Space-charge effects play a dominant role in many areas of physics. In high-power microwave devices using high-current, relativistic electron beams, it places a limit on the amount of radiation a device can produce. Because the beam's space-charge can actually reflect a portion of the beam, the ability to accurately predict the amount of current a device can carry is needed. This current value is known as the space-charge limited current. Because of the mathematical difficulties, this limit is typically estimated from a one-dimensional theory. This work presents a two-dimensional theory for calculating an upper-bound for the space-charge limited current of relativistic electron beams propagating in grounded coaxial drift tubes. Applicable to annular beams of arbitrary radius and thickness, the theory includes the effect introduced by a finite-length drift tube of circular cross-section. Using Green's second identity, the need to solve Poisson's equation is transferred to solving a Sturm-Liouville eigenvalue problem, which is easily solved by elementary methods. In general, the resulting eigenvalue, which is required to estimate the limiting current, must be numerically determined. However, analytic expressions can be found for frequently encountered limiting cases. Space-charge effects also produce the fundamental collective behavior found in plasmas, especially in plasma sheaths. A plasma sheath is the transition region between a bulk plasma and an adjacent plasma-facing surface. The sheath controls the loss of particles from the plasma in order to maintain neutrality. Using a fully kinetic theory, the problem of a planar sheath with a single-minimum electric potential profile is investigated. Appropriate for single charge-state ions of arbitrary temperature, the theory includes the emission of warm electrons from the surface as well as a net current through the sheath and is compared to particle-in-cell simulations. Approximate expressions are developed for estimating the sheath potential as well as the transition to space-charge saturation. The case of a space-charge limited sheath is discussed and compared to the familiar Child-Langmuir law.

This investigation examines band gap engineering of the GaAsN alloy by means of plasma ion implantation. The strong redshift of the alloy's band gap is suitable for telecommunication applications and thus stimulated much interest in recent years. Nitrogen (N) ion implantation into gallium arsenide (GaAs) results in a thin shallow N-rich layer below the surface. However, the violent implantation process also modifies the concentrations of gallium and arsenide. The core of this thesis is a novel method for prediction of the band gap from the conditions in the processing plasma.<p>The first important variable, the number of implanted ions, is obtained from the Lieberman model for the current during high-voltage Plasma Ion Implantation (PII). A review of the model's assumptions is provided as well as a comprehensive discussion of the implantation which includes error boundaries. The predicted and measured ion currents agree within error boundaries. The number of implanted ions can therefore be obtained from the prediction.<p>The distribution of the implanted ions was subsequently explored by simulations such as TRIM and TRIDYN. It was found that the nitrogen content in GaAs is limited by the sputtering of the surface atoms. Furthermore, the content of gallium increases near the surface while the content of arsenic decreases. The predicted ratios of the constituents in the implanted layer is such that the alloy cannot form by ion implantation alone; it could be reconciled by annealing.<p>Preliminary samples were produced and tested for the formation of the GaAsN alloy by Raman spectroscopy. No evidence for bonds between N and either Ga or As was found in the as-implanted samples. The thesis concludes with a discussion of the necessary steps to synthesize the GaAsN alloy.

This investigation examines band gap engineering of the GaAsN alloy by means of plasma ion implantation. The strong redshift of the alloy's band gap is suitable for telecommunication applications and thus stimulated much interest in recent years. Nitrogen (N) ion implantation into gallium arsenide (GaAs) results in a thin shallow N-rich layer below the surface. However, the violent implantation process also modifies the concentrations of gallium and arsenide. The core of this thesis is a novel method for prediction of the band gap from the conditions in the processing plasma.<p>The first important variable, the number of implanted ions, is obtained from the Lieberman model for the current during high-voltage Plasma Ion Implantation (PII). A review of the model's assumptions is provided as well as a comprehensive discussion of the implantation which includes error boundaries. The predicted and measured ion currents agree within error boundaries. The number of implanted ions can therefore be obtained from the prediction.<p>The distribution of the implanted ions was subsequently explored by simulations such as TRIM and TRIDYN. It was found that the nitrogen content in GaAs is limited by the sputtering of the surface atoms. Furthermore, the content of gallium increases near the surface while the content of arsenic decreases. The predicted ratios of the constituents in the implanted layer is such that the alloy cannot form by ion implantation alone; it could be reconciled by annealing.<p>Preliminary samples were produced and tested for the formation of the GaAsN alloy by Raman spectroscopy. No evidence for bonds between N and either Ga or As was found in the as-implanted samples. The thesis concludes with a discussion of the necessary steps to synthesize the GaAsN alloy.

Eines der größten Probleme bei der kontrollierten Kernfusion ist die immense thermische Belastung der mit dem Plasma in Berührung kommenden Materialien. Um den Energiefluß aus dem Plasma auf eine möglichst große Fläche zu verteilen, werden die betroffenen Komponenten in der Regel so angebracht, da"s das magnetische Feld annähernd parallel zur Oberfläche verläuft. Im Rahmen dieser Arbeit wurden ein spezieller drehbarer Meßkopf zur winkelabhängigen Messung des Strom- und Energieflusses entwickelt und ausführliche experimentelle Untersuchungen zur Winkelabhängigkeit der Teilchen- und Energieflüsse auf eine Fläche durchgeführt. Zum Verständnis der zu Grunde liegenden Mechanismen wird basierend auf den Gyrationsbahnen der Teilchen ein analytisches Modell entwickelt und dessen qualitative Übereinstimmung mit den experimentellen Befunden festgestellt. Die Durchführung der Experimente erfolgte am Plasmagenerator PSI-2, einem linearen Divertor-Simulator mit einem moderaten magnetischen Feld. Der Aufbau des Meßkopfes als ebene Sonde in einer isolierten Fläche enspricht dabei in etwa der einer sogenannten ,,flush-mounted probe''''. Die äußeren Maße der Sonde sind dabei vergleichbar mit dem Ionengyroradius ri}. Während die Elektronen bei den Experimenten stark magnetisiert sind, variieren die Bedingungen für die Ionen zwischen unmagnetisiert und magnetisiert je nach Ionenmasse und Magnetfeldstärke. Bei den Experimenten wurden verschiedene Größen der Plasmarandschicht als Funktionen des Winkels zwischen der Oberflächennormale der Sonde und dem Vektor des magnetischen Feldes bestimmt. / In fusion experiments, the energy flux to the target plates is an important issue. In order to spread the heat load, surfaces are usually designed to intersect magnetic field lines at very shallow angles. In the course of this work, a sensitive probe allowing simultaneous measurements of energy flux and current density as functions of a bias voltage was developed. Extensive experimental data on the particle and energy flux densities as functions of the angle between a surface and the confining magnetic field are provided. An analytical model is developed in order to reveal the physics involved; it is in good qualitative agreement with the experimental results. The experiments were conducted at the PSI-2 facility, a linear divertor simulator with moderate magnetic field strength. The probe was rotated in a spatially homogeneous plasma. The active area, a tungsten covered Peltier module, was immersed in a ceramic surface, closely resembling the geometry of a flush mounted probe. Its dimensions were comparable to the ion gyro radius ri. While the electrons were strongly magnetized, the ion conditions varied between unmagnetized and magnetized depending on the ion species. Sheath parameters were determined as functions of the angle alpha between the probe surface normal and the magnetic field.