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. / text

In this thesis the effect of the Hall term in the generalised Ohm's law on Alfvén (shear) and fast wave propagation and dissipation in the ion cyclotron frequency range is investigated. The damping of an initially Gaussian field perturbation in a uniform Hall MHD plasma is treated analytically. Subsequently a 2D Lagrangian remap code (Lare2d) is used to study the damping and phase mixing of initially Gaussian field perturbations and a harmonic series of boundary-driven perturbations in a uniform field (in the presence of a transverse equilibrium density gradient). The same code is then used to study a range of initially shear and fast-wave perturbations in the vicinity of a magnetic X-type null point. The magnetic energy associated with an initially Gaussian field perturbation in a uniform resistive plasma is shown to decay algebraically at a rate that is unaffected by the Hall term to leading order in kδ where k is wavenumber and δ is ion skin depth. A similar decay law applies to whistler perturbations in the limit kδ>>>1. We demonstrate that in both geometries considered, the inclusion of the Hall term reduces the effectiveness of phase-mixing in plasma heating. The reduction in the damping rate in the uniform field (non-uniform density) cases, arising from dispersive effects, tends to zero in both the weak and strong phase mixing limits. In the Hall MHD X-point case, minimal reductions are seen for initially shear wave pulses, suggesting that little or no phase-mixing takes place. Nonlinear fast wave pulses which interact with the initial X-point destabilise the local field sufficiently to generate multiple null pairs; subsequent oscillatory current sheet behaviour appears unaffected by earlier differences between the MHD and Hall MHD cases.

No description available.

In this thesis a model for saturated tearing mode islands is developed. The equations for the mode amplitudes are essentially those of R B White et al,after a pertubation expansion has been made. It is well known that these equations are not then analytic at the mode rational surface. In our model this problem is overcome when a suitable choice of the axisymmetric current density perturbation is added to the unperturbed equilibrium current density profile. The modelled axisymmetric current density perturbation flattens the unperturbed profile locally at the rational surface and is sufficient to induce an island. No modelling in the interior of the island is necessary. The axisymmetric perturbation has a free variable which adjusts the amount of local flattening. However, when the boundary conditions are taken into account, this free parameter is determined, and the problem becomes an eigenvalue problem. The boundary condition thus determines the amount of local flattening at the rational surface. The saturated island widths are determined using D.' (W) criterion. The model allows for non axsymmetric plasma surface in a simple way, requiring careful choice of D (W). The different criteria are compared to establish the validity of the use of such criteria for perturbed boundaries. In the cylindrical approximation, one or two modes may be included in the model. In the case of two modes, non-linear coupling via the current density profile is introduced. Toroidal coupling between modes can also be simply introduced. Two modes that are toroidally coupled are considered, but mode-mode coupling is ignored. The emphasis falls in large part on the boundary conditions. Various boundary conditions can be considered because distortion of the plasma surface can be fixed by wall effects, plasma rotation, external DC coil currents, plasma rotation with external coil currents, etc. Of particular interest is the case of toroidally coupled modes, coupled in turn to these external conditions as this is the first study of such a nature. Results flowing from the study include among others that: for the special case of circular boundaries the model agrees reasonably with the results of R B White et al. No significant difference was found between the D. I (W) criterion of P H Rutherford, which is valid for circular boundaries, and that of A H Reiman, which is also valid for perturbed boundaries, when the boundary is perturbed significantly. Toroidally coupled islands do not increase in size if the boundary condition of that particular mode is not changed. If a coil current of particular helicity is switched on, it will only affect the mode of that particular helicity. Toroidally induced sideband islands have approximately the same width as natural tearing islands when the size of the natural island is large. / Thesis (Ph.D.)-University of Natal, Durban, 1992.

The reversed-field pinch (RFP) is a device for magnetic confinement of fusion plasmas. The main objective of fusion plasma research is to realise cost-effective thermonuclear fusion power plants. The RFP is highly unstable as can be explained by the theory of magnetohydrodynamics (MHD). Feed-back control technology appears to enable a robustly stable RFP operation.  Experimental control and identification of nonaxisymmetric multimode MHD is pursued in this thesis. It is shown that nonparametric multivariate identification methods can be utilised to estimate MHD spectral characteristics from plant-friendly closed-loop operational input-output data. It is also shown that accurate tracking of the radial magnetic field boundary condition is experimentally possible in the RFP. These results appear generically useful as tools in both control and physics research in magnetic confinement fusion. / <p>QC 20120508</p>

We present a novel new method for modelling magnetized molecular cloud cores using submillimetre linear polarization maps from thermal dust emission. Our PolCat modelling software builds a three-dimensional core model via the use of consecutive parametrized coordinate transformations, and produces simulated polarization maps to fit to observational datasets. We utilize the Ferret evolutionary optimizer to search the parameter space to simultaneously minimize chi-squared for the intensity and polarization position angle maps separately. We have applied PolCat to multiple test problems and several datasets from the SCUPOL Legacy Catalogue. We find that PolCat is able to distinguish between maps of twisted and non-twisted field geometries and identify twist symmetry. Preliminary fits to several datasets show that the best potential field geometries to our sample cores contain field twists. Further research using a larger number of maps is required to determine if twisted fields are commonplace in cores.

Kontext: Die Sonnenkorona wird seit 1932 mit Koronographen beobachtet. Nur wenige Jahre später war klar, dass die Korona viel heißer ist als die sichtbare Sonnenoberfläche; seit dem ist der Mechanismus der koronalen Heizung ungeklärt. Viele Mechanismen wurden vorgeschlagen, die genügend Energie zur Basis der Korona liefern, es hat sich aber kein vollständig selbstkonsitentes Bild des Energietransports und der koronalen Dissipation etabliert. Ziele: Wir möchten ein selbstkosistentes Modell aufstellen, welches Bewegungen auf der Sonnenoberfläche enthält, welche das Magnetfeld verbiegen und verflechten, wodurch in der Korona Ströme induziert und Ohm’sch dissipiert werden. Die Modellbeschreibung soll durch den Vergleich von synthetischen mit realen Beobachtungen untermauert werden. Methoden: Wir treiben das 3D MHD Model mit beobachteten photosphärischen Magnetfeldern und Horizontalbewegungen an. Durch Wärmeleitung entlang des Feldes sowie Strahlungsverluste wird die koronale Energiebilanz realistisch. Wir synthetisieren Spektren in verschiedenen Emissionslinien mit einer Atom-Datenbank und der berechneten koronalen Plasmatemperatur sowie -dichte. Diese vergleichen wir mit entsprechenden Beobachtungen der Korona über der aktiven Region, mit der wir die Simulation antreiben. Wir vergleichen extrahierte Modell-Feldlinien mit empirischen und theoretischen Skalengesetzen, die die koronale Heizung entlang von Bögen voraussagen. Resultate: Im Modell bilden sich heiße koronale Bögen mit Temperaturen deutlich über 1 MK. Ihre 3D-Struktur entspricht den beobachteten koronalen Bögen; Doppler-Karten lassen auf ähnliche Plasmaströmungen entlang der Bögen schließen. An die Modell-Daten passen wir ein Skalengesetz an, welches von der Bogenlänge und der magnetischen Flussdichte an den Fußpunkten abhängt. Schlussfolgerungen: Aus der substanziellen Übereinstimmung zwischen Modell und Beobachtung schließen wir, dass das Modell eine genügende Beschreibung der Heizung und Wärmeleitung entlang von koronalen Bögen darstellt, um die Beobachtungen zu erklären.

Hypersonic vehicles generate shocks that can heat the air sufficiently to partially ionize the air and create an electrically conducting plasma that can be studied using the equations of single fluid magnetohydrodynamics (MHD). Introducing strong applied magnetic and electric fields into the flow could have beneficial effects such as reducing heat damage, providing a sort of MHD parachute, and generating electric power or thrust in the vehicle. The Low Diffusion E-CUSP (LDE) scheme with a fifth order WENO scheme has recently been developed by Zha et al. [1, 2]. The purpose of this work is to incorporate the low magnetic Reynolds number MHD model and the thermodynamics of high temperature air to the above CFD algorithm so that it can be used to simulate hypersonic flows with MHD effects. In this work we compare results treating air as chemically frozen, neglecting all high temperature real gas effects with results obtained treating the air as a real gas in thermodynamic equilibrium, whose thermodynamic properties are changed by the high temperature. The hypersonic flows at high altitudes considered in this study have low Reynolds numbers. The Reynolds numbers range from about 2000 to 5000 for Mach 6 flows and reach up to 1200000 for Mach 15 flows. Thus, the flows are treated as laminar for the former cases and as turbulent for the latter using the Baldwin-Lomax turbulence model.

The main objective of this thesis is to develop a comprehensive model with the capability of modeling both a high Reynolds number and high magnetic Reynolds number turbulent flow for application to supersonic combustor. The development of this model can be divided into three categories: one, the development of a self-consistent MHD numerical model capable of modeling magnetic turbulence in high magnetic Reynolds number applications. Second, the development of a gas discharge model which models the interaction of externally applied fields in conductive medium. Third, the development of models necessary for studying supersonic combustion applications with plasma-assistance such the extension of chemical kinetics models to extremely high temperature and non-equilibrium phenomenon.

Thesis (Ph.D.) - University of St Andrews, January 2008.