Browsing by Subject "Plasma physics"
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Item A radiative model for determining plasma dissociation using vacuum ultraviolet self-absorption spectroscopy(2013-05) Laity, George; Neuber, Andreas A.; Krompholz, Hermann G.; Hatfield, Lynn H.; Frank, KlausThis manuscript documents the first five years of collective knowledge gained from the Texas Tech University research program to study the emission and subsequent re-absorption of vacuum ultraviolet radiation present during the initiation of nano-second plasma discharges generated at atmospheric pressure. The initial experimental study resulted in direct observation of vacuum ultraviolet radiation produced by an open transient plasma at atmospheric pressure for the first time in the available literature. Upgrades to the spectral instrumentation enabled more efficient measurement of vacuum ultraviolet radiation for the wavelength range 115 - 135 nm, allowing for enhanced resolution in the recording of emission line profiles. A direct consequence of this effort was the conception of a passive optical diagnostic for measuring the absolute number density of atoms in the discharge plasma: the vacuum ultraviolet self-absorption spectroscopy (VUV-SAS) technique. An integral piece of this technique is a radiative transfer simulation for calculating the radiation trapping physics inside the plasma channel volume, executed in the MATLAB® environment and accelerated via GPU resources using the NVIDIA® CUDA architecture. The combination of experimental and modeling approaches resulted in successful demonstration of the VUV-SAS diagnostic for N2/H2 plasmas at atmospheric pressure, where spatially resolved N and H atom densities on the order 10^17 cm^-3 were observed without an invasive laser absorption diagnostic. Through approximation of the quasi-contiguous Stark broadening of H atoms in the discharge plasma, spatially resolved electron densities on the order 10^18 cm^-3 were observed along the plasma channel. All measured quantities are validated through detailed discussion of the relevant physics concerning the fast ionization shockwave characteristic to the inception of spark discharge plasmas. Finally, the extended VUV-SAS technique was successful in demonstrating the measurement of N and O atom densities present in air discharge plasmas, thereby finding practical application for a variety of future pulsed power laboratory experiments.Item Applications of Hamiltonian theory to plasma models(2016-05) Keramidas Charidakos, Ioannis; Morrison, Philip J.; Waelbroeck, F.; Horton, Wendell C.; Hazeltine, Richard; Fitzpatrick, Richard; Gamba, Irene M.Three applications of Hamiltonian Methods in Plasma Physics are presented. The first application is the development of a new, five-field, Hamiltonian gyrofluid model. It is comprised by evolution equations for the ion density, pressure and parallel temperature and electron density and pressure. It contains curvature and compressibility effects. The model is shown to satisfy a conserved energy and a Lie-Poisson bracket for it is given. Casimir invariants are calculated and through them, the normal fields of the system are recovered. Later, the model is linearized and shown to possess modes that are identified with the slab ITG, toroidal ITG and KBM modes. Both an electrostatic and an electromagnetic study are performed. Growth rates and critical parameters for instability are computed and compared to their fluid and kinetic counterparts. The accuracy of the model is shown to be between the fluid and the kinetic results, as was expected. Dissipation is added to the ideal system via the use of non-local terms that mimic Landau damping. The modes of the system are shown to undergo Krein bifurcations and their behavior once dissipation is turned on, strongly suggests that they are negative energy modes. A connection between the marginal stability condition of the ITG mode at high k┴ and the (missing) equation of perpendicular pressure is conjectured opening an interesting possibility for future research. The second application is a method for the derivation of reduced fluid models through the use of an action principle. The importance of the method lies in the fact that since all approximations are made directly at the level of the action, the models that result from the action minimization are guaranteed to retain the Hamiltonian character of their parent-model. The two-fluid action is given in Lagrangian variables and the two-fluid equations of motion are recovered by it's minimization. The Eulerian (field) equations of motion are retrieved through the Lagrange-to-Euler (L-E) map. New, single-fluid variables are defined but instead of being implemented at the level of the equations of motion, they are implemented directly in the action. The action is subjected to approximations. Different approximations lead to different models with the models of Lust, Extended MHD, Hall MHD and electron MHD being retrieved. The passing from Lagrangian to Eulerian variables in the single-fluid description requires a non-trivial modification of the E-L map. A note about the importance of quasineutrality in single-fluid models and its ramifications in the Lagrangian framework is given. Several invariants of the models are calculated via Noethers' Theorem. The third application concerns the imposition of constraints in Hamiltonian systems. Two worked examples of the method of Dirac are presented. The first one is on an electrostatic model which has the Hasegawa-Mima and RMHD as distinct limits. The constraint that leads to the Hasegawa-Mima is investigated. The calculations are demonstrated in detail and the reduced system is produced. A brief discussion of the dispersion relation of the reduced system concludes the first example. The second example is the imposition of quasineutrality and divergence-free current on the bracket of the two-fluid model. The various steps of the method are displayed and the example is completed with the verification that the new bracket satisfies the constraints. The possibility of performing the same calculation with single-fluid variables remains open for future research.Item Hamiltonian and Action Principle formulations of plasma fluid models(2015-05) Lingam, Manasvi; Morrison, Philip J.; Hazeltine, Richard; Waelbroeck, Francois; Breizman, Boris; Gamba, Irene MThe Hamiltonian and Action Principle (HAP) formulations of plasmas and fluids are explored in a wide variety of contexts. The principles involved in the construction of Action Principles are presented, and the reduction procedure to obtain the associated noncanonical Hamiltonian formulation is delineated. The HAP formulation is first applied to a 2D magnetohydrodynamics (MHD) model, and it is shown that one can include Finite Larmor Radius effects in a transparent manner. A simplified 2D limit of the famous Branginskii gyroviscous tensor is obtained, and the origins of a powerful tool - the gyromap - are traced to the presence of a gyroviscous term in the action. The noncanonical Hamiltonian formulation is used to extract the Casimirs of the model, and an Energy-Casimir method is used to derive the equilibria and stability; the former are shown to be generalizations of the Grad-Shafranov equation, and possess both flow and gyroviscous effects. The action principle of 2D MHD is generalized to encompass a wider class of gyroviscous fluids, and a suitable gyroviscous theory for liquid crystals is constructed. The next part of the thesis is devoted to examining several aspects of extended MHD models. It is shown that one can recover many such models from a parent action, viz. the two-fluid model. By performing systematic orderings in the action, extended MHD, Hall MHD and electron MHD are recovered. In order to obtain these models, novel techniques, such as non-local Lagrange-Euler maps which enable a transition between the two fluid frameworks, are introduced. A variant of extended MHD, dubbed inertial MHD, is studied via the HAP approach in the 2D limit. The model is endowed with the effects of electron inertia, but is shown to possess a remarkably high degree of similarity with (inertialess) ideal MHD. A reduced version of inertial MHD is shown to yield the famous Ottaviani-Porcelli model of reconnection. Similarities in the mathematical structure of several extended MHD models are explored in the Hamiltonian framework, and it is hypothesized that these features emerge via a unifying action principle. Prospects for future work, reliant on the HAP formulation, are also presented.Item Magnetic instabilities and resulting energy conversion in astrophysics(2013-08) Kagan, Daniel Ross; Milosavljević, MilošBecause the universe is primarily composed of plasma, the interaction of plasmas and magnetic fields is of great importance for astrophysics. In this dissertation, we investigate three magnetic instabilities and examine their possible effects on astrophysical objects. First, we model solar coronal structures as Double Beltrami states, which are the lowest energy equilibria of Hall magnetohydrodynamics. We find that these states can undergo a catastrophe with characteristics similar to those of a solar eruption, such as a flare or coronal mass ejection. We then investigate magnetic reconnection and particle acceleration in moderately magnetized relativistic pair plasmas with three-dimensional particle-in-cell simulations of a kinetic-scale current sheet. We find that in three dimensions the tearing instability produces a network of interconnected and interacting magnetic flux ropes. In its nonlinear evolution, the current sheet evolves toward a three-dimensional, disordered state in which the resulting flux rope segments contain magnetic substructure on kinetic scales and sites of temporally and spatially intermittent dissipation. We find that reconnection produces significant particle acceleration, primarily due to the electric field in the X-line regions between flux ropes; the resulting particle energy spectrum can extend to high Lorentz factors. We find that the highest energy particles are moderately beamed within.Item Mathematical analysis of equations in plasma physics(2009-12) White, Ryan Lee, 1982-; Hazeltine, R. D. (Richard D.); Morrison, PhilIn this paper, two equations from plasma physics are analyzed using two different mathematical procedures to yield information of interest for fusion energy. In the first case, Lie’s technique of computing symmetries of differential equations is applied to a specific case of the Grad-Shafranov equation. The case considered contains the majority of exact solutions from the literature. The full symmetry group is computed and new group-invariant solutions are obtained from these symmetries. The basic results and methods behind this technique are given along with several plots of the level sets or flux surfaces of the new solutions. In addition, a mathematical technique which was first used to prove the non-existence of solitons in quantum field theory is employed to derive an integral relation for any solution of the Sinh-Poisson equation. The original technique is modified to allow for a finite boundary and results are computed for two different boundary geometries.Item On the role of invariant objects in applications of dynamical systems(2012-05) Blazevski, Daniel, 1984-; Llave, Rafael de la; Chen, Thomas; Koch, Hans; Morrison, Phil; Ocampo, Cesar; Pavlovic, Natasa; Vasseur, AlexisIn this dissertation, we demonstrate the importance of invariant objects in many areas of applied research. The areas of application we consider are chemistry, celestial mechanics and aerospace engineering, plasma physics, and coupled map lattices. In the context of chemical reactions, stable and unstable manifolds of fixed points separate regions of phase space that lead to a certain outcome of the reaction. We study how these regions change under the influence of exposing the molecules to a laser. In celestial mechanics and aerospace engineering, we compute periodic orbits and their stable and unstable manifolds for a object of negligible mass (e.g. a satellite or spacecraft) under the presence of Jupiter and two of its moons, Europa and Ganymede. The periodic orbits serve as convenient spot to place a satellite for observation purposes, and computing their stable and unstable manifolds have been used in constructing low-energy transfers between the two moons. In plasma physics, an important and practical problem is to study barriers for heat transport in magnetically confined plasma undergoing fusion. We compute barriers for which heat cannot pass through. However, such barriers break down and lead to robust partial barriers. In this latter case, heat can flow across the barrier, but at a very slow rate. Finally, infinite dimensional coupled map lattice systems are considered in a wide variety of areas, most notably in statistical mechanics, neuroscience, and in the discretization of PDEs. We assume that the interaction amont the lattice sites decays with the distance of the sites, and assume the existence of an invariant whiskered torus that is localized near a collection of lattice sites. We prove that the torus has invariant stable and unstable manifolds that are also localized near the torus. This is an important step in understanding the global dynamics of such systems and opens the door to new possible results, most notably studying the problem of energy transfer between the sites.Item Plasma turbulence in the equatorial electrojet observations, theories, models, and simulations(2015-12) Hassan, Ehab Mohamed Ali Hussein; Morrison, Philip J.; Horton, Wendell; Fitzpatrick, Richard; Bengtson, Roger; Humphreys, ToddThe plasma turbulence in the equatorial electrojet due to the presence of two different plasma instability mechanisms has been observed and studied for more than seven decades. The sharp density-gradient and large conductivity give rise to gradient-drift and Farley-Buneman instabilities, respectively, of different scale-lengths. A new 2-D fluid model is derived by modifying the standard two-stream fluid model with the ion viscosity tensor and electron polarization drift, and is capable of describing both instabilities in a unified system. Numerical solution of the model in the linear regime demonstrates the capacity of the model to capture the salient characteristics of the two instabilities. Nonlinear simulations of the unified model of the equatorial electrojet instabilities reproduce many of the features that are found in radar observations and sounding rocket measurements under multiple solar and ionospheric conditions. The linear and nonlinear numerical results of the 2-D unified fluid model are found to be comparable to the fully kinetic and hybrid models which have high computational cost and small coverage area of the ionosphere. This gives the unified fluid model a superiority over those models. The distribution of the energy content in the system is studied and the rate of change of the energy content in the evolving fields obeys the law of energy conservation. The dynamics of the ions were found to have the largest portion of energy in their kinetic and internal thermal energy components. The redistribution of energy is characterized by a forward cascade generating small-scale structures. The bracket of the system dynamics in the nonlinear partial differential equation was proved to be a non-canonical Hamiltonian system as that bracket satisfies the Jacobi identity. The penetration of the variations in the interplanetary magnetic and electric fields in the solar winds to the dip equator is observed as a perfect match with the variations in the horizontal components of the geomagnetic and electric fields at the magnetic equator. Three years of concurrent measurements of the solar wind parameters at Advanced Composition Explorer (ACE) and Interplanetary Monitoring Platform (IMP) space missions used to establish a Kernel Density Estimation (KDE) functions for these parameters at the IMP-8 location. The KDE functions can be used to generate an ensemble of the solar wind parameters which has many applications in space weather forecasting and data-driven simulations. Also, categorized KDE functions ware established for the solar wind categories that have different origin from the Sun.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.Item Transport in higher dimensional phase spaces(2016-12) Curry, Christopher Timothy; Morrison, Philip J.; Horton, Jr., Claude W; Hazeltine, Richard; Matzner, Richard; Gamba, IreneWe use a four dimensional symplectic mapping, the coupled cubic-quadratic map, to provide evidence of Arnol’d Diffusion in phase space. We use the method of frequency analysis for dynamical systems to demonstrate the existence of regular orbits, and show that these orbits enclose weakly chaotic orbits which escape in finite time around the tori. A new collocation method for frequency analysis is employed by adapting it to allow for higher precision results. Arbitrary precision numerics are used to obtain highly accurate orbits for long timescales, and the adapted frequency method is used to obtain highly accurate frequencies of the mapping. We review the method of frequency analysis, demonstrate its effectiveness and accuracy in determining frequencies and finding tori in simple systems and low-dimensional mappings, and extend the results to higher dimensions. In the four dimensional mapping, we find several regular orbits with irrational frequency ratios, indicating the existence of tori in the phase space, as well as interior orbits that escape around these tori.