Global dynamics of the Rikitake system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Analytical attitude prediction of spin stabilized spacecrafts perturbed by magnetic residual torque

An analytical approach for spin-stabilized spacecraft attitude prediction is presented for the influence of the residual magnetic torques. Assuming an inclined dipole model for the Earth's magnetic field, an analytical averaging method is applied to obtain the mean residual torque every orbital period. The orbit mean anomaly is utilized to compute the average components of residual torque in the spacecraft body frame reference system. The theory is developed for time variations in the orbital elements, and non-circular orbits, giving rise to many curvature integrals. It is observed that the residual magnetic torque does not have component along the spin axis. The inclusion of this torque on the rotational motion differential equations of a spin stabilized spacecraft yields conditions to derive an analytical solution. The solution shows that residual torque does not affect the spin velocity magnitude, contributing only for the precession and the drift of the spin axis of the spacecraft. (c) 2005 COSPAR. Published by Elsevier Ltd. All rights reserved.

Conseqüências de uma tempestade geomagnética no posicionamento relativo com receptores GPS de simples freqüência

The error associated with the ionosphere depends on Total Electron Content (TEC) of the ionosphere. The geomagnetic field exerts strong influence in the TEC variation, because it controls the movement of the electrons. After solar events the magnetic lines of force can be compressed, characterizing the geomagnetic storm. The aim of this paper is to present to geodesic community the effects of a geomagnetic storm in the relative positioning. The processing of the data was accomplished with an interval of two hours, with a 430 km baseline. The analyze of the obtained results have been carried out from the discrepancies between the true coordinates and corresponding ones obtained in the processing of the baseline. The used data in this paper include the period of 30/03/2001 up to 02/04/2001. In March 31 a strong geomagnetic storm happened. One day after, that it corresponds to main phase of the storm, the values of the discrepancies decreased significantly. For instance, in 01:00-03:00 UT period, the value of the planimetric discrepancy reached 20 m in the storm day. However, in the main phase of the storm, the planimetric discrepancy decreased to 0.1 m.

Propagação da atitude de satélites artificiais estabilizados por rotação: torque residual médio com o modelo de quadripolo para o campo geomagnético

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Influência de estruturas geológicas bidimensionais no campo geoeletromagnético na presença do eletrojato equatorial

A Terra atua como um grande magneto esférico, cujo campo assemelha-se àquele gerado por um dipolo magnético. Este campo apresenta mudanças de intensidade que variam com a localização e a hora local. A parte principal do campo geomagnético se origina no interior da Terra através de processos eletromagnéticos. Extensivos estudos mostraram ainda que existem contribuições de origem externa ao planeta, principalmente de origem solar. Dentre estas fontes há anomalias do campo magnético que surgem a partir de um aumento diurno da corrente elétrica em uma estreita faixa da ionosfera, de direção leste-oeste, centrada no equador magnético e denominada Eletrojato Equatorial (EEJ). Ocasionalmente estas correntes podem apresentar reversões de fluxo, sendo denominadas Contra-Eletrojato (CEJ). Vários autores têm estudado os efeitos do EEJ e CEJ sobre as observações geoeletromagnéticas. Eles estão interessados no efeito combinado do EEJ e estruturas geológicas condutivas 1-D e 2-D. Nestes trabalhos a estrutura 2-D sempre se apresentava paralela ao eletrojato, o que é uma hipótese bastante restritiva ao se modelar ambientes geológicos mais realistas, em que corpos bidimensionais podem ter qualquer strike em relação ao EEJ. Neste trabalho apresentamos a solução deste problema sem esta restrição. Assim, mostramos os campos geoeletromagnéticos devidos a estruturas bidimensionais que possuam strike oblíquo em relação ao EEJ, através de perfis dos campos elétrico e magnéticos calculados na superfície e formando direção arbitrária à heterogeneidade condutiva 2-D. Com esta resposta avaliamos ainda qual a influência que estruturas bidimensionais exercem sobre a resposta magnetotelúrica, sob influência do Eletrojato Equatorial. Durante o desenvolvimento deste trabalho, utilizamos o método de elementos finitos, tendo por fonte eletromagnética o EEJ e o CEJ, que por sua vez foram representados por uma combinação de distribuições gaussianas de densidade de corrente. Estas fontes foram decompostas nas direções paralela e perpendicular à estrutura 2-D, resultando nos modos de propagação TE₁ e TE₂ e TM acoplados, respectivamente. Resolvemos o modo acoplado aplicando uma Transformada de Fourier nas equações de Maxwell e uma Transformada Inversa de Fourier na solução encontrada. De acordo com os experimentos numéricos realizados em um modelo interpretativo da Anomalia Condutiva da Bacia do Parnaíba, formado por uma enorme estrutura de 3000 ohm-m dentro de um corpo externo condutivo (1 ohm-m), concluímos que a presença do CEJ causa uma inversão na anomalia, se compararmos com o resultado do EEJ. Concluímos também que para as frequências mais altas as componentes do campo elétrico apresentam menor influência da parte interna do corpo 2-D do que da parte externa. Já para frequências mais baixas este comportamento se observa com as componentes do campo magnético. Com relação à frequência, vimos os efeitos do “skin-depth”, principalmente nas respostas magnéticas. Além disso, quando a estrutura 2-D está paralela ao eletrojato, o campo elétrico é insensível à estrutura interna do modelo para todos os valores de frequência utilizados. Com respeito ao ângulo θ_h entre a heterogeneidade e a fonte, vimos que o modo TM se manifesta naturalmente quando θ_h é diferente de 0°. Neste caso, o modo TE é composto por uma parte devido à componente da fonte paralela à heterogeneidade e a outra devido à componente da fonte perpendicular, que é acoplada ao modo TM. Assim, os campos calculados têm relação direta com o valor de θ_h. Analisando a influência do ângulo entre a direção do perfil dos campos e o strike da heterogeneidade verificamos que, à medida que θ_h se aproxima de 90°, os campos primários tornam-se variáveis para valores de θ_p diferentes de 90°. Estas variações causam uma assimetria na anomalia e dão uma idéia da inclinação da direção do perfil em relação aos corpos. Finalmente, concluímos que uma das influências que a distância entre o centro do EEJ e o centro da estrutura 2-D, causa sobre as componentes dos campos está relacionado às correntes reversas do EEJ e CEJ, pois a 500 km do centro da fonte estas correntes têm máxima intensidade. No entanto, com o aumento da distância, as anomalias diminuem de intensidade. Nas sondagens MT, nós também usamos o EEJ e o CEJ como fonte primária e comparamos nossos resultados com a resposta da onda plana. Deste modo observamos que as componentes do campo geoeletromagnético, usadas para calcular a impedância, têm influência do fator de acoplamento entre os modos TE₂ e TM. Além disso, esta influência se torna maior em meios resistivos e nas frequências mais baixas. No entanto, o fator de acoplamento não afeta os dados magnetotelúricos em frequências maiores de 10^-2 Hz. Para frequências da ordem de 10^-4 Hz os dados MT apresentam duas fontes de perturbação: a primeira e mais evidente é devido à presença fonte 2-D (EEJ e CEJ), que viola a hipótese da onda plana no método MT; e a segunda é causada pelo acoplamento entre os modos TE₂ e TM, pois quando a estrutura bidimensional está obliqua à fonte 2-D temos correntes elétricas adicionais ao longo da heterogeneidade. Concluimos assim, que o strike de uma grande estrutura condutiva bidimensional relativamente à direção do EEJ ou CEJ tem de fato influência sobre o campo geomagnético. Por outro lado, para estudos magnetotelúricos rasos (frequências maiores de 10^-3 Hz) o efeito do ângulo entre a estrutura geológica 2-D e a direção do EEJ não é tão importante. Contudo, em estudos de litosfera frequências menores de 10^-3 Hz) o acoplamento entre os modos TE₂ e TM não pode ser ignorado.

Tomografia da ionosfera a partir do GNSS e técnicas algébricas: estudo de caso para a região brasileira

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

First archeointensity results from Portuguese potteries (1550-1750 AD)

Geomagnetic field variations at archeomagnetic timescales can be obtained from well-dated heated structures and archeological potsherds. Here, we present the first archeointensity results obtained oil Portuguese ceramics (1550 to 1750 AD) collected at Brazilian archeological sites. The results are compared to those obtained from `Western Europe and currently available geomagnetic field models. Continuous thermomagnetic and IRM acquisitions curves indicate that Ti-poor titanomagnetite is responsible for the remanence in these ceramic fragments. Five fragments (24 samples) out of twelve analyzed yielded reliable intensity estimates. The row archeointensity data were corrected for TRM anisotropy and cooling rate effect. The mean dipole moments are obtained for three different age intervals: 1550 +/- 30 AD, 1600 +/- 30 AD and 1750 +/- 50 AD. Mean intensities vary from 37.9 +/- 4.2 mu T to 54.8 +/- 7.6 mu T in agreement with the previously reported data for 1550 AD and 1750 AD. Relatively weaker, but still highly dispersed, values were obtained for 1600 AD ceramics.

Archeointensity in Northeast Brazil over the past five centuries

This study presents the first archeointensity results from Northeast Brazil obtained from 14 groups of architectural brick fragments sampled in the city of Salvador, Bahia State (13 degrees S, 38.5 degrees W) and dated between the middle of the XVIth century and the beginning of the XIXth century. The dating is ascertained by historical documents complemented by archeological constraints, yielding in all cases age uncertainties of less than 50 years. Analyses were carried out using two experimental protocols: 1 the ""zero field-in field"" version of the classical Thellier and Thellier method as proposed by Coe (TT-ZI), including partial thermoremanent magnetization (pTRM) and pTRM-tail checks, and 2 the Triaxe procedure involving continuous high temperature magnetization measurements. Both TRM anisotropy and cooling rate effects were taken into account for the intensity determinations. The cooling rate effect was further explored for the TT-ZI protocol using three increasing slow cooling times (5 h, 10 h and 25 h) between 450 C and room temperature. Following archeological constraints, the slowest cooling time was retained in our study, yielding decreases of the raw intensity values by 4% to 14%. For each fragment, a mean intensity was computed and retained only when the data obtained from all specimens (between 2 and 6) satisfied a coherence test at similar to 5%. A total of 57 fragments (183 specimens) was considered for the computations of site-mean intensity values, with derived standard deviations of less than 8% of the corresponding means. When separately computed using the two experimental techniques, the site-mean intensity values always agree to within 5%. A good consistency is observed between intensity values of similar or close ages, which strengthen their reliability. Our data principally show a significant and continuous decrease in geomagnetic field intensity in Northeast Brazil between the first half of the XVIIth century and the XXth century. One result dated to the second half of the XVIth century further suggests that the geomagnetic field intensity reached a maximum around 1600 AD. This evolution is in good agreement with that expected in the city of Salvador from the available global geomagnetic field models. However, the accuracy of these models appears less well constrained between similar to 1550 AD and similar to 1650 AD. (C) 2010 Elsevier B.V. All rights reserved.

Giant magnetofossils and hyperthermal events

Magnetotactic bacteria biomineralize magnetic minerals with precisely controlled size, morphology, and stoichiometry. These cosmopolitan bacteria are widely observed in aquatic environments. If preserved after burial, the inorganic remains of magnetotactic bacteria act as magnetofossils that record ancient geomagnetic field variations. They also have potential to provide paleoenvironmental information. In contrast to conventional magnetofossils, giant magnetofossils (most likely produced by eukaryotic organisms) have only been reported once before from Paleocene-Eocene Thermal Maximum (PETM; 55.8 Ma) sediments on the New Jersey coastal plain. Here, using transmission electron microscopic observations, we present evidence for abundant giant magnetofossils, including previously reported elongated prisms and spindles, and new giant bullet-shaped magnetite crystals, in the Southern Ocean near Antarctica, not only during the PETM, but also shortly before and after the PETM. Moreover, we have discovered giant bullet-shaped magnetite crystals from the equatorial Indian Ocean during the Mid-Eocene Climatic Optimum (similar to 40 Ma). Our results indicate a more widespread geographic, environmental, and temporal distribution of giant magnetofossils in the geological record with a link to "hyperthermal" events. Enhanced global weathering during hyperthermals, and expanded suboxic diagenetic environments, probably provided more bioavailable iron that enabled biomineralization of giant magnetofossils. Our micromagnetic modelling indicates the presence of magnetic multi-domain (i.e., not ideal for navigation) and single domain (i.e., ideal for navigation) structures in the giant magnetite particles depending on their size, morphology and spatial arrangement. Different giant magnetite crystal morphologies appear to have had different biological functions, including magnetotaxis and other non-navigational purposes. Our observations suggest that hyperthermals provided ideal conditions for giant magnetofossils, and that these organisms were globally distributed. Much more work is needed to understand the interplay between magnetofossil morphology, climate, nutrient availability, and environmental variability.

Nonlinear Control of Magnetically Actuated Spacecraft

The topic of this thesis is the feedback stabilization of the attitude of magnetically actuated spacecraft. The use of magnetic coils is an attractive solution for the generation of control torques on small satellites flying inclined low Earth orbits, since magnetic control systems are characterized by reduced weight and cost, higher reliability, and require less power with respect to other kinds of actuators. At the same time, the possibility of smooth modulation of control torques reduces coupling of the attitude control system with flexible modes, thus preserving pointing precision with respect to the case when pulse-modulated thrusters are used. The principle based on the interaction between the Earth's magnetic field and the magnetic field generated by the set of coils introduces an inherent nonlinearity, because control torques can be delivered only in a plane that is orthogonal to the direction of the geomagnetic field vector. In other words, the system is underactuated, because the rotational degrees of freedom of the spacecraft, modeled as a rigid body, exceed the number of independent control actions. The solution of the control issue for underactuated spacecraft is also interesting in the case of actuator failure, e.g. after the loss of a reaction-wheel in a three-axes stabilized spacecraft with no redundancy. The application of well known control strategies is no longer possible in this case for both regulation and tracking, so that new methods have been suggested for tackling this particular problem. The main contribution of this thesis is to propose continuous time-varying controllers that globally stabilize the attitude of a spacecraft, when magneto-torquers alone are used and when a momentum-wheel supports magnetic control in order to overcome the inherent underactuation. A kinematic maneuver planning scheme, stability analyses, and detailed simulation results are also provided, with new theoretical developments and particular attention toward application considerations.

A multi-instrumental approach to the study of equatorial ionosphere over South America

An extensive study of the morphology and the dynamics of the equatorial ionosphere over South America is presented here. A multi parametric approach is used to describe the physical characteristics of the ionosphere in the regions where the combination of the thermospheric electric field and the horizontal geomagnetic field creates the so-called Equatorial Ionization Anomalies. Ground based measurements from GNSS receivers are used to link the Total Electron Content (TEC), its spatial gradients and the phenomenon known as scintillation that can lead to a GNSS signal degradation or even to a GNSS signal ‘loss of lock’. A new algorithm to highlight the features characterizing the TEC distribution is developed in the framework of this thesis and the results obtained are validated and used to improve the performance of a GNSS positioning technique (long baseline RTK). In addition, the correlation between scintillation and dynamics of the ionospheric irregularities is investigated. By means of a software, here implemented, the velocity of the ionospheric irregularities is evaluated using high sampling rate GNSS measurements. The results highlight the parallel behaviour of the amplitude scintillation index (S4) occurrence and the zonal velocity of the ionospheric irregularities at least during severe scintillations conditions (post-sunset hours). This suggests that scintillations are driven by TEC gradients as well as by the dynamics of the ionospheric plasma. Finally, given the importance of such studies for technological applications (e.g. GNSS high-precision applications), a validation of the NeQuick model (i.e. the model used in the new GALILEO satellites for TEC modelling) is performed. The NeQuick performance dramatically improves when data from HF radar sounding (ionograms) are ingested. A custom designed algorithm, based on the image recognition technique, is developed to properly select the ingested data, leading to further improvement of the NeQuick performance.

A remotely interrogated all-optical Rb-87 magnetometer

Atomic magnetometry was performed at Earth's magnetic field over a free-space distance of ten meters. Two laser beams aimed at a distant alkali-vapor cell excited and detected the Rb-87 magnetic resonance, allowing the magnetic field within the cell to be interrogated remotely. Operated as a driven oscillator, the magnetometer measured the geomagnetic field with less than or similar to 3.5 pT precision in a similar to 2 s data acquisition; this precision was likely limited by ambient field fluctuations. The sensor was also operated in self-oscillating mode with a 5.3 pT root Hz noise floor. Further optimization will yield a high-bandwidth, fully remote magnetometer with sub-pT sensitivity. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4747206]

New constraints on the gas age-ice age difference along the EPICA ice cores, 0-50 kyr

Gas is trapped in polar ice sheets at ~50–120 m below the surface and is therefore younger than the surrounding ice. Firn densification models are used to evaluate this ice age-gas age difference (Δage) in the past. However, such models need to be validated by data, in particular for periods colder than present day on the East Antarctic plateau. Here we bring new constraints to test a firn densification model applied to the EPICA Dome C (EDC) site for the last 50 kyr, by linking the EDC ice core to the EPICA Dronning Maud Land (EDML) ice core, both in the ice phase (using volcanic horizons) and in the gas phase (using rapid methane variations). We also use the structured 10Be peak, occurring 41 kyr before present (BP) and due to the low geomagnetic field associated with the Laschamp event, to experimentally estimate the Δage during this event. Our results seem to reveal an overestimate of the Δage by the firn densification model during the last glacial period at EDC. Tests with different accumulation rates and temperature scenarios do not entirely resolve this discrepancy. Although the exact reasons for the Δage overestimate at the two EPICA sites remain unknown at this stage, we conclude that current densification model simulations have deficits under glacial climatic conditions. Whatever the cause of the Δage overestimate, our finding suggests that the phase relationship between CO2 and EDC temperature previously inferred for the start of the last deglaciation (lag of CO2 by 800±600 yr) seems to be overestimated.

Magnetic properties of Cenozoic MORB and Cretaceous MORB from DSDP and ODP holes

The fact that the natural remanent magnetization (NRM) intensity of mid-oceanic-ridge basalt (MORB) samples shows systematic variations as a function of age has long been recognized: maximum as well as average intensities are generally high for very young samples, falling off rather rapidly to less than half the recent values in samples between 10 and 30 Ma, whereupon they slowly rise in the early Tertiary and Cretaceous to values that approach those of the very young samples. NRM intensities measured in this study follow the same trends as those observed in previous publications. In this study, we take a statistical approach and examine whether this pattern can be explained by variations in one or more of all previously proposed mechanisms: chemical composition of the magnetic minerals, abundance of these magnetization carriers, vectorial superposition of parallel or antiparallel components of magnetization, magnetic grain or domain size patterns, low-temperature oxidation to titanomaghemite, or geomagnetic field behavior. We find that the samples do not show any compositional, petrological, rock-magnetic, or paleomagnetic patterns that can explain the trends. Geomagnetic field intensity is the only effect that cannot be directly tested on the same samples, but it shows a similar pattern as our measured NRM intensities. We therefore conclude that the geomagnetic field strength was, on-average, significantly greater during the Cretaceous than during the Oligocene and Miocene.

Paleointensity record of Site 320-U1336

We present a high-resolution magnetostratigraphy and relative paleointensity (RPI) record derived from the upper 85 meters of IODP Site U1336, an equatorial Pacific early to middle Miocene succession recovered during Expedition 320/321. The magnetostratigraphy is well resolved with reversals typically located to within a few centimeters resulting in a well-constrained age model. The lowest normal polarity interval, from 85 to 74.87 meters, is interpreted as the upper part of Chron C6n (18.614-19.599 Ma). Another 33 magnetozones occur from 74.87 to 0.85 m, which are interpret to represent the continuous sequence of chrons from Chron C5Er (18.431-18.614 Ma) up to the top of Chron C5An.1n (12.014 Ma). We identify three new possible subchrons within Chron C5Cn.1n, Chron 5Bn.1r, and C5ABn. Sedimentation rates vary from about 7 to 15 m/Myr with a mean of about 10 m/Myr. We observe rapid, apparent changes in the sedimentation rate at geomagnetic reversals between ~16 and 19 Ma that indicate a calibration error in geomagnetic polarity timescale (ATNTS2004). The remanence is carried mainly by non-interacting particles of fine-grained magnetite, which have FORC distributions characteristic of biogenic magnetite. Given the relative homogeneity of the remanence carriers throughout the 85-m-thick succession and the quality with which the remanence is recorded, we have constructed a relative paleointensity (RPI) record that provides new insights into middle Miocene geomagnetic field behavior. The RPI record indicates a gradual decline in field strength between 18.5 Ma and 14.5 Ma, and indicates no discernible link between RPI and either chron duration or polarity state.