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.

In this thesis, we present the results from tests of two global magnetohydrodynamic (MHD) codes: the University of New Hampshire's OPEN-GGCM model and the University of Michigan's BATS-R-US model. We investigate their consistency with the theory of adiabatic particle drift in the inner and middle magnetosphere. Since the Rice Convection Model (RCM) uses the adiabatic particle drift as one of its basic assumptions, positive results of the tests will help us to establish a better physical model of the magnetosphere and ionosphere by coupling the RCM with one of these global MHD models. An introduction to the two models, the theory for the adiabatic particle drift, and the results from tests of OPEN-GGCM and BATS-R-US models are presented. By tracking individual magnetic tubes and comparing the quantities such as particle number N and theoretical invariant PV5/3 integrated along these flux tubes in different times, we find results of both the OPEN-GGCM and BATS-R-US models suggest that the conservation of the adiabatic invariant is very poor when using low-resolution simulation grid. Another test of the OPEN-GGCM simulation with higher grid resolution shows some improvement in PV5/3 conservation.

We have derived relativistically correct gyro- and bounce-averaged Hamiltonian equations of motion to describe the motions of non-isotropic proton distributions in the Earth's inner and middle magnetosphere. We have focused on the case of equatorially-mirroring protons, and we have modified the Magnetospheric Specification Model (MSM) to trace these particles. We call the new particle simulation the Radiation Belt Test Code (RBTC). We have modeled the March 1991 magnetic storm, which was an extremely strong magnetospheric compression in which protons were energized to 1 to 100 MeV on time scales of a few minutes. We have compared our results with CRESS data collected during the event, and with the simulation results of Hudson et al. (3). We see a significant flux increase, but it is not as large as the increase observed by CRRES. We conclude that our model correctly describes the gross features of high-energy magnetospheric protons, but that the present algorithm of the MSM is too computationally intensive to model these equations in a reasonable time, especially for the highest energy particles that we were interested in. Suggestions for improvements and alternative methods are suggested.

A significant effort is focused on understanding the behavior of the Earth's magnetosphere during times of southward interplanetary magnetic field, when the magnetosphere is in a driven state. In situ observations of the space environment provide us with real magnetic and electric field and plasma data with which to study magnetospheric processes, yet we lack the ability to experimentally control the parameters that influence these processes. On the other hand, a niche of computational modeling is the ability to experiment with these parameters in a straightforward effort to understand the magnetospheric response. The simulation model employed in this thesis (the Rice Convection Model-Equilibrium, or RCM-E) is unique in its ability to calculate the energy dependent drifts of plasma particles as well as their feedback on both the electric and magnetic fields. Three different RCM-E simulations are presented. First, the magnetospheric response to a moderate level of external driving is modeled, showing that the model reproduces several of the features of steady magnetospheric convection (SMC) events. The simulation is then repeated with a more rigorous calculation of the magnetic field that generally produces a higher quality result but suffers from excessive numerical noise in the important inner plasma sheet region. This simulation produces a more stressed magnetic field, but encounters numerical breakdown due largely to the numerical noise. The proper response to steady driving in the RCM-E is likely to be more stressed than the first simulation, yet more stable than the second simulation. Somewhat counter to conventional wisdom, these simulations suggest that enhanced convection by itself is insufficient to inject a ring current, since the magnetic field response acts to mitigate the injection. In the third simulation, a method for injecting plasma into the ring current without drastically affecting the near-Earth magnetic field configuration is demonstrated: significantly reduce the specific entropy of the injection source. The steady driving simulations apparently failed to produce a realistic ring current injection because the model equations conserve specific entropy as plasma is transported (adiabatic transport). These simulations suggest that a non-adiabatic plasma process---possibly the substorm---plays an important role in the dynamics of geomagnetic storms.