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.

Optical behaviour of cholesteric blue phases in electric fields

The optical behaviour of cholesteric mixtures of negative dielectric anisotrony under electric fields is reported. A mixture of S 311~ (31.35 %) + N 5 was employed. AC voltages (f = 1000 Hz) betweeen 0 and 150 volts were applied. Cells 23 micron thick, with internal SnO2 electrodes, were used.

Influence of substrate type and orientation on the morphology and optical properties of selective area growth of GaN and InGaN nanocolumns

A relevant issue concerning optoelectronic devices based on III-nitrides is the presence of strong polarization fields that may reduce efficiency.

Pulsating emission of droplets from an electrified meniscus.

A numerical description is given for the pulsating emission of droplets from an electrified meniscus of an inviscid liquid of infinite electrical conductivity which is injected at a constant flow rate into a region of uniform, continuous or time periodic, electric field. Under a continuous field, the meniscus attains a periodic regime in which bursts of tiny droplets are emitted from its tip. At low electric fields this regime consists of sequences of emission bursts interspersed with sequences of meniscus oscillations without droplet emission, while at higher fields the bursts occur periodically. These results are in qualitative agreement with experimental results in the literature. Under a time periodic electric field with square waveform, the electric stress that acts on the surface of the liquid while the field is on may generate a tip that emits tiny droplets or may accelerate part of the meniscus and lead to a second emission mode in which a few large droplets are emitted after the electric field is turned off. Conditions under which each emission mode or a combination of the two are realized are discussed for low frequency oscillatory fields. A simplified model is proposed for high electric field frequencies, of the order of the capillary frequency of the meniscus. This model allows computing the average emission rate as a function of the amplitude, duration and bias of the electric field square wave, and shows that droplet emission fails to follow the applied field above a certain frequency

Photovoltaic LiNbO3particles: Applications to Biomedicine/Biophotonics

Recently, a novel method to trap and pattern ensembles of nanoparticles has been proposed and tested. It relies on the photovoltaic (PV) properties of certain ferroelectric crystals such as LiNbO3 [1,2]. These crystals, when suitably doped, develop very high electric fields in response to illumination with light of suitable wavelength. The PV effect lies in the asymmetrical excitation of electrons giving rise to PV currents and associated space-charge fields (photorefractive effect). The field generated in the bulk of the sample propagates to the surrounding medium as evanescent fields. When dielectric or metal nanoparticles are deposited on the surface of the sample the evanescent fields give rise to either electrophoretic or dielectrophoretic forces, depending on the charge state of the particles, that induce the trapping and patterning effects [3,4]. The purpose of this work has been to explore the effects of such PV fields in the biology and biomedical areas. A first work was able to show the necrotic effects induced by such fields on He-La tumour cells grown on the surface of an illuminated iron-doped LiNbO3 crystal [5]. In principle, it is conceived that LiNbO3 nanoparticles may be advantageously used for such biomedical purposes considering the possibility of such nanoparticles being incorporated into the cells. Previous experiments using microparticles have been performed [5] with similar results to those achieved with the substrate. Therefore, the purpose of this work has been to fabricate and characterize the LiNbO3 nanoparticles and assess their necrotic effects when they are incorporated on a culture of tumour cells. Two different preparation methods have been used: 1) mechanical grinding from crystals, and 2) bottom-up sol-gel chemical synthesis from metal-ethoxide precursors. This later method leads to a more uniform size distribution of smaller particles (down to around 50 nm). Fig. 1(a) and 1(b) shows SEM images of the nanoparticles obtained with both method. An ad hoc software taking into account the physical properties of the crystal, particullarly donor and aceptor concentrations has been developped in order to estimate the electric field generated in noparticles. In a first stage simulations of the electric current of nanoparticles, in a conductive media, due to the PV effect have been carried out by MonteCarlo simulations using the Kutharev 1-centre transport model equations [6] . Special attention has been paid to the dependence on particle size and [Fe2+]/[Fe3+]. First results on cubic particles shows large dispersion for small sizes due to the random number of donors and its effective concentration (Fig 2). The necrotic (toxicity) effect of nanoparticles incorporated into a tumour cell culture subjected to 30 min. illumination with a blue LED is shown in Fig.3. For each type of nanoparticle the percent of cell survival in dark and illumination conditions has been plot as a function of the particle dilution factor. Fig. 1a corresponds to mechanical grinding particles whereas 1b and 1c refer to chemically synthesized particles with two oxidation states. The light effect is larger with mechanical grinding nanoparticles, but dark toxicity is also higher. For chemically synthesized nanoparticles dark toxicity is low but only in oxidized samples, where the PV effect is known to be larger, the light effect is appreciable. These preliminary results demonstrate that Fe:LiNbO· nanoparticles have a biological damaging effect on cells, although there are many points that should be clarified and much space for PV nanoparticles optimization. In particular, it appears necessary to determine the fraction of nanoparticles that become incorporated into the cells and the possible existence of threshold size effects. This work has been supported by MINECO under grant MAT2011-28379-C03.

Technology and characterization of GaN-HEMTs devices: high temperature and trapping effects

Los transistores de alta movilidad electrónica basados en GaN han sido objeto de una extensa investigación ya que tanto el GaN como sus aleaciones presentan unas excelentes propiedades eléctricas (alta movilidad, elevada concentración de portadores y campo eléctrico crítico alto). Aunque recientemente se han incluido en algunas aplicaciones comerciales, su expansión en el mercado está condicionada a la mejora de varios asuntos relacionados con su rendimiento y habilidad. Durante esta tesis se han abordado algunos de estos aspectos relevantes; por ejemplo, la fabricación de enhancement mode HEMTs, su funcionamiento a alta temperatura, el auto calentamiento y el atrapamiento de carga. Los HEMTs normalmente apagado o enhancement mode han atraído la atención de la comunidad científica dedicada al desarrollo de circuitos amplificadores y conmutadores de potencia, ya que su utilización disminuiría significativamente el consumo de potencia; además de requerir solamente una tensión de alimentación negativa, y reducir la complejidad del circuito y su coste. Durante esta tesis se han evaluado varias técnicas utilizadas para la fabricación de estos dispositivos: el ataque húmedo para conseguir el gate-recess en heterostructuras de InAl(Ga)N/GaN; y tratamientos basados en flúor (plasma CF4 e implantación de F) de la zona debajo de la puerta. Se han llevado a cabo ataques húmedos en heteroestructuras de InAl(Ga)N crecidas sobre sustratos de Si, SiC y zafiro. El ataque completo de la barrera se consiguió únicamente en las muestras con sustrato de Si. Por lo tanto, se puede deducir que la velocidad de ataque depende de la densidad de dislocaciones presentes en la estructura, ya que el Si presenta un peor ajuste del parámetro de red con el GaN. En relación a los tratamientos basados en flúor, se ha comprobado que es necesario realizar un recocido térmico después de la fabricación de la puerta para recuperar la heteroestructura de los daños causados durante dichos tratamientos. Además, el estudio de la evolución de la tensión umbral con el tiempo de recocido ha demostrado que en los HEMTs tratados con plasma ésta tiende a valores más negativos al aumentar el tiempo de recocido. Por el contrario, la tensión umbral de los HEMTs implantados se desplaza hacia valores más positivos, lo cual se atribuye a la introducción de iones de flúor a niveles más profundos de la heterostructura. Los transistores fabricados con plasma presentaron mejor funcionamiento en DC a temperatura ambiente que los implantados. Su estudio a alta temperatura ha revelado una reducción del funcionamiento de todos los dispositivos con la temperatura. Los valores iniciales de corriente de drenador y de transconductancia medidos a temperatura ambiente se recuperaron después del ciclo térmico, por lo que se deduce que dichos efectos térmicos son reversibles. Se han estudiado varios aspectos relacionados con el funcionamiento de los HEMTs a diferentes temperaturas. En primer lugar, se han evaluado las prestaciones de dispositivos de AlGaN/GaN sobre sustrato de Si con diferentes caps: GaN, in situ SiN e in situ SiN/GaN, desde 25 K hasta 550 K. Los transistores con in situ SiN presentaron los valores más altos de corriente drenador, transconductancia, y los valores más bajos de resistencia-ON, así como las mejores características en corte. Además, se ha confirmado que dichos dispositivos presentan gran robustez frente al estrés térmico. En segundo lugar, se ha estudiado el funcionamiento de transistores de InAlN/GaN con diferentes diseños y geometrías. Dichos dispositivos presentaron una reducción casi lineal de los parámetros en DC en el rango de temperaturas de 25°C hasta 225°C. Esto se debe principalmente a la dependencia térmica de la movilidad electrónica, y también a la reducción de la drift velocity con la temperatura. Además, los transistores con mayores longitudes de puerta mostraron una mayor reducción de su funcionamiento, lo cual se atribuye a que la drift velocity disminuye más considerablemente con la temperatura cuando el campo eléctrico es pequeño. De manera similar, al aumentar la distancia entre la puerta y el drenador, el funcionamiento del HEMT presentó una mayor reducción con la temperatura. Por lo tanto, se puede deducir que la degradación del funcionamiento de los HEMTs causada por el aumento de la temperatura depende tanto de la longitud de la puerta como de la distancia entre la puerta y el drenador. Por otra parte, la alta densidad de potencia generada en la región activa de estos transistores conlleva el auto calentamiento de los mismos por efecto Joule, lo cual puede degradar su funcionamiento y Habilidad. Durante esta tesis se ha desarrollado un simple método para la determinación de la temperatura del canal basado en medidas eléctricas. La aplicación de dicha técnica junto con la realización de simulaciones electrotérmicas han posibilitado el estudio de varios aspectos relacionados con el autocalentamiento. Por ejemplo, se han evaluado sus efectos en dispositivos sobre Si, SiC, y zafiro. Los transistores sobre SiC han mostrado menores efectos gracias a la mayor conductividad térmica del SiC, lo cual confirma el papel clave que desempeña el sustrato en el autocalentamiento. Se ha observado que la geometría del dispositivo tiene cierta influencia en dichos efectos, destacando que la distribución del calor generado en la zona del canal depende de la distancia entre la puerta y el drenador. Además, se ha demostrado que la temperatura ambiente tiene un considerable impacto en el autocalentamiento, lo que se atribuye principalmente a la dependencia térmica de la conductividad térmica de las capas y sustrato que forman la heterostructura. Por último, se han realizado numerosas medidas en pulsado para estudiar el atrapamiento de carga en HEMTs sobre sustratos de SiC con barreras de AlGaN y de InAlN. Los resultados obtenidos en los transistores con barrera de AlGaN han presentado una disminución de la corriente de drenador y de la transconductancia sin mostrar un cambio en la tensión umbral. Por lo tanto, se puede deducir que la posible localización de las trampas es la región de acceso entre la puerta y el drenador. Por el contrario, la reducción de la corriente de drenador observada en los dispositivos con barrera de InAlN llevaba asociado un cambio significativo en la tensión umbral, lo que implica la existencia de trampas situadas en la zona debajo de la puerta. Además, el significativo aumento del valor de la resistencia-ON y la degradación de la transconductancia revelan la presencia de trampas en la zona de acceso entre la puerta y el drenador. La evaluación de los efectos del atrapamiento de carga en dispositivos con diferentes geometrías ha demostrado que dichos efectos son menos notables en aquellos transistores con mayor longitud de puerta o mayor distancia entre puerta y drenador. Esta dependencia con la geometría se puede explicar considerando que la longitud y densidad de trampas de la puerta virtual son independientes de las dimensiones del dispositivo. Finalmente se puede deducir que para conseguir el diseño óptimo durante la fase de diseño no sólo hay que tener en cuenta la aplicación final sino también la influencia que tiene la geometría en los diferentes aspectos estudiados (funcionamiento a alta temperatura, autocalentamiento, y atrapamiento de carga). ABSTRACT GaN-based high electron mobility transistors have been under extensive research due to the excellent electrical properties of GaN and its related alloys (high carrier concentration, high mobility, and high critical electric field). Although these devices have been recently included in commercial applications, some performance and reliability issues need to be addressed for their expansion in the market. Some of these relevant aspects have been studied during this thesis; for instance, the fabrication of enhancement mode HEMTs, the device performance at high temperature, the self-heating and the charge trapping. Enhancement mode HEMTs have become more attractive mainly because their use leads to a significant reduction of the power consumption during the stand-by state. Moreover, they enable the fabrication of simpler power amplifier circuits and high-power switches because they allow the elimination of negativepolarity voltage supply, reducing significantly the circuit complexity and system cost. In this thesis, different techniques for the fabrication of these devices have been assessed: wet-etching for achieving the gate-recess in InAl(Ga)N/GaN devices and two different fluorine-based treatments (CF4 plasma and F implantation). Regarding the wet-etching, experiments have been carried out in InAl(Ga)N/GaN grown on different substrates: Si, sapphire, and SiC. The total recess of the barrier was achieved after 3 min of etching in devices grown on Si substrate. This suggests that the etch rate can critically depend on the dislocations present in the structure, since the Si exhibits the highest mismatch to GaN. Concerning the fluorine-based treatments, a post-gate thermal annealing was required to recover the damages caused to the structure during the fluorine-treatments. The study of the threshold voltage as a function of this annealing time has revealed that in the case of the plasma-treated devices it become more negative with the time increase. On the contrary, the threshold voltage of implanted HEMTs showed a positive shift when the annealing time was increased, which is attributed to the deep F implantation profile. Plasma-treated HEMTs have exhibited better DC performance at room temperature than the implanted devices. Their study at high temperature has revealed that their performance decreases with temperature. The initial performance measured at room temperature was recovered after the thermal cycle regardless of the fluorine treatment; therefore, the thermal effects were reversible. Thermal issues related to the device performance at different temperature have been addressed. Firstly, AlGaN/GaN HEMTs grown on Si substrate with different cap layers: GaN, in situ SiN, or in situ SiN/GaN, have been assessed from 25 K to 550 K. In situ SiN cap layer has been demonstrated to improve the device performance since HEMTs with this cap layer have exhibited the highest drain current and transconductance values, the lowest on-resistance, as well as the best off-state characteristics. Moreover, the evaluation of thermal stress impact on the device performance has confirmed the robustness of devices with in situ cap. Secondly, the high temperature performance of InAlN/GaN HEMTs with different layouts and geometries have been assessed. The devices under study have exhibited an almost linear reduction of the main DC parameters operating in a temperature range from room temperature to 225°C. This was mainly due to the thermal dependence of the electron mobility, and secondly to the drift velocity decrease with temperature. Moreover, HEMTs with large gate length values have exhibited a great reduction of the device performance. This was attributed to the greater decrease of the drift velocity for low electric fields. Similarly, the increase of the gate-to-drain distance led to a greater reduction of drain current and transconductance values. Therefore, this thermal performance degradation has been found to be dependent on both the gate length and the gate-to-drain distance. It was observed that the very high power density in the active region of these transistors leads to Joule self-heating, resulting in an increase of the device temperature, which can degrade the device performance and reliability. A simple electrical method have been developed during this work to determine the channel temperature. Furthermore, the application of this technique together with the performance of electro-thermal simulations have enabled the evaluation of different aspects related to the self-heating. For instance, the influence of the substrate have been confirmed by the study of devices grown on Si, SiC, and Sapphire. HEMTs grown on SiC substrate have been confirmed to exhibit the lowest self-heating effects thanks to its highest thermal conductivity. In addition to this, the distribution of the generated heat in the channel has been demonstrated to be dependent on the gate-to-drain distance. Besides the substrate and the geometry of the device, the ambient temperature has also been found to be relevant for the self-heating effects, mainly due to the temperature-dependent thermal conductivity of the layers and the substrate. Trapping effects have been evaluated by means of pulsed measurements in AlGaN and InAIN barrier devices. AlGaN barrier HEMTs have exhibited a de crease in drain current and transconductance without measurable threshold voltage change, suggesting the location of the traps in the gate-to-drain access region. On the contrary, InAIN barrier devices have showed a drain current associated with a positive shift of threshold voltage, which indicated that the traps were possibly located under the gate region. Moreover, a significant increase of the ON-resistance as well as a transconductance reduction were observed, revealing the presence of traps on the gate-drain access region. On the other hand, the assessment of devices with different geometries have demonstrated that the trapping effects are more noticeable in devices with either short gate length or the gate-to-drain distance. This can be attributed to the fact that the length and the trap density of the virtual gate are independent on the device geometry. Finally, it can be deduced that besides the final application requirements, the influence of the device geometry on the performance at high temperature, on the self-heating, as well as on the trapping effects need to be taken into account during the device design stage to achieve the optimal layout.

Análisis y simulación numérica de problemas electrohidrodinámicos relacionados con el electrospray

La presente tesis es un estudio analítico y numérico del electrospray. En la configuración más sencilla, un caudal constante del líquido a atomizar, que debe tener una cierta conductividad eléctrica, se inyecta en un medio dieléctrico (un gas u otro líquido inmiscible con el primero) a través de un tubo capilar metálico. Entre este tubo y un electrodo lejano se aplica un voltaje continuo que origina un campo eléctrico en el líquido conductor y en el espacio que lo rodea. El campo eléctrico induce una corriente eléctrica en el líquido, que acumula carga en su superficie, y da lugar a un esfuerzo eléctrico sobre la superficie, que tiende a alargarla en la dirección del campo eléctrico. El líquido forma un menisco en el extremo del tubo capilar cuando el campo eléctrico es suficientemente intenso y el caudal suficientemente pequeño. Las variaciones de presión y los esfuerzos viscosos asociados al movimiento del líquido son despreciables en la mayor parte de este menisco, siendo dominantes los esfuerzos eléctrico y de tensión superficial que actúan sobre la superficie del líquido. En el modo de funcionamiento llamado de conochorro, el balance de estos esfuerzos hace que el menisco adopte una forma cónica (el cono de Taylor) en una región intermedia entre el extremo del tubo y la punta del menisco. La velocidad del líquido aumenta al acercarse al vértice del cono, lo cual propicia que las variaciones de la presión en el líquido generadas por la inercia o por la viscosidad entren en juego, desequilibrando el balance de esfuerzos mencionado antes. Como consecuencia, del vértice del cono sale un delgado chorro de líquido, que transporta la carga eléctrica que se acumula en la superficie. La acción del campo eléctrico tangente a la superficie sobre esta carga origina una tracción eléctrica que tiende a alargar el chorro. Esta tracción no es relevante en el menisco, donde el campo eléctrico tangente a la superficie es muy pequeño, pero se hace importante en el chorro, donde es la causa del movimiento del líquido. Lejos del cono, el chorro puede o bien desarrollar una inestabilidad asimétrica que lo transforma en una espiral (whipping) o bien romperse en un spray de gotas prácticamente monodispersas cargadas eléctricamente. La corriente eléctrica transportada por el líquido es la suma de la corriente de conducción en el interior del líquido y la corriente debida a la convección de la carga acumulada en su superficie. La primera domina en el menisco y la segunda en el chorro lejano, mientras que las dos son comparables en una región intermedia de transferencia de corriente situada al comienzo del chorro aunque aguas abajo de la región de transición cono-chorro, en la que el menisco deja de ser un cono de Taylor. Para un campo exterior dado, la acumulación de carga eléctrica en la superficie del líquido reduce el campo eléctrico en el interior del mismo, que llega a anularse cuando la carga alcanza un estado final de equilibrio. El tiempo característico de este proceso es el tiempo de relajación dieléctrica, que es una propiedad del líquido. Cuando el tiempo de residencia del líquido en la región de transición cono-chorro (o en otra región del campo fluido) es grande frente al tiempo de relajación dieléctrica, la carga superficial sigue una sucesión de estados de equilibrio y apantalla al líquido del campo exterior. Cuando esta condición deja de cumplirse, aparecen efectos de relajación de carga, que se traducen en que el campo exterior penetra en el líquido, a no ser que su constante dieléctrica sea muy alta, en cuyo caso el campo inducido por la carga de polarización evita la entrada del campo exterior en el menisco y en una cierta región del chorro. La carga eléctrica en equilibrio en la superficie de un menisco cónico intensifica el campo eléctrico y determina su variación espacial hasta distancias aguas abajo del menisco del orden de su tamaño. Este campo, calculado por Taylor, es independiente del voltaje aplicado, por lo que las condiciones locales del flujo y el valor de la corriente eléctrica son también independientes del voltaje en tanto los tamaños de las regiones que determinan estas propiedades sean pequeños frente al tamaño del menisco. Los resultados experimentales publicados en la literatura muestran que existe un caudal mínimo para el que el modo cono-chorro que acabamos de describir deja de existir. El valor medio y la desviación típica de la distribución de tamaños de las gotas generadas por un electrospray son mínimos cuando se opera cerca del caudal mínimo. A pesar de que los mecanismos responsables del caudal mínimo han sido muy estudiados, no hay aún una teoría completa del mismo, si bien su existencia parece estar ligada a la aparición de efectos de relajación de carga en la región de transición cono-chorro. En esta tesis, se presentan estimaciones de orden de magnitud, algunas existentes y otras nuevas, que muestran los balances dominantes responsables de las distintas regiones de la estructura asintótica de la solución en varios casos de interés. Cuando la inercia del líquido juega un papel en la transición cono-chorro, los resultados muestran que la región de transferencia de corriente, donde la mayor parte de la corriente pasa a la superficie, está en el chorro aguas abajo de la región de transición cono-chorro. Los efectos de relajación de carga aparecen de forma simultánea en el chorro y la región de transición cuando el caudal se disminuye hasta valores de un cierto orden. Para caudales aún menores, los efectos de relajación de carga se notan en el menisco, en una región grande comparada con la de transición cono-chorro. Cuando el efecto de las fuerzas de viscosidad es dominante en la región de transición, la región de transferencia de corriente está en el chorro pero muy próxima a la región de transición cono-chorro. Al ir disminuyendo el caudal, los efectos de relajación de carga aparecen progresivamente en el chorro, en la región de transición y por último en el menisco. Cuando el caudal es mucho mayor que el mínimo del modo cono-chorro, el menisco deja de ser cónico. El campo eléctrico debido al voltaje aplicado domina en la región de transferencia de corriente, y tanto la corriente eléctrica como el tamaño de las diferentes regiones del problema pasan a depender del voltaje aplicado. Como resultado de esta dependencia, el plano caudal-voltaje se divide en diferentes regiones que se analizan separadamente. Para caudales suficientemente grandes, la inercia del líquido termina dominando frente a las fuerzas de la viscosidad. Estos resultados teóricos se han validado con simulaciones numéricas. Para ello se ha formulado un modelo simplificado del flujo, el campo eléctrico y el transporte de carga en el menisco y el chorro del electrospray. El movimiento del líquido se supone casi unidireccional y se describe usando la aproximación de Cosserat para un chorro esbelto. Esta aproximación, ampliamente usada en la literatura, permite simular con relativa facilidad múltiples casos y cubrir amplios rangos de valores de los parámetros reteniendo los efectos de la viscosidad y la inercia del líquido. Los campos eléctricos dentro y fuera del liquido están acoplados y se calculan sin simplificación alguna usando un método de elementos de contorno. La solución estacionaria del problema se calcula mediante un método iterativo. Para explorar el espacio de los parámetros, se comienza calculando una solución para valores fijos de las propiedades del líquido, el voltaje aplicado y el caudal. A continuación, se usa un método de continuación que permite delinear la frontera del dominio de existencia del modo cono-chorro, donde el método iterativo deja de converger. Cuando el efecto de la inercia del líquido domina en la región de transición cono-chorro, el caudal mínimo para el cual el método iterativo deja de converger es del orden del valor estimado del caudal para el que comienza a haber efectos de relajación de carga en el chorro y el cono. Aunque las simulaciones no convergen por debajo de dicho caudal, el valor de la corriente eléctrica para valores del caudal ligeramente mayores parece ajustarse a las estimaciones para caudales menores, reflejando un posible cambio en los balances aplicables. Por el contrario, cuando las fuerzas viscosas dominan en la región de transición, se pueden obtener soluciones estacionarias para caudales bastante menores que aquel para el que aparecen efectos de relajación de carga en la región de transición cono-chorro. Los resultados numéricos obtenidos para estos pequeños caudales se ajustan perfectamente a las estimaciones de orden de magnitud que se describen en la memoria. Por último, se incluyen como anexos dos estudios teóricos que han surgido de forma natural durante el desarrollo de la tesis. El primero hace referencia a la singularidad en el campo eléctrico que aparece en la línea de contacto entre el líquido y el tubo capilar en la mayoría de las simulaciones. Primero se estudia en qué situaciones el campo eléctrico tiende a infinito en la línea de contacto. Después, se comprueba que dicha singularidad no supone un fallo en la descripción del problema y que además no afecta a la solución lejos de la línea de contacto. También se analiza si los esfuerzos eléctricos infinitamente grandes a los que da lugar dicha singularidad pueden ser compensados por el resto de esfuerzos que actúan en la superficie del líquido. El segundo estudio busca determinar el tamaño de la región de apantallamiento en un chorro de líquido dieléctrico sin carga superficial. En esta región, el campo exterior es compensado parcialmente por el campo que induce la carga de polarización en la superficie del líquido, de forma que en el interior del líquido el campo eléctrico es mucho menor que en el exterior. Una región como ésta aparece en las estimaciones cuando los efectos de relajación de carga son importantes en la región de transferencia de corriente en el chorro. ABSTRACT This aim of this dissertation is a theoretical and numerical analysis of an electrospray. In its most simple configuration, a constant flow rate of the liquid to be atomized, which has to be an electrical conductor, is injected into a dielectric medium (a gas or another inmiscible fluid) through a metallic capillary tube. A constant voltage is applied between this tube and a distant electrode that produces an electric field in the liquid and the surrounding medium. This electric field induces an electric current in the liquid that accumulates charge at its surface and leads to electric stresses that stretch the surface in the direction of the electric field. A meniscus appears on the end of the capillary tube when the electric field is sufficiently high and the flow rate is small. Pressure variations and viscous stresses due to the motion of the liquid are negligible in most of the meniscus, where normal electric and surface tension stresses acting on the surface are dominant. In the so-called cone-jet mode, the balance of these stresses forces the surface to adopt a conical shape -Taylor cone- in a intermediate region between the end of the tube and the tip of the meniscus. When approaching the cone apex, the velocity of the liquid increases and leads to pressure variations that eventually disturb the balance of surfaces tension and electric stresses. A thin jet emerges then from the tip of the meniscus that transports the charge accumulated at its surface. The electric field tangent to the surface of the jet acts on this charge and continuously stretches the jet. This electric force is negligible in the meniscus, where the component of the electric field tangent to the surface is small, but becomes very important in the jet. Far from the cone, the jet can either develop an asymmetrical instability named “whipping”, whereby the jet winds into a spiral, or break into a spray of small, nearly monodisperse, charged droplets. The electric current transported by the liquid has two components, the conduction current in the bulk of the liquid and the convection current due to the transport of the surface charge by the flow. The first component dominates in the meniscus, the second one in the far jet, and both are comparable in a current transfer region located in the jet downstream of the cone-jet transition region where the meniscus ceases to be a Taylor cone. Given an external electric field, the charge that accumulates at the surface of the liquid reduces the electric field inside the liquid, until an equilibrium is reached in which the electric field induced by the surface charge counters the external electric field and shields the liquid from this field. The characteristic time of this process is the electric relaxation time, which is a property of the liquid. When the residence time of the liquid in the cone-jet transition region (or in other region of the flow) is greater than the electric relaxation time, the surface charge follows a succession of equilibrium states and continuously shield the liquid from the external field. When this condition is not satisfied, charge relaxation effects appear and the external field penetrates into the liquid unless the liquid permittivity is large. For very polar liquids, the field due to the polarization charge at the surface prevents the external field from entering the liquid in the cone and in certain region of the jet. The charge at the surface of a conical meniscus intensifies the electric field around the cone, determining its spatial variation up to distances downstream of the apex of the order of the size of the meniscus. This electric field, first computed by Taylor, is independent of the applied voltage. Therefore local flow characteristics and the electric current carried by the jet are also independent of the applied voltage provided the size of the regions that determine these magnitudes are small compared with the size of the meniscus. Many experiments in the literature show the existence of a minimum flow rate below which the cone-jet mode cannot be established. The mean value and the standard deviation of the electrospray droplet size distribution are minimum when the device is operated near the minimum flow rate. There is no complete explanation of the minimum flow rate, even though possible mechanisms have been extensively studied. The existence of a minimum flow rate seems to be connected with the appearance of charge relaxation effects in the transition region. In this dissertation, order of magnitude estimations are worked out that show the dominant balances in the different regions of the asymptotic structure of the solution for different conditions of interest. When the inertia of the liquid plays a role in the cone-jet transition region, the region where most of the electric current is transfered to the surface lies in the jet downstream the cone-jet transition region. When the flow rate decreases to a certain value, charge relaxation effects appear simultaneously in the jet and in the transition region. For smaller values of the flow rate, charge relaxation effects are important in a region of the meniscus larger than the transition region. When viscous forces dominate in the flow in the cone-jet transition region, the current transfer region is located in the jet immediately after the transition region. When flow rate is decreased, charge relaxation effects appears gradually, first in the jet, then in the transition region, and finally in the meniscus. When flow rate is much larger than the cone-jet mode minimum, the meniscus ceases to be a cone. The electric current and the structure of the solution begin to depend on the applied voltage. The flow rate-voltage plane splits into different regions that are analyzed separately. For sufficiently large flow rates, the effect of the inertia of the liquid always becomes greater than the effect of the viscous forces. A set of numerical simulations have been carried out in order to validate the theoretical results. A simplified model of the problem has been devised to compute the flow, the electric field and the surface charge in the meniscus and the jet of an electrospray. The motion of the liquid is assumed to be quasi-unidirectional and described by Cosserat’s approximation for a slender jet. This widely used approximation allows to easily compute multiple configurations and to explore wide ranges of values of the governing parameters, retaining the effects of the viscosity and the inertia of the liquid. Electric fields inside and outside the liquid are coupled and are computed without any simplification using a boundary elements method. The stationary solution of the problem is obtained by means of an iterative method. To explore the parameter space, a solution is first computed for a set of values of the liquid properties, the flow rate and the applied voltage, an then a continuation method is used to find the boundaries of the cone-jet mode domain of existence, where the iterative method ceases to converge. When the inertia of the liquid dominates in the cone-jet transition region, the iterative method ceases to converge for values of the flow rate for which order-of-magnitude estimates first predict charge relaxation effects to be important in the cone and the jet. The electric current computed for values of the flow rate slightly above the minimum for which convergence is obtained seems to agree with estimates worked out for lower flow rates. When viscous forces dominate in the transition region, stationary solutions can be obtained for flow rates significantly smaller than the one for which charge relaxation effects first appear in the transition region. Numerical results obtained for those small values of the flow rate agree with our order of magnitude estimates. Theoretical analyses of two issues that have arisen naturally during the thesis are summarized in two appendices. The first appendix contains a study of the singularity of the electric field that most of the simulations show at the contact line between the liquid and the capillary tube. The electric field near the contact line is analyzed to determine the ranges of geometrical configurations and liquid permittivity where a singularity appears. Further estimates show that this singularity does not entail a failure in the description of the problem and does not affect the solution far from the contact line. The infinite electric stresses that appear at the contact line can be effectively balanced by surface tension. The second appendix contains an analysis of the size and slenderness of the shielded region of a dielectric liquid in the absence of free surface charge. In this region, the external electric field is partially offset by the polarization charge so that the inner electric field is much lower than the outer one. A similar region appears in the estimates when charge relaxation effects are important in the current transfer region.

The peculiar electrical response of liquid crystal-carbon nanotube systems as seen by impedance spectroscopy

Conductive nanoparticles, especially elongated ones such as carbon nanotubes, dramatically modify the electrical behavior of liquid crystal cells. These nanoparticles are known to reorient with liquid crystals in electric fields, causing significant variations of conductivity at minute concentrations of tens or hundreds ppm. The above notwithstanding, impedance spectroscopy of doped cells in the frequency range customarily employed by liquid crystal devices, 100 Hz?10 kHz, shows a relatively simple resistor/capacitor response where the components of the cell can be univocally assigned to single components of the electrical equivalent circuit. However, widening the frequency range up to 1 MHz or beyond reveals a complex behavior that cannot be explained with the same simple EEC. Moreover, the system impedance varies with the application of electric fields, their effect remaining after removing the field. Carbon nanotubes are reoriented together with liquid crystal reorientation when applying voltage, but barely reoriented back upon liquid crystal relaxation once the voltage is removed. Results demonstrate a remarkable variation in the impedance of the dielectric blend formed by liquid crystal and carbon nanotubes, the irreversible orientation of the carbon nanotubes and possible permanent contacts between electrodes.

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.

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.

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.

An Asymptotic Solution for Surface Fields on a Dielectric-Coated Circular Cylinder with an Effective Impedance Boundary Condition.

Reverberation chambers are well known for providing a random-like electric field distribution. Detection of directivity or gain thereof requires an adequate procedure and smart post-processing. In this paper, a new method is proposed for estimating the directivity of radiating devices in a reverberation chamber (RC). The method is based on the Rician K-factor whose estimation in an RC benefits from recent improvements. Directivity estimation relies on the accurate determination of the K-factor with respect to a reference antenna. Good agreement is reported with measurements carried out in near-field anechoic chamber (AC) and using a near-field to far-field transformation.

Surface Impedance Characterization for UTD Based Solution with IBC for Surface Fields on a Dielectric-Coated PEC Circular Cylinder

A novel formulation for the surface impedance characterization is introduced for the canonical problem of surface fields on a perfect electric conductor (PEC) circular cylinder with a dielectric coating due to a electric current source using the Uniform Theory of Diffraction (UTD) with an Impedance Boundary Condition (IBC). The approach is based on a TE/TM assumption of the surface fields from the original problem. Where this surface impedance fails, an optimization is performed to minimize the error in the SD Green?s function between the original problem and the equivalent one with the IBC. This new approach requires small changes in the available UTD based solution with IBC to include the geodesic ray angle and length dependence in the surface impedance formulas. This asymptotic method, accurate for large separations between source and observer points, in combination with spectral domain (SD) Green?s functions for multidielectric coatings leads to a new hybrid SD-UTD with IBC to calculate mutual coupling among microstrip patches on a multilayer dielectric-coated PEC circular cylinder. Results are compared with the eigenfunction solution in SD, where a very good agreement is met.

Ion correlations due to high-frequency electric field and their effect on the nonlinear plasma conductivity

The influence of a strong, high‐frequency electric field on the ion‐ion correlations in a fully ionized plasma is investigated in the limit of infinite ion mass, starting with the Bogoliubov‐Born‐Green‐Kirkwood‐Yvon hierarchy of equations; a significant departure from the thermal correlations is found. It is shown that the above effect may substantially modify earlier results on the nonlinear high‐frequency plasma conductivity.

Electrostatic plasma instabilities excited by a high-frequency electric field. AT(30-1)-1238-MATT-669

An analysis of the electrostatic plasma instabilities excited by the application of a strong, uniform, alternating electric field is made on the basis of the Vlasov equation. A very general dispersion relation is obtained and discussed. Under the assumption W 2 O » C 2 pi. (where wO is the applied frequency and wpi the ion plasma frequency) a detailed analysis is given for wavelengths of the order of or large compared with the Debye length. It is found that there are two types of instabilities: resonant (or parametric) and nonresonant. The second is caused by the relative streaming of ions and electrons, generated by the field; it seems to exist only if wO is less than the electron plasma frequency wpe. The instability only appears if the field exceeds a certain threshold, which is found.