Cette thèse présente les avancées dans l'étude des étoiles naines blanches magnétiques. L'étude des étoiles naines blanches en général, le state final d'évolution de près de 95% des étoiles de notre galaxie, permet d'obtenir de l'information cruciale sur leurs progéniteurs. Se pencher sur les propriétés des champs magnétiques des étoiles naines blanches par opposition à celles de leur progéniteur, beaucoup plus difficiles à observer en partie à cause de la faible intensité du champ, est bien plus réalisable. Plusieurs hypothèses ont été formulées afin de décrire l'origine et l'évolution de ces objets atypiques. Que les champs soient d'origine fossile suite à l'évolution d'une étoile isolée et conservation du flux magnétique, ou créés lors de la rotation rapide de la fusion de deux étoiles, il nous faut bien comprendre leur résultat, les naines blanches magnétiques, avant de pouvoir retracer leur évolution. Toutefois, les modèles de naines blanches magnétiques d'aujourd'hui reposent sur un nombre d'approximation, qui ne sont valides jusqu'à une relativement faible intensité de champ. Ceci a été la motivation derrière ce projet de doctorat. Nous avons implémenté un traitement des raies d'absorption utilisant le calcul des énergies de transition de l'atome d'hydrogène et d'hélium sous champs magnétiques arbitraires. Ces calculs, fournis par le groupe de l'université de Tübingen en Allemagne, ont utilisé une approche numérique à la résolution de l'Hamiltonien de l'atome d'hydrogène et d'hélium en présence d'un champ magnétique d'intensité arbitraire. Cet ajout aux modèles d'atmosphères permet de modéliser la position et l'intensité des raies d'absorption dans le spectre des étoiles. Une procédure de discrétisation de la surface visible de l'étoile nous permet de modéliser des champs magnétiques avec une géométrie arbitraire, tel qu'un dipôle décentré et incliné par rapport à l'observateur. Ces nouveaux outils ont été utilisés afin d'étudier en premier lieu un ensemble des naines blanches magnétiques avec une atmosphère riche en hydrogène. De ces résultats, nous avons déterminé une distribution de masse de ces étoiles, avec une masse moyenne significativement plus élevée que leurs homologues non-magnétiques, tels qu'attendu par les théories d'évolution binaires. Les informations extraites des différentes caractéristiques des distributions obtenues suite à cette analyse ne nous permettent cependant pas de favoriser une hypothèse d'évolution plutôt qu'une autre. Suite à ceci, celles avec une atmosphère riche en hélium ont été les prochaines à être analysées. Nous avons ainsi déterminé rigoureusement, pour la première fois, les paramètres magnétiques de ces étoiles riches en hélium. / This thesis presents advances in the study of magnetic white dwarf stars. The study of white dwarf stars in general, the final state of evolution of nearly 95% of the stars in our galaxy, provides crucial information about their progenitors. It is much more feasible to study the magnetic field properties of white dwarf stars as opposed to their progenitor stars, which are much more difficult to observe in part because of the weak field strength. Several hypotheses have been formulated to describe the origin and evolution of these atypical objects. Whether the fields are of fossil origin following the evolution of an isolated star and conservation of magnetic flux, or created during the rapid rotation of the merger of two stars, we need to understand their result, the magnetic white dwarfs, before we can trace their evolution. However, today's models of magnetic white dwarfs rely on a number of approximations, which are only valid up to relatively low field strengths. This was the motivation behind this doctoral thesis. We have implemented a treatment of the absorption lines using the calculation of the transition energies of the hydrogen and helium atom under arbitrary magnetic fields. These calculations, provided by the group of the University of Tubingen in Germany, used a numerical approach to the resolution of the Hamiltonian of the hydrogen and helium atom in the presence of a magnetic field of arbitrary intensity. This addition to atmospheric models allows to model the position and intensity of absorption lines in the spectrum of stars. A discretization procedure of the visible surface of the star allows us to model magnetic fields with an arbitrary geometry, such as an offset and inclined dipole. These new tools have been used to study first a set of magnetic white dwarfs with a hydrogen-rich atmosphere. From these results, we have determined a mass distribution of these stars, with an average mass significantly higher than their non-magnetic counterparts, as expected by the binary evolution theories. The information extracted from the different characteristics of the distributions obtained from this analysis does not however allow us to favor one evolutionary hypothesis over another. Following this, those with a helium rich atmosphere were the next to be analyzed. We have thus determined rigorously, for the first time, the magnetic parameters of these helium-rich stars.

In narrow electron bands in which the Coulomb interaction energy becomes comparable to the bandwidth, interactions can drive new quantum phases. In this dissertation, we achieve narrow bands by twisting two atomically thin layers of the semiconducting van der Waals material WSe₂. The resulting moiré potential from the twist angle modulates the electronic bands, yielding minibands of tens of meV on the valence band. We perform transport measurements at cryogenic temperatures and observe signatures of collective phases over twist angles that range from 4 to 5.1°. At half-band filling, a correlated insulator appeared that is tunable with both twist angle and displacement field. Near the boundary between ordered and disordered quantum phases, several experiments have demonstrated metallic behaviour that defies the Landau Fermi paradigm. We find that the metal-insulator transition as a function of both density and displacement field is continuous. At the metal–insulator boundary, the resistivity displays strange metal behaviour at low temperatures, with dissipation comparable to that at the Planckian limit. Further into the metallic phase, Fermi liquid behaviour is recovered at low temperature, and this evolves into a quantum critical fan at intermediate temperatures, before eventually reaching an anomalous saturated regime near room temperature. An analysis of the residual resistivity indicates the presence of strong quantum fluctuations in the insulating phase. We further show via magnetotransport measurements that new correlated electronic phases can exist independent of moiré commensurability, and are instead driven by weak interactions in twisted WSe₂. The first of these phases is an antiferromagnetic metal that is driven by proximity to the van Hove singularity (vHS), which trails a range of incommensurate dopings. The temperature, magnetic field and density dependence of the Hall effect carry signatures of the reconstructed Fermi surface due to itinerant magnetic ordering. The second is an excitonic metal-insulator phase that exists at high external magnetic field in the vicinity of half-filling of the moiré superlattice. For a 4.2° sample, magnetic field dependence of the longitudinal resistance shows metallic behavior at fields above 5 T, but transitions to an insulating state above ∼ 24 T. A detailed analysis of of the Landau fans and the high field 𝝆_𝜘𝛾 near the gap rules out the possibility of a trivial insulator. We propose an Ising excitonic insulator as the most likely scenario. Moreover, in the electron-imbalanced excitonic metal, a set of correlated Landau levels emerge. The observation of tunable collective phases in a simple band, which hosts only two holes per unit cell at full filling, establishes twisted bilayer transition metal dichalcogenides as an ideal platform to study correlated physics in two dimensions on a triangular lattice.

Cette thèse de doctorat présente les résultats d'un relevé spectropolarimétrique visant la détection directe de champs magnétiques dans le vent d'étoiles Wolf-Rayet (WR). Les observations furent entièrement obtenues à partir du spectropolarimètre ESPaDOnS, installé sur le télescope de l'observatoire Canada-France-Hawaii. Ce projet débuta par l'observation d'un étoile très variable de type WN4 appelée EZ CMa = WR6 = HD 50896 et se poursuivit par l'observation de 11 autres étoiles WR de notre galaxie. La méthode analytique utilisée dans cette étude vise à examiner les spectres de polarisation circulaire (Stokes V) et à identifier, au travers des raies d'émission, les signatures spectrales engendrées par la présence de champs magnétiques de type split monopole dans les vents des étoiles observées. Afin de pallier à la présence de polarisation linéaire dans les données de polarisation circulaire, le cross-talk entre les spectres Stokes Q et U et le spectre Stokes V fut modélisé et éliminé avant de procéder à l'analyse magnétique. En somme, aucun champ magnétique n'est détecté de manière significative dans les 12 étoiles observées. Toutefois, une détection marginale est signalée pour les étoiles WR134, WR137 et WR138 puisque quelques-unes de leur raies spectrales semblent indiquer la présence d'une signature magnétique. Pour chacune de ces trois étoiles, la valeur la plus probable du champ magnétique présent dans le vent stellaire est respectivement de B ~ 200, 130 et 80 G. En ce qui concerne les autres étoiles pour lesquelles aucune détection magnétique ne fut obtenue, la limite supérieure moyenne de l'intensité du champ qui pourrait être présent dans les données, sans toutefois être détecté, est évaluée à 500 G. Finalement, les résultats de cette étude ne peuvent confirmer l'origine magnétique des régions d'interaction en co-rotation (CIR) observées chez plusieurs étoiles WR. En effet, aucun champ magnétique n'est détecté de façon convaincante chez les quatre étoiles pour lesquelles la présence de CIR est soupçonnée. / This thesis presents the results of a spectropolarimetric survey aimed at detecting directly the presence of magnetic fields in Wolf-Rayet (WR) stars. The search for the elusive WR fields began by observing the highly variable WN4 star EZ CMa = WR6 = HD 50896 and continued among a sample of eleven bright WR stars. All observations were obtained using the highly-efficient ESPaDOnS spectropolarimeter at the Canada-France-Hawaii telescope. The methodology used in this study attempts to detect the characteristic circular polarization (Stokes V) pattern in strong emission lines that is expected to arise as a consequence of a global magnetic field with a split monopole configuration. Since Stokes V data were affected by significant cross-talk from linear polarization to circular polarization, the spurious cross-talk signal was removed prior to applying the magnetic analysis. In the end, no magnetic fields are unambiguously detected in any of the observed stars. Nonetheless, the data show evidence supporting marginal detections for WR134, WR137 and WR138 for which the most probable field intensities, in the observable parts of the stellar winds, are B ~ 200, 130 and 80 G, respectively. In the case of non-detections, the average field strength upper-limit for the magnetic field is B ~ 500 G. Finally, this study cannot confirm the magnetic origin of co-rotating interaction regions observed in several WR stars since, out of 4 stars showing CIR-type variability, none showed decisive evidence for the presence of magnetic fields.

High image fidelity in Magnetic Resonance Imaging (MRI) relies on precise magnetic field control of encoding gradient fields and background B0 magnetic fields. To ensure a high degree of accuracy in the spatial location of the proton spins and the resultant object geometry, conventional image encoding using linear gradient fields, as well as advanced techniques with non-linear encoding, requires field generating hardware capable of excellent field shaping capabilities and accuracy. Non-homogeneous B0 background fields in MR imaging cause faster relaxation, signal dropout, and geometry distortion, resulting in inferior image quality and reduced diagnostic accuracy. Besides manufacturing imperfections in the magnet and site conditions, the magnetic field inside the imaging object is not homogeneous due to the differences in geometries and magnetic properties of individual human tissues, which is recognized as the primary source of B0 variation in MRI. Considering the differences of B0 conditions across subjects, it is essential for MR imaging to utilize flexible B0 shimming techniques such as active shimming in order to produce a highly homogeneous B0 field. The control capability and optimized control strategy for these magnetic fields require the development of new hardware and methodologies. B0 background field generated by the magnet and the encoding gradient field from gradient coil are two critical pillars of MR imaging. Since the multi-coil array provides advanced shim capability and is proven to be capable of imaging encoding with a compact size, it is considered a perfect component as a combination of B0 shim coil and encoding gradient coil for an accessible head-only MR scanner. MR scanners like this type provide unique features that will enable researchers to develop new MRI methodologies and conduct research into the functionalities of the human brain through more natural human behaviors. Its clinical applications will be more accessible to the general population for disease screening and diagnosis due to its portability and low energy requirements. Since the multi-coil array has the advantage of smaller volume and wall thickness than the traditional gradient coil, its design and implementation is challenging because of its compact space, irregular curved shape of coil elements, mechanical reliability requirements during scan and good thermal control for long working periods. It was the challenges involved in the design and implementation of the multi-coil array that initiated the first project of my dissertation. In this project, we present 1) a novel molding method for the construction of resin-impregnated wire patterns with irregular curved shapes along with a microcontroller-driven motorized machine for automated coil construction, 2) the design and validation of a water-cooling system using multiple parallel pipes impregnated with thermal epoxy, 3) a quality-controlled procedure of building the multi-coil array employing the technique of vacuum resin infusion. A multi-coil array was fabricated successfully and evaluated in multiple sites and then integrated into the first-prototype of the accessible head-only MR scanner. The similar quality of experimental images from the fabricated multi-coil array compared to those from conventional gradient coils indicates that the multi-coil array can effectively shape fields for both image encoding and B0 shimming. Our lab has shown that multi-coil technology offers advanced shim capability when imaging the human brain, but it could potentially benefit the imaging of other organs like the heart. The MR imaging of the heart is subject to dark band artifacts or signal loss caused by B0 inhomogeneity, which can result in misinterpretation of lesions and a reduction in diagnostic accuracy. It has been demonstrated in a recent study that the use of multi-coil techniques can significantly reduce B0 inhomogeneity within the heart based on shim analysis using in vivo B0 maps. Multi-coil arrays are not a standard configuration in commercial scanners but are normally used for research, B0 shimming is typically implemented by using the commonly-installed spherical harmonic shim coils in the first, second, and potentially third orders. The development of multi-coil technology, more in-depth design of the coil structure and geometry as well as the optimal use of the current spherical harmonic shim technology require a thorough understanding of cardiac B0 conditions across subjects and at a population level. Since the in vivo cardiac B0 measurement is not a routine clinical protocol and dedicated in vivo measurement for a large sample size are extremely labor intensive and expensive, the lack of such B0 data is a long-standing problem, especially for the subject groups like pediatric or elderly patients who cannot undergo B0 map measurement with breath hold. This challenge could be resolved by the use of B0 simulation on the basis of structural images from different imaging modalities, assuming that the B0 distributions inside the human heart depends on the anatomical structures surrounding heart and across the entire body. The challenge and assumption led to my second project regarding B0 magnetic field simulation in the human heart. We proposed a novel B0 simulation approach based on chest-abdomen-pelvis structural CT images and validated it using in vivo acquired B0 maps in the heart from the same subjects. This B0 simulation approach was then applied to CT images from more than one thousand subjects and the resultant large set of simulated B0 maps were analyzed with different shim types for searching optimal shim solution based on popular spherical harmonic decomposition. The derived B0 conditions were also statistically analyzed for potential correlation and linear association with demographic parameters of these subjects for investigating potential population-based shim strategy. By the use of in vivo acquisition, we also investigated the B0 magnetic field variation across cardiac cycle and evaluated the impact of these variations on in vivo cardiac B0 shimming. The results of this study allow us to better understand the primary sources and characteristics of B0 distributions in the heart as well as pave the way for developing optimal B0 shim methods within heart in both subject-specific and population-based manners.

Ever since the discovery of van der Waals materials, the condensed matter community has developed a wide spectrum of techniques to probe various phases in these fascinating materials. Among these phases, correlated phenomena are of great importance to physicists, and recent progress on moiré heterostructures offers a highly flexible and tunable platform to study them. It has been established in previous works that twisted WSe₂, a type of semiconductor in the van der Waals family, has great potential in hosting a large number of correlated phases and phase transitions. However, it is believed that commensurability plays a critical role in the stability of correlations. In this thesis, we demonstrate correlated physics in twisted WSe₂ beyond commensurate fillings, as well as their magnetic field dependence, via electric transport measurements. At modest magnetic fields, a Stoner-like instability in the system near van Hove singularities causes a reconstruction of the Fermi surface. On the other hand, at extremely high magnetic fields, the system exhibits reentrant insulating behaviors that are possibly due to the presence of strong excitonic interactions. Furthermore, correlated topological states are observed away from half-filling in the imbalanced excitonic metallic regime. This wide range of tunability once again proves moiré heterostructures as a promising platform to simulate quantum correlation effects on a lattice.

Magnetic flux emergence is the subject of how magnetic fields from the solar interior can rise and expand into the atmosphere to produce active regions. It is the link that joins dynamics in the convection zone with dynamics in the atmosphere. In this thesis, we study many aspects of magnetic flux emergence through mathematical modelling and computer simulations. Our primary aim is to understand the key physical processes that lie behind emergence. The first chapter introduces flux emergence and the theoretical framework, magnetohydrodynamics (MHD), that describes it. In the second chapter, we discuss the numerical techniques used to solve the highly non-linear problems that arise from flux emergence. The third chapter summarizes the current literature. In the fourth chapter, we consider how changing the geometry and parameter values of the initial magnetic field can affect the dynamic evolution of the emerging magnetic field. For an initial toroidal magnetic field, it is found that its axis can emerge to the corona if the tube’s initial field strength is large enough. The fifth chapter describes how flux emergence models can produce large-scale solar eruptions. A 2.5D model of the breakout model, using only dynamic flux emergence, fails to produce any large scale eruptions. A 3D model of toroidal emergence with an overlying magnetic field does, however, produce multiple large-scale eruptions and the form of these is related to the breakout model. The sixth chapter is concerned with signatures of flux emergence and how to identify emerging twisted magnetic structures correctly. Here, a flux emergence model produces signatures found in observations. The signatures from the model, however, have different underlying physical mechanisms to the original interpretations of the observations. The thesis concludes with some final thoughts on current trends in theoretical magnetic flux emergence and possible future directions.

In this thesis examples of translationally invariant one-dimensional (1D) Vlasov-Maxwell (VM) equilibria are investigated. The 1D VM equilibrium equations are equivalent to the motion of a pseudoparticle in a conservative pseudopotential, with the pseudopotential being proportional to one of the diagonal components of the plasma pressure tensor. A necessary condition on the pseudopotential (plasma pressure) to allow for force-free 1D VM equilibria is formulated. It is shown that linear force-free 1D VM solutions correspond to the case where the pseudopotential is an attractive central potential. The pseudopotential for the force-free Harris sheet is found and a Fourier transform method is used to find the corresponding distribution function. The solution is extended to include a family of equilibria that describe the transition between the Harris sheet and the force-free Harris sheet. These equilibria are used in 2.5D particle-in-cell simulations of magnetic reconnection. The structure of the diffusion region is compared for simulations starting from anti-parallel magnetic field configurations with different strengths of guide field and self-consistent linear and non-linear force-free magnetic fields. It is shown that gradients of off-diagonal components of the electron pressure tensor are the dominant terms that give rise to the reconnection electric field. The typical scale length of the electron pressure tensor components in the weak guide field case is of the order of the electron bounce widths in a field reversal. In the strong guide field case the scale length reduces to the electron Larmor radius in the guide magnetic field.

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