Browsing by Subject "Magnetohydrodynamics"
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Item Aspects of relativistic Hamiltonian physics(2015-08) D'Avignon, Eric Cavell; Morrison, Philip J.; Shepley, Lawrence; Rindler, Wolfgang; Mahajan, Swadesh; Hazeltine, Richard; Shvets, GennadyThis dissertation presents various new results in relativistic Hamiltonian plasma physics. It begins with an overview of Hamiltonian physics, with an emphasis on noncanonical brackets, and presents various nonrelativistic systems to be generalized later on. There then follows an exposition on action principles for Hall and Extended MHD, which allow the derivation of the noncanonical Hamiltonian brackets for those systems. I next discuss the transition to relativistic Hamiltonian systems, and the special difficulties that arise in this step. A detailed exploration of relativistic Hamiltonian MHD follows, using a novel bracket formulation. This chapter also investigates alternative brackets, gauge degeneracies, and Casimir invariants. Next I lay out the connection between Lagrangian and Eulerian MHD (both in Hamiltonian forms), and present some early work on a bracket-based formulation of the relativistic Navier-Stokes equation. The next chapters develop various results using an antisymmetric relativistic spin tensor, and several unexpected and intriguing physical consequences of the Jacobi identity. I conclude with a program of future research and several useful appendices.Item Global instabilities in rotating magnetized plasmas(2009-05) Pino, Jesse Ethan, 1981-; Mahajan, Swadesh M.; Hazeltine, R. D. (Richard D.)The Magnetorotational Instability (MRI) is believed to be the primary mechanism for angular momentum transfer in astrophysical accretion disks. This instability, which exists in ionized disks in the presence of weak magnetic fields, can either transfer angular momentum directly, or give rise to anomalous viscosity via non-linear turbulence. While many previous analytical treatments are concerned with the local theory of the MRI, when the length scale of rotation shear is comparable to the length scale of the most unstable modes, a global analysis is necessary. In this dissertation we investigate the global theory of the linear MRI. In particular, we show how rotation shear can localize global modes and how the global growth rates can differ signicantly from the local approximation in certain cases. Changes in the equilibrium density are considered. In addition, the effects of Hall Magnetohydrodynamics on the MRI are studied in both the local and global cases.Item Magneto-hydrodynamics simulation study of high density thermal plasmas in plasma acceleration devices(2013-08) Sitaraman, Hariswaran; Raja, Laxminarayan L.The development of a Magneto-hydrodynamics (MHD) numerical tool to study high density thermal plasmas in plasma acceleration devices is presented. The MHD governing equations represent eight conservation equations for the evolution of density, momentum, energy and induced magnetic fields in a plasma. A matrix-free implicit method is developed to solve these conservation equations within the framework of an unstructured grid finite volume formulation. The analytic form of the convective flux Jacobian is derived for general unstructured grids. A Lower Upper Symmetric Gauss Seidel (LU-SGS) technique is developed as part of the implicit scheme. A coloring based algorithm for parallelization of this technique is also presented and its computational efficiency is compared with a global matrix solve technique that uses the GMRES (Generalized Minimum Residual) algorithm available in the PETSc (Portable Extensible Toolkit for Scientific computation) libraries. The verification cases used for this study are the MHD shock tube problem in one, two and three dimensions, the oblique shock and the Hartmann flow problem. It is seen that the matrix free method is comparatively faster and shows excellent scaling on multiple cores compared to the global matrix solve technique. The numerical model was thus verified against the above mentioned standard test cases and two application problems were studied. These include the simulation of plasma deflagration phenomenon in a coaxial plasma accelerator and a novel high speed flow control device called the Rail Plasma Actuator (RailPAc). Experimental studies on coaxial plasma accelerators have revealed two different modes of operation based on the delay between gas loading and discharge ignition. Longer delays lead to the detonation or the snowplow mode while shorter delays lead to the relatively efficient stationary or deflagration mode. One of the theories that explain the two different modes is based on plasma resistivity. A numerical modeling study is presented here in the context of a coaxial plasma accelerator and the effect of plasma resistivity is dealt with in detail. The simulated results pertaining to axial distribution of radial currents are compared with experimental measurements which show good agreement with each other. The simulations show that magnetic field diffusion is dominant at lower conductivities which tend to form a stationary region of high current density close to the inlet end of the device. Higher conductivities led to the formation of propagating current sheet like features due to greater convection of magnetic field. This study also validates the theory behind the two modes of operation based on plasma resistivity. The RailPAc (Rail Plasma Actuator) is a novel flow control device that uses the magnetic Lorentz forces for fluid flow actuation at atmospheric pressures. Experimental studies reveal actuation ~ 10-100 m/s can be achieved with this device which is much larger than conventional electro-hydrodynamic (EHD) force based plasma actuators. A magneto-hydrodynamics simulation study of this device is presented. The model is further developed to incorporate applied electric and magnetic fields seen in this device. The snowplow model which is typically used for studying pulsed plasma thrusters is used to predict the arc velocities which agrees well with experimental measurements. Two dimensional simulations were performed to study the effect of Lorentz forcing and heating effects on fluid flow actuation. Actuation on the order of 100 m/s is attained at the head of the current sheet due to the effect of Lorentz forcing alone. The inclusion of heating effects led to isotropic blast wave like actuation which is detrimental to the performance of RailPAc. This study also revealed the deficiencies of a single fluid model and a more accurate multi-fluid approach is proposed for future work.Item Relativistic electron beam-plasma instability and interaction with electromagnetic wave(Texas Tech University, 1995-12) Masten, John B.A plasma particle simulation was undertaken to study the growth rate of the relativistic beam-plasma electromagnetic instability. The linear dispersion relation for the relativistic beam-plasma electromagnetic instability is derived and solved numerically for the growth rate of the electromagnetic field. The linear growth rate is numerically tabulated as a function of beam velocity and wavenumber. The results are compared with plasma particle simulations conducted using MAGIC, a particle in cell code developed by Mission Research Corporation under the auspices of the Air Force Office of Scientific Research. The resulting growth rates, as a function of beam velocity and wavenumber, from the particle simulation agree with the linear theory. The saturation of the beam-plasma instability agrees with the quasi-linear theory. Electromagnetic turbulence develops from the relativistic beam-plasma instability. The interaction of the electromagnetic turbulence with an incident electromagnetic wave, at w=wp where wp is the plasma frequency, is studied by the use of the Fourier spectrum. A scattered wave spectrum is observed at w =2wp.Item Rotating mirror plasmas in the quest of magnetofluid states(2006) Quevedo, Hernan Javier; Bengtson, Roger D.; Mahajan, Swadesh M.The goal of this dissertation is to describe and discuss the first steps taken by the Magneto Bernoulli eXperiment (MBX) to create magnetofluid states in the laboratory using a rotating plasma in an external mirror magnetic field. The terminology magnetofluid has been introduced to characterize a plasma model, based on 2-fluid theory, that treats the flow and the magnetic field in a symmetrical way. Many interesting astrophysical and laboratory problems involve large flows and fall in this category. Based on the set of parameters where MBX should run, we set up the experiment, and added different probes to diagnose the rotating plasma. We have also installed a data acquisition system, and set up an archive system (to store the data) that can be accessed worldwide. Experimental results demonstrate that supersonic flows can be generated with biasing electrodes at the throat of the mirror magnetic field. Alfvenic flows needed for a transition to magnetofluid states could not be reached because the initial plasma density was too low. At low bias (slow rotational speed) the plasma has E × B/B2 drift rotation and the magnetic fields lines are equipotentials. With a higher bias, we observed large potential drops along the field lines. We also observed an asymmetry in the polarity of the bias which leads to constraints in the control of the sheared plasma flow. We present a model that captures many of these features. In conjunction with experimental efforts we develop a theory for a rotating plasma embedded in an external mirror magnetic field. An analytic solution that involves rigid rotation of the plasma shows important differences between a 2-fluid system and ideal MHD. We find high non equipotential magnetic lines and asymmetry to compare with the experimental results.Item Tearing mode dynamics in tokamak plasmas(2016-05) Vergos, Nikolaos; Fitzpatrick, Richard, 1963-; Hazeltine, Richard; Breizman, Boris; Waelbroeck, Francois; Hallock, GaryOne of the most problematic instabilities in tokamak plasmas is tearing modes; they are driven by current and pressure gradients, and involve a reconfiguration of the magnetic and velocity fields localized into a narrow region located at a resonant magnetic surface. While the equilibrium magnetic field lines are located on concentric nested toroidal flux surfaces, the instability creates magnetic islands in which field lines connect flux tubes together, allowing for a high radial heat transport, and, thus, resulting in a loss of confinement, and, potentially, disruptions. In order for the magnetic field lines to break and reconnect, we need to take into account the resistivity of the plasma and solve the resistive magnetohydrodynamics (MHD) equations. The analytical solution consists of a boundary layer analysis (asymptotic matching) and takes advantage of the small radial width of the region where the perturbations vary significantly. Indeed, ideal magnetohydrodynamics can be used everywhere except in that narrow region where the full resistive problem must be solved. This dissertation addresses two related problems in the study of resistive tearing modes, and their interactions with externally induced resonant magnetic perturbations (error-fields). First, an in-depth investigation of the bifurcated states of a rotating, quasi-cylindrical, tokamak plasma in the presence of a resonant error-field is performed, within the context of constant-ψ resistive MHD theory. The response of the rotating plasma is studied in both the linear, and the nonlinear regime. In general, there is a "forbidden band" of tearing mode rotation frequencies that separates a branch of high-frequency solutions from a branch of low-frequency solutions. When a high-frequency solution crosses the upper boundary of the forbidden band there is a bifurcation to a low-frequency solution, and vice versa. Second, the analysis is extended to include the study of braking and locking of tearing mode rotation by the interaction of the mode with an error-field. It is found that this interaction can brake the plasma rotation, suppress magnetic island evolution and drive locked modes.