High-power solar arrays for satellite power systems are presently being planned with dimensions of kilometers, and with tens of kilovolts distributed over their surface. Such systems will face many plasma interaction problems, such as power leakage to the plasma, enhanced surface damage due to particle focusing, and anomalous arcing to name a few. In most cases, these effects cannot be adequately modeled without detailed knowledge of the plasma-sheath structure and space charge effects. A computer program (PANEL) has been developed to model the solar power satellite (SPS)-plasma interaction by an iterative solution of the coupled Poisson and Vlasov equations. PANEL uses the "inside-out" method and a finite difference scheme to calculate densities and potentials at selected points on either a two or three dimensional grid. PANEL was originally developed by Dr. Lee W. Parker to solve the Laplace equation for the potential distribution about a planar spacecraft and to calculate the plasma currents to the spacecraft surface. After some improvements, this version was tested and used to model the plasma interaction of the MSFC/Rockwell design for the SPS. Those results are presented in chapter three. More recently, with the aid of Dr. Parker, charge density calculation routines have been added to PANEL to include space charge effects. These routines along with some necessary improvements have been installed, resulting in the present version of PANEL. Among these improvements are: selectable boundary conditions, stop and start capability, a grid cell division technique to improve trajectory accuracy, and a method of phase space boundary tracking that greatly increases program efficiency by avoiding the repeated tracing of most trajectories. In this thesis, the history of the spacecraft charging problem is reviewed, the theory of the plasma screening process is discussed and extended, program theory is developed, and a series of models is presented. These models are primarily two-dimensional (2-D) for two reasons; one being that large 3-D models require more computing time than I have been able to afford, and the other being that most analytic models suitable for testing PANEL are 1-D and the 3-D capabilities were not required. These models include PANEL's predictions for two variations on the Child-Langmuir diode problem and two models of the interaction of an infinitely long one meter wide solar array with a dense 10 eV plasma. These models are part of an ongoing effort to adapt PANEL to augment the laboratory studies of a 1 x 10 meter solar array in a simulated low Earth orbit plasma being conducted in the Chamber A facilities at the NASA/Johnson Space Center. Also included are two 3-D test models. One is a "point potential" in a hot plasma and is compared to the Debye theory of plasma screening. The other is a flat disc in charge free space. For the Child-Langmuir diode problem, a good agreement is obtained between PANEL results and the classical theory. This is viewed as a confirming test of PANEL. Conversely, in the solar array models, the agreement between the PANEL and Child-Langmuir predictions for the plasma sheath thickness is presented as a numerical confirmation of the use of the Child-Langmuir diode theory to estimate plasma sheath thickness in the spacecraft charging problem.

This body of work deals with a detailed analysis of plasma, magnetic, and electric field data from Pioneer Venus Orbiter (PVO) to determine if the data are consistent with the possibility of lightning on Venus. This has been a strong topic of debate in the planetary physics community. In a recent Nature article [Ingersoll, 2007], Ingersoll provides a synopsis of the case against lightning on Venus. He states that there should not be lightning on Venus, whose clouds, at roughly 55-60km above the surface, are like terrestrial smog clouds, which do not produce lightning. Ingersoll then goes on to recount that no visible evidence (flashes) has been detected on the night or day-side of Venus. An article published by Gurnett [ Gurnett, et al., 2001] details the non-detection of high frequency radio waves characteristic of terrestrial lightning (0.125 to 16MHz) during Cassini's two fly-bys of Venus, contrasted with the definite detection of RF waves during Cassini's later earth fly-by. However, the detection of low frequency whistler waves by Venus Express has revived claims that the source of these whistler waves is lightning in the lower atmosphere of Venus [ Russell, et al., 2007]. Numerous other papers have been published on different aspects of the debate, such as a paper addressing telemetry interference being incorrectly interpreted as evidence for lightning [Taylor, et al., 1988], another paper suggesting the detected events are a local phenomenon [Taylor, et al., 1983], and a paper documenting some of the optical searches for Venusian lightning [Taylor, et al. , 1994]. This work is a comprehensive reconsideration of 14 years of PVO plasma data on a season by season basis, as the spacecraft goes to low altitudes on the night-side of Venus. In this effort, intelligent software filters have been developed to find, sort, and analyze the frequency of occurrence of low frequency whistler waves. The results of this investigation show that the source cannot be in the lower atmosphere of Venus, since at the lowest altitudes (140-156km), the signals disappear. Therefore, an ionospheric source for these whistler waves must be considered.

Is the magnetic field in the Earth's magnetotail static? if yes, why? if not, what causes the magnetic field to change and how does it evolve with time? These questions have haunted magnetospheric physicists for the past decade. Although significant progress has been made in this area of research, a consensus still does not exist. This thesis approaches the problem from the most fundamental basis--Faraday's law relating the curl of the electric field to the time variation of the magnetic field. If we can reach an independent theory that relates the electric field to the magnetic field, the whole problem can, at least in principle, be solved. This thesis pursues the problem both physically and mathematically. Our answers to the questions listed at the beginning are: (1) the magnetic field is generally not static; (2) the change is powered by the energy transfer from the solar wind to the magnetosphere, the agent that effects the change is plasma injection from the high-latitude plasma mantle; (3) the time-dependence is closely related to the velocity distribution of the mantle plasma; A decrease of B$\sb{\rm z}$ in the near tail and a flux buildup at the farther end of tail are two primary features of the time evolution; (4) a dense, drifting plasma mantle causes an intensive reconfiguration in the plasma sheet and is likely to lead to plasma sheet instability. The general results of the thesis are supportive of Hones' phenomenological model of the tail evolution (Hones, 1977).

A three dimensional B-field model of the Earth's magnetosphere satisfying the condition $\nabla$ $\cdot$ B = 0 is described. Highly flexible ring and cross-tail current systems are combined with the vacuum B-field model of Voigt (1981), a fully shielded dipole within a fixed magnetopause geometry. The ring current consists of nested eastward and westward flowing current distributions which tilt with and remain axially symmetric about the magnetic dipole axis. To include realistic flexing of the current sheet with dipole tilt, the intensity and position of the westward flowing cross-tail current in the midnight meridian can be represented by arbitrary functions of the distance along the magnetotail. Model configurations are completely specified by four initial physical input parameters: the dipole tilt angle, the magnetopause stand-off distance, the geomagnetic index D$\sp{\rm st}$, and the midnight equatorward boundary of the diffuse aurora. These parameters determine the relative position and strength of both the ring and cross-tail currents and provide for a diverse array of configurations including many degrees of magnetotail field stretching. The resulting equatorial flux levels, $\triangle$B profiles, and the dipole tilt-dependent shape and position of the neutral sheet compare well with observations. With additional input parameters, the reconfiguration of the geomagnetic tail during magnetospheric substorms is modeled and incorporated into a magnetic field simulation of an observed substorm event. The ring and cross-tail currents, as prescribed by the set of initial input parameters, follow a physically reasonable sequence of development and magnetic flux densities are in general agreement with geosynchronous observations of the event.

Data from the Helios 1 spacecraft have been used to determine an empirical value for the polytropic index for the free-streaming solar wind. Application of this non-adiabatic polytropic index to a two-dimensional solar wind computer model to simulate the effects of thermal heat conduction has been investigated. The current project involves the insertion of this empirically-derived polytropic index into a magnetohydrodynamic model of solar wind propagation. This computer model is used to predict the time for shocks originating at the Sun to travel to Earth. This information is important for the protection of Earth-orbiting satellites. The model is a two and one-half-dimensional numerical code that solves the magnetohydrodynamic equations using the two-step Lax-Wendroff scheme. The shock jump ratios of the plasma parameters are determined using the Rankine-Hugoniot relations. In addition, the shock model requires a representative background solar wind as an initial condition. The original background solar wind is similar to the results obtained by Parker (Astrophysical Journal, 1958) and Weber and Davis (Astrophysical Journal, 1967). Changes to this initial condition are made by applying the non-adiabatic polytropic index to a three-dimensional, steady-state, magnetohydrodynamic model of the solar wind. The adjustments to the steady-state model produce a background solar wind that compares well to Helios 1 data. This new background solar wind is used as the initial condition for the 2D shock model. The shock model is also adjusted to include the effects of heat conduction. Comparison of model results with observational data indicate that these changes produce average transit times that are only 45 minutes late. Before the changes to the 2D shock model and its initial solar wind condition were made, the average prediction time was two hours late. Adjusting the shock model to include the effects of heat conduction but using the original background solar wind produces an average transit time that is less than one hour early. A few specific events are discussed in greater detail.

Motivation for the study of hot, dense ($\sim$solid density) plasmas has historically been in connection with stellar interiors. In recent years, however, there has been a growing interest in such plasmas due to their relevance to short wavelength (EUV and x-ray) lasers, inertial confinement fusion, and optical harmonic generation. In constrast to the stellar plasmas, these laboratory plasmas are typically composed of high-z elements and are not in thermal equilibrium. Descriptions of nonthermal plasma experiments must necessarily involve the consideration of the various atomic processes and the rates at which they occur. Traditionally, the rates of collisional atomic processes are calculated by considering a binary collision picture. For example, a single electron may be taken to collisionally excite an ion. A cross section may be defined for this process and, multiplying by a flux, the rate may be obtained. In a high density plasma this binary picture clearly breaks down as the electrons no longer act independently of each other. The cross section is ill-defined in this regime and another approach is needed to obtain rates. In this thesis an approach based on computing rates without recourse to a cross section is presented. In this approach, binary collisions are replaced by stochastic density fluctuations. It is then these density fluctuations which drive transitions in the ions. Furthermore, the oscillator strengths for the transitions are computed in screened Coulomb potentials which reflect the average polarization of the plasma near the ion. Numerical computations are presented for the collisional ionization rate. The effects of screening in the plasma-ion interaction are investigated for $He\sp+$ ions in a plasma near solid density. It is shown that dynamic screening plays an important role in this process. Then, density effects in the oscillator strength are explored for both $He\sp+$ and $Ar\sp{+17}.$ Approximations which introduce a nonorthogonality between the initial and final states is shown to introduce a nonnegligible error. Changes in the bound state energy levels are included in the calculation as well and are shown to dramatically increase the ionization rate over the low density result. Finally, a calculation is presented in which the final state wavefunctions are found exactly within a (density-dependent) screened Coulomb potential.

A magnetohydrodynamics (MHD) computer simulation code is tested for numerical accuracy and physical plausibility. Comparisons are made between numerical results and simple linear theory. The adverse affects of numerical dispersion and diffusion are analyzed. Applications for both an Earth-like and pole-on magnetospheric simulation are investigated.

We propose that the "bursty bulk flows" are "bubbles" in the Earth's plasma sheet. Specifically, they are flux tubes that have lower values of $pV\sp{5/3}$ than their neighbors, where p is the thermal pressure of the particles and V is the volume of a tube containing one unit of magnetic flux. Whether they are created by reconnection or some other mechanism, the bubbles are propelled earthward by a magnetic-buoyancy force, which is related to the interchange instability. Most of the major observed characteristics of the bursty bulk flows can be interpreted naturally in terms of the bubble picture. We propose a new "stratified fluid" picture of the plasma sheet, based on the idea that bubbles constitute the crucial transport mechanism. Results from simple mathematical models of plasma-sheet transport support the idea that bubbles can resolve the pressure-balance inconsistency.

This thesis addresses a fundamental question in magnetospheric physics, which is whether steady state convection could theoretically exist in the Earth's plasma sheet. By constructing a numerical two-dimensional magnetohydrostatic equilibrium magnetosphere that is consistent with the condition of steady, lossless, adiabatic, plasma-sheet convection, we disprove assertions made by Erickson and Wolf (1980), Schindler and Birn (1982), and Birn and Schindler (1985), concerning the non-existence of a physical steady-state solution within the ideal MHD limit (isotropic pressure, perfect conductivity). The computed steady-state magnetic field model, however, is different both from averaged observations and from standard magnetic-field models in that the equatorial magnetic field strength B$\sb{\rm ze}$ exhibits a very deep broad minimum in the inner plasma sheet. Somewhat similar results were also found in Erickson's (1985) quasi-static adiabatic convection models, in which a shallow, sharp B$\sb{\rm ze}$-minimum developed tailward of the inner-edge of the plasma sheet during the course of earthward convection. To study tearing instability of the configurations that possess a B$\sb{\rm ze}$-minimum in the near-earth plasma sheet in the presence of resistivity, a time-dependent numerical resistive MHD code has been developed. By performing the simulations with two types of initial equilibrium magnetic-field configurations, including the standard model in which B$\sb{\rm ze}$ decreases monotonically down the tail, which is inconsistent with steady-state adiabatic convection, we find that the existence of a B$\sb{\rm ze}$-minimum greatly enhances the growth of resistive tearing-mode instability and that the neutral line is likely to form near the initial B$\sb{\rm ze}$-minimum. In the framework of collisionless plasma theory, it is argued that ideal MHD is likely to be violated near the B$\sb{\rm ze}$-minimum, making the steady-state model susceptible to the collisionless tearing-mode instability. In this respect, our results are consistent with the previous assertions that steady-state convection cannot be sustained in the Earth's plasma sheet. In other words, our calculations suggest that the magnetotail structure associated with adiabatic earthward convection is intrinsically unstable even if the solar wind condition is precisely steady, which may explain why magnetospheric substorms should occur and why the neutral line associated with the substorm should occur in the near-earth plasma sheet.

In this thesis, we develop a dynamical mean field approach to strongly correlated electron systems. Our approach is based on the standard limit of infinite dimensions but goes beyond that by treating inter-unit-cell interactions on an equal footing with intra-unit-cell ones. We then apply this approach to the extended Hubbard model. We identify a non-Fermi liquid state in this model. This novel state displays the intriguing phenomenon of spin-charge separation.