This thesis is concerned with several problems in general relativity and low energy string theory that are pertinent to the time evolution of the gravitational field. We present a formulation of the Einstein field equations in terms of variational techniques borrowed from geometric analysis. These equations yield the evolution equations for the Cauchy problems of both general relativity and low energy string theory. We then proceed to investigate the evolutionary linear stability of Schwarzschild-like solutions in higher dimensional relativity called black strings. These objects are determined to be linearly unstable. This motivates a further stability analysis of the charged p-brane solutions of low energy string theory. We show that one can eliminate linear instabilities in p-branes for sufficiently large values of charge. We also consider the characteristic problem of general relativistic magnetohydrodynamics (GRMHD). We compute the eigenvalues and eigenvectors of GRMHD and establish degeneracy conditions. Finally, we consider the initial value problem for axisymmetric GRMHD. We formulate the general Einstein and MHD equations under the assumption of a stationary axisymmetric spacetime without assuming the circularity condition.

Until now the quantum field theory (QFT) that successfully describes the electric, weak and strong interactions (three out of the four fundamental forces) between particles is the Standard Model, but it omits gravity. The prime candidate for a quantum theory of gravity is string theory. However, recent developments in string theory suggest that a portion of the alternative quantum field theories that are being considered, are incompatible with gravity. In 2005, this led string theorists to outline the conditions an effective field theory (EFT) should satisfy in order to be consistent with a quantum theory of gravity. These conditions are the ones that separate the so-called landscape from the swampland. An EFT that satisfies these conditions is said to reside in the landscape, while EFTs that do not satisfy these conditions belong to the swampland. This mapping out of EFTs to the swampland gives rise to a number of predictions that are related to the physics of the Early universe and the nature of dark energy. The de Sitter conjecture and the Trans-Planckian censorship conjecture are some of these conditions and will be the main focus of this thesis. The main purpose behind this work is to gain a deep understanding of each criterium, as well as unravel their implications and predictions related to the dynamics of the Early Universe. We do this by writing a pedagogical introduction of the topic and by introducing some possible alternative to the inflationary scenario, cosmologies that seem to be consistent with the aforementioned constraints.

Um das mikroskopische Verhalten der Gravitation zu beschreiben, ist es nötig, Quantenfeldtheorie und allgemeine Relativitätstheorie in einer vereinheitlichten Sprache zu formulieren. Eine Möglichkeit dieses Problem anzugehen ist es, die Punktteilchen der Quantenfeldtheorie durch fadenförmige Strings zu ersetzen. Allerdings erfordert die mathematische Konsistenz, dass sich die String in höherdimensionalen Raum-Zeiten bewegen; dies macht es jedoch sehr schwer, physikalische Konsequenzen zu extrahieren. Eine mögliche Lösung dieses Problems ist die Verwendung von String-Dualitäten, welche die Stringtheorie mittels holographischer Beschreibungen mit Eichtheorien auf dem Rand der Raum-Zeit verbinden. Die Dualitäten sind begründete Vermutungen, die die String- und Eichtheorie bei unterschiedlichen Werten der Kopplung gleichsetzen. Nicht zuletzt deshalb ist eine direkte Überprüfung der Dualitäten schwierig durchführbar. Hier hilft jedoch die sehr bemerkenswerte Tatsache, dass eine verborgene Eigenschaft der Vermutungen Integrabilität zu sein scheint, welche eine Extrapolation zwischen starker und schwacher Kopplung ermöglicht. Desweiteren kann das gesamte Spektrum, in gewissen vereinfachenden Grenzfällen, durch einen kompakten Satz von Bethe-Gleichungen ausgedrückt werden. Die Bethe-Gleichungen, welche aus Eichtheorierechnungen hergeleitet und geraten werden, bieten ein exzellentes Hilfsmittel, die vermuteten Dualitäten zu prüfen. Durch das Vergleichen der Vorhersagen der Gleichungen und expliziten Berechnungen in der Stringtheorie erhält man starke Argumente für die Gültigkeit der Vermutung und der angenommenen Integrabilität. / In this thesis we study superstring theory on AdS$_5\, \times\,$S$^5$, AdS$_3\,\times\,$S$^3$ and $\adsfour$. A shared feature of each theory is that their corresponding symmetry algebras allows for a decomposition under a $\mathbb{Z}_4$ grading. The grading can be realized through an automorphism which allows for a convenient construction of the string Lagrangians directly in terms of graded components. We adopt a uniform light-cone gauge and expand in a near plane wave limit, or equivalently, an expansion in transverse string coordinates. With a main focus on the two critical string theories, we perform a perturbative quantization up to quartic order in the number of fields. Each string theory is, through holographic descriptions, conjectured to be dual to lower dimensional gauge theories. The conjectures imply that the conformal dimensions of single trace operators in gauge theory should be equal to the energy of string states. What is more, through the use of integrable methods, one can write down a set of Bethe equations whose solutions encode the full spectral problem. One main theme of this thesis is to match the predictions of these equations, written in a language suitable for the light-cone gauge we employ, against explicit string theory calculations. We do this for a large class of string states and the perfect agreement we find lends strong support for the validity of the conjectures.

Einer der Hauptzweige innerhalb der String-Theorie, der sich um die Konstruktion phänomenologisch relevanter Modelle bemüht, beschäftigt sich mit sich schneidenden D-Branen. Nach einer allgemeinen Einleitung in die Stringtheorie, werden sowohl Torus- als auch Z_N-Orientifolde detailliert dargestellt. Es wird auf das Bild von D9-Branen mit externen B-Feldern eingegangen, aber das Hauptaugenmerk liegt auf dem T-dualen Bild sich schneidender D6-Branen. Die Forderung nach einer Abwesenheit von R-R und NS-NS Tadpolen wird im Formalismus der konformen Feldtheorie hergeleitet. Verschiedene Aspekte der chiralen und nicht-chiralen masselosen Spektren geschlossener und offener Strings werden behandelt, wie Raumzeit-Anomalien, der generalisierte Green-Schwarz-Mechanismus und verschiedene Mechanismen zur Brechung der Eichgruppen. Anschließend werden sowohl der supersymmetrische wie auch der nicht-supersymmetrische Zugang zur Bildung niederenergetischer Modelle diskutiert. Das Problem komplexer Strukturinstabilitäten auf dem Torus wird erfolgreich in einem Z_3-Orientifold-Modell behoben. Es wird ein dem Standard-Modell ähnliches Drei-Generationen-Modell konstruiert, das neben den üblichen Eichgruppen noch eine zusätzliche globale B-L-Symmetrie besitzt. Somit sind weder der elektroschwache Higgs-Mechanismus noch die üblichen Yukawa-Kopplungen in diesem Modell realisiert. Es wird gezeigt, daß der natürliche Ursprung dieses Modells ein flipped SU(5)-GUT-Modell ist. Die Stringskala muß hierbei wenigstens von der Größenordnung der GUT-Skala angenommen werden. Anschließend werden supersymmetrische Modelle auf dem Z_4-Orbifold besprochen, einem Hintergrund, der auch exzeptionelle 3-Zyklen zuläßt. Es werden fraktionale D-Branen explizit konstruiert. Schließlich wird als Beispiel ein Pati-Salam-Modell dargestellt, welches drei Fermion-Generationen besitzt. Dieses Modell ergibt sich nach der Anwendung verschiedener Branenrekombinations-mechanismen und beinhaltet nicht-flache und nicht-faktorisierbare D-Branen. Es wird ebenfalls gezeigt, wie dieses Modell auf ein MSSM-artiges Modell heruntergebrochen werden kann, welches eine masselose Hyperladung besitzt. Im letzten Teil wird der Frage nachgegangen, ob instabile Modulusfelder des Sektors geschlossener oder offener Strings möglicherweise für die Phase der Inflation innerhalb der kosmischen Entwicklung unseres Universums verantwortlich gewesen sein können. Damit dies der Fall sein kann, müssen potentielle Inflaton-Kandidaten die Slow-Roll-Bedingung erfüllen. Dies ist in der diskutierten Modellklasse für die geschlossenen String-Felder nur für den sehr speziellen Fall möglich, daß einige Felder als eingefroren behandelt werden und zudem ein spezielles Koordinatensystem verwendet wird. Im Sektor der offenen Strings konnte auf One-loop-Niveau kein Modulusfeld die Bedingung erfüllen. / Intersecting branes have been the subject of an elaborate string model building for several years. After a general introduction into string theory, this work introduces in detail the toroidal and Z_N-orientifolds. The picture involving D9-branes with B-fluxes is shortly reviewed, but the main discussion employs the T-dual picture of intersecting D6-branes. The derivation of the R-R and NS-NS tadpole cancellation conditions in the conformal field theory is shown in great detail. Various aspects of the open and closed chiral and non-chiral massless spectrum are discussed, involving spacetime anomalies and the generalized Green-Schwarz mechanism. An introduction into possible gauge breaking mechanisms is given, too. Afterwards, both N=1 supersymmetric and non-supersymmetric approaches to low energy model building are treated. Firstly, the problem of complex structure instabilities in toroidal OmegaR-orientifolds is approached by a Z_3-orbifolded model. In particular, a stable non-supersymmetric standard-like model with three fermion generations is discussed. This model features the standard model gauge groups at the same time as having a massless hypercharge, but possessing an additional global B-L symmetry. The electroweak Higgs mechanism and the Yukawa couplings are not realized in the usual way. It is shown that this model descends naturally from a flipped SU(5) GUT model, where the string scale has to be at least of the order of the GUT scale. Secondly, supersymmetric models on the Z_4-orbifold are discussed, involving exceptional 3-cycles and the explicit construction of fractional D-branes. A three generation Pati-Salam model is constructed as a particular example, where several brane recombination mechanisms are used, yielding non-flat and non-factorizable branes. This model even can be broken down to a MSSM-like model with a massless hypercharge. Finally, the possibility if unstable closed and open string moduli could have played the role of the inflaton in the evolution of the universe is being explored. In the closed string sector, the important slow-rolling requirement can only be fulfilled for very specific cases, where some moduli are frozen and a special choice of coordinates is taken. In the open string sector, inflation does not seem to be possible at all.

Diese Dissertation konzentriert sich auf die perturbative Berechnung von Streuamplituden in der Stringtheorie, insbesondere auf Ein-Schleifen-Amplituden für geschlossene Strings. In diesem Fall ist die Weltfläche ein Torus oder eine Riemannsche Fläche vom Geschlecht eins, wobei Punktierungen externe Strings repräsentieren. Der Torus besitzt eine SL(2,Z)-Symmetrie (die modulare Gruppe), die reiche mathematische Eigenschaften offenbart, die für das Verständnis der Amplituden in der Stringtheorie von zentraler Bedeutung sind. Die Niedrigenergie-Entwicklung der Streuamplituden für geschlossene Strings auf Genus-eins-Niveau wird durch die Integration von Korrelatoren der konformen Feldtheorie über den Modulraum des punktierten Torus bestimmt. Dieser Prozess zerfällt in zwei Integrale: eines über den Konfigurationsraum der Einfügungspunkte und eines über den Modulraum der Tori. Das erste Integral führt zu nicht-holomorphen modularen Formen, die als modulare Graphenformen (MGFs) bekannt sind. Diese Arbeit wendet Techniken aus der algebraischen Geometrie und Zahlentheorie an, um MGFs als iterierte Integrale von holomorphen Eisensteinreihen und deren komplexer Konjugation zu analysieren. Mithilfe von Zetageneratoren zeigt die Fourier-Entwicklung der MGFs das Auftreten von mehrfachen Zetawerten und deren einfachwertigen Versionen. Der Prozess wird auf nicht-holomorphe modulare Formen ausgeweitet, die aus iterierten Integralen holomorpher modularer Formen konstruiert sind und holomorphe Spitzenformen einbeziehen. Diese Konstrukte helfen bei der Definition der modularen Vervollständigung der dreifachen Eisenstein-Integrale, wobei Koeffizienten auftreten, die multiple Zetawerte, L-Werte der Spitzenformen und neue Perioden enthalten. Auf modularer Tiefe drei wird eine Basis der MGFs unter Verwendung von Lösungen der Laplace-Gleichungen konstruiert, die es ermöglicht, MGFs über den Modulraum des Torus zu integrieren. / This thesis focuses on the perturbative calculation of scattering amplitudes in string theory, particularly at one-loop for closed strings. At this level, the worldsheet is a torus, or genus-one Riemann surface, with punctures representing external strings. The torus possesses an SL(2,Z) symmetry (the modular group), which reveals rich mathematical properties crucial to understanding string theory amplitudes. The low-energy expansion of genus-one closed-string scattering amplitudes is derived by integrating conformal field theory correlators over the moduli space of the punctured torus. This process splits into two integrals: one over the configuration space of insertion points and the other over the moduli space of tori. The first integral introduces non-holomorphic modular forms known as modular graph forms (MGFs). This work applies techniques from algebraic geometry and number theory to analyze MGFs as iterated integrals of holomorphic Eisenstein series and their complex conjugates. Using zeta generators, the Fourier expansion of MGFs reveals the presence of multiple zeta values and their single-valued versions. The study extends to non-holomorphic modular forms constructed from iterated integrals of holomorphic modular forms, incorporating holomorphic cusp forms. These constructs help define the modular completion of triple Eisenstein integrals, yielding coefficients involving multiple zeta values, L-values of cusp forms, and new periods. At modular depth three, a basis of MGFs is constructed using solutions to Laplace equations, allowing for the integration of MGFs over the torus moduli space.

Travail réalisé en cotutelle avec l'université Paris-Diderot et le Commissariat à l'Energie Atomique sous la direction de John Harnad et Bertrand Eynard. / Cette thèse traite des aspects géométriques et d'intégrabilité associés aux modèles de matrices aléatoires. Son but est de présenter diverses applications des modèles de matrices aléatoires allant de la géométrie algébrique aux équations aux dérivées partielles des systèmes intégrables. Ces différentes applications permettent en particulier de montrer en quoi les modèles de matrices possèdent une grande richesse d'un point de vue mathématique. Ainsi, cette thèse abordera d'abord l'étude de la jonction de deux intervalles du support de la densité des valeurs propres au voisinage d'un point singulier. On montrera plus précisément en quoi ce régime limite particulier aboutit aux équations universelles de la hiérarchie de Painlevé II des systèmes intégrables. Ensuite, l'approche des polynômes (bi)-orthogonaux, introduite par Mehta pour le calcul des fonctions de partition, permettra d'énoncer des problèmes de Riemann-Hilbert et d'isomonodromies associés aux modèles de matrices, faisant ainsi le lien avec la théorie de Jimbo-Miwa-Ueno. On montrera en particulier que le cas des modèles à deux matrices hermitiens se transpose à un cas dégénéré de la théorie isomonodromique de Jimbo-Miwa-Ueno qui sera alors généralisé. La méthode des équations de boucles avec ses notions centrales de courbe spectrale et de développement topologique permettra quant à elle de faire le lien avec les invariants symplectiques de géométrie algébrique introduits récemment par Eynard et Orantin. Ce dernier point fera également l'objet d'une généralisation aux modèles de matrices non-hermitien (beta quelconque) ouvrant ainsi la voie à la ``géométrie algébrique quantique'' et à la généralisation de ces invariants symplectiques pour des courbes ``quantiques''. Enfin, une dernière partie sera consacrée aux liens étroits entre les modèles de matrices et les problèmes de combinatoire. En particulier, l'accent sera mis sur les aspects géométriques de la théorie des cordes topologiques avec la construction explicite d'un modèle de matrices aléatoires donnant le dénombrement des invariants de Gromov-Witten pour les variétés de Calabi-Yau toriques de dimension complexe trois utilisées en théorie des cordes topologiques. L'étendue des domaines abordés étant très vaste, l'objectif de la thèse est de présenter de façon la plus simple possible chacun des domaines mentionnés précédemment et d'analyser en quoi les modèles de matrices peuvent apporter une aide précieuse dans leur résolution. Le fil conducteur étant les modèles matriciels, chaque partie a été conçue pour être abordable pour un spécialiste des modèles de matrices ne connaissant pas forcément tous les domaines d'application présentés ici. / This thesis deals with the geometric and integrable aspects associated with random matrix models. Its purpose is to provide various applications of random matrix theory, from algebraic geometry to partial differential equations of integrable systems. The variety of these applications shows why matrix models are important from a mathematical point of view. First, the thesis will focus on the study of the merging of two intervals of the eigenvalues density near a singular point. Specifically, we will show why this special limit gives universal equations from the Painlevé II hierarchy of integrable systems theory. Then, following the approach of (bi) orthogonal polynomials introduced by Mehta to compute partition functions, we will find Riemann-Hilbert and isomonodromic problems connected to matrix models, making the link with the theory of Jimbo, Miwa and Ueno. In particular, we will describe how the hermitian two-matrix models provide a degenerate case of Jimbo-Miwa-Ueno's theory that we will generalize in this context. Furthermore, the loop equations method, with its central notions of spectral curve and topological expansion, will lead to the symplectic invariants of algebraic geometry recently proposed by Eynard and Orantin. This last point will be generalized to the case of non-hermitian matrix models (arbitrary beta) paving the way to ``quantum algebraic geometry'' and to the generalization of symplectic invariants to ``quantum curves''. Finally, this set up will be applied to combinatorics in the context of topological string theory, with the explicit computation of an hermitian random matrix model enumerating the Gromov-Witten invariants of a toric Calabi-Yau threefold. Since the range of the applications encountered is large, we try to present every domain in a simple way and explain how random matrix models can bring new insights to those fields. The common element of the thesis being matrix models, each part has been written so that readers unfamiliar with the domains of application but familiar with matrix models should be able to understand it.

We introduce slow-roll inflation in string theory on both a conceptual level and a detailed one. In order to do this we first briefly review important concepts of inflation and string theory. We then reconstruct models of string inflation in the so-called Racetrack scenario for two different cases where the difference being the number of Kähler moduli used as inflaton. Furthermore, we briefly relate our results to the more recent discussion on whether AdS/dS solutions actually exist in string theory. In this instance our results seem to indicate that uplifting is a crucial component to obtain AdS/dS solutions.

This work is divided into two major topics: many-worlds (or multiverse) theories in cosmology and Richard Dawids string theory-based epistemology, or non-empirical confirmation theory, as he calls it. The former is discussed in part I and the latter in part II of this dissertation. These topics are not intertwined in this work, as are not the essays that compose each chapter: in part I, first chapter, probability arguments that are presented in the literature as indications a multiverse must exist are accessed, whereas the second chapter is concerned with analyzing the metaphysical view that motivates many-world theory building, namely, the need to find unconditioned explanations in physics. Non-empirical confirmation theory is built upon three arguments, the No Alternatives Argument, the Meta-Inductive Argument from the Success of Other Theories in the Research Program and the Unexpected Explanatory Coherence Argument. Each compose a chapter in part II of this work, as they encode different philosophical issues that require for their assessment different tools from the philosophers arsenal. Skeptical conclusions are drawn at the end of each chapter. The wide spectrum of questions this work touches are designed to give at least slight indication that critical exploration of foundational theories made upon grounds familiar to philosophers can be found as internal to scientific practice itself, if that practice is concerned with the discovery, refinement and revision of fundamental theories. / Este trabalho divide-se em dois grandes tópicos: teorias de muitos mundos (ou multiverso) em cosmologia e a epistemologia não-empírica, embasada na teoria das cordas, de Richard Dawid. O primeiro é discutido na parte I e o segundo compõe a parte II deste trabalho. Tais tópicos não estão ligados, e a problemática desenvolvida em cada capítulo deste trabalho é, em larga medida, independente das demais: no primeiro capítulo da parte I argumentos probabilísticos indicados a literatura em prol da existência de muitos mundos são analisados, enquanto no segundo capítulo os pressupostos metafísicos que motivam a construção de teorias de muitos mundos em cosmologia, a saber, o fundamentalismo que busca explicações não-condicionadas para os fenômenos com os quais lida a física, são discutidos. A teoria da confirmação não-empírica de Dawid, tema da segunda parte deste trabalho, tem por base três argumentos, a saber, o argumento das alternativas inexistentes, o argumento meta-indutivo do sucesso de outras teorias no programa de pesquisa e o argumento da coerência explanatória inesperada. Cada um destes argumentos é tema de um capítulo neste trabalho, posto que desvelam problemáticas filosóficas distintas que requerem, por sua natureza, ferramentas de análise diferentes. Conclusões céticas são indicadas ao final de cada capítulo. O amplo espectro de questões que aborda este trabalho é desenhado com o propósito de fornecer ao menos vaga indicação de que a exploração crítica de teorias fundamentais, levadas a cabo a partir de vieses familiares ao filósofo, pode ser vista como interna à própria prática científica, se esta prática é preocupada com a descoberta, refinamento e revisão de teorias fundamentais.

Cette thèse porte sur diverses applications de la théorie des cordes topologiques basée sur différents types de variétés de Calabi-Yau (CY). Le premier type considéré est la variété torique CY, qui est intimement liée aux problèmes spectraux des différents opérateurs. L'exemple particulier considéré dans la thèse ressemble beaucoup au modèle de Harper-Hofstadter en physique de la matière condensée. Nous étudions d’abord les secteurs non perturbatifs dans ce modèle et proposons une nouvelle façon de les calculer en utilisant la théorie topologique des cordes. Dans la deuxième partie de la thèse, nous considérons les fonctions de partition sur des variétés de CY elliptiquement fibrées. Celles-ci présentent un comportement modulaire intéressant. Nous montrons que pour les géométries qui ne conduisent pas à des symétries de jauge non abéliennes, les fonctions de partition des cordes topologiques peuvent être reconstruites avec seulement les invariants de Gromov-Witten du genre zéro. Finalement, nous discutons des travaux en cours concernant la relation entre les fonctions de partitionnement des cordes topologiques sur les soi-disant arbres de Higgsing dans la théorie de F. / This thesis focuses on various applications of topological string theory based on different types of Calabi-Yau (CY) manifolds. The first type considered is the toric CY manifold, which is intimately related to spectral problems of difference operators. The particular example considered in the thesis closely resembles the Harper-Hofstadter model in condensed matter physics. We first study the non-perturbative sectors in this model, and then propose a new way to compute them using topological string theory. In the second part of the thesis, we consider partition functions on elliptically fibered CY manifolds. These exhibit interesting modular behavior. We show that for geometries which don't lead to non-abelian gauge symmetries, the topological string partition functions can be reconstructed based solely on genus zero Gromov-Witten invariants. Finally, we discuss ongoing work regarding the relation of the topological string partition functions on the so-called Higgsing trees in F-theory.

In the nanoscale metrology industry, there is a need for low-cost instruments, which have the ability to probe the structrure and elemental composition of thin films. This dissertation, describes the research performed to design and simulate a miniature Cylindrical Mirror Analyzer, (CMA), and Auger Electron Spectrometer, (AES). The CMA includes an integrated coaxial thermionic electron source. Electron optics simulations were performed using the Finite Element Method, (FEM), software COMSOL. To address the large Secondary Electron, (SE), noise, inherent in AES spectra, this research also included experiments to create structures in materials, which were intended to suppress SE backgound noise in the CMA. Laser Beam Machining, (LBM), of copper substrates was used to create copper pillars with very high surface areas, which were designed to supress SE’s. The LBM was performed with a Lumera SUPER RAPID‐HE model Neodymium Vanadate laser. The laser has a peak output power of 30 megawatts, has a 5x lens and a spot size of 16 μm. The laser wavelength is in the infrared at 1064 nm, a pulse width of 15 picoseconds, and pulse repetition rate up to 100 kHz. The spectrometer used in this research is intended for use when performing chemical analysis of the surface of bulk materials and thin films. It is applicable for metrology of thin films, as low as 0.4 nm in thickness, without the need to perform destructive sample thinning, which is required in Scanning Tranmission Electron Microscopy, (STEM). The spectrometer design is based on the well known and widely used coaxial cylinder capacitor design known as the Cylindrical Mirror Analyzer, (CMA). The coaxial tube arrangement of the CMA allows for placing an electron source,which is mounted in the center of the inner cylinder of the spectrometer. Simulation of the electron source with an Einzel Lens was also performed. In addtion, experiments with thin film coatings and Laser Beam Machining to supress Secondary Electron emission noise within the Auger electron spectrum were completed. Design geometry for the miniature CMA were modeled using Computer Aided Design, (CAD). Fixed Boundary Conditions, (BC), were applied and the geometry was then meshed for FEM. The electrostatic potential was then solved using the Poisson equation at each point. Having found the solution to the electrostatic potentials, electron flight simulations were performed and compared with the analytical solution. From several commercially available FEM modeling packages, COMSOL Multiphysics was chosen as the research platform for modeling of the spectrometer design. The CMA in this design was reduced in size by a factor of 4 to 5. This enabled mounting the CMA on a 2 ¾ in flange compared to the commercial PHI model 660 CMA which mounts onto a 10 in flange. Results from the Scanning Electron Microscopy measurements of the Secondary Electron emission characteristics of the LBM electron suppressor will also be presented.