C��digo h��brido avanzado de motores de plasma de efecto Hall

La propulsi��n el��ctrica constituye hoy una tecnolog��a muy competitiva y de gran proyecci��n de futuro. Dentro de los diversos motores de plasma existentes, el motor de efecto Hall ha adquirido una gran madurez y constituye un medio de propulsi��n id��neo para un rango amplio de misiones. En la presente Tesis se estudian los motores Hall con geometr��a convencional y paredes diel��ctricas. La compleja interacci��n entre los m��ltiples fen��menos f��sicos presentes hace que sea dif��cil la simulaci��n del plasma en estos motores. Los modelos h��bridos son los que representan un mejor compromiso entre precisi��n y tiempo de c��lculo. Se basan en utilizar un modelo fluido para los electrones y algoritmos de din��mica de part��culas PIC (Particle-In- Cell) para los iones y los neutros. Permiten hacer uso de la hip��tesis de cuasineutralidad del plasma, a cambio de resolver separadamente las capas l��mite (o vainas) que se forman en torno a las paredes de la c��mara. Partiendo de un c��digo h��brido existente, llamado HPHall-2, el objetivo de la Tesis doctoral ha sido el desarrollo de un c��digo h��brido avanzado que mejorara la simulaci��n de la descarga de plasma en un motor de efecto Hall. Las actualizaciones y mejoras realizadas en las diferentes partes que componen el c��digo comprenden tanto aspectos te��ricos como num��ricos. Fruto de la extensa revisi��n de la algoritmia del c��digo HPHall-2 se han conseguido reducir los errores de precisi��n un orden de magnitud, y se ha incrementado notablemente su consistencia y robustez, permitiendo la simulaci��n del motor en un amplio rango de condiciones. Algunos aspectos relevantes a destacar en el subc��digo de part��culas son: la implementaci��n de un nuevo algoritmo de pesado que permite determinar de forma m��s precisa el flujo de las magnitudes del plasma; la implementaci��n de un nuevo algoritmo de control de poblaci��n, que permite tener suficiente n��mero de part��culas cerca de las paredes de la c��mara, donde los gradientes son mayores y las condiciones de c��lculo son m��s cr��ticas; las mejoras en los balances de masa y energ��a; y un mejor c��lculo del campo el��ctrico en una malla no uniforme. Merece especial atenci��n el cumplimiento de la condici��n de Bohm en el borde de vaina, que en los c��digos h��bridos representa una condici��n de contorno necesaria para obtener una soluci��n consistente con el modelo de interacci��n plasma-pared, y que en HPHall-2 a��n no se hab��a resuelto satisfactoriamente. En esta Tesis se ha implementado el criterio cin��tico de Bohm para una poblaci��n de iones con diferentes cargas el��ctricas y una gran dispersi��n de velocidades. En el c��digo, el cumplimiento de la condici��n cin��tica de Bohm se consigue por medio de un algoritmo que introduce una fina capa de aceleraci��n nocolisional adyacente a la vaina y mide adecuadamente el flujo de part��culas en el espacio y en el tiempo. Las mejoras realizadas en el subc��digo de electrones incrementan la capacidad de simulaci��n del c��digo, especialmente en la regi��n aguas abajo del motor, donde se simula la neutralizaci��n del chorro del plasma por medio de un modelo de c��todo volum��trico. Sin abordar el estudio detallado de la turbulencia del plasma, se implementan modelos sencillos de ajuste de la difusi��n an��mala de Bohm, que permiten reproducir los valores experimentales del potencial y la temperatura del plasma, as�� como la corriente de descarga del motor. En cuanto a los aspectos te��ricos, se hace especial ��nfasis en la interacci��n plasma-pared y en la din��mica de los electrones secundarios libres en el interior del plasma, cuestiones que representan hoy en d��a problemas abiertos en la simulaci��n de los motores Hall. Los nuevos modelos desarrollados buscan una imagen m��s fiel a la realidad. As��, se implementa el modelo de vaina de termalizaci��n parcial, que considera una funci��n de distribuci��n no-Maxwelliana para los electrones primarios y contabiliza unas p��rdidas energ��ticas m��s cercanas a la realidad. Respecto a los electrones secundarios, se realiza un estudio cin��tico simplificado para evaluar su grado de confinamiento en el plasma, y mediante un modelo fluido en el l��mite no-colisional, se determinan las densidades y energ��as de los electrones secundarios libres, as�� como su posible efecto en la ionizaci��n. El resultado obtenido muestra que los electrones secundarios se pierden en las paredes r��pidamente, por lo que su efecto en el plasma es despreciable, no as�� en las vainas, donde determinan el salto de potencial. Por ��ltimo, el trabajo te��rico y de simulaci��n num��rica se complementa con el trabajo experimental realizado en el Pnnceton Plasma Physics Laboratory, en el que se analiza el interesante transitorio inicial que experimenta el motor en el proceso de arranque. Del estudio se extrae que la presencia de gases residuales adheridos a las paredes juegan un papel relevante, y se recomienda, en general, la purga completa del motor antes del modo normal de operaci��n. El resultado final de la investigaci��n muestra que el c��digo h��brido desarrollado representa una buena herramienta de simulaci��n de un motor Hall. Reproduce adecuadamente la f��sica del motor, proporcionando resultados similares a los experimentales, y demuestra ser un buen laboratorio num��rico para estudiar el plasma en el interior del motor. Abstract Electric propulsion is today a very competitive technology and has a great projection into the future. Among the various existing plasma thrusters, the Hall effect thruster has acquired a considerable maturity and constitutes an ideal means of propulsion for a wide range of missions. In the present Thesis only Hall thrusters with conventional geometry and dielectric walls are studied. The complex interaction between multiple physical phenomena makes difficult the plasma simulation in these engines. Hybrid models are those representing a better compromise between precision and computational cost. They use a fluid model for electrons and Particle-In-Cell (PIC) algorithms for ions and neutrals. The hypothesis of plasma quasineutrality is invoked, which requires to solve separately the sheaths formed around the chamber walls. On the basis of an existing hybrid code, called HPHall-2, the aim of this doctoral Thesis is to develop an advanced hybrid code that better simulates the plasma discharge in a Hall effect thruster. Updates and improvements of the code include both theoretical and numerical issues. The extensive revision of the algorithms has succeeded in reducing the accuracy errors in one order of magnitude, and the consistency and robustness of the code have been notably increased, allowing the simulation of the thruster in a wide range of conditions. The most relevant achievements related to the particle subcode are: the implementation of a new weighing algorithm that determines more accurately the plasma flux magnitudes; the implementation of a new algorithm to control the particle population, assuring enough number of particles near the chamber walls, where there are strong gradients and the conditions to perform good computations are more critical; improvements in the mass and energy balances; and a new algorithm to compute the electric field in a non-uniform mesh. It deserves special attention the fulfilment of the Bohm condition at the edge of the sheath, which represents a boundary condition necessary to match consistently the hybrid code solution with the plasma-wall interaction, and remained as a question unsatisfactory solved in the HPHall-2 code. In this Thesis, the kinetic Bohm criterion has been implemented for an ion particle population with different electric charges and a large dispersion in their velocities. In the code, the fulfilment of the kinetic Bohm condition is accomplished by an algorithm that introduces a thin non-collisional layer next to the sheaths, producing the ion acceleration, and measures properly the flux of particles in time and space. The improvements made in the electron subcode increase the code simulation capabilities, specially in the region downstream of the thruster, where the neutralization of the plasma jet is simulated using a volumetric cathode model. Without addressing the detailed study of the plasma turbulence, simple models for a parametric adjustment of the anomalous Bohm difussion are implemented in the code. They allow to reproduce the experimental values of the plasma potential and the electron temperature, as well as the discharge current of the thruster. Regarding the theoretical issues, special emphasis has been made in the plasma-wall interaction of the thruster and in the dynamics of free secondary electrons within the plasma, questions that still remain unsolved in the simulation of Hall thrusters. The new developed models look for results closer to reality, such as the partial thermalization sheath model, that assumes a non-Maxwellian distribution functions for primary electrons, and better computes the energy losses at the walls. The evaluation of secondary electrons confinement within the chamber is addressed by a simplified kinetic study; and using a collisionless fluid model, the densities and energies of free secondary electrons are computed, as well as their effect on the plasma ionization. Simulations show that secondary electrons are quickly lost at walls, with a negligible effect in the bulk of the plasma, but they determine the potential fall at sheaths. Finally, numerical simulation and theoretical work is complemented by the experimental work carried out at the Princeton Plasma Physics Laboratory, devoted to analyze the interesting transitional regime experienced by the thruster in the startup process. It is concluded that the gas impurities adhered to the thruster walls play a relevant role in the transitional regime and, as a general recomendation, a complete purge of the thruster before starting its normal mode of operation it is suggested. The final result of the research conducted in this Thesis shows that the developed code represents a good tool for the simulation of Hall thrusters. The code reproduces properly the physics of the thruster, with results similar to the experimental ones, and represents a good numerical laboratory to study the plasma inside the thruster.

Transition from isentropic to isothermal expansion in laser produced plasma

The transition that the expansion flow of laser-produced plasmas experiences when one moves from long, low intensity pulses (temperature vanishing at the isentropic plasma-vacuum front,lying at finite distance) to short, intense ones (non-zero, uniform temperature at the plasma-vacuum front, lying at infinity) is studied. For plznar geometry and lqge ion number Z, the transition occurs for dq5/dt=0.14(27/8)k712Z���1zn$/m4f, 12nK,,; mi, and K are laser intensity, critical density,ion mass, and Spitzer���s heat conduction coefficient. This result remains valid for finite Zit,h ough the numerical factor in d$/dt is different. Shorter wavelength lasers and higher 4 plasmas allow faster rising pulses below transition.

Resonant absorption in a plasma step profile

Resonant absorption of p-polarized light shined on a plane-layered plasma with a step profile, is discussed as a function of wavelength (or critical density n,) of the light: for simplicity the incidence angle is assumed small. If n, lies within or above the step, the absorption A is given by Ginzburg���s result modified by strong reflections at the foot and top of the step. The absorption above is total for particular values of nc and U. For n, crossing the top of the density step the absorption is not monotonical: it exhibits a minimum that vanishes for zero radius of curvature U there and zero collision frequency 1��� (A - Iln VI-���). The results are applied to the profile produced by irradiating a solid target with a high-intensity pulse that steepens the plasma by radiation pressure.

Plasma kinetics issues in an ESA study for a plasma laboratory in space

A study supported by the European Space Agency (ESA), in the context of its General Studies Programme, performed an investigation of the possible use of space for studies in pure and applied plasma physics, in areas not traditionally covered by ���space plasma physics���. A set of experiments have been identified that can potentially provide access to new phenomena and to allow advances in several fields of plasma science. These experiments concern phenomena on a spatial scale (101���104 m) intermediate between what is achievable on the ground and the usual solar system plasma observations. Detailed feasibility studies have been performed for three experiments: active magnetic experiments, largescale discharges and long tether���plasma interactions. The perspectives opened by these experiments are discussed for magnetic reconnection, instabilities, MHD turbulence, atomic excited states kinetics, weakly ionized plasmas,plasma diagnostics, artificial auroras and atmospheric studies. The discussion is also supported by results of numerical simulations and estimates.

The ESA "Plasma Laboratory in Space" study

The European Space Agency has initiated, in the context of its General Studies Programme, a study of the possible use of space for studies in pure and applied plasma physics, in areas not traditionally covered by ���space plasma physics���. A team of experts has been set-up to review a broad range of area including industrial plasma physics and pure plasma physics, astrophysical and solar-terrestrial areas. A set of experiments have been identified that can potentially provide access to new phenomena and to allow advances in several fields of plasma science. These experiments concern phenomena on spatial scale (102 to104 m) intermediate between what is achievable on ground experiment and usual solar system plasma observations.

Fast calculation of LTE opacities for ICF plasmas

The accurate computation of radioactive opacities is needed in several research fields such as astrophysics, magnetic fusion or ICF target physics analysis, in which the radiation transport is an important feature to determine in detail. Radiation transport plays an important role in the transport of energy in dense plasma and it is strongly influenced by the variation of plasma opacity with density and temperature, as well as, photon energy. In this work we present some new features of the opacity code ATMED [1]. This code has been designed to compute the spectral radioactive opacity as well as the Rosseland and Planck means for single element and mixture plasmas. The model presented is fast, stable and reasonably accurate into its range of application and it can be a useful tool to simulate ICF experiments in plasma laboratory.

Modelling of spectral properties and population kinetics studies of inertial fusi��n and laboratory astrophysical plasmas

Fundamental research and modelling in plasma atomic physics continue to be essential for providing basic understanding of many different topics relevant to high-energy-density plasmas. The Atomic Physics Group at the Institute of Nuclear Fusion has accumulated experience over the years in developing a collection of computational models and tools for determining the atomic energy structure, ionization balance and radiative properties of, mainly, inertial fusion and laser-produced plasmas in a variety of conditions. In this work, we discuss some of the latest advances and results of our research, with emphasis on inertial fusion and laboratory-astrophysical applications.

Plasma���wall interaction in laser inertial fusion reactors: novel proposals for radiation tests of first wall materials

Dry-wall laser inertial fusion (LIF) chambers will have to withstand strong bursts of fast charged particles which will deposit tens of kJ m���2 and implant more than 1018 particles m���2 in a few microseconds at a repetition rate of some Hz. Large chamber dimensions and resistant plasma-facing materials must be combined to guarantee the chamber performance as long as possible under the expected threats: heating, fatigue, cracking, formation of defects, retention of light species, swelling and erosion. Current and novel radiation resistant materials for the first wall need to be validated under realistic conditions. However, at present there is a lack of facilities which can reproduce such ion environments. This contribution proposes the use of ultra-intense lasers and high-intense pulsed ion beams (HIPIB) to recreate the plasma conditions in LIF reactors. By target normal sheath acceleration, ultra-intense lasers can generate very short and energetic ion pulses with a spectral distribution similar to that of the inertial fusion ion bursts, suitable to validate fusion materials and to investigate the barely known propagation of those bursts through background plasmas/gases present in the reactor chamber. HIPIB technologies, initially developed for inertial fusion driver systems, provide huge intensity pulses which meet the irradiation conditions expected in the first wall of LIF chambers and thus can be used for the validation of materials too.

Plasma���wall interaction in laser inertial fusion reactors: novel proposals for radiation tests of first wall materials

Dry-wall laser inertial fusion (LIF) chambers will have to withstand strong bursts of fast charged particles which will deposit tens of kJ m���2 and implant more than 1018 particles m���2 in a few microseconds at a repetition rate of some Hz. Large chamber dimensions and resistant plasma-facing materials must be combined to guarantee the chamber performance as long as possible under the expected threats: heating, fatigue, cracking, formation of defects, retention of light species, swelling and erosion. Current and novel radiation resistant materials for the first wall need to be validated under realistic conditions. However, at present there is a lack of facilities which can reproduce such ion environments. This contribution proposes the use of ultra-intense lasers and high-intense pulsed ion beams (HIPIB) to recreate the plasma conditions in LIF reactors. By target normal sheath acceleration, ultra-intense lasers can generate very short and energetic ion pulses with a spectral distribution similar to that of the inertial fusion ion bursts, suitable to validate fusion materials and to investigate the barely known propagation of those bursts through background plasmas/gases present in the reactor chamber. HIPIB technologies, initially developed for inertial fusion driver systems, provide huge intensity pulses which meet the irradiation conditions expected in the first wall of LIF chambers and thus can be used for the validation of materials too.

Inverse bremsstrahlung absorption in spherical laser targets

Inverse bremsstrahlung has been incorporated into an analytical model of the expanding corona of a laser-irradiated spherical target. Absorption decreases slowly with increasing intensity, in agreement with some numerical simulations, and contrary to estimates from simple models in use up to now, which are optimistic at low values of intensity and very pessimistic at high values. Present results agree well with experimental data from many laboratories; substantial absorption is found up to moderate intensities,say below IOl5 W cm-2 for 1.06 pm light. Anomalous absorption, wher, included in the analysis, leaves practically unaffected the ablation pressure and mass ablation rate, for given absorbed intensity. Universal results are given in dimensionless fom.

Nonlocal electron heat-flux

Electron thermal conduction in a not quite collisional unmagnetlzed plasma is analysed. The failure of classical results for temperature scale-length up to 100 times larger than thermal mean-free-path for electron scattering, and large ion-charge number Z , is discussed. Recent results from a nonlocal model of conduction at large Z are reviewed. Closed form expressions for Braginskii's coefficients a ,/3 , y for Z =0(1) are derived. An extension of the nonlocal model for Z =0(1) is discussed.

Electron cooling in probe collection from magnetized plasmas with anomalous transport

The electron-retarding range of the current-voltage characteristic of a flat Langmuir probe perpendicular to a strong magnetic field in a fully ionized plasma is analysed allowing for anomalous (Bohm) cross-field transport and temperature changes in the collection process. With probe size and ion thermal gyroradius comparable, and smaller than the electron mean free path, there is an outer quasineutral region with ion viscosity determinant in allowing nonambipolar parallel and cross flow. A potential overshoot lying either at the base or inside the quasineutral region both makes ions follow Boltzmann's law at negative bias and extends the electron-retarding range to probe bias e(j)p ~ +2Too. Electron heating and cooling occur roughly at positive and negative bias, with a re-minimum around efa ~ - 2 7 ^ ; far from the probe heat conduction cools and heats electrons at and radially away from the probe axis, respectively. The potential overshoot with no thermal effects would reduce the electron current Ie, making the In Ie versus 4>p graph downwards-concave,but cooling further reduces Ie substantially, and may tilt the slope upwards past the temperature minimum. The domain of strict validity of our analysis is narrow in case of low ion mass (deuterium), breaking down with the ion Boltzmann law.

Self-similar deflagration in laser half-plasmas

The self-similar motion of a half-space plasma, generated by a linear pulse of laser radiation absorbed anomalously at the critical density, has been studied. The resulting plasma structure has been completely determined for [pulse duration (critical density)maximum irradiation] large enough