Analysis of the flow field in a laser engine represents a difficult computational problem involving combinations of complex physical and gas-dynamical processes. Following a brief discussion of these processes a calculation procedure using primitive variables formulation on a non-staggered grid system is introduced. Based on this procedure, a Pressure Based Navier-Stokes Solver (PBNS) is developed using a generalized curvilinear coordinate system. The solver is first tested in application to a subsonic compressible flow over an insulated flat plate and to a flow in an axisymmetric converging-diverging nozzle. Next, the PBNS code is used to analyze the flowfield and performance of a laser thruster. The physical/numerical model includes the geometric ray tracing for the laser beam, beam power absorption, plasma radiation losses, and plasma thermophysical and optical properties. Equilibrium hydrogen is used as a flowing gas and its properties are calculated using the Hydrogen Properties Calculation (HPC) based on the the methods of statistical thermodynamics. Two thruster configurations, two laser types (CO₂ and iodide), various laser power levels, and various injection conditions are tested. The results of these tests include the temperature, pressure, velocity and Mach number contours, as well as table of the laser beam power absorbed, radiation losses to the thruster walls, thrust level and specific impulse. The maximum specific impulse obtained in these tests is 1537 sec for a CO₂ laser thruster and 827 sec for an iodide laser thruster. Up to 100% power absorption can be achieved, however, the radiation losses from the hot plasma are quite high disallowing a full conversion of the absorbed power into the thermal energy of the propellant. The PBNS code can be used to study the effects of various design parameters on the performance of a laser thruster and provide guidelines for the preliminary design of a laser engine. / Ph. D.

The use of aerodynamic forces to assist in certain orbital transfers can greatly reduce the fuel consumption as compared with corresponding all-propulsive transfers. Therefore, in seeking minimum fuel trajectories, aeroassisted transfers need to be investigated. A review of the current literature indicates that such problems have been solved almost exclusively via optimal control theory formulations that result in continuously varying control laws. The use of a piecewise-constant strategy allows the controls to vary to a degree necessary to affect changes in the desired state dependent parameters while simplifying the optimization process. In the process of searching for a tool to produce numerical results, the current research investigates three candidate methods of solving the parameter optimization problem of minimum fuel aeroassisted orbital transfer with piecewise-constant controls. A method based on implicitly integrating the state trajectory is chosen over methods which analytically and explicitly integrate the state trajectory. The implicit method offers improved performance over the explicit method while presenting a more correct solution than the analytic method. The analytic method is shown to suffer from approximations that lead to undesirable solutions. Analytic expressions for the characteristic velocities of Hohmann and idealized aeroassisted transfers are presented and compared. For a large number of transfers from high Earth orbit to low Earth orbit, the aeroassisted mode requires less fuel. Numerical results are presented for minimum fuel transfer from geosynchronous Earth orbit to low earth orbit for a variety of control strategies. The piecewise-constant strategies are seen to provide solutions which are comparable to those found via optimal control theory. / Master of Science

Thesis (Ph. D.)--University of Hawaii at Manoa, 1991. / Includes bibliographical references (leaves 152-154) / Microfiche. / xvi,154 leaves, bound ill. 29 cm

The problem of developing a generalized impulse as a function of a set of parameters is investigated. The proposed generalized impulse alters an existing orbit by producing, over some period of time, a change in velocity, ΔV, as well as a change in position, Δr. The generalized impulse is described by parameters associated with an instantaneous change in velocity as well as parameters associated with an atmospheric skip trajectory. Closed form solutions are obtained through several changes of independent variable, the use of modified Chapman variables and the consequent analytical integration of the uncoupled equations. The closed form solutions contain between two and six parameters depending on the complexity of the desired skip trajectory. Fuel optimal transfer orbits are obtained using the generalized impulse along with Keplerian arcs and instantaneous changes in velocity. Families of coplanar and noncoplanar transfers for circular orbit to circular orbit are numerically generated. The generated transfer trajectories involve the rendezvous of two vehicles. The orbits are not globally optimal but rather optimal for the specified number and type of velocity impulses specified. The optimal solution to the nonlinear problem is determined via sequential quadratic programming which satisfies the Kuhn-Tucker optimality conditions for constrained minimization. It is found that for transfer between coplanar and noncoplanar orbits, solutions using the generalized impulse compare favorably with solutions obtained by optimal control theory. Numerical solution to complex problems involving transfer from general orbit to general orbit were not obtained. / Master of Science

In this work, we describe all the possible radiative processes occurring in a low temperature hydrogen plasma. Some of the fundamental concepts involving ionized gases and collision phenomena are presented, and a rigorous approach is used to show that classical mechanics is quite appropriate to our study. As an application to a laser engine, we investigate the effects of the maximum temperature, the temperature gradient, the stretching of the plasma shape, the engine pressure, and the equivalent sphere radius, on the total emitted power, including absorbing mechanisms through the equation of radiative transfer. Graphs related to spectral radiative exitances are included, and a complete set of graphs of the total power, permitting interpolations with respect to the above relevant parameters, are also provided. / Master of Science

Le contexte de ce travail est le contrôle optimal géométrique appliqué à la mécanique céleste et au contrôle quantique. On s’est tout d’abord intéressé au problème de transfert orbital de satellite autour de la Terre à consommation minimale,qui amena à la réalisation du code HamPath, permettant tout d’abord la résolution de problème de contrôle optimal dont la loi de commande est lisse. Il se base sur le Principe du Maximum de Pontryagin (PMP) et sur la notion de point conjugué. Ce programme combine méthode de tir, méthodes homotopiques différentielles et calcul des conditions d’optimalité du deuxième ordre. Nous nous intéressons par la suite au contrôle quantique. On étudie tout d’abord le contrôle d’un système composé de deux types de particules de spin 1/2 ayant des temps de relaxation différents et dont la dynamique est gouvernée par les équations de Bloch. Ces deux sous-systèmes,correspondant aux deux types de particules, sont couplés par un même contrôle (un champ electromagnétique), le but étant alors d’amener la magnétisation des particules du premier type à zéro tout en maximisant celle du second (dans un système de coordonnées bien choisi). Ce modèle intervient en imagerie médicale par Résonance Magnétique Nucléaire et consiste à maximiser le contraste entre deux régions d’une même image. L’utilisation des outils géométriques et numériques aura permis de donner une très bonne synthèse sous-optimale pour deux cas particuliers (mélange sang oxygéné/désoxygéné et liquide cérébrospinal/eau). La dernière contribution de cette thèse porte sur l’étude d’un système quantique à deux niveaux d’énergie dontl a dynamique est régie par les équations de Lindblad. Le modèle est basé sur la minimisation d’énergie du transfert. On se restreint à un cas particulier pour lequelle Hamiltonien donné par le PMP est Liouville intégrable. On décrit alors les lieux conjugués et de coupure pour ce problème riemannien avec dérive / This work is about geometric optimal control applied to celestial and quantum mechanics. We first dealt with the minimum fuel consumption problem of transfering a satellite around the Earth. This brought to the creation of the code HamPath which permits first of all to solve optimal control problem for which the command law is smooth. It is based on the Pontryagin Maximum Principle (PMP) and on the notion of conjugate point. This program combines shooting method, differential homotopic methods and tools to compute second order optimality conditions. Then we are interested in quantum control. We study first a system which consists in two different particles of spin 1/2 having two different relaxation time. Both sub-systems are driven by the same control. The problem consists in bringing to zero the magnetization of one of the two system while maximizing the magnetization of the second one. This problem comes from constrast imaging in Nuclear Magnetic Resonance and consists in maximising the contrast between two areas of the image. The use of geometrical and numerical tools has given a very precise sub-optimal synthesis for two particular cases (deoxygenated/oxygenated blood and cerebrospinal fluid/water cases). The last contribution of this thesis is about the Lindblad equations in the two-level case. The model is based upon the minimisation of the transfer energy. We restrict the study to a particular case for which the Hamiltonian given by the PMP is Liouville integrable.We describe the conjugate and cut loci for this Riemannian with drift problem