A fossil magnetic field embedded in the radiative core of the Sun has been thought possible for some time now. However, such a fossil magnetic field has, a priori, not been considered a visible phenomenon due to the effects of turbulence in the solar convection zone. Since a well developed theory (referred to herein as magnetohydrodynamic dynamo theory) exists for describing the regeneration of magnetic fields in astrophysical objects like the Sun, it is possible to quantitatively evaluate the interaction of a fossil magnetic field with the magnetohydrodynamic dynamo operating in the solar convection zone. In this work, after a brief description of the basic dynamo equations, a spherical model calculation of the solar dynamo is introduced. First, we calculate the interaction of a fossil magnetic field with a dynamo in which the regeneration mechanisms of cyclonic convection and large-scale, nonuniform rotation are confined to spherical shells. It is argued that the amount of amplification or suppression of a fossil magnetic field will be smallest for a uniform distribution of cyclonic convection and nonuniform rotation, as expected in the Sun. Secondly, we calculate the interaction of a fossil magnetic field with a dynamo having a uniform distribution of cyclonic convection and large-scale, nonuniform rotation. We find that the dipole or quadrupole moments of a fossil magnetic field are suppressed by factors of -0.35 and -0.37, respectively. The dynamo modified fossil field, superimposed on the theoretically calculated magnetic fields of the solar magnetic cycle, are compared with the actual sunspot cycle and solar magnetic fields as observed by others, indicating that a fossil magnetic field may be responsible for asymmetries in the sunspot cycle and an observed solar magnetic quadrupole moment. Further observations and reduction of the data are required before the presence of a fossil magnetic field can be established. A discussion is given of the implications for the Sun if a fossil magnetic field is observed and identified. It is considered most likely that a fossil magnetic field would be a remnant of the possible Hayashi phase of a fully convective, protosun. Other possibilities also exist.

O ciclo solar é um dos fenômenos magnéticos mais interessantes do Universo. Embora ele tinha sido descoberto há mais de 150 anos, até agora permanece um problema em aberto para a Astrofísica. Há diferentes tipos de observações que sugerem que o ciclo solar corresponde a um processo de dínamo operando em algum lugar do interior solar. Parker foi o primeiro a tentar explicar o dínamo solar como um processo hidro-magnético acerca de 50 anos atrás. Desde então, embora tenha havido avanços significativos nas observações e investigações teóricas e numéricas, uma resposta definitiva para o dínamo solar ainda não existe. Acredita-se que no caso do Sol, pelo menos dois processos são necessários para completar o ciclo magnético observado: a transformação de um campo poloidal inicial em um campo toroidal, um processo conhecido como efeito , o qual se deve ao cisalhamento em grande escala ocasionado pela rotação diferencial; e a transformação do campo toroidal em um novo campo poloidal de polaridade oposta ao inicial. Esse segundo processo é menos conhecido e motivo de intensas discussões e pesquisas. Duas hipóteses principais foram formuladas para explicar a natureza deste processo, usualmente conhecido como efeito : a primeira, baseada na idéia de Parker de um mecanismo turbulento onde os campos poloidais resultam de movimentos convectivos ciclônicos operando em tubos de fluxo toroidais em pequena escala. Esses modelos se depararam, no entanto, com um serio inconveniente: na fase não-linear, i.e., quando a reação dinâmica do campo magnético ao fluido torna-se importante, o efeito pode ser amortecido de forma catastrófica, levando a um dínamo pouco efetivo. A segunda hipótese é baseada nas idéias de Babcock (1961) e Leighton (1969) (BL), que propuseram que o campo poloidal forma-se devido à emergência e decaimento posterior das regiões bipolares ativas. Neste modelo a circulação meridional tem um papel fundamental pois atua como mecanismo de transporte do fluxo magnético, de tal forma que a escala de tempo advectivo deve dominar sobre a escala de tempo difusiva. Por essa razão essa classe de modelos é comumente conhecida como modelo de dínamo dominado pelo transporte de fluxo, ou dínamo advectivo. Os modelos de dínamo dominados pelo transporte de fluxo são relativamente bem sucedidos em reproduzir as características em grande escala do ciclo solar, tornando-se populares entre a comunidade de Física solar, no entanto, também apresentam vários problemas amplamente discutidos na literatura. O objetivo principal deste trabalho foi identificar as principais limitações dessa classe de modelos e explorar as suas possíveis soluções. Para tal, construímos um modelo numérico bi-dimensional de dínamo cinemático baseado na teoria de campo médio e investigamos primeiro os efeitos da geometria e da espessura da tacoclina solar na amplificação do dínamo. Depois, consideramos o processo de bombeamento magnético turbulento como um mecanismo alternativo de transporte de fluxo magnético, e finalmente, incluímos a reação dinâmica do campo magnético sobre a difusividade magnética turbulenta, um processo conhecido como amortecimento de . Verificamos que é possível construir-se um modelo de dínamo dominado pelo transporte de fluxo capaz de reproduzir as observações ao considerar-se uma tacoclina de espessura fina localizada abaixo da zona convectiva. Isto limita a criação de intensos campos toroidais não desejados nas altas latitudes. Verificamos também ser importante considerar o bombeamento magnético, pois ele provê advecção do fluxo magnético para o equador e para a base da camada convectiva, o que resulta em uma correta distribuição latitudinal e temporal dos campos toroidais e também permite certa penetração desses campos nas regiões mais estáveis onde podem adquirir maior amplificação. Esse mecanismo é ainda importante para produzir a paridade correta do campo (anti-simétrica) nos dois hemisférios do Sol. Também encontramos que o amortecimento da difusividade magnética é um mecanismo fundamental para a formação de pequenas estruturas de campo toroidal com maior tempo de vida, identificadas com os tubos de fluxo, que acredita-se existirem na base da zona de convecção. Além do mais, os campos magnéticos formados graças ao amortecimento de podem ser até ~2 vezes mais intensos que as estruturas magnéticas formadas sem o seu amortecimento. Por fim, nos últimos anos, alguns trabalhos teóricos vêm chamando a atenção para o papel da conservação da helicidade magnética no processo de dínamo, dando nova vida a modelos de dínamo turbulento, como originalmente proposto por Parker. Com o objetivo de investigar o papel da helicidade magnética e de buscar uma descrição dinâmica mais realista do mecanismo de dínamo, construímos recentemente um modelo numérico de convecção tridimensional (utilizando o código MHD, PLUTO) que tenta reproduzir o cenário natural do interior solar onde teria lugar o processo de dínamo. Exploramos a evolução de um campo magnético semente imposto sobre um estado convectivo estacionário. Os resultados preliminares indicam que a convecção pode facilmente excitar o efeito de dínamo, inclusive em casos sem rotação. Porém, nos casos com rotação, o dínamo parece produzir uma maior quantidade de campo magnético médio com relação aos casos sem a rotação nos quais o campo flutuante é dominante. Estes resultados suportam a existência de um dínamo turbulento y validam a teoria de campo médio, mas uma a análise mais detalhada ainda é necessária. / The solar cycle is one of the most interesting magnetic phenomenon in the Universe. Even though it was discovered more than 150 years ago, it remains until now as an open problem in Astrophysics. There are several observational evidences that suggest that the solar cycle corresponds to a dynamo process operating at some place of the solar interior. Parker, in 1955, was the first to try to explain the solar dynamo as hydromagnetic phenomena. Since then, although there has been important improvements in the observations, theory and numerical simulations, a definitive model for the solar dynamo is still missing. There is common agreement that in the solar case, at least two processes are necessary to close the dynamo loop: the transformation of an initial poloidal field into a toroidal field, the so called Omega effect, which is due to a large scale shear caused by the diferential rotation, and the transformation of the toroidal field into a new poloidal field of opposite polarity, which is still a poorly understood process that has been the subject of intense debate and research. Two main hypotheses have been formulated in order to explain the nature of this effect, usually denominated alpha effect: the first one is based on Parker\'s idea of a turbulent mechanism where the poloidal field results from cyclonic convective motions operating at small scales in the toroidal field ropes. These models, however face an important limitation: in the non-linear regime, i.e. when the back reaction of the toroidal field on the motions becomes important, the alpha effect can be catastrophically quenched leading to an ineffective dynamo. The second hypotheses is based on the formulation of Babcock (1961) and Leighton (1969) (BL), who proposed that the poloidal field is formed due to the emergence and decay of bipolar magnetic regions. In this model the meridional circulation plays an important role by acting as conveyor belt of the magnetic flux, so that the advection time must be dominant over the diffusion time. For this reason these models are often called flux-transport dynamo models. The flux-transport dynamo models has been relatively successful in reproducing the large scale features of the solar cycle, and have become popular between the solar community. However, they also present several problems that have been widely discussed in the literature. The main goal of this work was to identify the main problems concerning the flux-transport dynamo model and to explore possible solutions for them. For this aim, we have built a two-dimensional kinematic numerical model based on the mean-field theory in order to explore first the effects of the geometry and thickness of the solar tachocline on the dynamo amplification. Then, we considered the turbulent pumping as an alternative magnetic flux advection mechanism, and finally, we included the non-linear back-reaction of the magnetic field on the turbulent magnetic diffusivity, a process known as eta-quenching. We have found that it is possible to build a flux-transport dynamo model able to reproduce the observations as long as a thin tachocline located below the convective zone is considered. This helps to prevent the amplification of undesirable strong toroidal fields at the high latitudes. We have also found that it is important to consider the turbulent magnetic pumping mechanism, because it provides magnetic field advection both equatorward and inwards, that results in a correct latitudinal and temporal distribution of the toroidal field and also allows the penetration of the toroidal fields down into the stable layers where they can acquire further amplification. Besides, this mechanism plays an important role in reproducing the correct field parity (anti-symmetric) on both solar hemispheres. We have also found that the eta-quenching may lead to the formation of long-lived small structures of toroidal field which resemble the flux-tubes that are believed to exist at the base of the convection zone. The magnetic fields that are formed thanks to the eta-quenching can be up to ~ twice as larger as the magnetic structures which are developed without this effect. Finally, a number of theoretical works in the last years have called the attention to the role of magnetic helicity conservation in the dynamo processes, giving a new life to the turbulent dynamo model as proposed by Parker. With the aim to study the role of magnetic helicity and explore a more realistic dynamical description of the dynamo mechanism, we have also recently built a 3D convective numerical model (based on the MHD-Goudunov type PLUTO code) where we try to reproduce the natural scenario of the solar interior where the dynamo might take place. We have studied the evolution of a seed field embedded in an initially steady state convection layer. Our preliminary results indicate that convection can easily drive the dynamo action, even in the case without rotation. However, in the rotating cases, the dynamo appears to produce a larger amount of large scale (coherent) magnetic field when compared to the case without rotation where small scale fluctuating fields are dominant. These results support the existence of a turbulent mean field dynamo, but furthermore detailed analysis is still required.

One of the extraordinary properties of the Sun is the observed range of motion scales from the convection granules to the cyclic variation of magnetic activity. The Sun's magnetic field exhibits coherence in space and time on much larger scales than the turbulent convection that ultimately powers the dynamo. Motivated by the scale separation considerations, in this thesis we study the parametric scale selection of dynamo action. Although helioseismology has made a lot of progress in the study of the solar interior, the precise motions of plasma are still unknown. In this work, we assume that the model flow is forced with helical viscous body forces acting on different characteristic scales and weak and strong large-scale shear flows that are believed to be present near the base of the convection zone. In this thesis, we look for numerical evidence of a large-scale magnetic field relative to the characteristic scale of the model flow. The investigation is based on the simulations of incompressible MHD equations in elongated triply-periodic domains. To commence the investigation, a linear stability analysis of the coarsening instability in a one-dimensional periodic system is performed to study the stability threshold in the mean-field limit that assumes large scale separation in the system. The simulations are used to discriminate between different forms of the mean-field α -effect and domain aspect ratio. The notion of scale selection refers to methods for estimating characteristic scales. We define the dynamo scale through the characteristic scales of the underlying model flow, forcing and the realised magnetic field. The aspect ratio of the elongated domains plays a crucial role in all considered cases. In Part II, we examine the dynamo generated by the imposed model flows. The transition from large-scale dynamo at the onset to small-scale dynamo as we increase Rm is smooth and takes place in two stages: a fast transition into a predominantly small-scale magnetic energy state and a slower transition into even smaller scales. The long wavelength perturbation imposed on the ABC flow in the modulated case is not preserved in the eigenmodes of the magnetic field. In the presence of the linear (semi-linear shearing-box approximation) and the sinusoidal shearing motions, the field again undergoes a smooth transition at the slow non-sheared rate, which is associated with the balance of the advection and diffusion terms in the induction equation. Part III considers the nonlinear extension of the analysis in Part II, where the incompressible cellular and sheared flows interact with the exponentially growing magnetic field via the Lorentz force in the dynamical regime. Both sheared and non-sheared helical cellular flows become unstable to large-scale perturbations even in the limit of high viscosity. Due to the helical properties of the imposed forcing, the inverse cascade of helicity leads to energy accumulation in the largest scales of the domain, albeit the characteristic lengthscale exhibits the transitional nature at a highly reduced rate in the mean-field limit. As Rm is increased, the transition resembles that of the kinematic regime. The unique properties of the anisotropic shear reduce the componentality of the system, which in turn is able to half the rate of transition from the large-scale dynamo at the onset to a small-scale one.

This thesis is based on a study conducted at the City Library Dynamo in Gothenburg where data have been collected through qualitative interviews with young people aged 15 - 25 years. Our intention was to examine what young people think about the City Library Dynamo as a venue, and how they perceive its activities and functions.In order to compare two different cultural venues for young people, where Dynamo is one, interviews were also conducted at a location other than the library, at Arena 29, a cultural activity house for young people in Gothenburg. Twelve qualitative and semi-structured interviews were conducted in order to collect data which was then transcribed and structured. As a theoretical framework we have used the new model for the public library, developed by Hvenegaard, Jochumsen and Skot-Hansen 2010.Our result shows a thoroughly positive image of the City Library Dynamo, particularly as a meeting and study place. Young people stated that they felt welcome and that the City Library Dynamo was designed and tailored to match their needs. Through our interviews, we understood that the need to feel recognized and welcomed is primary for this age group, regardless the type of institution. / Program: Bibliotekarie

When a ferromagnet is heated, it loses its magnetism. Stars and planets have magnetic fields, as does the Earth. But it is known that the center of the Earth is very hot. Therefore, to sustain the large magnetic field of a planet, we cannot look to simple ferromagnetism like that of a bar magnet, but we have to look at the movement of electric charges within the Earth’s molten core to generate magnetic field. This magnetic field sustainment against ohmic dissipation by turbulent flow is referred to as the turbulent dynamo effect. Theoretical research into the mechanisms that create the dynamo has been actively pursued for several decades, culminating recently in massive computer simulations of the Earth’s core. Most of these studies have employed the equations of magnetohydrodynamics (MHD), a nonlinear theory of electrically conducting fluids. The EDQNM (Eddy-Damped Quasi-Normal Markovian) closure is a statistical model designed so that the turbulence equations derived from Navier-Stokes dynamics can be closed and satisfy the realizability condition of positivity of the kinetic energy spectrum. In case of MHD turbulence, realizability requires more work. We have proved in an earlier work that equations analogous to those expected of the EDQNM closure for MHD without mean fields satisfy the appropriate realizability conditions (Turner and Pratt 1999). In this work, we discuss requirements needed to make the MHD equations realizable with mean fields, extending those of neutral fluid turbulence by Turner [1]. Finally, we discuss direct numerical simulations and the correspondence of the statistical theories with simulation results.

Sous l'effet combiné de la rotation rapide et de l'interaction gravitationnelle avec une lune avoisinante, un corps céleste est elliptiquement déformé (marées). Dans les zones liquides à l'intérieur de la planète, cette déformation rend les lignes de courant elliptiques. Cet écoulement elliptique peut être instable, et des ondes inertielles peuvent croître à des amplitudes importantes. Ce mécanisme offre donc un alternatif à la convection pour exciter des écoulements dans les intérieurs planétaires, et donc aussi pour la génération du champ magnétique par effet dynamo. En première instance, il est important de mieux comprendre comment l'écoulement elliptique évolue après sa déstabilisation initiale. Nous proposons un modèle théorique, et nous étudions les scénarios de transition vers des écoulements de plus en plus complexes dans un système modèle en géométrie cylindrique. Nous mettons en place une expérience qui vise à étudier le même problématique, utilisant un métal liquide comme fluide, et mettant l'ensemble sous champ. Nous montrons qu'il est possible de se servir du champ magnétique induit comme méthode de détection des écoulements excités par l'instabilité. A champ magnétique imposé fort, la force de Lorentz devient non-négligeable et nous montrons comment celle-ci agit sur l'instabilité elliptique. Des études en géométrie cylindrique et sphéroïdales sont présentées. Le problème de la dynamo elliptique est de grande importance à l'échelle géophysique. Par une approche numérique, nous trouvons que les ondes inertielles, peuvent exciter une dynamo. Nous proposons une modélisation théorique pour le mécanisme de la dynamo d'ondes inertielles.

Cette thèse s'inscrit dans le contexte général de l'étude des processus dynamiques intervenant dans les étoiles tels que la convection, la rotation ou le champ magnétique et de leurs interactions non-linéaires. Les résultats de simulations numériques obtenus avec le code 2D éléments finis STELEM et le code pseudo-spectral 3D ASH sont présentés. La première partie de cette thèse concerne la modélisation globale de la dynamo solaire, mécanisme de régénération du champ magnétique. Via des simulations numériques 2D utilisant la théorie des champs moyens, j'ai pu étudier l'influence d'une circulation méridienne au profil complexe dans les modèles de Babcock-Leighton. Même si ces modèles sont capables de reproduire une période de 22 ans, de nombreuses caractéristiques du cycle telles que la migration des taches solaires vers l'équateur sont perdues. Nous montrons que des doutes peuvent être formulés sur la capacité de ces modèles à rendre compte du fonctionnement réel de la dynamo solaire. Dans l'objectif de mieux contraindre les effets de la variabilité du cycle solaire sur le climat terrestre, nous présentons ensuite un premier effort d'application en physique solaire de techniques de prédiction sophistiquées utilisées en météorologie. J'ai également pu effectuer les premiers calculs MHD 3D en géométrie sphérique d'une des étapes clés de la dynamo : l'évolution non-linéaire de structures magnétiques de la base de la zone convective vers la surface où elles émergent sous forme de régions actives. Les effets globaux de la force de courbure magnétique et des écoulements moyens sont pris en compte. Des champs faibles sont susceptibles d'être modulés par les mouvements convectifs, favorisant ainsi l'émergence à des longitudes privilégiées. Nous montrons qu'il est nécessaire de prendre en compte l'effet de la convection dans l'angle de tilt et non d'expliquer la loi de Joy uniquement par la rotation et la force de Coriolis induite. L'introduction d'une atmosphère dans ces modèles est une étape vers une vision 3D globale du Soleil.

Au cours de cette thèse, nous avons étudié les mécanismes d'induction à l'origine de l'instabilité dynamo dans des écoulements de métaux liquides à grand nombre de Reynolds magnétique (Rm). Les écoulements considérés sont pleinement turbulents et présentent des fluctuations sur une large gamme d'échelles spatio-temporelles. En mesurant le champ induit lorsqu'un champ extérieur est appliqué à un écoulement de gallium liquide (Rm<5) ou de sodium liquide (Rm<50), nous nous sommes intéressé aux questions suivantes : Existe-t-il un effet coopératif des petites échelles de la turbulence pouvant contribuer au champ induit à grande échelle ? Si les résultats de la théorie de champ moyen suggèrent la possibilité d'un effet coopératif pouvant induire un champ magnétique à grande échelle, les mesures effectuées dans les expériences du tore de Perm, et VKG de Lyon, montrent que la contribution des petites échelles est négligeable devant celle des grandes échelles de l'écoulement. Comment décrire les effets d'induction produits par les mouvements à grande échelle ? En mesurant, à bas Rm(Rm<5), les profils de champ induit le long d'un rayon dans l'expérience VKG, nous montrons que l'écoulement de von Karman contrarotatif présente un comportement turbulent à grande échelle. L'écoulement passe 50% du temps dans des configurations très éloignées de sa structure moyenne, ce qui provoque de larges fluctuations des mécanismes d'induction, et peut les rendre inefficaces pendant des durées supérieures au temps de diffusion magnétique. Les résultats expérimentaux obtenus, tant dans le gallium que dans le sodium, suggèrent que le caractère turbulent de l'écoulement ne peut avoir qu'un impact faible sur le seuil de l'instabilité alors les fluctuations aux grandes échelles de l'écoulement peuvent remettre en question l'analyse cinématique basées sur le seul écoulement moyen.Dans une seconde partie de la thèse, nous explorons numériquement les mécanismes d'induction dans un écoulement constitué d'un ensemble de colonnes hélicitaires organisées le long d'un anneau. Pour un tel écoulement qui reproduit la structure des colonnes de Busse de la convection thermique dans le noyau terrestre, nous montrons, à l'aide d'une technique itérative, que des modes dipolaires et quadrupolaires peuvent être entretenus. Le quadrupôle semble toujours favorisé par rapport au dipôle et le bouclage du cycle dynamo se fait entre les composantes radiale et toroïdale du champ magnétique. Les résultats obtenus pour ce système simple soulignent le lien étroit existant entre la géométrie de l'expérience dynamo de Karlsruhe et le problème de la génération du champ magnétique terrestre dans le modèle de convection de Busse.

Many of the celestial bodies we know are found to be magnetized:the Earth, many of the planets so far discovered, the Sun and other stars,the interstellar space, the Milky Way and other galaxies.The reason for that is still to be fully understood, and this work is meant to be a step in that direction. The dynamics of the interstellar medium is dominated by events likesupernovae explosions that can be modelled as irrotational flows.The first part of this thesis is dedicated to the analysis of some characteristics of these flows, in particular how they influencethe typical turbulent magnetic diffusivity of a medium, and it is shownthat the diffusivity is generally enhanced, except for some specific casessuch as steady potential flows, where it can be lowered.Moreover, it is examined how such flows can develop vorticity when they occur in environments affected by rotation or shear,or that are not barotropic. Secondly, we examine helical flows, that are of basic importance for the phenomenon of the amplification of magnetic fields, namely the dynamo.Magnetic helicity can arise from the occurrence of an instability: here we focus on theinstability of purely toroidal magnetic fields, also known as Tayler instability.It is possible to give a topological interpretation of magnetic helicity.Using this point of view, and being aware that magnetic helicity is a conserved quantity in non-resistive flows,it is illustrated how helical systems preserve magnetic structureslonger than non-helical ones. The final part of the thesis deals directly with dynamos.It is shown how to evaluate dynamo transport coefficients with two of the most commonly used techniques, namely theimposed-field and the test-field methods.After that, it is analyzed how dynamos are affected by advectionof magnetic fields and material away from the domain in which theyoperate.It is demonstrated that the presence of an outflow, likestellar or galactic winds in real astrophysical cases,alleviates the so-calledcatastrophic quenching, that is the damping of a dynamoin highly conductive media, thus allowing the dynamo process to work better. / <p>At the time of the doctoral defence the following paper was unpublished and had a status as follows: Paper nr 5: Submitted</p>

The Sun, by the virtue of its proximity to Earth, serves as an excellent astrophysical laboratory for testing our theoretical ideas. The Sun displays a plethora of visually awe-inspiring phenomena including flares, prominences, sunspots, corona, CMEs and uncountable others. It is now known that it is the magnetic field of the Sun which governs all these and also the geomagnetic storms at the Earth, which owes its presence to the interaction between the geomagnetic field and the all-pervading Solar magnetic field in the interplanetary medium. Since the solar magnetic field affects the interplanetary space around the Earth in a profound manner, it is absolutely essential that we develop a comprehensive understanding of the generation and manifestation of magnetic fields of the Sun. This thesis aims at developing a state-of-the-art dynamo code SURYA1taking into account important results from helioseismology and magnetohydrodynamics. This dynamo code is then used to study various phenomenon associated with solar activity including evolution of solar parity, response to stochastic fluctuations, helicity of active regions and prediction of future solar cycles. Within last few years dynamo theorists seem to have reached a consensus on the basic characteristics of a solar dynamo model. The solar dynamo is now believed to be comprised of three basic processes: (i)The toroidal field is produced by stretching of poloidal field lines primarily inside the tachocline – the region of strong radial shear at the bottom of the convection zone. (ii) The toroidal field so formed rises to the surface due to magnetic buoyancy to form active regions. (iii) Poloidal field is generated at the surface due to decay of tilted active regions – an idea attributed to Babcock (1961) & Leighton (1969). The meridional circulation then carries the poloidal field produced near the surface to the tachocline. The profile of the solar differential rotation has now been mapped by helioseismology and so has been the poleward branch of meridional circulation near the surface. The model I describe in this thesis is a two-dimensional kinematic solar dynamo model in a full sphere. Our dynamo model Surya was developed over the years in stages by Prof. Arnab Rai Choudhuri, Dr. Mausumi Dikpati, Dr. Dibyendu Nandy and myself. We provide all the technical details of our model in Chap. 2 of this thesis. In this model we assume the equatorward branch of the meridional circulation (which hasn’t been observed yet), to penetrate slightly below the tachocline (Nandy & Choudhuri 2002, Science, 296, 1671). Such a meridional circulation plays an important role in suppressing the magnetic flux eruptions at high latitudes. The only non-linearity included in the model is the prescription of magnetic buoyancy. Our model is shown to reproduce various aspects of observational data, including the phase relation between sunspots and the weak, efficient. An important characteristic of our code is that it displays solar-like dipolar parity (anti-symmetric toroidal fields across equator) when certain reasonable conditions are satisfied, the most important condition being the requirement that the poloidal field should diffuse efficiently to get coupled across the equator. When the magnetic coupling between the hemispheres is enhanced by either increasing the diffusion or introducing an α ff distributed throughout the convection zone, we find that the solutions in the two hemispheres evolve together with a single period even when we make the meridional circulation or the α effect different in the two hemispheres. The effect of diffusive coupling in our model is investigated in Chap. 3. After having explored the regular behaviour of the solar cycle using the dynamo code we proceed to study the irregularities of the Solar cycle.We introduce stochastic fluctuations in the poloidal source term at the solar surface keeping the meridional circulation steady for all the numerical experiments. The dynamo displays oscillatory behaviour with variable cycle amplitudes in presence of fluctuations with amplitudes as large as 200%. We also find a statistically significant correlation between the strength of polar fields at the endofone cycle and the sunspot number of the next cycle. In contrast to this there exist a very poor correlation between the sunspot number of a cycle and the polar field formed at its end. This suggests that during the declining phase of the sunspot cycle poloidal field generation from decaying spots takes place via the Babcock-Leighton mechanism which involves randomness and destroys the correlation between sunspot number of a cycle and the polar at its end. In addition to this we also see that the time series of asymmetries in the sunspot activity follows the time series of asymmetries in the polar field strength with a lag of 5 years. We also compare our finding with available observational data. Although systematic measurements of the Sun’s polar magnetic field exist only from mid-1970s, other proxies can be used to infer the polar field at earlier times. The observational data indicate a strong correlation between the polar field at a sunspot minimum and the strength of the next cycle, although the strength of the cycle is not correlated well with the polar field produced at its end. We use these findings about the correlation of polar fields with sunspots to develop an elegant method for predicting future solar cycles. We feed observational data for polar fields during the minima of cycle n into our dynamo model and run the code till the next minima in order to simulate the sunspot number curve for cycle n+1. Our results fit the observed sunspot numbers of cycles 21-23 reasonably well and predict that cycle 24 will be about 30–35% weaker than cycle 23. We fit that the magnetic diffusivity in the model plays an important role in determining the magnetic memory of the Solar dynamo. For low diffusivity, the amplitude of a sunspot cycle appears to be a complex function of the history of the polar field of earlier cycles. Only if the magnetic diffusivity within the convection zone is assumed to be high (of order 1012cms−1), we are able to explain the correlation between the polar fiat a minimum and the next cycle. We give several independent arguments that the diffusivity must be of this order. In a dynamo model with diffusivity like this, the poloidal field generated at the mid-latitudes is advected toward the poles by the meridional circulation and simultaneously diffuses towards the tachocline, where the toroidal field for the next cycle is produced. The above ideas are put forward in Chap. 6. We next come to an important product of the dynamo process namely the magnetic helicity. It has been shown independently by many research groups that the mean value of the normalized current helicity αp= B (Δ×B)/B2in solar active regions is of the order of 10−8m−1, predominantly negative in the northern hemisphere, positive in the southern hemisphere. Choudhuri (2003, Sol. Phys., 215, 31)developed a model for production of the helicity of the required sign in a Babcock-Leighton Dynamo by wrapping of poloidal field lines around a fluxtube rising through the convection zone. In Chap. 7 we calculate helicities of solar active regions based on this idea. Rough estimates based on this idea compare favourably with the observed magnitude of helicity. We use our solar dynamo model to study how helicity varies with latitude and time. At the time of solar maximum, our theoretical model gives negative helicity in the northern hemisphere and positive helicity in the south, in accordance with observed hemispheric trends. However, we fit that during a short interval at the beginning of a cycle, helicities tend to be opposite of the preferred hemispheric trends. After calculating the sign and magnitude of helicity of the sunspots we worry about the distribution of helicity inside a sunspot. In Chap. 8 we model the penetration of a wrapped up background poloidal field into a toroidal magnetic flux tube rising through the solar convective zone. The rise of the straight, cylindrical flux tube is followed by numerically solving the induction equation in a comoving Lagrangian frame, while an external poloidal magnetic field is assumed to be radially advected onto the tube with a speed corresponding to the rise velocity. One prediction of our model is the existence of a ring of reverse current helicity on the periphery of active regions. On the other hand, the amplitude of the resulting twist depends sensitively on the assumed structure (ffvs. concentrated/intermittent) of the active region magnetic field right before its emergence, and on the assumed vertical profile of the poloidal field. Nevertheless, in the model with the most plausible choice of assumptions a mean twist comparable to the observational results. Our results indicate that the contribution of this mechanism to the twist can be quite find under favourable circumstances it can potentially account for most of the current helicity observed in active regions.