In this thesis, the relationship between several high-latitude phenomena and the ionospheric conductance in both hemispheres is studied theoretically and experimentally. </p>Theoretically, the high-latitude electrodynamics is studied by considering currents in the magnetosphere-ionosphere system resulting from the ionospheric sheet current redistribution between the conjugate ionospheres. It is shown that strong flow between the conjugate ionospheres, the interhemispheric currents (IHC), can be set up if the conductance distribution is asymmetric in the conjugate ionospheric regions. Such conditions are typical for solstices owing to the differences in the solar illumination. Analytical and numerical modeling shows that IHCs can appear in the regions of strong conductance gradient, more specifically around the solar terminator line, and that the intensity of the IHCs can be comparable to the intensity of the well known Region 1/Region 2 currents. The effect of IHC excitation on observable magnetic perturbations on the ground is investigated. It is shown that in the vicinity of the solar terminator line, the pattern of magnetic perturbation can be such that an apparent equivalent current vortex can be detected. In addition, strong conductance gradients are shown to affect significantly the quality of the ionospheric plasma flow estimates from the ground-based magnetometer data. </p>Experimentally, the effect of the nightside ionospheric conductance on occurrence of substorms, global storm sudden commencement and radar auroras is investigated. To characterize substorm occurrence, new parameters, the derivatives of the classical AE and AO indices, are introduced. It is shown that the seasonal and diurnal variations of these parameters are controlled by the total nightside ionospheric conductance in the conjugate regions. The substorm onsets preferentially occur at low levels of the total conductance, which is consistent with the idea of the substorm triggering through the magnetosphere-ionosphere feedback instability. It is hypothesized that the total conductance affects the global storm onsets as well. To check this idea, the 33-year sudden storm commencement (SSC) data are considered. The semiannual, annual, semidiurnal, and diurnal variations in the SSC occurrence rate are found to be significant and these components exhibit a strong relationship with the total conductance of the high-latitude ionospheres. Finally, the SuperDARN midnight echo occurrence is shown to correlate, for some radars, with the total conductance minima and presumably with electric field maxima, which is consistent with general expectation that the F-region irregularities occur preferentially during times of enhanced electric fields. The gradients of the high-latitude conductance can also lead to significant errors in the plasma convection estimates from the ground-based magnetometers, and to investigate this effect a statistical assessment of the difference between the true plasma convection (SuperDARN) and the magnetometer-inferred equivalent convection direction is performed. The largest differences are found for the transition region between the dark and sunlit ionospheres and in the midnight sector where strong conductance gradients are expected due to particle precipitation. Consideration of regular conductance gradients due to solar illumination improves the agreement between the radar and magnetometer data. Finally, an attempt is made to demonstrate the effects of conductance upon the properties of traveling convection vortices (TCVs). Joint SuperDARN and magnetometer data reveal that there is resemblance between the magnetometer and radar inferred TCV images on a scale of thousands of kilometers. However, on a smaller scale of hundreds of kilometers, significant differences are observed.

In this work, I will describe a new statistical tool: the canonical bicoherence, which is a combination of the canonical coherence and the bicoherence. I will provide its definitions, properties, estimation by multitaper methods and statistics, and estimate the variance of the estimates by the weighted jackknife method. I will discuss its applicability and usefulness in nonlinear quadratic phase coupling detection and analysis for multivariate random processes. Furthermore, I will develop the time-varying canonical bicoherence for the nonlinear analysis of non-stationary random processes. In this thesis, the canonical bicoherence is mainly applied in two types of data: a) three-component geomagnetic field data, and b) high-dimensional brain electroencephalogram data. Both results obtained will be linked with physical or physiological interpretations. In particular, this thesis is the first work where the novel method of ``canonical bicoherence'' is introduced and applied to the nonlinear quadratic phase coupling detection and analysis for multivariate random processes. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2008-10-31 15:03:57.596

Thesis (MScEng)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Geomagnetic storms are primarily driven by the rapid transfer of energy from the solar wind to the magnetosphere. The mechanism of energy transfer involves the merging of the interplanetary magnetic field to the geomagnetic field in a process known as magnetic reconnection. This leads to an influx of energetic, charged particles into the magnetosphere so that current systems are enhanced. Specifically, an increase in the equatorial ring current leads to a decrease in the surface field. Geomagnetic storms are thus characterized by a strong decline in the horizontal components of the geomagnetic field, lasting from several hours to days. The intensity of a storm is described by the disturbed storm-time index, which is essentially a measure of the deviation from the typical quiet day variation along the equator. Severe storms can lead to the disruption of high frequency (HF) communications as a consequence of a strongly perturbed ionosphere. By the same token, the global positioning system (GPS) can become highly unreliable during magnetically disturbed conditions, yielding distance errors as large as 50 meters. The impact of geomagnetic activity and other solar-driven processes on technology systems are collectively known as space weather. Magnetic field sensing thus forms an important part of space weather forecasting and is vital to space science research as a means of improving our understanding of solar wind-magnetosphere interactions. This study examines the use of magnetometers built as SQUIDs (Superconducting Quantum Interference Devices) for monitoring the geomagnetic field for space weather forecasting purposes. A basic theory of superconductivity is presented and subsequently the key aspects governing the operation of SQUIDs are discussed. Space weather is also introduced with respect to the various processes on the sun that perturb the magnetosphere and hence the geomagnetic field. The method of analysis was basically to Fourier-transform the data using the Wiener-Khintchine theorem. A systematic approach to Fourier analysis is thus presented, demonstrating the superiority of the Wiener-Khintchine theorem in noise reduction. The suitability of SQUID magnetometers for space science research is demonstrated by a comparative study between SQUID and fluxgate datasets for magnetic storms during 2011. Strong correlation was observed between the frequency content of the SQUID and fluxgate signals. This result supports South Africa’s SQUID project, currently undertaken as a collaborative effort between SANSA Space Science and the Department of Electrical and Electronic Engineering at Stellenbosch University. This thesis thus lays a foundation for future research involving advanced magnetometry using SQUIDs. / AFRIKAANSE OPSOMMING: Geomagnetiese storms word hoofsaaklik gedryf deur die vinnige oordrag van energie van die sonwind na die magnetosfeer. Die meganisme van energie oordrag behels die samesmelting van die interplanetêre magneetveld met die geomagneetveld, in 'n proses wat bekend staan as magnetiese heraansluiting. Dit lei tot 'n instroming van energieke elektries-gelaaide deeltjies, tot in die magnetosfeer, met die gevolg dat magnetosferiese elektriese stroomstelsels versterk word. 'n Toename in die ekwatoriale ringstrome lei spesifiek tot 'n afname in die horisontale komponent van die geomagnetiese veld. Geomagnetiese storms word dus gekenmerk deur 'n sterk afname in die horisontale komponent van die geomagnetiese veld, ‘n afname wat etlike ure tot dae kan duur. Die intensiteit van 'n storm word beskryf deur die storm-tyd versteurings indeks , 'n maatstaf van die afwyking van die tipiese stil dag magnetiese variasie langs die ewenaar. Ernstige storms kan lei tot die ontwrigting van hoë frekwensie (HF) kommunikasie as 'n gevolg van 'n erg versteurde ionosfeer. Soortgelyk kan die Globale Posisionering Stelsel (GPS) hoogs onbetroubaar word tydens magneties versteurde toestande, en posisiefoute so groot as 50 meter veroorsaak. Die impak van geomagnetiese aktiwiteit en ander sonkrag gedrewe prosesse op tegnologie is gesamentlik bekend as ruimteweer. Magneetveldmetinge vorm dus 'n belangrike deel van ruimteweervoorspelling en is noodsaaklik vir ruimtewetenskaplike navorsing as 'n middel om die sonwind-magnetosfeer interaksies beter te verstaan. Hierdie studie ondersoek die gebruik van SQUID (Engels: Superconducting Quantum Interference Device) magnetometers vir die monitering van die geomagnetiese veld vir ruimteweervoorspellingsdoeleindes. ’n Basiese teorie van supergeleiding word aangebied, waarvolgens die sleutelaspekte van SQUIDs bespreek word. Ruimteweer word ook voorgestel in terme van die verskillende prosesse op die son wat die aarde se magnetosfeer en dus die geomagnetiese veld versteur. Die analisemetode wat hier gebruik word, is om die Fourier-transform van data met die Wiener-Khintchine theorema te bereken. A sistematiese metode vir Fourier-analise word aangebied, wat die superiorireit van die Wiener-Khintchine teorema vir ruisvermindering demonstreer. Die geskiktheid van SQUID magnetometers vir ruimtewetenskaplike navorsing word gedemonstreer deur ’n vergelykende studie tussen SQUID- en vloedhek-datastelle vir magnetiese storms gedurende 2011. Sterk korrelasie is waargeneem tussen die frekwensie-inhoud van die SQUID- en vloedhekseine. Hierdie resultate ondersteun Suid-Afrika se SQUID-projek, wat tans as ’n samewerkingspoging tussen SANSA Space Science en die Departement Elektriese en Elektroniese Ingenieurswese aan die Universiteit van Stellenbosch bedryf word. Hierdie tesis lê ’n fondasie vir toekomstige navorsing oor gevorderde magnetometrie met SQUIDs.

A zone of high magnetization along the SE margin of Paleoproterozoic Laurentia in the United States is indicated by magnetic anomaly data. The SE edge corresponds to the geochemical Neodymium mantle derivation model age (TDM) boundary and the entire anomaly overlies the Paleoproterozoic Mazatzal Province. Two-dimensional gravity and magnetic models across the Nd boundary are created with Moho constrained from receiver functions with gravity, sedimentary thickness and the base of the crustal magnetization. Upper crustal magnetization does not show strong variation across this boundary and much of the strong magnetization appears to lie in the middle crust. Using magnetic modeling of several potential geologic scenarios, we estimate magnetization, depth extent, and width of this zone of high magnetization. The anomaly has variable width (~ 300 km) with amplitude of approximately 200 nT. Pre-1.55Ga Paleoproterozoic mid crustal blocks have significantly higher average effective susceptibility (0.06 SI) than those of the post-1.55Ga Mesoproterozoic (0.01 SI). In two of the three profiles, the Paleoproterozoic zone of high magnetization has the highest average susceptibility indicating the Mazatzal province is innately highly magnetic. The zone may have formed either by magmatism associated with westward subduction or from highly magnetic terranes wedging between accreting island arcs.

The thermosphere-ionosphere regions are mainly controlled by the solar, but also by geomagnetic activity. In this case study, the Earth’s ionospheric response to the 25-26 August 2018 intense geomagnetic storm is investigated using the International GNSS System (IGS) Total Electron Content (TEC) observations. During this major storm, the minimum disturbance storm time (Dst) index reached -174 nT. We use observations and model simulations to analyse the ionospheric response during the initial phase and the main phase of the magnetic storm. A significant difference between storm day and quiet day TEC is observed. The O/N2 ratio observed from the GUVI instrument onboard the TIMED satellite is used to analyse the storm effect. The result shows a clear depletion of the O/N2 ratio in the high latitude region, and an enhancement in the low latitude region during the main phase of the storm. Furthermore, the Coupled Thermosphere Ionosphere Plasmasphere electrodynamics (CTIPe) model simulations were used. The results suggest that the CTIPe model can capture the ionospheric variations during storms. / Die Regionen der Ionosphären und Thermosphäre werden hauptsächlich von der Sonne sowie auch von geomagnetische Aktivität beeinflusst. In dieser Fallstudie wurde die ionosphärische Reaktion der Erde auf den starken geomagnetischen Sturm vom 25./26. August 2018 unter Verwendung der Gesamtelektronengehaltsdaten (Total Electron Content, TEC) vom Internationalen GNSS Service untersucht. Während dieses großen Sturms wurde ein ”Disturbance Storm Time Index” Dst von -174 nT erreicht. Beobachtungen und Modellsimulationen wurden verwendet, um die ionosphärische Reaktion während der Anfangsphase und der Hauptphase des magnetischen Sturms zu untersuchen. Ein signifikanter Unterschied zwischen TEC während eines Sturmtages und eines ruhigen Tages wurde beobachtet. Das vom GUVI-Instrument an Bord des TIMED-Satelliten beobachtete O/N2 -Verhältnis wurde verwendet, um den Sturmeffekt weiter zu untersuchen. Das Ergebnis zeigt eine deutliche Abnahme/Zunahme des O/N2 Verhältnis in hohen/niedrigen Breiten während der Hauptphase des Sturms. Darüber hinaus wurde das Coupled Thermosphere Ionosphere Plasmasphere ectrodynamics (CTIPe) Modell verwendet. Die Ergebnisse legen nahe, dass das CTIPe-Modell die ionosphärischen Schwankungen während eines Sturms erfassen kann.

Les travaux présentés dans ce mémoire constituent une contribution à la conception de méthodes systématiques pour l’analyse et la commande de systèmes périodiques et incertains. Une partie importante de cette thèse est également consacrée au contrôle d’attitude de satellites dont la dynamique se prête naturellement à une représentation sous forme de modèles périodiques soumis à des incertitudes. La première partie propose une présentation unifiée des résultats d’analyse et de synthèse de modèles périodiques et incertains à temps-discret via des méthodes basées sur des inégalités linéaires matricielles (LMI) et en s’appuyant sur la théorie de Lyapunov. Par la suite, l’accent est mis sur une nouvelle classe de correcteurs périodiques à mémoire pour lesquels l’entrée de commande est construite en utilisant l’historique des états du système conservés en mémoire. Des exemples numériques démontrent que ces nouveaux degrés de liberté permettent de repousser les limites des performances robustes. La seconde partie s’intéresse aux aspects de périodicité et de robustesse du contrôle d’attitude de satellite rencontrés notamment lors de l’utilisation des magnéto-coupleurs. Ces actionneurs s’appuient sur le champ géomagnétique variant périodiquement le long de l’orbite du satellite. Différentes stratégies de commande sont mises en œuvre et comparées entre elles avec le souci constant de tenir compte des principales limitations des actionneurs. Cette démarche conduit à une nouvelle loi de commande périodique régulant le moment cinétique des roues à réactions sans perturber le contrôle d’attitude dont l’effort de commande est réparti sur l’ensemble des actionneurs. / This manuscript reviews contributions to the development of systematic methods for analysis and control of periodic uncertain systems. An important part of this thesis is also dedicated to the design of attitude control systems for satellites whose dynamics is naturally represented as a periodic model subject to uncertainties. The first part is devoted to the developpement of a unifying presentation of the analysis and synthesis results of periodic, uncertain and discrete-time models via methods relying on linear matrix inequalities (LMI) and based on Lyapunov theory. Subsequently, the focus is on a new class of periodic control laws with memory for which the control input is constructed using history of the states of the system kept in memory. Numerical experiments show that these new degrees of freedom can outperformed the existing results. The second part deals with periodic and robustness aspects of attitude control of a satellite using magnetorquers. These actuators use the geomagnetic field that varies periodically along the orbital trajectory. Different control strategies are implemented and compared with one another with the constant concern of taking the main limitations of the actuators into account. This approach leads to a new control law regulating the momentum of the reaction wheels without disturbing attitude control for which the control effort is shared by all actuators.

Parmi les méthodes de reconstitution de l'histoire du champ géomagnétique, l'étude des variations de la production atmosphérique d'isotopes cosmogéniques s'est récemment développé. Cette production est modulée au premier ordre et aux échelles multimillénaires par l'intensité du champ géomagnétique. Son enregistrement dans les archives de l'environnement terrestre en apporte une lecture indépendante, donc complémentaire des méthodes paléomagnétiques. Ce travail vise à retracer les changements de taux de production de 10Be enregistrés dans les sédiments marins, afin de restituer les variations du moment géomagnétique depuis environ 800 000 ans. Les rapports 10Be/9Be authigéniques mesurés par Spectrométrie de Masse par Accélérateur le long de trois séquences de différentes latitudes, permettent de caractériser la production globale de 10Be sur deux intervalles de temps. (1) Lors de la baisse du moment dipolaire associée à l'excursion Laschamp (~41 000 ans BP), la surproduction de 10Be à 38°N et 2°S, confirmée par des mesures de 10Be/230Thxs, est identique à celle restituée dans les glaces du Groenland. (2) L'étude menée sur une carotte prélevée à l'équateur couvrant l'intervalle 800 000 – 250 000 ans BP (époque Brunhes), révèle les phases successives de surproduction globale de 10Be déclenchées par les chutes de moment dipolaires liées à l'inversion Brunhes-Matuyama d'une part et d'autre part à une dizaine d'excursions documentées. La calibration de ces enregistrements avec des valeurs absolues disponibles dans la littérature permet la quantification des moments dipolaires. / Among the methods for reconstructing the geomagnetic field history, studying the variations in cosmogenic isotopes production in the atmosphere has recently developed. At multi millennial scales, this production is mainly modulated by the geomagnetic field intensity. Its record in terrestrial archives provides an independent reading to complement paleomagnetic methods. This work aims at tracing the changes in 10Be production rates recorded in marine sediments, in order to reproduce the geomagnetic variations for the past 800,000 years. Authigenic 10Be/9Be ratios measured using Accelerator Mass Spectrometry along three sequences from different latitudes, characterize the 10Be global production during two time intervals. (1) During the dipole moment low associated with the Laschamp excursion (~ 41,000 years BP), the 10Be overproduction at 38°N and 2°S, confirmed by measurements of 10Be/230Thxs, is identical to that recorded in the Greenland ice sheet. (2) Studying a core collected near the equator and covering the interval 800,000 – 250,000 years BP (Brunhes epoch) reveals the successive phases of global 10Be overproductions triggered by dipole moment lows associated to the Brunhes-Matuyama reversal and also to several other documented excursions. Calibrating these records with absolute values available in the literature allows quantifying dipole moments. These are then compared to paleomagnetic reference reconstructions over the same time series. Bearing out the number and extent of these dipole field lows allows considering to refine their chronology before using their features to get a better understanding of the geodynamo rhythms throughout the last Million years.

The design of an attitude control system for a flexible spacecraft using magnetic actuation is considered. The nonlinear, linear, and modal equations of motion are developed for a general flexible body. Magnetic control is shown to be instantaneously underactuated, and is only controllable in the time-varying sense. A PD-like control scheme is proposed to address the attitude control problem for the linear system. Control gain limitations are shown to exist for the purely magnetic control. A hybrid control scheme is also proposed that relaxes these restrictions by adding a minimum control effort from an alternate three-axis actuation system. Floquet and passivity theory are used to obtain gain selection criteria that ensure a stable closed-loop system, which would aid in the design of a hybrid controller for a flexible spacecraft. The ability of the linearized system to predict the stability of the corresponding nonlinear system is also investigated.

The design of an attitude control system for a flexible spacecraft using magnetic actuation is considered. The nonlinear, linear, and modal equations of motion are developed for a general flexible body. Magnetic control is shown to be instantaneously underactuated, and is only controllable in the time-varying sense. A PD-like control scheme is proposed to address the attitude control problem for the linear system. Control gain limitations are shown to exist for the purely magnetic control. A hybrid control scheme is also proposed that relaxes these restrictions by adding a minimum control effort from an alternate three-axis actuation system. Floquet and passivity theory are used to obtain gain selection criteria that ensure a stable closed-loop system, which would aid in the design of a hybrid controller for a flexible spacecraft. The ability of the linearized system to predict the stability of the corresponding nonlinear system is also investigated.

The use of magnetometers combined with unmanned aerial vehicles (UAVs) is an emerging market for commercial and military applications. This study presents the methodology used to magnetically characterize a novel fixed-wing vertical take-off and landing (VTOL) UAV. The most challenging aspect of integrating magnetometers on manned or unmanned aircraft is minimizing the amount of magnetic noise generated by the aircraft’s onboard components. As magnetometer technology has improved in recent years magnetometer payloads have decreased in size. As a result, there has been an increase in opportunities to employ small to medium UAV with magnetometer applications. However, in comparison to manned aviation, small UAVs have smaller distance scales between sources of interference and sensors. Therefore, more robust magnetic characterization techniques are required specifically for UAVs. This characterization determined the most suitable position for the magnetometer payload by evaluating the aircraft’s static-field magnetic signature. For each aircraft component, the permanent and induced magnetic dipole moment characteristics were determined experimentally. These dipole characteristics were used to build three dimensional magnetic models of the aircraft. By assembling the dipoles in 3D space, analytical and numerical static-field solutions were obtained using MATLAB computational and COMSOL finite element analysis frameworks. Finally, Tolles and Lawson aeromagnetic compensation coefficients were computed and compared to evaluate the maneuver noise for various payload locations. The magnetic models were used to study the sensitivity of the aircraft configuration and to simultaneously predict the effects at potential sensor locations. The study concluded by predicting that a wingtip location was the area of lowest magnetic interference. / Graduate