• A simulation study of magnetic reconnection processes at the dayside magnetopause

      Shi, Yong; Lee, L. C.; Akasofu, S-I.; Gatterdam, R.; Gosink, J.; Swift, D. W. (1989-12)
      In this thesis, the day side reconnection processes are studied by using computer simulations. First, the global magnetic reconnection patterns at the dayside magnetopause are studied based on a two-dimensional incompressible magnetohydrodynamic (MHD) code. It is found that multiple X line reconnection may prevail at the dayside magnetopause when the magnetic Reynolds number is large (> 200). The formation and subsequent poleward convection of magnetic islands are observed in the simulation. The Alfvén Mach number of the solar wind, MAsw , cam also change the reconnection patterns. For a large reconnection tends to occur at the higher latitude region. Secondly, the structure of the dayside reconnection layer is studied by a two-dimensional compressible MHD simulation. In a highly asymmetric configuration typical of the dayside magnetopause, the pair of slow shocks bounding the reconnection layer in Petschek’s symmetric model is found to be replaced by an intermediate shock on the magnetosheath side and a weak slow shock on the magnetospheric side. In addition, a mechanism for the enhancement of By, which is observed in the magnetopause current layer and magnetic flux tubes, is proposed.
    • Solar Flare Soft X -Ray Irradiance And Its Impact On The Earth's Upper Atmosphere

      Rodgers, Erica M.; Bailey, Scott (2007)
      Solar flares dramatically enhance the soft X-ray region of the solar spectrum. The enhancement is more significant than previously thought, and the solar soft X-ray instruments aboard the Thermosphere Ionosphere Mesosphere Energetics Dynamics (TIMED) and Solar Radiation and Climate Experiment (SORCE) satellites have observed more flares than expected. This dissertation presents a state-of-the-art analysis used to determine flare spectra from TIMED and SORCE solar observations. A relationship is established between Geostationary Operational Environmental Satellite (GOES) flare 0.1-0.8 nm irradiances and XPS flare 0.1-2 and 0.1-7 nm irradiances. Solar flares primarily enhance the soft X-ray irradiance in the 0.1-2 nm range, and rapidly modify the energy input to the lower thermosphere. Most of the excess flare 0.1-2 nm irradiance comes from 1-2 nm. Thus, flares deposit a large amount of their energy between 100-110 km. One of the key effects of this energy deposition is to modify nitric oxide (NO), which plays an important role in the energy balance of the thermosphere as it is a source of radiative cooling through infrared emissions. The density of NO is highly variable as a function of time and latitude, and reaches a maximum in the same altitude region where the flare irradiance is absorbed. This dissertation also presents valid comparisons between Student Nitric Oxide Explorer (SNOE) satellite NO observations and those predicted by a photochemical thermospheric model to provide a better understanding of low latitude flare enhanced NO column density. Large flares can deposit the same amount of 0.1-2 and 0.1-7 nm energy to the thermosphere during a relatively short time as the Sun normally deposits in one day. The NO column density doubles as the daily integrated energy to the thermosphere doubles.
    • Solar magnetic fields: source, evolution, and interaction with planetary magnetospheres

      Burkholder, Brandon; Delamere, Peter; Otto, Antonius; Newman, David; Ng, Chung-Sang; Connor, Hyunju (2019-08)
      Magnetized plasmas with twisted and filamented magnetic fields are pervasive throughout the heliosphere. In the solar magnetic field, photospheric convection on scale sizes from granules to differential rotation is responsible for driven magnetic reconnection. These reconnection sites are closely related to the magnetic topology, which is highly complex as the magnetic field is structured by a network of many thousands of magnetic flux concentrations. The coronal plasma overlying this "magnetic carpet" is the source of the solar wind flow, which has been found to be turbulent as close to the sun as our observations can currently resolve. At 1 AU, observations have also revealed a highly structured solar wind which we posit in this thesis originates in the corona rather than forming in-transit. Further, the solar wind-magnetosphere interaction depends on variability in the solar wind. When the boundary between solar wind plasma and magnetospheric plasma is unstable to the growth of Kelvin-Helmholtz waves, driven magnetic reconnection can occur on the magnetopause boundary. Such reconnection allows magnetic field to thread the boundary and transport can take place. We quantify the solar wind interaction for a corotation dominated system in terms of the mass and momentum transport driven by Kelvin-Helmholtz instabilities. Model-data comparisons are performed in this thesis using both the magnetohydrodynamic and hybrid-kinetic approaches for fluid simulations.
    • Spectroscopic study of sprites

      Kanmae, Takeshi; 神前 丈; Stanbaek-Nielsen, Hans; Olson, John; Lummerzheim, Dirk; Simpson, William; Hampton, Donald (2014-12)
      Optical emissions from sprites--large electric discharges in the mesosphere caused by intense lightning strokes--have been studied for decades. Studies have identified that sprite emissions are primarily composed of molecular band emissions of nitrogen and notably identified the near ultraviolet and blue emission from the N₂⁺ First Negative system, which provided direct evidence of ionization in sprites. This implies that further evidence of the ionization may be provided by the visible and near infrared emission from the N₂⁺ Meinel system, which is more accessible from ground-based platforms, though anticipated strong quenching in the mesosphere and below have made the presence of the emission somewhat controversial. To investigate the presence of the Meinel emission along the vertical extent of sprites, we made ground-based spectral observations in 2005. The observed spectra were mainly composed of the N₂ First Positive system, and no or little indication of the Meinel bands were found. This study suggests that the quenching is indeed severe at sprite altitude, and it is difficult to study the ionization process in sprites via the Meinel emission. In addition, the data allowed us to investigate details of the First Positive emission from sprites. The observed First Positive spectra showed that the vibrational distribution of the upper state varies along the vertical extent of sprites, which is in agreement with previous reports, and furthermore this study indicates that the variation is associated with altitude, implying that collisional energy transfer processes play roles in exciting the First Positive emission, particularly at lower altitudes. Recent high-speed imaging observations have revealed the very dynamic nature of sprites: they develop within a few to 10 ms in forms of streamers and columnar glows. The underlying electron energies in these features have been inferred from their emissions in previous measurements, but they lacked either sufficient temporal or spatial resolution. To investigate the underlying electron energies, we made airborne spectral observations in 2009 with a slitless spectrograph, which provided temporal and spatial resolution improved over the previous measurements. The observed spectra clearly showed that the streamers consistently had a higher fraction of blue emission compared to the glows, indicating that the more energetic nature of the streamers. From the fractional blue emissions, the local electric fields were inferred to be 0.7 to 1.5Ek in the streamers and 0.3 to 0.6Ek in the glows, where Ek is the conventional breakdown electric field. The results support the interpretation of sprites as scaled analogs of streamer discharges observed in laboratory experiments.
    • Spectroscopy of the N₂ Vegard-Kaplan bands in the dayglow

      Yonker, Justin (2005-05)
      A synthetic spectrum of the N₂ Vegard-Kaplan (VK) bands is developed for dayglow conditions at thermospheric altitudes. Due to the change in electron spin, the A³Eu state is metastable (lifetime 2-3 s.) and excited from the X¹Eg⁺ ground state primarily by photo-electron impact. Cascade from higher-energy triplets contributes to the A³Eu⁺ population and, due to its long lifetime, losses due to quenching are significant. Because of quenching, the VK bands were the last of the major N₂ emissions to be observed, as is explained in an historical review of the work of Vegard and Kaplan. Taking as inputs the solar soft x-ray measurements of the Student Nitric Oxide Explorer (SNOE), the model computes steady-state, ro-vibrational A³Eu⁺ populations and generates the synthetic VK spectrum in Rayleighs. Comparison with observations is hampered by a lack of VK data for days within the SNOE mission (1998-2003). As such, model results for a day in 1999 are compared with VK observations from 1992. The error is within 50% for altitudes below 150 km, above which it steadily decreases to 8% at 280 km. These errors are reasonable considering the unknown solar conditions of the 1992 observations.
    • Structure of reconnection layers in the magnetosphere

      Lin, Yu; Lee, Lou-Chuang; Hawkins, J. G.; Sentman, D. D.; Smith, R. W.; Swift, D. W. (1993)
      Magnetic reconnection can lead to the formation of observed boundary layers at the dayside magnetopause and in the nightside plasma sheet of the magnetosphere. In this thesis, the structure of these reconnection layers is studied by solving the one-dimensional Riemann problem for the evolution of a current sheet. Analytical method, resistive MHD simulations, and hybrid simulations are used. Based on the ideal MHD formulation, rotational discontinuities, slow shocks, slow expansion waves, and contact discontinuity are present in the dayside reconnection layer. Fast expansion waves are also present in the solution of the Riemann problem, but they quickly propagate out of the reconnection layer. Our study provides a coherent picture for the transition from the reconnection layer with two slow shocks in Petschek's model to the reconnection layer with a rotational discontinuity and a slow expansion wave in Levy et al.'s model. In the resistive MHD simulations, the rotational discontinuities are replaced by intermediate shocks or time-dependent intermediate shocks. In the hybrid simulations, the time-dependent intermediate shock quickly evolves to a steady rotational discontinuity, and the contact discontinuity does not exist. The magnetotail reconnection layer consists of two slow shocks. Hybrid simulations of slow shocks indicate that there exists a critical number, $M\sb{c}$, such that for slow shocks with an intermediate Mach number $M\sb{I} \ge M\sb{c}$, a large-amplitude rotational wavetrain is present in the downstream region. For slow shocks with $M\sb{I} < M\sb{c}$, the downstream wavetrain does not exist. Chaotic ion orbits in the downstream wave provide an efficient mechanism for ion heating and wave damping and explain the existence of the critical number $M\sb{c}$ in slow shocks.
    • Studying auroral microphysics using multiple optically tracked rocket sub-payloads

      Vann, Joshua M.; Conde, Mark; Delamere, Peter; Hampton, Donald (2018-12)
      There is insufficient knowledge of scale length parameters associated with ionospheric plasma structures. Using a novel technique combining rocket-based instrument data with ground-based optical and instrumental data measurements, ISINGLASS attempts to determine the spatial scale lengths over which parameter differences in auroral arcs present in the upper ionosphere. Determination of such scale lengths has the propensity to strengthen preexisting models of magnetosphere-ionosphere interactions. While analysis is not complete and the extent of such scale lengths is still unknown, after completion of the experiment phase of the mission, differences in measurements have been found that cannot be accounted for through experimental error. This shows the existence of a critical scale length within the distances measured, and the techniques used present a reliable method with which to launch a future campaign.
    • Suprathermal electron tails in a beam-plasma instability

      Hollerbach, Uwe; Swift, W.; Stenbaek-Nielsen, H. C.; Rees, M. H.; Kan, J. R. (1987-09)
      This study investigated the suprathermal electron tails produced in a beam-plasma instability, and their scaling with beam and background densities. A periodic one-dimensional electrostatic simulation was used to study the suprathermal tails. Electrons were treated as particles, and ions were treated as a fluid. The simulation showed that ion dynamics are required for the formation of the suprathermal tails, as expected from the theory of the oscillating two-stream instability. The energy of the suprathermal tails is directly proportional to the beam density, and does not depend strongly on the background density. There is a slight decrease in the energy of the suprathermal tails as the background density increases. A novel numerical effect was also found: a three-plasmon interaction caused by the modification of the Langmuir wave dispersion relation when high-order splines are used as particle shape factors.
    • Synchronization in biological systems

      Klaas, Jonathan P. (2004-12)
      Synchronization, the adjustment of rhythms via coupling, is an essentially nonlinear effect in coupled dynamical systems. Synchronization is observed in many systems, for example the moon's periods of rotation and revolution, in pendulums suspended from a common support, in swarms of fireflies that flash in unison, and in biological circadian rhythms. Circadian rhythms are periodic fluctuations in multiple physiological systems that have evolved as a consequence of the daily rotation of the earth. These rhythms have been observed in organisms ranging from cyanobacteria to man. In this thesis we will present a conceptually simple model of circadian rhythms to yield insight into the activity patterns of mice in light and food restriction experiments. The model consists of two coupled van der Pol oscillators that are driven by an external periodic influence representing food availability. The results of the model are compared to circadian data of mice collected by Dr. Abel Bult-Ito (Institute of Artic Biology).
    • The Characterization Of The Infrasonic Noise Field And Its Effects On Least Squares Estimation

      Galbraith, Joseph; Szuverla, Kurt (2007)
      Localization of the source of an acoustic wave propagating through the atmosphere is not a new problem. Location methods date back to World War I, when sound location was used to determine enemy artillery positions. Since the drafting of the Comprehensive Nuclear-Test-Ban Treaty in 1996 there has been increased interest in the accurate location of distant sources using infrasound. A standard method of acoustic source location is triangulation of the source from multi-array back azimuth estimates. For waves traveling long distances through the atmosphere, the most appropriate method of estimating the back azimuth is the least squares estimate (LSE). Under the assumption of an acoustic signal corrupted with additive Gaussian, white, uncorrelated noise the LSE is theoretically the minimum variance, unbiased estimate of the slowness vector. The infrasonic noise field present at most arrays is known to violate the assumption of white, uncorrelated noise. The following work characterizes the noise field at two infrasound arrays operated by the University of Alaska Fairbanks, The power distribution and coherence of the noise fields was determined from atmospheric pressure measurements collected from 2003-2006. The estimated power distribution and coherence of the noise field were not the white, uncorrelated noise field assumed in the analytic derivation of the LSE of the slowness vector. The performance of the LSE of azimuth and trace velocity with the empirically derived noise field was numerically compared to its performance under the standard noise assumptions. The effect of violating the correlation assumption was also investigated. The inclusion of clutter in the noise field introduced a dependence to the performance of the LSE on the relative signal amplitude. If the signal-to-clutter ratio was above 10 dB, the parameter estimates made with the correlated noise field were comparable to the estimates made with uncorrelated noise. From the results of these numerical studies, it was determined that the assumption of Gaussian, white, uncorrelated noise had little effect on the performance of the LSE at signal-to-noise ratios greater than 10 dB, but tended to over estimate the performance of the LSE at lower signal-to-noise ratios.
    • The Dynamics And Morphology Of Sprites

      Moudry, Dana; Sentman, Dave (2003)
      In 1999 the University of Alaska Fairbanks fielded a 1000 fields-per-second intensified CCD camera to study sprites and associated upper atmospheric phenomena occurring above active thunderstorms as part of the NASA Sprites99 campaign. The exceptional clarity and definition obtained by this camera the night of August 18, 1999, provides the most detailed image record of these phenomena that has been obtained to date. The result of a frame-by-frame analysis of the data permits an orderly classification of upper atmospheric optical phenomena, and is the subject matter of this thesis. The images show that both elves and halos, which are diffuse emissions preceding sprites, are largely spatially unstructured. Observations of sprites initiating outside of main parts of halos, and without a halo, suggest sprites are initiated primarily from locations of atmospheric composition and density inhomogeneities. All sprites appear to start as tendrils descending from approximately 75 km altitude, and may form other dynamic or stationary features. Dynamic features include downward developing tendrils and upward developing branches. Stationary features include beads, columns, and diffuse "puffs," all of which have durations greater than 1 ms. Stationary sprite features are responsible for a significant fraction of the total optical emissions of sprites. Velocities of sprite tendrils were measured. After initial speeds of 106--107 m/s, sprite tendrils may slow to 105 m/s. Similarly, on some occasions the dim optical emission left behind by the descending tendrils may expand horizontally, with speeds on the order of 105 m/s. The volume excited by the sprite tendrils may rebrighten after 30--100 ms in the form of one of three different sprite after effects collectively termed "crawlers." A "smooth crawler" consists of several beads moving upward (~105 m/s) without a large vertical extent, with "smooth" dynamics at 1 ms timescale. "Embers" are bead-like forms which send a downward-propagating luminous structure towards the cloudtop at speeds of 106 m/s, and have irregular dynamics at 1 ms timescales. In TV-rate observations, the downward-propagating structure of an ember is averaged out and appears as a vertically-extended ribbon above the clouds. The third kind of crawler, so-called "palm tree," appears similar to an ember at TV-rates, but with a wider crown at top.
    • The effect of rate, frequency, and form of migration on host parasite population dynamics

      Mottet, Geneva; Drown, Devin M.; Newman, David; Wackerbauer, Renate (2019-08)
      What is the effect of migration on host-parasite population dynamics? Animals live in a landscape where they move between patches. They are also locked in host-parasite conflicts. Host-parasite interactions are modeled with consumer resource functions. I constructed models using two different consumer resource functions (the Lotka Volterra system and the Saturating Type II system). The first model was a conservative system. The second was dissipative and more biologically realistic. I examined the effect of rate of migration, time between migration events, and form of migration. I found that the time between migration events had the largest effect on the synchronization in host-parasites population dynamics between the patches. Decreased time between migration events increased the fraction of simulation to completely synchronize and decreased the time it took to do so. In the first model, I observed simulations with a low rate of migration took a long time to synchronization and with a high rate of migration took a short time to synchronize. There was a phase transition between these two amounts of time it took to synchronize. In the second model, simulations done at low rates of migration did not synchronize while with increased migration rates the fraction of simulations to synchronize increased. I found in some simulations of parasite only migration that the patches synchronized faster. My results imply that parasite only migration to islands could have a greater impact on the extinction risk on islands further from the mainland than other forms of migration.
    • The generalized Ohm's law in collisionless magnetic reconnection

      Cai, Heng-Jin; Lee, L. C.; Jiang, T. M.; Morack, J. L.; Sentman, D. D.; Swift, D. W. (1995)
      Magnetic reconnection is an important process in space environments. As a result of magnetic reconnection, the magnetic field topology changes, which requires the breakdown of the frozen-in condition in ideal magnetofluids. In a collisional plasma, the resistivity associated with Coulomb collisions of charged particles is responsible for the breakdown of frozen-in condition. In a collisionless plasma, however, the cause of the breakdown of frozen-in condition remains unanswered. We address this problem by investigating the generalized Ohm's law and the force balance near magnetic neutral lines based on two-dimensional particle simulations. In a particle simulation with one active species, it is found that a weakly anisotropic and skewed velocity distribution is formed near the magnetic X line, leading to the presence of off-diagonal elements of plasma pressure tensor. The gradients of the off-diagonal pressure terms transport plasma momentum away from the X line to balance the reconnection electric field. The presence of the reconnection electric field results in the breakdown of frozen-in condition. The importance of both electron and ion off-diagonal pressure tensor terms in the generalized Ohm's law near neutral lines is further confirmed in full particle simulations. The generation of the off-diagonal pressure terms can be explained in terms of the thermal dispersion of particle motions and the response of particle distribution function in the electric and magnetic fields near the neutral lines. In the particle simulations, we also find the presence of a new dynamo process, in which a large amount of new magnetic flux near the magnetic O line is generated. This dynamo process is not allowed in resistive magnetofluids. However, in a collisionless plasma, the plasma inertia and momentum transport due to the off-diagonal plasma pressure terms can lead to E $\cdot$ J < 0 near the magnetic O line and make the dynamo process possible.
    • The morphology and electrodynamics of the boreal polar winter cusp

      McHarg, Matthew G.; Olson, J. J. (1993)
      The major result of this thesis is the magnetic signatures of the dayside cusp region. These signatures were determined by comparing the magnetic observations to optical observations of different energy particle precipitation regions observed in the cusp. In this thesis, the cusp is defined as the location of most direct entry of magnetosheath particles into the ionosphere. Optical observations show that the observing station rotates daily beneath regions of different incident energy particles. Typically, the station passes from a region in the morning of high energy particles into a region near magnetic noon of very low energy precipitation, and then returns to a region of high energy precipitation after magnetic noon. A tentative identification of the cusp is made on the basis of these observations. The optical observations also are used to determine the upward field aligned current density, which is found to be most intense in the region identified as the cusp. The magnetic field measurements are found to correlate with the optical measurements. When the characteristic energy is high, the spectrogram shows large amplitude broad band signals. The Pc5 component of these oscillations is right hand polarized in the morning, and left hand polarized in the afternoon. During the time the optics detect precipitation with a minimum characteristic energy, the magnetic spectrogram shows a unique narrow band tone at 3-5 mHz. The occurrence statistics of the magnetic oscillations are compared to DMSP satellite observations of the cusp and low latitude boundary layer. The pulses that make the narrow band tone are found to come in wave trains that are phase coherent. These trains of coherent pulses are found to be separated by phase jumps from adjacent wave trains. These jumps in phase occur when a new field aligned current appears on the equatorward edge of the cusp. This combination of phase coherent wave trains associated with poleward propagating auroral forms which are shown to contain intense field aligned currents may be the signature of newly reconnected flux tubes in the ionosphere.
    • The quasiparallel collisionless shock wave: A simulation study

      Mandt, Mark Edward; Kan, J. R.; Das, D.; Lee, L. C.; Olson, J. V.; Swift, D. W. (1988)
      The structure of the quasi-parallel collisionless shock wave is studied via a numerical simulation model. The model is compared to observations and theoretical predictions and within its limitations appears to reproduce the true shock structure reasonably well. Three electron equations of state and their effects on the simulation are examined. It is found that only the isotropic-adiabatic electron equation of state yields acceptable results in the simulation at high Mach numbers. The scale lengths of the shock are measured, normalized by the natural scale lengths of the plasma, and plotted as a function of the Alfven Mach number. It is found that the wavelength of the upstream waves follows that predicted for a phase standing whistler quite well and the scalelength of the jump in the magnitude of the magnetic field is generally greater than, but approximately equal to this wavelength. For Alfven Mach numbers $M\sb{A} >$ 2.5, waves are generated in the downstream region. Their wavelength and the scale length of the plasma transition are larger than the natural scale lengths of the plasma. The ion heating is seen to occur in two stages. In the first stage which occurs upstream of the principal shock ramp, the heating can be characterized by a polytropic power law equation of state with an exponent much greater than the isentropic-adiabatic rate of $\gamma$ = 5/3. The second stage of heating which occurs from the principal shock ramp to the downstream region is characterized by an exponent on the order of the isentropic-adiabatic rate. The results show that the ion heating occurs mainly around the principle density jump near the center of the shock transition region, while the increase in entropy takes place mainly in the upstream side of the shock transition region. It is suggested that the ion heating is a consequence of the non-adiabatic scattering of the ions through the magnetic field of the shock and its upstream precursor wave.
    • Transient spatiotemporal chaos in a diffusively and synaptically coupled Morris-Lecar neuronal network

      Lafranceschina, Jacopo; Wackerbauer, Renate; Newman, David E.; Szuberla, Curt A. L. (2014-05)
      Transient spatiotemporal chaos was reported in models for chemical reactions and in experiments for turbulence in shear flow. This study shows that transient spatiotemporal chaos also exists in a diffusively coupled Morris-Lecar (ML) neuronal network, with a collapse to either a global rest state or to a state of pulse propagation. Adding synaptic coupling to this network reduces the average lifetime of spatiotemporal chaos for small to intermediate coupling strengths and almost all numbers of synapses. For large coupling strengths, close to the threshold of excitation, the average lifetime increases beyond the value for only diffusive coupling, and the collapse to the rest state dominates over the collapse to a traveling pulse state. The regime of spatiotemporal chaos is characterized by a slightly increasing Lyapunov exponent and degree of phase coherence as the number of synaptic links increases. In contrast to the diffusive network, the pulse solution must not be asymptotic in the presence of synapses. The fact that chaos could be transient in higher dimensional systems, such as the one being explored in this study, point to its presence in every day life. Transient spatiotemporal chaos in a network of coupled neurons and the associated chaotic saddle provide a possibility for switching between metastable states observed in information processing and brain function. Such transient dynamics have been observed experimentally by Mazor, when stimulating projection neurons in the locust antennal lobe with different odors.
    • Transient spatiotemporal chaos in a Morris-Lecar neuronal ring network collapses to either the rest state or a traveling pulse

      Keplinger, Keegan (2012-12)
      Transient spatiotemporal dynamics exists in an electrically coupled Morris-Lecar neuronal ring network, a theoretical model of an axo-axonic gap junction network. The lifetime of spatiotemporal chaos was found to grow exponentially with network size. Transient dynamics regularly collapses from a chaotic state to either the resting potential or a traveling pulse, indicating the existence of a chaotic saddle. For special conditions, a chaotic attractor can arise in the Morris-Lecar network to which transient chaos can collapse. The short-term outcome of a Morris-Lecar ring network is determined as a function of perturbation configuration. Perturbing small clusters of nearby neurons in the network consistently induced chaos on a resting network. Perturbation on a chaotic network can induce collapse in the network, but transient chaos becomes more resistant to collapse by perturbation when greater external current is applied.
    • Transient spatiotemporal chaos on complex networks

      Rawoot, Safia (2004-12)
      Some of today's most important questions regard complex dynamical systems with many interacting components. Network models provide a means to gain insight into such systems. This thesis focuses on a network model based upon the Gray-Scott cubic autocatalytic reaction-diffusion system that manifests transient spatiotemporal chaos. Motivated by recent studies on the small-world topology discovered by Watts and Strogatz, the network's original regular ring topology was modified by the addition of a few irregular connections. The effects of these added connections on the system's transience as well on the dynamics local to the added connections were examined. It was found that the addition of a single connection can significantly effect the transient time of spatiotemporal chaos and that the addition of two connections can transform the system's spatiotemporal chaos from transient to asymptotic. These findings suggest that small modifications to a network's topology can greatly affect its behavior.
    • Two- and three-dimensional study of the Kelvin-Helmholtz instability, magnetic reconnection and their mutual interaction at the magnetospheric boundary

      Chen, Qinxue; Otto, Antonius; Watkins, Brenton; Sentman, Davis; Smith, Roger (1997)
      Magnetic reconnection and the Kelvin-Helmholtz (KH) instability regulate the transport of magnetic flux, plasma, momentum and energy from the solar wind into the magnetosphere. In this thesis, I use two-dimensional and three-dimensional MHD simulations to investigate the KH instability, magnetic reconnection, and their relationship. Two basic flow and magnetic field configurations are distinguished at the Earth's magnetopause: (1) configurations where the difference in plasma velocity between the two sides of the boundary $\Delta$v (velocity shear) is parallel to the difference of the magnetic field $\Delta$b (magnetic shear), and (2) configurations where the velocity shear is perpendicular to the magnetic shear. For configuration (1), either magnetic reconnection is modified by the shear flow, or the KH instability is modified by the magnetic shear and resistivity. The evolution of the basic configuration (2) requires three dimensions. In this case, both processes can operate simultaneously in different planes. If the KH instability grows faster initially, it can wrap up the current layer and thereby initiate a very fast and turbulent reconnection process. The resulting magnetic turbulence can provide the first explanation of often very turbulent structures of the magnetopause current layer. For the first time, it is quantitatively confirmed that the KH instability operates at the magnetospheric boundary at low latitudes.
    • Two-dimensional Bernstein-Greene-Kruskal modes in a magnetized plasma with kinetic effects from electrons and ions

      Tang, Han; Chung-Sang, Ng; Delamere, Peter; Newman, David (2020-05)
      Electrostatic structures are observed in various of space environments including the auroral acceleration region, the solar wind region and the magnetosphere. The Bernstein-Greene-Kruskal (BGK) mode, one of the non-linear solutions to the Vlasov-Poisson system, is a potential explanation to these phenomena. Specifically, two dimensional (2D) BGK modes can be constructed through solving the Vlasov-Poisson-Ampère system with the assumption of a uniform ion background. This thesis discusses the existence and features of the 2D BGK modes with kinetic effects from both electrons and ions. Specifically, we construct electron or ion BGK modes with finite temperature ratio between ions and electrons. More general cases, the electron-ion 2D BGK mode with the participation of both non-Boltzmann electron and ion distributions are constructed and analyzed as well.