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The polar electric potential imposed on the ionosphere by coupling between the earth's magnetosphere and the solar wind has been shown to have a non-linear response to the interplanetary electric field (IEF). This dissertation presents an empirical study of this polar cap potential saturation phenomenon. First, the saturation of the reverse convection potential under northward is demonstrated using bin-averaged SuperDARN data. Then, the saturation reverse convection potential is shown to saturate at a higher value at higher solar wind plasma beta. The reverse convection flow velocity is then compared with cross-polar cap flows under southward IMF under summer, winter and equinox conditions. It is demonstrated that the reverse convection flow exhibits the opposite seasonal behavior to cross polar cap flow under southward IMF. Then, an interhemispheric case study is performed to provide an explanation for the seasonal behavior of the reverse convection potential. It is found using DMSP particle precipitation data that the reverse convection cells in the winter circulate at least partially on closed field lines. Finally, SuperDARN and DMSP data are merged to provide polar cap potential measurements for a statistical study of polar cap potential saturation under southward IMF. It is found that the extent of polar cap potential saturation increases with increasing Alfvenic Mach number, and has no significant relation to Alfven wing transmission coefficient or solar wind dynamic pressure. / Ph. D.

The results of an investigation of the reverse convection potentials in the day side high latitude ionosphere during periods of steady northward interplanetary magnetic field (IMF) are reported. While it has been shown that the polar cap potential in the ionosphere exhibits non-linear saturation behavior when the IMF becomes increasingly southward, it has yet to be shown whether the high latitude reverse convection cells in response to increasingly northward IMF exhibit similar behavior. Solar wind data from the ACE satellite from 1998 to 2005 was used to search for events in the solar wind when the IMF is northward and the interplanetary electric field is stable for more than 40 minutes. Bin-averaged SuperDARN convection data was used with a spherical harmonic fit applied to calculate the average potential pattern for each northward IMF bin. Results show that the reverse convection cells do, in fact, exhibit non-linear saturation behavior. The saturation potential is approximately 20 kV and is achieved when the electric coupling function reaches between 18 and 30 kV/RE. / Master of Science

The turbulen flow in an asymmetric diffuser has been en studied by the means of Reynold average Navier-Stokes equations with both differential and explict algebraic expressions to model the Reynolds stress tensor. Modifications to the differential stress model have been derived, using the inverse turbulence timescale to obtain the dissipation of turbuence kinetic energy. The explicit algebraic Reynolds stress model has been used in combination with a two-equation platform to close the system of equations. Modifications made to the transport equation for the inverse turbulence timescale has made it possible to substantially relax the deman on near-wall resolution of this quantity. The rapid growth wth present in the original formulation can be treated as an explicit function of the wall-normal distance. In order to use the new formulation for the transport equation, an equation has as been derived to obtain the shortest distance bettwee a point and the closest wall, regardles of the geometric complexity of the domain. An explicit algebraic expression to model the passive scalar flux vector has been investigated using a comparison with a standard eddy-diffusivity model in the asymmetric diffuser. Results show a substantial improvement of the complexity of the scalar field and scalar flux vector in sepaarated flows. Automated code generation has been used in all the above studies to generate versatile model testing tools for general two-dimensional geometries. Finite element formulations are used for these tools.

<p>The turbulen flow in an asymmetric diffuser has been en studied by the means of Reynold average Navier-Stokes equations with both differential and explict algebraic expressions to model the Reynolds stress tensor. Modifications to the differential stress model have been derived, using the inverse turbulence timescale to obtain the dissipation of turbuence kinetic energy. The explicit algebraic Reynolds stress model has been used in combination with a two-equation platform to close the system of equations. Modifications made to the transport equation for the inverse turbulence timescale has made it possible to substantially relax the deman on near-wall resolution of this quantity. The rapid growth wth present in the original formulation can be treated as an explicit function of the wall-normal distance. In order to use the new formulation for the transport equation, an equation has as been derived to obtain the shortest distance bettwee a point and the closest wall, regardles of the geometric complexity of the domain. An explicit algebraic expression to model the passive scalar flux vector has been investigated using a comparison with a standard eddy-diffusivity model in the asymmetric diffuser. Results show a substantial improvement of the complexity of the scalar field and scalar flux vector in sepaarated flows. Automated code generation has been used in all the above studies to generate versatile model testing tools for general two-dimensional geometries. Finite element formulations are used for these tools.</p>

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<p dir="ltr">Calculating space-charge limited current (SCLC) is a critical problem in plasma physics and intense particle beams. Accurate calculations are important for validation and verification of particle-in-cell (PIC) simulations. The theoretical assessment of SCLC is complicated by the nonlinearity of the Poisson equation when combined with the energy balance and continuity equations. This dissertation provides several theoretical tools to convert the nonlinear Poisson equation into a corresponding linear differential equation, which is then solved for numerous geometries of practical interest.</p><p dir="ltr">The first and second chapters briefly summarize the application of variational calculus (VC) to solve for one-dimensional (1D) SCLC in cylindrical and spherical diode geometries by extremizing the current in the gap. Next, conformal mapping (CM) is presented to convert the concentric cylindrical diode geometry into a planar geometry to obtain the same SCLC solution as VC. In the next chapter, SCLC is determined for several geometries with curvilinear electron flow that cannot be solved using VC because the Poisson equation cannot be written easily. We then map a hyperboloid tip onto a plane to form a non-Euclidean disk (Poincaré disk). These mappings on to Poincaré disk are utilized to solve for SCLC in tip-to-tip and tip-to-plane geometries. Lie symmetries are then introduced to solve for SCLC with nonzero monoenergetic injection velocity, recovering the solutions for concentric cylinders, concentric spheres, tip-to-plane, and tip-to-tip for zero injection velocity. We then extend the SCLC calculations to account for any geometry in multiple dimensions by using VC and vacuum capacitance. First, we derive a relationship between the space-charge limited (SCL) potential and vacuum potential that holds for any geometry. This relationship is utilized to obtain exact closed-form solutions for SCLC in two-dimensional (2D) and three-dimensional (3D) planar geometries considering emission from the full surface of the cathode. PIC simulations using VSim were performed that agreed with the SCLC in 2D diode with a maximum error of 13%. In the final chapters, we extend these multidimensional SCLC calculations to nonzero monoenergetic emission. The SCLC in any orthogonal diode in any number of dimensions is obtained by relating it to the vacuum capacitance. The current in the bifurcation regime is also derived from first-principles from vacuum capacitance. The simulations performed in VSim agreed with the theory with a maximum error of 7%.</p><p dir="ltr">These mathematical techniques form a set of powerful tools that extend prior studies by yielding exact and approximate SCLC in numerous nonplanar and multidimensional diode geometries, thereby not requiring expensive and time-consuming PIC simulations. While more experiments are required to benchmark the validity of these calculations, these results may ultimately prove useful by providing a rapid first-principles approach to determine SCLC for many geometries that can be used to assess the validity of PIC simulations and facilitate multiphysics simulations.</p>

<p>It is demonstrated that control software updates for the magnetic confinement fusion experiment EXTRAP T2R can enable novel studies of plasma physics. Specifically, it is shown that the boundary radial magnetic field in T2R can be maintained at finite levels by feedback. System identification methods to measure in situ magnetohydrodynamic stability are developed and applied with encouraging results. Subsequently, results from closed-loop identification are used for retooling the T2R regulator. The track of research here pursued could possibly be relevant for future thermonuclear fusion reactors.</p> / QC 20100518

The transport of heat that results from turbulence is a major factor limiting the temperature gradient, and thus the performance, of fusion devices. We use nonlinear simulations to show that a toroidal equilibrium scale sheared flow can completely suppress the turbulence across a wide range of flow gradient and temperature gradient values. We demonstrate the existence of a bifurcation across this range whereby the plasma may transition from a low flow gradient and temperature gradient state to a higher flow gradient and temperature gradient state. We show further that the maximum temperature gradient that can be reached by such a transition is limited by the existence, at high flow gradient, of subcritical turbulence driven by the parallel velocity gradient (PVG). We use linear simulations and analytic calculations to examine the properties of the transiently growing modes which give rise to this subcritical turbulence, and conclude that there may be a critical value of the ratio of the PVG to the suppressing perpendicular gradient of the velocity (in a tokamak this ratio is equal to q/ε where q is the magnetic safety factor and ε the inverse aspect ra- tio) below which the PVG is unable to drive subcritical turbulence. In light of this, we use nonlinear simulations to calculate, as a function of three parameters (the perpendicular flow shear, q/ε and the temperature gradient), the surface within that parameter space which divides the regions where turbulence can and cannot be sustained: the zero- turbulence manifold. We are unable to conclude that there is in fact a critical value of q/ε below which PVG-driven turbulence is eliminated. Nevertheless, we demonstrate that at low values of q/ε, the maximum critical temperature gradient that can be reached without generating turbulence (and thus, we infer, the maximum temperature gradient that could be reached in the transport bifurcation) is dramatically increased. Thus, we anticipate that a fusion device for which, across a significant portion of the minor radius, the magnetic shear is low, the ratio q/ε is low and the toroidal flow shear is strong, will achieve high levels of energy confinement and thus high performance.