measuring Unit (CMU), radius 55 mm. Both one- and two-dimensional MHD calculations have been performed, with emphasis on studies of Rayleigh-Taylor instability in the presence of strength and on liner/glide plane interactions. One-dimensional MHD calculations using the experimental current profile confirm that a peak generator current of 100-105 MA yields radial liner dynamics which are consistent with both glide plane and CMU impact diagnostics. These calculations indicate that the liner reached velocities of 6.9-7.5 km/s before CMU impact. Kinetic energy of the liner, integrated across its radial cross-section, is between 18-22 MJ. Since the initial goal was to accelerate the liner to at least 20 MJ, these calculations are consistent with overall success. Two-dimensional MHD calculations were employed for more detailed comparisons with the measured data set. The complete data set consisted of over 250 separate probe traces. From these data and from their correlation with the MHD calculations, we can conclude that the liner deviated from simple cylindrical shape during its implosion. Two-dimensional calculations have clarified our understanding of the mechanisms responsible for these deformations. Many calculations with initial outer edge perturbations have been performed to assess the role of Rayleigh-Taylor instability. Perturbation wavelengths between 4-32 mm and amplitudes between 8-240 {mu}m have been simulated with the experimental current profiles. When strength is omitted short wavelengths are observed to grow to significant levels; material strength stabilizes such modes in the calculations.
Date: August 1, 1997
Creator: Faehl, R.J.; Sheehey, P.T. & Reinovsky, R.E.
Partner: UNT Libraries Government Documents Department

Radiation MHD modeling of a proposed dynamic hohlraum

Description: In this paper we report 2D radiation magnetohydrodynamic simulations of a dynamic hohlraum target designed to be driven by the Z accelerator at Sandia National Laboratory, Albuquerque New Mexico. Z generates currents up 20 MA with a rise time of 100 ns and peak electrical power of 40 TW. In this design we attempt to reduce the effects of magneto-Rayleigh Taylor (RT) modes by using a distributed initial density profile. Earlier work showed that ``tailoring`` the initial density profile could reduce the sheath acceleration and the number of e-foldings that the RT instability grows during the implosion . As the sheath moves in radially, fresh material is swept up or ``snow plowed``, providing a back pressure that counters the J x B force. A special profile can be found in which the unstable outer surface of the sheath implodes at constant velocity, reducing the classical growth rate to zero, although residual Richtmeyer-Meshkov type instability (instability of the snow-plow shock front) may be present. In practice, it is hard to create tailored initial density profiles due to the difficulty of machining and otherwise manipulating very low density materials. It becomes easier to manufacture these complex targets as the current, energy and load mass increase with large drivers. Z is the first fast pulse power device with enough energy to consider loads of this type.
Date: July 1, 1997
Creator: Hammer, J.H.; De Groot, J.S.; Tabak, M.; Toor, A. & Zimmerman, G.B.
Partner: UNT Libraries Government Documents Department

Particle acceleration from reconnection in the geomagnetic tail

Description: Acceleration of charged particles in the near geomagnetic tail, associated with a dynamic magnetic reconnection process, was investigated by a combined effort of data analysis, using Los Alamos data from geosynchronous orbit, MHD modeling of the dynamic evolution of the magnetotail, and test particle tracing in the electric and magnetic fields obtained from the MHD simulation.
Date: August 1, 1997
Creator: Birn, J.; Borovsky, J.E.; Thomsen, M.F.; McComas, D.J.; Reeves, G.D.; Belian, R.D. et al.
Partner: UNT Libraries Government Documents Department

A kinetic-MHD model for studying low frequency multiscale phenomena

Description: A nonlinear kinetic-MHD model for studying low frequency multiscale phenomena has been developed by taking advantage of the single fluid MHD model`s simplicity and by properly accounting for core ion finite Larmor radius (FLR) effects and major kinetic effects of energetic particles. The kinetic-MHD model treats the low energy core plasma by a generalized MHD description and energetic particles kinetically; the coupling between the dynamics of these two components of plasmas is through the plasma pressure. The generalized MHD model for core plasma includes core ion FLR effects which provide a finite parallel electric field, a modified perpendicular velocity from the {bold E} {times} {bold B} drift, and a gyroviscosity tensor, which are neglected in the usual single fluid MHD description. The perturbed core plasma electron and ion densities, velocity and pressure tensor are determined from both the low frequency and high frequency gyro-kinetic equations. From the quasineutrality condition, we obtain the parallel electric field, which arises from the ion gryoradius effects. The kinetic-MHD model is closed by generalized pressure laws for the core and energetic plasmas. When ion gryoradius radius is on the order of the plasma equilibrium scale length, the Vlasov description may be adopted to describe the energetic particle dynamics. From the kinetic-MHD model we derive eigenmode equations for low frequency waves such as shear/kinetic Alfven waves (KAW) and ballooning-mirror modes. The kinetic-MHD model has been successfully applied to study ballooning-mirror instabilities to understand the field-aligned structure and instability threshold of compressional Pc 5 waves in the ring current region. It is also demonstrated that the ion FLR effects in the dispersion relation of KAWs are properly retained; note that these are not properly included in the popularly employed two-fluid equations because the gryoviscosity contribution is usually not retained. 18 refs., 2 figs.
Date: May 1, 1996
Creator: Cheng, C. Z. & Johnson, J. R.
Partner: UNT Libraries Government Documents Department