The theory of electrostatic probes in strong magnetic fields : Thesis submitted to the Faculty of The Graduate School of the University of Colorado for the Degree Doctor of Philosophy Department of Aerospace Engineering Science

A theory is developed of an electrostatic probe in a fully-ionized plasma in the presence of a strong magnetic field. The ratio of electron Larmor radius to probe transverse dimension is assumed to be small. Poisson's equation, together with kinetic equations for ions and electrons are considered. An asymptotic perturbation method of multiple scales is used by considering the characteristic lengths appearing in the problem. The leading behavior of the solution is found. The results obtained appear to apply to weaker fields also, agreeing with the solutions known in the limit of no magnetic field. The range of potentials for wich results are presented is limited. The basic effects produced by the field are a depletion of the plasma near the probe and a non-monotonic potential surrounding the probe. The ion saturation current is not changed but changes appear in both the floating potential Vf and the slope of the current-voltage diagram at Vf. The transition region extends beyond the space potential Vs,at wich point the current is largely reduced. The diagram does not have an exponential form in this region as commonly assumed. There exists saturation in electron collection. The extent to which the plasma is disturbed is determined. A cylindrical probe has no solution because of a logarithmic singularity at infinity. Extensions of the theory are considered.

Vortex pinning vs superconducting wire network: origin of periodic oscillations induced by applied magnetic fields in superconducting films with arrays of nanomagnets

Hybrid magnetic arrays embedded in superconducting films are ideal systems to study the competition between different physical (such as the coherence length) and structural length scales such as are available in artificially produced structures. This interplay leads to oscillation in many magnetically dependent superconducting properties such as the critical currents, resistivity and magnetization. These effects are generally analyzed using two distinct models based on vortex pinning or wire network. In this work, we show that for magnetic dot arrays, as opposed to antidot (i.e. holes) arrays, vortex pinning is the main mechanism for field induced oscillations in resistance R(H), critical current Ic(H), magnetization M(H) and ac-susceptibility χ ac(H) in a broad temperature range. Due to the coherence length divergence at Tc, a crossover to wire network behaviour is experimentally found. While pinning occurs in a wide temperature range up to Tc, wire network behaviour is only present in a very narrow temperature window close to Tc. In this temperature interval, contributions from both mechanisms are operational but can be experimentally distinguished.

Passenger Exposure to Magnetic Fields due to the Batteries of an Electric Vehicle

In electric vehicles, passengers sit very close to an electric system of significant power. The high currents achieved in these vehicles mean that the passengers could be exposed to significant magnetic fields. One of the electric devices present in the power train are the batteries. In this paper, a methodology to evaluate the magnetic field created by these batteries is presented. First, the magnetic field generated by a single battery is analyzed using finite elements simulations. Results are compared to laboratory measurements, taken from a real battery, in order to validate the model. After this, the magnetic field created by a complete battery pack is estimated and results are discussed.

Theory of a Probe in a Strong Magnetic Field. AT(30-1)-1238-MATT 599

A kinetic approach is used to develop a theory of electrostatic probes in a fully ionized plasma in the presence of a magnetic field. A consistent asymptotic expansion is obtained assuming that the electron Larmor radius is small compared to the radius of the probe. The order of magnitude of neglected terms is given. It is found that the electric potential within the tube of force defined by the cross section of the probe decays non-mono tonic ally from the probe; this bump disappears at a certain probe voltage and the theory is valid up to this voltage. The transition region, which extends beyond plasma potential, is not exponential. The possible saturation of the electron current is discussed. Restricted numerical results are given; they seem to be useful for weaker magnetic fields down to the zero-field limit. Extensions of the theory a r e considered.

Analysis and Design Considerations of an Electric Vehicle Powertrain regarding Energy Efficiency and Magnetic Field Exposure

En esta tesis se analiza el sistema de tracción de un vehículo eléctrico de batería desde el punto de vista de la eficiencia energética y de la exposición a campos magnéticos por parte de los pasajeros (radiación electromagnética). Este estudio incluye tanto el sistema de almacenamiento de energía como la máquina eléctrica, junto con la electrónica de potencia y los sistemas de control asociados a ambos. Los análisis y los resultados presentados en este texto están basados en modelos matemáticos, simulaciones por ordenador y ensayos experimentales a escala de laboratorio. La investigación llevada a cabo durante esta tesis tuvo siempre un marcado enfoque industrial, a pesar de estar desarrollada en un entorno de considerable carácter universitario. Las líneas de investigación acometidas tuvieron como destinatario final al diseñador y al fabricante del vehículo, a pesar de lo cual algunos de los resultados obtenidos son preliminares y/o excesivamente académicos para resultar de interés industrial. En el ámbito de la eficiencia energética, esta tesis estudia sistemas híbridos de almacenamiento de energía basados en una combinación de baterías de litio y supercondensadores. Este tipo de sistemas son analizados desde el punto de vista de la eficiencia mediante modelos matemáticos y simulaciones, cuantificando el impacto de ésta en otros parámetros tales como el envejecimiento de las baterías. Respecto a la máquina eléctrica, el estudio se ha centrado en máquinas síncronas de imanes permanentes. El análisis de la eficiencia considera tanto el diseño de la máquina como la estrategia de control, dejando parcialmente de lado el inversor y la técnica de modulación (que son incluidos en el estudio como fuentes adicionales de pérdidas, pero no como potenciales fuentes de optimización de la eficiencia). En este sentido, tanto la topología del inversor (trifásico, basado en IGBTs) como la técnica de modulación (control de corriente en banda de histéresis) se establecen desde el principio. El segundo aspecto estudiado en esta tesis es la exposición a campos magnéticos por parte de los pasajeros. Este tema se enfoca desde un punto de vista predictivo, y no desde un punto de vista de diagnóstico, puesto que se ha desarrollado una metodología para estimar el campo magnético generado por los dispositivos de potencia de un vehículo eléctrico. Esta metodología ha sido validada mediante ensayos de laboratorio. Otros aspectos importantes de esta contribución, además de la metodología en sí misma, son las consecuencias que se derivan de ella (por ejemplo, recomendaciones de diseño) y la comprensión del problema proporcionada por esta. Las principales contribuciones de esta tesis se listan a continuación: una recopilación de modelos de pérdidas correspondientes a la mayoría de dispositivos de potencia presentes en un vehículo eléctrico de batería, una metodología para analizar el funcionamiento de un sistema híbrido de almacenamiento de energía para aplicaciones de tracción, una explicación de cómo ponderar energéticamente los puntos de operación par-velocidad de un vehículo eléctrico (de utilidad para evaluar el rendimiento de una máquina eléctrica, por ejemplo), una propuesta de incluir un convertidor DC-DC en el sistema de tracción para minimizar las pérdidas globales del accionamiento (a pesar de las nuevas pérdidas introducidas por el propio DC-DC), una breve comparación entre dos tipos distintos de algoritmos de minimización de pérdidas para máquinas síncronas de imanes permanentes, una metodología predictiva para estimar la exposición a campos magnéticos por parte de los pasajeros de un vehículo eléctrico (debida a los equipos de potencia), y finalmente algunas conclusiones y recomendaciones de diseño respecto a dicha exposición a campos magnéticos. ABSTRACT This dissertation analyzes the powertrain of a battery electric vehicle, focusing on energy efficiency and passenger exposure to electromagnetic fields (electromagnetic radiation). This study comprises the energy storage system as well as the electric machine, along with their associated power electronics and control systems. The analysis and conclusions presented in this dissertation are based on mathematical models, computer simulations and laboratory scale tests. The research performed during this thesis was intended to be of industrial nature, despite being developed in a university. In this sense, the work described in this document was carried out thinking of both the designer and the manufacturer of the vehicle. However, some of the results obtained lack industrial readiness, and therefore they remain utterly academic. Regarding energy efficiency, hybrid energy storage systems consisting in lithium batteries, supercapacitors and up to two DC-DC power converters are considered. These kind of systems are analyzed by means of mathematical models and simulations from the energy efficiency point of view, quantifying its impact on other relevant aspects such as battery aging. Concerning the electric machine, permanent magnet synchronous machines are studied in this work. The energy efficiency analysis comprises the machine design and the control strategy, while the inverter and its modulation technique are taken into account but only as sources of further power losses, and not as potential sources for further efficiency optimization. In this sense, both the inverter topology (3-phase IGBT-based inverter) and the switching technique (hysteresis current control) are fixed from the beginning. The second aspect studied in this work is passenger exposure to magnetic fields. This topic is approached from the prediction point of view, rather than from the diagnosis point of view. In other words, a methodology to estimate the magnetic field generated by the power devices of an electric vehicle is proposed and analyzed in this dissertation. This methodology has been validated by laboratory tests. The most important aspects of this contribution, apart from the methodology itself, are the consequences (for instance, design guidelines) and the understanding of the magnetic radiation issue provided by it. The main contributions of this dissertation are listed next: a compilation of loss models for most of the power devices found in a battery electric vehicle powertrain, a simulation-based methodology to analyze hybrid energy storage performance in traction applications, an explanation of how to assign energy-based weights to different operating points in traction drives (useful when assessing electrical machine performance, for instance), a proposal to include one DC-DC converter in electric powertrains to minimize overall power losses in the system (despite the new losses added by the DC-DC), a brief comparison between two kinds of loss-minimization algorithms for permanent magnet synchronous machines in terms of adaptability and energy efficiency, a predictive methodology to estimate passenger magnetic field exposure due to power devices in an electric vehicle, and finally some useful conclusions and design guidelines concerning magnetic field exposure.

Potential theory

In this chapter we will introduce the reader to the techniques of the Boundary Element Method applied to simple Laplacian problems. Most classical applications refer to electrostatic and magnetic fields, but the Laplacian operator also governs problems such as Saint-Venant torsion, irrotational flow, fluid flow through porous media and the added fluid mass in fluidstructure interaction problems. This short list, to which it would be possible to add many other physical problems governed by the same equation, is an indication of the importance of the numerical treatment of the Laplacian operator. Potential theory has pioneered the use of BEM since the papers of Jaswon and Hess. An interesting introduction to the topic is given by Cruse. In the last five years a renaissance of integral methods has been detected. This can be followed in the books by Jaswon and Symm and by Brebbia or Brebbia and Walker.In this chapter we shall maintain an elementary level and follow a classical scheme in order to make the content accessible to the reader who has just started to study the technique. The whole emphasis has been put on the socalled "direct" method because it is the one which appears to offer more advantages. In this section we recall the classical concepts of potential theory and establish the basic equations of the method. Later on we discuss the discretization philosophy, the implementation of different kinds of elements and the advantages of substructuring which is unavoidable when dealing with heterogeneous materials.

Anisotropic magnetoresistive study in bilayer NiFe-NiO for sensor applications

Related with the detection of weak magnetic fields, the anisotropic magnetoresistive (AMR) effect is widely utilized in sensor applications. Exchange coupling between an antiferromagnet (AF) and the ferromagnet (FM) has been known as a significant parameter in the field sensitivity of magnetoresistance because of pinning effects on magnetic domain in FM layer by the bias field in AF. In this work we have studied the thermal evolution of the magnetization reversal processes in nanocrystalline exchange biased Ni80Fe20/Ni-O bilayers with large training effects and we report the anisotropic magnetoresistance ratio arising from field orientation in the bilayer.

Anisotropic magnetoresistive study in bilayer NiFe-NiO for sensor applications

Related with the detection of weak magnetic fields, the anisotropic magnetoresistive(AMR) effect is widely utilized in sensor applications. Exchange coupling between an antiferromagnet (AF) and the ferromagnet (FM) has been known as a significant parameter in the field sensitivity of magnetoresistance because of pinning effects on magnetic domain in FM layer by the bias field in AF. In this work we have studied the thermal evolution of the magnetization reversal processes in nanocrystalline exchange biased Ni80Fe20/Ni-O bilayers with large training effects and we report the anisotropic magnetoresistance ratio arising from field orientation in the bilayer.

Drifting plasma collection by a positive biased tether wire in LEO-like plasma conditions: current measurement and plasma diagnostic

BETs is a three-year project financed by the Space Program of the European Commission, aimed at developing an efficient deorbit system that could be carried on board any future satellite launched into Low Earth Orbit (LEO). The operational system involves a conductive tape-tether left bare to establish anodic contact with the ambient plasma as a giant Langmuir probe. As a part of this project, we are carrying out both numerical and experimental approaches to estimate the collected current by the positive part of the tether. This paper deals with experimental measurements performed in the IONospheric Atmosphere Simulator (JONAS) plasma chamber of the Onera-Space Environment Department. The JONAS facility is a 9- m3 vacuum chamber equipped with a plasma source providing drifting plasma simulating LEO conditions in terms of density and temperature. A thin metallic cylinder, simulating the tether, is set inside the chamber and polarized up to 1000 V. The Earth's magnetic field is neutralized inside the chamber. In a first time, tether collected current versus tether polarization is measured for different plasma source energies and densities. In complement, several types of Langmuir probes are used at the same location to allow the extraction of both ion densities and electron parameters by computer modeling (classical Langmuir probe characteristics are not accurate enough in the present situation). These two measurements permit estimation of the discrepancies between the theoretical collection laws, orbital motion limited law in particular, and the experimental data in LEO-like conditions without magnetic fields. In a second time, the spatial variations and the time evolutions of the plasma properties around the tether are investigated. Spherical and emissive Langmuir probes are also used for a more extensive characterization of the plasma in space and time dependent analysis. Results show the ion depletion because of the wake effect and the accumulation of- ions upstream of the tether. In some regimes (at large positive potential), oscillations are observed on the tether collected current and on Langmuir probe collected current in specific sites.

Multimodal integration of functional and structural brain connectivity. An application to the characterization of Mild Cognitive Impairment

La investigación para el conocimiento del cerebro es una ciencia joven, su inicio se remonta a Santiago Ramón y Cajal en 1888. Desde esta fecha a nuestro tiempo la neurociencia ha avanzado mucho en el desarrollo de técnicas que permiten su estudio. Desde la neurociencia cognitiva hoy se explican muchos modelos que nos permiten acercar a nuestro entendimiento a capacidades cognitivas complejas. Aun así hablamos de una ciencia casi en pañales que tiene un lago recorrido por delante. Una de las claves del éxito en los estudios de la función cerebral ha sido convertirse en una disciplina que combina conocimientos de diversas áreas: de la física, de las matemáticas, de la estadística y de la psicología. Esta es la razón por la que a lo largo de este trabajo se entremezclan conceptos de diferentes campos con el objetivo de avanzar en el conocimiento de un tema tan complejo como el que nos ocupa: el entendimiento de la mente humana. Concretamente, esta tesis ha estado dirigida a la integración multimodal de la magnetoencefalografía (MEG) y la resonancia magnética ponderada en difusión (dMRI). Estas técnicas son sensibles, respectivamente, a los campos magnéticos emitidos por las corrientes neuronales, y a la microestructura de la materia blanca cerebral. A lo largo de este trabajo hemos visto que la combinación de estas técnicas permiten descubrir sinergias estructurofuncionales en el procesamiento de la información en el cerebro sano y en el curso de patologías neurológicas. Más específicamente en este trabajo se ha estudiado la relación entre la conectividad funcional y estructural y en cómo fusionarlas. Para ello, se ha cuantificado la conectividad funcional mediante el estudio de la sincronización de fase o la correlación de amplitudes entre series temporales, de esta forma se ha conseguido un índice que mide la similitud entre grupos neuronales o regiones cerebrales. Adicionalmente, la cuantificación de la conectividad estructural a partir de imágenes de resonancia magnética ponderadas en difusión, ha permitido hallar índices de la integridad de materia blanca o de la fuerza de las conexiones estructurales entre regiones. Estas medidas fueron combinadas en los capítulos 3, 4 y 5 de este trabajo siguiendo tres aproximaciones que iban desde el nivel más bajo al más alto de integración. Finalmente se utilizó la información fusionada de MEG y dMRI para la caracterización de grupos de sujetos con deterioro cognitivo leve, la detección de esta patología resulta relevante en la identificación precoz de la enfermedad de Alzheimer. Esta tesis está dividida en seis capítulos. En el capítulos 1 se establece un contexto para la introducción de la connectómica dentro de los campos de la neuroimagen y la neurociencia. Posteriormente en este capítulo se describen los objetivos de la tesis, y los objetivos específicos de cada una de las publicaciones científicas que resultaron de este trabajo. En el capítulo 2 se describen los métodos para cada técnica que fue empleada: conectividad estructural, conectividad funcional en resting state, redes cerebrales complejas y teoría de grafos y finalmente se describe la condición de deterioro cognitivo leve y el estado actual en la búsqueda de nuevos biomarcadores diagnósticos. En los capítulos 3, 4 y 5 se han incluido los artículos científicos que fueron producidos a lo largo de esta tesis. Estos han sido incluidos en el formato de la revista en que fueron publicados, estando divididos en introducción, materiales y métodos, resultados y discusión. Todos los métodos que fueron empleados en los artículos están descritos en el capítulo 2 de la tesis. Finalmente, en el capítulo 6 se concluyen los resultados generales de la tesis y se discuten de forma específica los resultados de cada artículo. ABSTRACT In this thesis I apply concepts from mathematics, physics and statistics to the neurosciences. This field benefits from the collaborative work of multidisciplinary teams where physicians, psychologists, engineers and other specialists fight for a common well: the understanding of the brain. Research on this field is still in its early years, being its birth attributed to the neuronal theory of Santiago Ramo´n y Cajal in 1888. In more than one hundred years only a very little percentage of the brain functioning has been discovered, and still much more needs to be explored. Isolated techniques aim at unraveling the system that supports our cognition, nevertheless in order to provide solid evidence in such a field multimodal techniques have arisen, with them we will be able to improve current knowledge about human cognition. Here we focus on the multimodal integration of magnetoencephalography (MEG) and diffusion weighted magnetic resonance imaging. These techniques are sensitive to the magnetic fields emitted by the neuronal currents and to the white matter microstructure, respectively. The combination of such techniques could bring up evidences about structural-functional synergies in the brain information processing and which part of this synergy fails in specific neurological pathologies. In particular, we are interested in the relationship between functional and structural connectivity, and how two integrate this information. We quantify the functional connectivity by studying the phase synchronization or the amplitude correlation between time series obtained by MEG, and so we get an index indicating similarity between neuronal entities, i.e. brain regions. In addition we quantify structural connectivity by performing diffusion tensor estimation from the diffusion weighted images, thus obtaining an indicator of the integrity of the white matter or, if preferred, the strength of the structural connections between regions. These quantifications are then combined following three different approaches, from the lowest to the highest level of integration, in chapters 3, 4 and 5. We finally apply the fused information to the characterization or prediction of mild cognitive impairment, a clinical entity which is considered as an early step in the continuum pathological process of dementia. The dissertation is divided in six chapters. In chapter 1 I introduce connectomics within the fields of neuroimaging and neuroscience. Later in this chapter we describe the objectives of this thesis, and the specific objectives of each of the scientific publications that were produced as result of this work. In chapter 2 I describe the methods for each of the techniques that were employed, namely structural connectivity, resting state functional connectivity, complex brain networks and graph theory, and finally, I describe the clinical condition of mild cognitive impairment and the current state of the art in the search for early biomarkers. In chapters 3, 4 and 5 I have included the scientific publications that were generated along this work. They have been included in in their original format and they contain introduction, materials and methods, results and discussion. All methods that were employed in these papers have been described in chapter 2. Finally, in chapter 6 I summarize all the results from this thesis, both locally for each of the scientific publications and globally for the whole work.

Design of a Semi-analytical Method to Describe Plasma-Wall Interactions

Electric probes are objects immersed in the plasma with sharp boundaries which collect of emit charged particles. Consequently, the nearby plasma evolves under abrupt imposed and/or naturally emerging conditions. There could be localized currents, different time scales for plasma species evolution, charge separation and absorbing-emitting walls. The traditional numerical schemes based on differences often transform these disparate boundary conditions into computational singularities. This is the case of models using advection-diffusion differential equations with source-sink terms (also called Fokker-Planck equations). These equations are used in both, fluid and kinetic descriptions, to obtain the distribution functions or the density for each plasma species close to the boundaries. We present a resolution method grounded on an integral advancing scheme by using approximate Green's functions, also called short-time propagators. All the integrals, as a path integration process, are numerically calculated, what states a robust grid-free computational integral method, which is unconditionally stable for any time step. Hence, the sharp boundary conditions, as the current emission from a wall, can be treated during the short-time regime providing solutions that works as if they were known for each time step analytically. The form of the propagator (typically a multivariate Gaussian) is not unique and it can be adjusted during the advancing scheme to preserve the conserved quantities of the problem. The effects of the electric or magnetic fields can be incorporated into the iterative algorithm. The method allows smooth transitions of the evolving solutions even when abrupt discontinuities are present. In this work it is proposed a procedure to incorporate, for the very first time, the boundary conditions in the numerical integral scheme. This numerical scheme is applied to model the plasma bulk interaction with a charge-emitting electrode, dealing with fluid diffusion equations combined with Poisson equation self-consistently. It has been checked the stability of this computational method under any number of iterations, even for advancing in time electrons and ions having different time scales. This work establishes the basis to deal in future work with problems related to plasma thrusters or emissive probes in electromagnetic fields.

Lock-in amplifiers for AMR sensors

Anisotropic magnetoresistive (AMR) magnetic sensors are often chosen as the magnetic transducer for magnetic field sensing in applications with low to moderate magnetic field resolution because of the relative low mass of the sensor and their ease of use. They measure magnetic fields in the order of the Earth magnetic field (with typical sensitivities of 1‰/G or 10−2‰/μT), have typical minimum detectable fields in order of nT and even 0.1 nT but they are seriously limited by the thermal drifts due to the variation of the resistivity with temperature (∼2.5‰/°C) and the variation of the magnetoresistive effect with temperature (which affects both the sensitivity of the sensors: ∼2.7‰/°C, and the offset: ±0.5‰/°C). Therefore, for lower magnetic fields, fluxgate vector sensors are generally preferred. In the present work these limitations of AMR sensors are outlined and studied. Three methods based on lock-in amplifiers are proposed as low noise techniques. Their performance has been simulated, experimentally tested and comparatively discussed. The developed model has been also used to derive a technique for temperature compensation of AMR response. The final goal to implement these techniques in a space qualified applied specific integrated circuit (ASIC) for Mars in situ exploration with compact miniaturized magnetometers.

Suppression of the intrinsic stochastic pinning of domain walls in magnetic nanostripes

Nanofabrication has allowed the development of new concepts such as magnetic logic and race-track memory, both of which are based on the displacement of magnetic domain walls on magnetic nanostripes. One of the issues that has to be solved before devices can meet the market demands is the stochastic behaviour of the domain wall movement in magnetic nanostripes. Here we show that the stochastic nature of the domain wall motion in permalloy nanostripes can be suppressed at very low fields (0.6-2.7 Oe). We also find different field regimes for this stochastic motion that match well with the domain wall propagation modes. The highest pinning probability is found around the precessional mode and, interestingly, it does not depend on the external field in this regime. These results constitute an experimental evidence of the intrinsic nature of the stochastic pinning of domain walls in soft magnetic nanostripes

Theory of a probe in a strong magnetic field

An asymptotic analysis of the Langmuir-probe problem in a quiescent, fully ionized plasma in a strong magnetic field is performed, for electron cyclotron radius and Debye length much smaller than probe radius, and this not larger than either ion cyclotron radius or mean free path. It is found that the electric potential, which is not confined to a sheath, controls the diffusion far from the probe; inside the magnetic tube bounded by the probe cross section the potential overshoots to a large value before decaying to its value in the body of the plasma. The electron current is independent of the shape of the body along the field and increases with ion temperature; due to the overshoot in the potential, (1) the current at negative voltages does not vary exponentially, (2) its magnitude is strongly reduced by the field, and (3) the usual sharp knee at space potential, disappears. In the regions of the C-V diagram studied the ion current is negligible or unaffected by the field. Some numerical results are presented.The theory, which fails beyond certain positive voltage, fields useful results for weak fields, too.

Evaluation of the Magnetic Field Generated by the Inverter of an Electric Vehicle

In hybrid and electric vehicles, passengers sit very close to an electric system of significant power, which means that they may be subjected to high electromagnetic fields. The hazards of long-term exposure to these fields must be taken into account when designing electric vehicles and their components. Among all the electric devices present in the power train, the electronic converter is the most difficult to analyze, given that it works with different frequencies. In this paper, a methodology to evaluate the magnetic field created by a power electronics converter is proposed. After a brief overview of the recommendations of electromagnetic fields exposure, the magnetic field produced by an inverter is analyzed using finite element techniques. The results obtained are compared to laboratory measurements, taken from a real inverter, in order to validate the model. Finally, results are used to draw some conclusions regarding vehicle design criteria and magnetic shielding efficiency.