SIMULATIONS OF WINDS OF WEAK-LINED T TAURI STARS. II. THE EFFECTS OF A TILTED MAGNETOSPHERE AND PLANETARY INTERACTIONS

Based on our previous work, we investigate here the effects on the wind and magnetospheric structures of weak-lined T Tauri stars due to a misalignment between the axis of rotation of the star and its magnetic dipole moment vector. In such a configuration, the system loses the axisymmetry presented in the aligned case, requiring a fully three-dimensional (3D) approach. We perform 3D numerical magnetohydrodynamic simulations of stellar winds and study the effects caused by different model parameters, namely the misalignment angle theta(t), the stellar period of rotation, the plasma-beta, and the heating index.. Our simulations take into account the interplay between the wind and the stellar magnetic field during the time evolution. The system reaches a periodic behavior with the same rotational period of the star. We show that the magnetic field lines present an oscillatory pattern. Furthermore, we obtain that by increasing theta(t), the wind velocity increases, especially in the case of strong magnetic field and relatively rapid stellar rotation. Our 3D, time-dependent wind models allow us to study the interaction of a magnetized wind with a magnetized extrasolar planet. Such interaction gives rise to reconnection, generating electrons that propagate along the planet`s magnetic field lines and produce electron cyclotron radiation at radio wavelengths. The power released in the interaction depends on the planet`s magnetic field intensity, its orbital radius, and on the stellar wind local characteristics. We find that a close-in Jupiter-like planet orbiting at 0.05 AU presents a radio power that is similar to 5 orders of magnitude larger than the one observed in Jupiter, which suggests that the stellar wind from a young star has the potential to generate strong planetary radio emission that could be detected in the near future with LOFAR. This radio power varies according to the phase of rotation of the star. For three selected simulations, we find a variation of the radio power of a factor 1.3-3.7, depending on theta(t). Moreover, we extend the investigation done in Vidotto et al. and analyze whether winds from misaligned stellar magnetospheres could cause a significant effect on planetary migration. Compared to the aligned case, we show that the timescale tau(w) for an appreciable radial motion of the planet is shorter for larger misalignment angles. While for the aligned case tau(w) similar or equal to 100 Myr, for a stellar magnetosphere tilted by theta(t) = 30 degrees, tau(w) ranges from similar to 40 to 70 Myr for a planet located at a radius of 0.05 AU. Further reduction on tau(w) might occur for even larger misalignment angles and/or different wind parameters.

THREE-DIMENSIONAL NUMERICAL SIMULATIONS OF MAGNETIZED WINDS OF SOLAR-LIKE STARS

By means of self-consistent three-dimensional magnetohydrodynamics (MHD) numerical simulations, we analyze magnetized solar-like stellar winds and their dependence on the plasma-beta parameter (the ratio between thermal and magnetic energy densities). This is the first study to perform such analysis solving the fully ideal three-dimensional MHD equations. We adopt in our simulations a heating parameter described by gamma, which is responsible for the thermal acceleration of the wind. We analyze winds with polar magnetic field intensities ranging from 1 to 20 G. We show that the wind structure presents characteristics that are similar to the solar coronal wind. The steady-state magnetic field topology for all cases is similar, presenting a configuration of helmet streamer-type, with zones of closed field lines and open field lines coexisting. Higher magnetic field intensities lead to faster and hotter winds. For the maximum magnetic intensity simulated of 20 G and solar coronal base density, the wind velocity reaches values of similar to 1000 km s(-1) at r similar to 20r(0) and a maximum temperature of similar to 6 x 10(6) K at r similar to 6r(0). The increase of the field intensity generates a larger ""dead zone"" in the wind, i.e., the closed loops that inhibit matter to escape from latitudes lower than similar to 45 degrees extend farther away from the star. The Lorentz force leads naturally to a latitude-dependent wind. We show that by increasing the density and maintaining B(0) = 20 G the system recover back to slower and cooler winds. For a fixed gamma, we show that the key parameter in determining the wind velocity profile is the beta-parameter at the coronal base. Therefore, there is a group of magnetized flows that would present the same terminal velocity despite its thermal and magnetic energy densities, as long as the plasma-beta parameter is the same. This degeneracy, however, can be removed if we compare other physical parameters of the wind, such as the mass-loss rate. We analyze the influence of gamma in our results and we show that it is also important in determining the wind structure.

Um estudo da abundância de lítio, rotação, atividade cromosférica e magnetismo das estrelas análogas e gêmeas solares

The study physical process that control the stellar evolution is strength influenced by several stellar parameters, like as rotational velocity, convective envelope mass deepening, and magnetic field intensity. In this study we analyzed the interconnection of some stellar parameters, as Lithium abundance A(Li), chromospheric activity and magnetic field intensity as well as the variation of these parameters as a function of age, rotational velocity, and the convective envelope mass deepening for a selected sample of solar analogs and twins stars. In particular, we analyzed the convective envelope mass deepening and the dispersion of lithium abundance for these stars. We also studied the evolution of rotation in subgiants stars, because its belong to the following evolutionary stage of solar analogs, and twins stars. For this analyze, we compute evolutionary models with the TGEC code to derive the evolutionary stage, as well as the convective envelope mass deepening, and derive more precisely the stellar mass, and age for this 118 stars. Our Investigation shows a considerable dispersion of lithium abundance for the solar analogs stars. We also realize that this dispersion is not by the convective zone deep, in this way we observed which the scattering of A(Li) can not be explained by classical theories of mixing in the convective zone. In conclusion we have that are necessary extra-mixing process to explain this decrease of Lithium abundance in solar analogs and twins stars. We analyzed the subgiant stars because this are the subsequent evolutionary stage after the solar analogs and twins stars. For this analysis, we compute the rotational period for 30 subgiants stars observed by Co- RoT satellite. For this task we apply two different methods: Lomb-Scargle algorithm, and the Plavchan Periodogram. We apply the TGEC code we compute models with internal distribution of angular momentum to confront the predict results with the models, and the observational results. With this analyze, we showed which solid body rotation models are incompatible with the physical interpretation of observational results. As a result of our study we still concluded that the magnetic field, convective envelope mass deepening, and internal redistribution of angular momentum are essential to explain the evolution of low-mass stars, and its observational characteristics. Based on population synthesis simulation, we concluded that the solar neighborhood presents a considerable quantity of solar twins when compared with the discovered set nowadays. Altogether we foresee the existence around 400 solar analogs in the solar neighborhood (distance of 100 pc). We also study the angular momentum of solar analogs and twins, in this study we concluded that added angular momentum from a Jupiter type planet, putted in the Jupiter position, is not enough to explain the angular momentum predicted by Kraft law (Kraft 1970)

Efeitos de interface em bicamadas magnéticas

We study magnetic interface roughness in F/AF bilayers. Two kinds of roughness were considered. The first one consists of isolated defects that divide the substrate in two regions, each one with an AF sub-lattice. The interface exchange coupling is considered uniform and presents a sudden change in the defects line, favoring Neel wall nucleation. Our results show the interface field dependence of the threshold thickness for the reorientation of the magnetization in the ferromagnetic film. Angular profiles show the relaxation of the magnetization, from Neel wall, at the interface, to reoriented state, at the surface. External magnetic field, perpendicular to the easy axis of the substrate, favors the reoriented state. Depending, of the external magnetic field intensity, parallel to the easy axis of the AF, the magnetization profile at surface can be parallel or perpendicular to the field direction. The second one treats of distributed deffects, periodically. The shape hysteresis curves, exchange bias and coercivity were characterized by interface field intensity and roughness pattern. Our results show that dipolar effects decrease the exchange bias and coercivity

Artificial neural networks applied in study of atmospheric parameters to high voltage substations concerning lightning

This gaper demonstrates that artificial neural networks can be used effectively for estimation of parameters related to study of atmospheric conditions to high voltage substations design. Specifically, the neural networks are used to compute the variation of electrical field intensity and critical disruptive voltage in substations taking into account several atmospheric factors, such as pressure, temperature, humidity, so on. Examples of simulation of tests are presented to validate the proposed approach. The results that were obtained by experimental evidences and numerical simulations allowed the verification of the influence of the atmospheric conditions on design of substations concerning lightning.

Effect of electron magnetic trapping in a plasma immersion ion implantation system

In this work we describe a two-dimensional computer simulation of magnetic field enhanced plasma immersion implantation system. Negative bias voltage of 10.0 kV is applied to a cylindrical target located on the axis of a grounded vacuum chamber filled with uniform nitrogen plasma. A pair of external coils creates a static magnetic field with main vector component along the axial direction. Thus, a system of crossed ExB field is generated inside the vessel forcing plasma electrons to rotate in azimuthal direction. In addition, the axial variation of the magnetic field intensity produces magnetic mirror effect that enables axial particle confinement. It is found that high-density plasma regions are formed around the target due to intense background gas ionization by the trapped electrons. Effect of the magnetic field on the sheath dynamics and the implantation current density of the PIII system is investigated. By changing the magnetic field axial profile (varying coils separation) an enhancement of about 30% of the retained dose can be achieved. The results of the simulation show that the magnetic mirror configuration brings additional benefits to the PIII process, permitting more precise control of the implanted dose.

Investigando o campo magnético das estrelas análogas e gêmeas solares através da espectropolarimetria

This study proposes an observing program focused on the investigation of the stellar magnetism and dynamo evolution in cool active solar-like stars. More mainly in the solar analogs and twins. Observations of stars of our base were carried out with two spectropolarimeter (ESPaDOnS@CFHT and NARVAL@TBL). The analyse of stars in stage different allows an understanding of the dependence of magnetic activity on basic stellar parameters such as rotation, mass, age and depth of the convection zone. This study provides measures necessary for testing dynamo theories. The 65 targets for this project are solar type stars with mass spanning from 0:9 M=Mfi 1:075 solar masses and at different evolutionary stages. Our two main science objectives were, (i) To determine how the magnetic field evolved from the ZAMS to the TO (turn off) for stars with 0:9 M=Mfi 1:075; (ii) To determine the impact of convective depth and rotation on magnetic of cool stars of solar type. The main result from this study was the characterization of the dependence of magnetic field intensity as function of age, Rossby number and the convective zone deepening. This context, the availability of ESPaDOnS and NARVAL opens an exceptional possibility to study the magnetic properties of Sun-like stars by means of spectropolarimetric observations

Evaluation and identification of lightning models by artificial neural networks

This paper describes a novel approach for mapping lightning models using artificial neural networks. The networks acts as identifier of structural features of the lightning models so that output parameters can be estimated and generalized from an input parameter set. Simulation examples are presented to validate the proposed approach. More specifically, the neural networks are used to compute electrical field intensity and critical disruptive voltage taking into account several atmospheric and structural factors, such as pressure, temperature, humidity, distance between phases, height of bus bars, and wave forms. A comparative analysis with other approaches is also provided to illustrate this new methodology.

Uma metodologia para predição do campo elétrico de radiodifusão sonora em ondas médias utilizando inferências bayesianas

A adoção de sistemas digitais de radiodifusão sonora, que estão em fase de testes no país, permite realizar novos estudos visando um melhor planejamento para a implementação dessas novas emissoras. O que significa reavaliar os principais modelos de radiopropagação existentes ou propor novas alternativas para atender as demandas inerentes dos sistemas digitais. Os modelos atuais, conforme Recomendações ITU-R P. 1546 e ITU-R P. 1812, não condizem fielmente com a realidade de algumas regiões do Brasil, principalmente com as regiões de clima tropical, como a Região Amazônica, seja pelo elevado índice pluviométrico seja pela vasta flora existente. A partir dos modelos adequados ao canal de propagação, torna-se viável desenvolver ferramentas de planejamento de cobertura mais precisas e eficientes. A utilização destas ferramentas é cabível tanto para a ANATEL, para a elaboração dos planos básicos de distribuição de canais quanto para os radiodifusores. No presente trabalho é apresentada uma metodologia utilizando a inteligência computacional, baseada em Inferênciass Baysianas, para predição da intensidade de campo elétrico, a qual pode ser aplicada ao planejamento ou expansão de áreas de cobertura em sistemas de radiodifusão para frequências na faixa de ondas médias (de 300 kHz a 3MHz). Esta metodologia gera valores de campo elétrico estimados a partir dos valores de altitude do terreno (através de análises de tabelas de probabilidade condicional) e estabelece a comparação destes com valores de campo elétrico medidos. Os dados utilizados neste trabalho foram coletados na região central do Brasil, próximo à cidade de Brasília. O sinal transmitido era um sinal de rádio AM transmitido na frequência de 980 kHz. De posse dos dados coletados durante as campanhas de medição, foram realizadas simulações utilizando tabelas de probabilidade condicional geradas por Inferências Bayesianas. Assim, é proposto um método para predizer valores de campo elétrico com base na correlação entre o campo elétrico medido e altitude, através da utilização de inteligência computacional. Se comparados a inúmeros trabalhos existentes na literatura que têm o mesmo objetivo, os resultados encontrados neste trabalho validam o uso da metodologia para determinar o campo elétrico de radiodifusão sonora em ondas médias utilizando Inferências Bayesianas.

Desenvolvimento de um magnetometro a precessão nuclear

O objetivo desta tese foi desenvolver um magnetômetro à precessão nuclear para prospecção geofísica e estações-base magnéticas. O magnetômetro à precessão nuclear mede a intensidade total do campo magnético. Seu funcionamento é baseado na ressonância magnética nuclear. A medida de campo é feita pela de terminação da freqüência de precessão de núcleos de hidrogênio – prótons - de líquidos não viscosos no campo magnético terrestre. O magnetômetro é constituído de duas partes: o sensor e o instrumento de medida. O sensor é uma bobina solenoidal, cujo núcleo é preenchido com o líquido. Três líquidos diferentes foram testados; água, propanol e um querosene sintético. Optou-se pelo uso do querosene porque oferece maior amplitude no sinal de precessão, dando, conseqüentemente, maior relação sinal/ ruído. O sistema de medida contém os circuitos de sintonia e amplificação do sinal e, os circuitos lógicos para a programação da operação e contagem da freqüência de precessão. Cada ciclo de medida tem duração de 3 segundos, sendo 2,3s para a polarização e 0,7s para a recepção do sinal. São possíveis dois modos de operação: manual, reciclando automaticamente e por controle remoto. O sinal de precessão é amplificado seletivamente em uma das 14 faixas de sintonia, que cobrem medidas entre 22000 e 95000 gammas. A freqüência de precessão é multiplicada por um fator de 64 e contada durante um tempo igual a 0,36699s, determinado com base na razão giromagnética do próton. O número de pulsos contados é numericamente igual ao valor do campo magnético em gammas. A resposta pode ser lida em mostradores digitais ou na saída BCD paralela quando operando por controle remoto. A precisão da medida é de 1 gamma. O instrumento foi testado no campo para avaliar a relação sinal/ruído, gradiente suportável e consumo de potência. Nos testes de aplicação do protótipo, foram obtidos dados de variação diurna e realizaram-se levantamentos magnético de reconhecimento e detalhe em um sítio arqueológico na Ilha de Marajó, Pará. As respostas dos testes foram comparados com dois magnetômetros comerciais - o GP-70, McPhar e o G-816, Geometrics e, ainda, com dados do Observatório Magnético de Tatuoca-Pa. Em todos os casos, a comparação dos dados mostrou bom desempenho do magnetômetro em teste.

Predição de campo elétrico para TV digital usando Funções de Green diádicas

Este trabalho oferece um método para a predição da intensidade de campo elétrico para TV Digital utilizando a Função de Green diádica. A Diádica é uma ferramenta matemática eficiente que tem simplicidade simbólica e robustez permitindo, assim, que algumas características do meio (como permissividade, condutividade e permeabilidade, por exemplo) sejam consideradas na elaboração do modelo de campo elétrico, bem como levar em conta a anisotropia do meio. Na maior parte dos trabalhos correlatos, que utilizam as funções de Green diádicas, estão relacionados na faixa de VHF. Este trabalho irá apresentar desde os conceitos básicos das diádicas, desenvolvendo-a para o cálculo de um modelo que permita predizer o campo elétrico para a faixa de UHF, na qual os sistemas de TV Digital se encontram. Uma explanação teórica e um desenvolvimento matemático serão feitos de forma que um entendimento claro e objetivo sejam alcançados no estudo das funções de Green diádicas, numa parte da teoria do eletromagnetismo. Testes foram realizados para confirmar a aplicabilidade da formulação sugerida, fazendo simulações que realizem uma comparação entre os dados medidos, de duas emissoras de TV situadas na cidade de Belém, e o modelo de Okumura-Hata modificado, mostrando resultados satisfatórios, tanto para frequências na faixa de VHF e UHF.

Inversion method for obtaining electrical parameters for soil in the rural region in Brazil

This paper presents an inversion methodology through weighted least squares to obtain the electrical parameters for the soil of a typical mid-western region in Brazil using the model based in the formalism of the parabolic equations to calculate the electric field intensity received. To validate this methodology, the results of the radio signal measurement campaign conducted in six radial routes leaving the city of Brasilia, Federal District, where the transmitter was located, were used. The measurements were compared to computer simulations and, thus, the optimal values for the electric conductivity and relative permittivity for the soil of the region could be estimated. Finally, a quantitative analysis of these parameters was performed with the values found in the literature, which demonstrated the effectiveness of the proposed methodology.

Estudo para correção dos sensores da rede de monitoramento do campo elétrico em função do campo elétrico de tempo bom

A monitoring network of atmospheric electric field covering the Vale do Paraiba region was implemented. The sensors were located on different sites with different altitude and geographic topology. The present work reports the study carried on those sensors in order to verify the necessity of using some correction factor to the measured local electric field intensity due to effects of local environment. The measurements were done in continuous 24 hours per day with the data recorded on registers in each device accumulating information during a period of four months. The relation between the electric field values by each sensor was compared to the reference located on Sao Jose dos Campos city using the same period. In a graphical analysis using the local field intensity and the reference, the data were fitted to a straight line obtained by minimum square method. Variation up to 95% was observed between the field values in some sensors. Another method was proposed, comparing the mean values of the electric field in a function of time. The variation in some sensors reached up to 133%. We conclude that the variations are due to local atmospheric conditions and no correction factor is required on the electric field sensors

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.

Statistical properties of Radio Halos and the re-acceleration model

Galaxy clusters occupy a special position in the cosmic hierarchy as they are the largest bound structures in the Universe. There is now general agreement on a hierarchical picture for the formation of cosmic structures, in which galaxy clusters are supposed to form by accretion of matter and merging between smaller units. During merger events, shocks are driven by the gravity of the dark matter in the diffuse barionic component, which is heated up to the observed temperature. Radio and hard-X ray observations have discovered non-thermal components mixed with the thermal Intra Cluster Medium (ICM) and this is of great importance as it calls for a “revision” of the physics of the ICM. The bulk of present information comes from the radio observations which discovered an increasing number of Mpcsized emissions from the ICM, Radio Halos (at the cluster center) and Radio Relics (at the cluster periphery). These sources are due to synchrotron emission from ultra relativistic electrons diffusing through µG turbulent magnetic fields. Radio Halos are the most spectacular evidence of non-thermal components in the ICM and understanding the origin and evolution of these sources represents one of the most challenging goal of the theory of the ICM. Cluster mergers are the most energetic events in the Universe and a fraction of the energy dissipated during these mergers could be channelled into the amplification of the magnetic fields and into the acceleration of high energy particles via shocks and turbulence driven by these mergers. Present observations of Radio Halos (and possibly of hard X-rays) can be best interpreted in terms of the reacceleration scenario in which MHD turbulence injected during these cluster mergers re-accelerates high energy particles in the ICM. The physics involved in this scenario is very complex and model details are difficult to test, however this model clearly predicts some simple properties of Radio Halos (and resulting IC emission in the hard X-ray band) which are almost independent of the details of the adopted physics. In particular in the re-acceleration scenario MHD turbulence is injected and dissipated during cluster mergers and thus Radio Halos (and also the resulting hard X-ray IC emission) should be transient phenomena (with a typical lifetime <» 1 Gyr) associated with dynamically disturbed clusters. The physics of the re-acceleration scenario should produce an unavoidable cut-off in the spectrum of the re-accelerated electrons, which is due to the balance between turbulent acceleration and radiative losses. The energy at which this cut-off occurs, and thus the maximum frequency at which synchrotron radiation is produced, depends essentially on the efficiency of the acceleration mechanism so that observations at high frequencies are expected to catch only the most efficient phenomena while, in principle, low frequency radio surveys may found these phenomena much common in the Universe. These basic properties should leave an important imprint in the statistical properties of Radio Halos (and of non-thermal phenomena in general) which, however, have not been addressed yet by present modellings. The main focus of this PhD thesis is to calculate, for the first time, the expected statistics of Radio Halos in the context of the re-acceleration scenario. In particular, we shall address the following main questions: • Is it possible to model “self-consistently” the evolution of these sources together with that of the parent clusters? • How the occurrence of Radio Halos is expected to change with cluster mass and to evolve with redshift? How the efficiency to catch Radio Halos in galaxy clusters changes with the observing radio frequency? • How many Radio Halos are expected to form in the Universe? At which redshift is expected the bulk of these sources? • Is it possible to reproduce in the re-acceleration scenario the observed occurrence and number of Radio Halos in the Universe and the observed correlations between thermal and non-thermal properties of galaxy clusters? • Is it possible to constrain the magnetic field intensity and profile in galaxy clusters and the energetic of turbulence in the ICM from the comparison between model expectations and observations? Several astrophysical ingredients are necessary to model the evolution and statistical properties of Radio Halos in the context of re-acceleration model and to address the points given above. For these reason we deserve some space in this PhD thesis to review the important aspects of the physics of the ICM which are of interest to catch our goals. In Chapt. 1 we discuss the physics of galaxy clusters, and in particular, the clusters formation process; in Chapt. 2 we review the main observational properties of non-thermal components in the ICM; and in Chapt. 3 we focus on the physics of magnetic field and of particle acceleration in galaxy clusters. As a relevant application, the theory of Alfv´enic particle acceleration is applied in Chapt. 4 where we report the most important results from calculations we have done in the framework of the re-acceleration scenario. In this Chapter we show that a fraction of the energy of fluid turbulence driven in the ICM by the cluster mergers can be channelled into the injection of Alfv´en waves at small scales and that these waves can efficiently re-accelerate particles and trigger Radio Halos and hard X-ray emission. The main part of this PhD work, the calculation of the statistical properties of Radio Halos and non-thermal phenomena as expected in the context of the re-acceleration model and their comparison with observations, is presented in Chapts.5, 6, 7 and 8. In Chapt.5 we present a first approach to semi-analytical calculations of statistical properties of giant Radio Halos. The main goal of this Chapter is to model cluster formation, the injection of turbulence in the ICM and the resulting particle acceleration process. We adopt the semi–analytic extended Press & Schechter (PS) theory to follow the formation of a large synthetic population of galaxy clusters and assume that during a merger a fraction of the PdV work done by the infalling subclusters in passing through the most massive one is injected in the form of magnetosonic waves. Then the processes of stochastic acceleration of the relativistic electrons by these waves and the properties of the ensuing synchrotron (Radio Halos) and inverse Compton (IC, hard X-ray) emission of merging clusters are computed under the assumption of a constant rms average magnetic field strength in emitting volume. The main finding of these calculations is that giant Radio Halos are naturally expected only in the more massive clusters, and that the expected fraction of clusters with Radio Halos is consistent with the observed one. In Chapt. 6 we extend the previous calculations by including a scaling of the magnetic field strength with cluster mass. The inclusion of this scaling allows us to derive the expected correlations between the synchrotron radio power of Radio Halos and the X-ray properties (T, LX) and mass of the hosting clusters. For the first time, we show that these correlations, calculated in the context of the re-acceleration model, are consistent with the observed ones for typical µG strengths of the average B intensity in massive clusters. The calculations presented in this Chapter allow us to derive the evolution of the probability to form Radio Halos as a function of the cluster mass and redshift. The most relevant finding presented in this Chapter is that the luminosity functions of giant Radio Halos at 1.4 GHz are expected to peak around a radio power » 1024 W/Hz and to flatten (or cut-off) at lower radio powers because of the decrease of the electron re-acceleration efficiency in smaller galaxy clusters. In Chapt. 6 we also derive the expected number counts of Radio Halos and compare them with available observations: we claim that » 100 Radio Halos in the Universe can be observed at 1.4 GHz with deep surveys, while more than 1000 Radio Halos are expected to be discovered in the next future by LOFAR at 150 MHz. This is the first (and so far unique) model expectation for the number counts of Radio Halos at lower frequency and allows to design future radio surveys. Based on the results of Chapt. 6, in Chapt.7 we present a work in progress on a “revision” of the occurrence of Radio Halos. We combine past results from the NVSS radio survey (z » 0.05 − 0.2) with our ongoing GMRT Radio Halos Pointed Observations of 50 X-ray luminous galaxy clusters (at z » 0.2−0.4) and discuss the possibility to test our model expectations with the number counts of Radio Halos at z » 0.05 − 0.4. The most relevant limitation in the calculations presented in Chapt. 5 and 6 is the assumption of an “averaged” size of Radio Halos independently of their radio luminosity and of the mass of the parent clusters. This assumption cannot be released in the context of the PS formalism used to describe the formation process of clusters, while a more detailed analysis of the physics of cluster mergers and of the injection process of turbulence in the ICM would require an approach based on numerical (possible MHD) simulations of a very large volume of the Universe which is however well beyond the aim of this PhD thesis. On the other hand, in Chapt.8 we report our discovery of novel correlations between the size (RH) of Radio Halos and their radio power and between RH and the cluster mass within the Radio Halo region, MH. In particular this last “geometrical” MH − RH correlation allows us to “observationally” overcome the limitation of the “average” size of Radio Halos. Thus in this Chapter, by making use of this “geometrical” correlation and of a simplified form of the re-acceleration model based on the results of Chapt. 5 and 6 we are able to discuss expected correlations between the synchrotron power and the thermal cluster quantities relative to the radio emitting region. This is a new powerful tool of investigation and we show that all the observed correlations (PR − RH, PR − MH, PR − T, PR − LX, . . . ) now become well understood in the context of the re-acceleration model. In addition, we find that observationally the size of Radio Halos scales non-linearly with the virial radius of the parent cluster, and this immediately means that the fraction of the cluster volume which is radio emitting increases with cluster mass and thus that the non-thermal component in clusters is not self-similar.