Electromagnetic wave propagation and absorption in electrodeless plasma thrusters

The thesis aims at developing a numerical code to study the electromagnetic wave-plasma interaction phenomena critical for the operation of electrodeless thrusters, particularly, the Electron Cyclotron Resonance (ECR) Thruster under development in the European H2020 MINOTOR project. Current in-space Electric Propulsion technologies are presented with special attention to their advantageous characteristics compared to conventional techniques. Among those, electrodeless thrusters emerge as efficient and durable alternatives for future propulsion systems. The main limitation hindering the implementation of these devices is the complicated physical phenomena governing the fundamental operational stages i.e. the plasma heating and ionization, and the acceleration of charged particles. The present work is devoted to the study of the plasma heating mechanism by electromagnetic wave interaction. As presented in the chapter on electromagnetic theory, this is a complex physical problem with a considerable amount of phenomena going on; such as absorption, re ection, resonance or cuto . Numerical methods are a suitable tool to address the specific behavior taking place inside a thruster and better understand the physics underneath. Furthermore, future numerical codes should be capable of simulating the complete thruster operation by integrating the plasma wave interaction code with additional ion and neutral, electron, and magnetic nozzle codes. Full simulations will serve to shorten design cycles and complement laboratory testing during the preliminary design phase. This thesis manly focuses on the implementation and verification of the 2D wave-plasma code fdwaves while presenting important concepts on electromagnetism, plasma physics and numerical methods. Specifically, a two dimensional Finite Di erence and Frequency Domain method is used to discretize the Maxwell's Equations. Numerical wave normal surfaces are plotted using von Neumann stability analysis implemented in the wave-explorer code and compared using solutions to the analytic dispersion relation. This is shown to be truly useful to evaluate the behavior of numerical schemes in terms of spurious propagation and divergence from the physical solution. Preliminary results are shown, firstly, propagation through vacuum serving as a verification method for the code due to the existence of straightforward analytic solutions, then, wave behavior in homogeneous cold plasma media is presented. The work carried out in this thesis is intended to be continued in the future, as a consequence, a considerable number of tools currently under study or development are presented. Special mention should be made of the new code for arbitrary geometry simulation fdmesher, non-uniform grids and the Perfectly Matched Layer (PML) boundary conditions.Ingeniería Aeroespacial (Plan 2010

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La solución de algunas EDO de Riccati

En este artículo, se presenta un enfoque nuevo y eficaz para determinar la solución general de la ecuación diferencial no lineal de Riccati cuando los coeficientes son variables y están relacionados entre sí mediante otra ecuación diferencial ordinaria. La ecuación de Riccati se convierte de una vez a una ecuación diferencial ordinaria de Bernoulli y tiene la ventaja que no se necesita conocer a priori una solución particular. Estos métodos de solución permiten explicar este tipo de EDO de manera sencilla en las aulas

Markoff-Rosenberger triples in arithmetic progression

We study the solutions of the Rosenberg--Markoff equation ax^2+by^2+cz^2 = dxyz (a generalization of the well--known Markoff equation). We specifically focus on looking for solutions in arithmetic progression that lie in the ring of integers of a number field. With the help of previous work by Alvanos and Poulakis, we give a complete decision algorithm, which allows us to prove finiteness results concerning these particular solutions. Finally, some extensive computations are presented regarding two particular cases: the generalized Markoff equation x^2+y^2+z^2 = dxyz over quadratic fields and the classic Markoff equation x^2+y^2+z^2 = 3xyz over an arbitrary number field.Comment: To appear in Journal of Symbolic Computatio