Academic literature on the topic 'Simulation of magnetic fields'

Les dispersions col·loïdals, un terme encunyat pel científic escocès Thomas Graham el 1861, han estat objecte d’interès en diferents àrees científiques durant més d'un segle. Una dispersió col·loïdal es caracteritza per l’existència d'una fase dispersa uniformement distribuïda dins un medi dispersiu. Diferents compostos entren dins aquesta categoria, com els aerosols (fum, boira, núvols o pols), les escumes, les emulsions (maionesa o llet) o els gels (mantega o melmelada). Les millores recents en la síntesi de partícules i l'estabilitat col·loïdal han impulsat la millora en el disseny de nous col·loides, conferint-los les propietats requerides en cada aplicació. Entre la gran varietat de dispersions col·loïdals (existents en la naturalesa o dissenyades per l'home), hem estudiat un tipus singular de dispersions on les partícules col·loïdals mostren un comportament superparamagnetic anomenades dispersions col·loïdals superparamagnètiques. En aquestes dispersions, sorgeixen característiques sorprenents quan un camp magnètic extern és aplicat, com a conseqüència del balanç entre les interaccions característiques entre col·loides i la interacció magnètica anisotròpica dipol-dipol entre les partícules col·loïdals constituents. Al llarg d'aquesta tesi s'ha utilitzat diferents models teòrics i de simulació per tractar diferents fenòmens que apareixen en aquestes dispersions col·loïdals superparamagnètiques. Per una banda, hem mostrat com l’aplicació de camps magnètics uniformes a aquestes dispersions indueix l’agregació reversible de les partícules superparamagnètiques. A la vista dels models teòrics i simulacions, hem proposat un nou criteri basat en les propietats físiques de les dispersions col·loïdals per predir la formació d'agregats, i la seva validesa s'ha discutit comparant el comportament predit amb resultats experimentals. Hem aportat evidencies de la existència d'un estat d'equilibri on els agregats assoleixen una distribució de mides estable, un fet ja suggerit amb anterioritat però establert sense prou claredat. També ens hem centrat en la descripció de la cinètica de creixement d'aquests agregats i en la seva implicació en diferents fenòmens observats experimentalment. La necessitat d'assolir escales de temps grans, com en certes situacions experimentals, ha motivat el desenvolupament de nous models i estratègies de simulació per reduir els temps de càlcul requerits en simulacions estàndard. Hem presentat un nou model de simulació que proporciona un mètode fiable i més ràpid per descriure la formació d'estructures en forma de cadena que apareixen en dispersions superparamagnètiques. El model ha estat validat comparant-ne els resultats obtinguts amb altres resultats de simulacions estàndard de Dinàmica de Langevin i s'ha aplicat a situacions experimentals, com ara el temps de relaxació T2 dels protons en solucions aquoses de nanopartícules superparamagnètiques. Mencionar també que aquest model de simulació ha estat implementat i el corresponent programari s’ha posat a disposició de la comunitat científica de forma gratuïta, concebut com una eina de simulació que pot ser ampliada fàcilment per resoldre altres problemes d’interès. Per altra banda, també hem discutit diferents efectes que sorgeixen com a conseqüència de l’aplicació de camps magnètics inhomogenis a aquestes dispersions superparamagnètiques. En concret, hem estudiat el moviment de les partícules magnètiques disperses en fluids a través de camps magnètics inhomogenis, el que es coneix com magnetoforesi. Per a tal efecte, hem centrat els esforços en la descripció de la separació magnètica de col·loides mitjançant l’aplicació de gradients de camp magnètic uniformes, des de dispersions superparamagnètiques a mescles de col·loides amb diferent resposta magnètica. Hem validat aquests models teòrics comparant-los amb simulacions per ordinador i n’hem discutit la seva utilitat comparant-ne les prediccions amb resultats experimentals. L’anàlisi racional d'aquests resultats proporciona un marc idoni per a millorar el disseny i el rendiment de diferents separadors magnètics, així com plantejar noves estratègies de separació, com per exemple la separació cooperativa en dispersions superparamagnètiques. Existeixen, encara, problemes oberts que esperem que aquest treball ajudi a afrontar com, per exemple, entendre la interconnexió entre les estructures induïdes en dispersions superparamagnètiques i la seva dinàmica d’agregació. Aquest és un aspecte important en una gran varietat d'aplicacions industrials i de laboratori com són els processos de separació magnètica, tractament d’aigües residuals i eliminació de contaminants, immunoassaigs en aplicacions clíniques o la creació de nous materials supramoleculars. Tanmateix, esperem que els resultats que es presenten al llarg d'aquest document encoratgin nous estudis dins el camp de col·loides magnètics, ja sigui perfeccionant els resultats i mètodes aquí presentats o contribuint al desenvolupament de noves estratègies per afrontar problemes encara per resoldre.<br>Colloidal dispersions, a term coined by the Scottish scientist Thomas Graham in 1861, have been the subject of interest in different scientific areas during more than a century. A colloidal dispersion is characterized by the existence of a dispersed phase uniformly distributed throughout a dispersion medium. Many different compounds fall in this category like aerosols (smog, fog, clouds or dust), foams, emulsions (mayonnaise or milk) or gels (butter or jelly). Recent improvements in particle synthesis and colloidal stability have boosted the controlled design of new colloids on demand, targeting the required properties for each application. Among the large variety of different colloidal dispersions (either found in nature or man-made), we have studied a singular type of such dispersions where the colloids have a superparamagnetic behavior called superparamagnetic colloidal dispersions. In these dispersions, surprising features arise under the application of an external magnetic field, as a consequence of the interplay between characteristic colloidal interactions and the anisotropic magnetic dipole-dipole interaction between their constituent colloidal particles. Along this thesis we have used different theoretical and simulation methods to discuss a number of phenomena appearing in superparamagnetic colloidal dispersions. On the one hand, we have shown that the application of a uniform magnetic field to such dispersions may induce the reversible aggregation of superparamagnetic particles. In view of theoretical models and computer simulations, a new criterion based on the physical properties of the colloidal dispersion has been proposed to predict the formation of aggregates, and its validity has been discussed by comparing the predicted behavior with experimental results. We have provided evidences of the existence of an equilibrium state, where aggregate sizes acquire a steady distribution, an issue previously suggested but unclear up to now. We have also focused our attention on the growth kinetics of the aggregates and its implications in different phenomena observed in experiments. The need to reach the large time scales of some experiments has motivated the development of new models and simulation strategies to overcome the large time consuming calculations required in standard simulations. We have presented a new simulation model that provides a faster and reliable approach to address the formation of chain-like structures in superparamagnetic dispersions. The model has been validated by direct comparison with standard Langevin Dynamics simulations and has been applied to experimental situations like the T2 relaxation time of protons in aqueous solutions of superparamagnetic nanoparticles. Let us mention that the simulation model has been implemented and the corresponding computer code is free and available to the scientific community, envisaged as a new modeling tool readily extensible to other problems of interest. On the other hand, we have analyzed different effects arising as a consequence of the application of inhomogeneous magnetic fields to such superparamagnetic dispersions. Specifically, we have studied the controlled motion of magnetic particles dispersed in a liquid medium by using inhomogeneous magnetic fields, what is known as magnetophoresis. To do so, we have focused the efforts on the description of the magnetic separation of colloids by the application of uniform magnetic field gradients, from superparamagnetic dispersions to mixtures of colloids with different magnetic response. We have validated the theoretical models adopted against computer simulations and we have discussed their usefulness by comparing the predictions obtained with experimental results. The rational analysis of these results provides a proper starting framework to enhance the design and performance of different magnetic separators, as well as to shape new separation strategies, like the cooperative magnetophoretic separation in superparamagnetic dispersions. There exists, of course, open problems that we hope this work will help to deal with. For instance, a better understanding of the interplay between the induced structures in superparamagnetic dispersions and their aggregation kinetics. This is an important issue in a vast variety of industrial and lab applications as, for example, in magnetic separation-based processes, waste-water treatment and pollutant removal, immunoassays in clinical applications or in the assisted assembly of new supramolecular materials. Nevertheless, we hope that the results presented along this document could encourage further studies in magnetic colloids science, either refining the results and approaches provided here or developing new strategies to face unsolved problems.

付記する学位プログラム名: 京都大学卓越大学院プログラム「先端光・電子デバイス創成学」<br>京都大学<br>新制・課程博士<br>博士(工学)<br>甲第23205号<br>工博第4849号<br>京都大学大学院工学研究科電気工学専攻<br>(主査)教授 小林 哲生, 教授 松尾 哲司, 特定教授 中村 武恒<br>学位規則第4条第1項該当<br>Doctor of Philosophy (Engineering)<br>Kyoto University<br>DFAM

Magnetic fields play a key role in a wide variety of phenomena found on the Sun. One such phenomena is the Coronal Mass Ejection (CME) where a large amount of material is ejected from the Sun. CME’s may directly affect the earth, therefore understanding their origin is of key importance for space weather and the near-Earth environment. In this thesis, the nature and evolution of solar magnetic fields is considered through a combination of Magnetic Flux Transport Simulations and Potential Field Source Surface Models. The Magnetic Flux Transport Simulations produce a realistic description of the evolution and distribution of the radial magnetic field at the level of the solar photosphere. This is then applied as a lower boundary condition for the Potential Field Source Surface Models which prescribe a coronal magnetic field. Using these two techniques, the location and variation of coronal null points, a key element in the Magnetic Breakout Model of CMEs, are determined. Results show that the number of coronal null points follow a cyclic variation in phase with the solar cycle. In addition, they preferentially form at lower latitudes as a result of the complex active latitude field. Although a significant number of coronal nulls may exist at any one time (≈ 17), it is shown that only half may satisfy the necessary condition for breakout. From this it is concluded that while the Magnetic Breakout Model of CMEs is an important model in understanding the origin of the CMEs, other processes must occur in order to explain the observed number of CMEs. Finally, the Magnetic Flux Transport Simulations are applied to stellar magnetic fields and in particular to the fast rotating star HD171488. From this speculative study it is shown that the Magnetic Flux Transport Simulations constructed for the Sun may be applied in very different stellar circumstances and that for HD171488 a significantly higher rate of meridional flow (1200-1400 ms⁻¹) is required to match observed magnetic field distributions.

Design of magnetic component is a key factor in achieving high frequency, high power-density converters. Planar magnetics are widely used in bias power supplies for the benefits of low profile and their compatibility with printed-circuit boards (PCB). The coupled inductors with winding layers sandwiched between two core plates are studied in this dissertation in order to model the self-inductance, winding loss, and core loss. The most challenging task for the plate-core inductor is to model the magnetic field with finite core dimensions, very non-uniform flux pattern, and large fringing flux. The winding is placed near the edge of the core to maximize the energy within the limited footprint and the amount of energy stored outside the core volume is not negligible. The proportional-reluctance, equal-flux (PREF) model is developed to build the contours with equal amount of flux by governing the reluctance of the flux path. The shapes of the flux lines are modeled by different functions that guided by the finite-element simulation (FES). The field from the flux lines enables calculation of inductance, winding loss, and core loss, etc. The inductance matrix including self-inductance and mutual inductance of a coupled inductor is important for circuit simulation and evaluation. The derivation of the inductance matrix of inductors with plate-core structure is described in Chapter 2. Two conditions are defined as common-mode (CM) field and differential-mode (DM) field in order to compute the matrix parameters. The proportional-reluctance, equal-flux (PREF) model introduced is employed to find the CM field distribution, and the DM field distribution is found from functions analogous to that of a solenoid's field. The inductance calculated are verified by flex-circuit prototypes with various dimensions, and the application of the inductance model is presented at the last with normalized parameters to cover structures within a wide-range. In circuit where coupled inductors are used instead of transformers, the phase shift between the primary and secondary side is not always 180 degrees. Therefore, it is important to model the winding loss for a coupled inductor accurately. The winding loss can be calculated from the resistance matrix, which is independent of excitations but only relates to the frequency and geometry. The methodology to derive the resistance matrix from winding losses of coupled inductors is discussed. Winding loss model with 2D magnetic field is improved by including the additional eddy current loss for better accuracy for the plate-core structures. The resistance matrix calculated from the model is verified by both measurement results and finite-element simulation (FES) of coupled-inductor prototypes. Accurate core loss model is required for designing magnetic components in power converters. Most existing core loss models are based on frequency domain calculation and they cannot be implemented in SPICE simulations. The core loss model in the time domain is discussed in Chapter 5 for arbitrary current excitations. An effective ac flux density is derived to simplify the core loss calculation with non-uniform field distribution. A sub-circuit for core loss simulation is established in LTSPICE that is capable of being integrated to the power stage simulation. Transient behavior and accurate simulation results from the LTSPICE matches very well with the FES results. An equivalent circuit for coupled windings is developed for inductors with significant fringing effect. The equivalent circuit is derived from a physical model that captures the flux paths by having a leakage inductor and two mutual inductors on the primary and secondary side. A mutual resistor is added to each side in parallel with one mutual inductor to model the winding loss with open circuit and phase-shift impact. Two time-varying resistors are employed to represent the core loss in the time-domain. The equivalent circuit is verified by both finite-element simulation (FES) and prototypes fabricated with flexible circuit.<br>Ph. D.

Magnetic flux continually emerges from the Sun, rising through the solar interior, emerging at the photosphere in the form of sunspots and expanding into the atmosphere. Observations of sunspot rotations have been reported for over a century and are often accompanied by solar eruptions and flaring activity. In this thesis, we present 3D numerical simulations of the emergence of twisted flux tubes from the uppermost layers of the solar interior, examining the rotational movements of sunspots in the photospheric plane. The basic experiment introduces the mechanism and characteristics of sunspot rotation by a clear calculation of rotation angle, vorticity, magnetic helicity and energy, whereby we find an untwisting of the interior portion of the field, accompanied by an injection of twist into the atmospheric field. We extend this model by altering the initial field strength and twist of the sub-photospheric tube. This comparison reveals the rotation angle, helicity and current show a direct dependence on field strength. An increase in field strength increases the rotation angle, the length of fieldlines extending into the atmosphere, and the magnetic energy transported to the atmosphere. The fieldline length is crucial as we predict the twist per unit length equilibrates to a lower value on longer fieldlines, and hence possesses a larger rotation angle. No such direct dependence is found when varying the twist but there is a clear ordering in rotation angle, helicity, and energy, with more highly twisted tubes undergoing larger rotation angles. We believe the final angle of rotation is reached when the system achieves a constant degree of twist along the length of fieldlines. By extrapolating the size of the modelled active region, we find rotation angles and rates comparable with those observed. In addition, we explore sunspot rotation caused by sub-photospheric velocities twisting the footpoints of flux tubes.

Le travail réalisé au cours de cette thèse concerne le développement du système de bobines de l'expérience n2EDM à l'Institut Paul Sherrer (PSI). Le but de cette expérience est de mettre en évidence de nouvelles sources de violation CP à travers la mesure du moment dipolaire électrique du neutron. L'actuelle limite supérieure sur la mesure de nEDM, $2.9 \cross 10^{-26}$ e.cm (90\% C.L.) à été obtenue par la collaboration RAL-Sussex-ILL en 2006.L'expérience n2EDM vise à améliorer d'un ordre de grandeur la sensibilité statistique en gardant sous contrôle les effets systématiques. Cela requiert la production d'un champ magnétique très uniforme. Les non-uniformités de ce dernier sont en effet responsable de la dépolarisation des neutrons et impliqués dans plusieurs effets systématiques.Dans le premier chapitre, les motivations physiques sont discutées.Le second chapitre décrit le principe de mesure de l'expérience n2EDM, ainsi que l'importance de l'uniformité du champ magnétique. Le chapitre s'achève par une présentation globale du dispositif expérimental.Le troisième chapitre présente le logiciel COMSOL et discute du design et des performances de la bobine B$_{0}$, en charge de la production du champ magnétique principal.Dans le quatrième chapitre, le système de bobines correctrices chargées de corriger les non-uniformités du champ magnétique et celles devant produire des gradients spécifiques sont présentées.Finalement, le cinquième et dernier chapitre présente l'étude des dipôles magnétiques localisés et de leur influence sur l'expérience<br>This work presents the design of the coils system developed for the n2EDM experiment at the Paul Sherrer Institute (PSI). The goal of this experiment is to reveal new sources of CP violation through the measurement of the neutron electric dipole moment. The current upper limit of the nEDM measurement, $2.9 \cross 10^{-26}$ e.cm (90\% C.L.) was achieved by the RAL-Sussex-ILL collaboration in 2006.The n2EDM experiment aims at improving by one order of magnitude the statistical sensitivity while keeping under control the systematics effects. It requires to produce a very uniform field, its non-uniformities being responsible of the neutron's depolarization and of severals systematic effects.In the first chapter, the theoretical motivation are discussed.The second chapter describes the measurement principle of the n2EDM experiment, as well as the importance of the magnetic field uniformity. This chapter ends by an overview of the apparatus.The third chapter introduces the COMSOL software and discuss the design and the performances of the B0 coil, in charge of the production of the main magnetic field.In the fourth chapter, the correcting coils used to suppress the non-uniformities of the magnetic field and the ones which produce specific gradients are presented.Finally, the fifth and last chapter talks about the study of localised magnetic dipoles and their influence on the experiment

Cette thèse consiste en l'étude expérimentale et numérique des processus de formation des particules de suie au sein des flammes laminaires non-pré-mélangées et partiellement prémélangées sous l'influence d'un champ magnétique ou d'une stimulation acoustique. Dans une premiére étape, la capacité du code CIAO à prédire la fraction volumique de suie dans une flamme axisymétrique est étudiée. Par la suite, deux flammes subissant une stimulation acoustique ont été étudiées. Les résultats peuvent être utilisés pour améliorer les modèles de suie futurs, en particulier concernant les différentes échelles temporelles de la chimie en phase gazeuse, et la formation d'hydrocarbures polyaromatiques (PAH) et de suie couplée avec des flux transitoires. Pour étudier la formation des particules de suie sous l'influence de gradients de champ magnétique, un brûleur de type Santoro est utilisé. Les techniques de mesure utilisées dans le cadre de cette thèse sont l'imagerie directe à haute cadence, la technique Background Oriented Schlieren (BOS) et la méthode d'Absorption/Emission Modulée (MAE). Une augmentation de la fraction volumique de suie intégrée a été mise en évidence lorsque le gradient de champ magnétique est ascendant. Une analyse de stabilité linéaire locale appliquée à l'écoulement non-visqueux est présentée pour une flamme sous l'influence de la perturbation magnétique envisagée. Le gradient de champ magnétique provoque alors une réduction du taux d'amplification. De fait, l'étude est complété par l'identification d'un domaine où les flammes qui oscillent naturellement peuvent être stabilisées et contrôlées par des gradients de champ magnétique<br>In this thesis light is shed on the soot formation processes in laminar coflow flames influenced by magnetic field gradients and acoustic forcing. Both influences have been assessed experimentally and numerically. First, the CIAO in-house code's ability to predict soot volume fraction fields in a steady coflow flame is studied. Then, two acoustically forced cases were studied. These findings are used to improve future soot models, especially, concerning the different time scales of gas phase chemistry and the formation of polycyclic aromatic hydrocarbons (PAH) and soot coupled with unsteady flows. To investigate soot formation under magnetic field gradients, a Santoro type burner is used. The measurement techniques applied in the course of this thesis are high-speed luminosity measurements, Background Oriented Schlieren (BOS) and one- and two-color Modulated Absorption/Emission (MAE) techniques. The magnetic field impact on soot formation was first studied experimentally in steady laminar flames. A scaling of soot production similar to the increased integrated soot volume fraction with increased oxygen content in the coflow was documented. A local inviscid stability analysis is presented for an ethylene coflow flame to investigate the flame's response to small perturbations of the mean velocity, temperature, fuel, and oxygen massfraction under magnetic field exposure. The magnetic field is found to reduce the perturbations' growth rate. The magnetic field study is completed by identifying a domain where naturally oscillating flames can be stabilized and controlled by magnetic field gradients