A Homegrown DSMC-PIC Model for Electric Propulsion

Powering spacecraft with electric propulsion is becoming more common, especially in CubeSat-class satellites. On account of the risk of spacecraft interactions, it is important to have robust analysis and modeling tools of electric propulsion engines, particularly of the plasma plume. The Navier-Stokes equations used in classic continuum computational fluid dynamics do not apply to the rarefied plasma, and therefore another method must be used to model the flow. A good solution is to use the DSMC method, which uses a combination of particle modeling and statistical methods for modeling the simulated molecules. A DSMC simulation known as SINATRA has been developed with the goal to model electric propulsion plumes. SINATRA uses an octree mesh, is written in C++, and is designed to be expanded by further research. SINATRA has been initially validated through several tests and comparisons to theoretical data and other DSMC models. This thesis examines expanding the functionality of SINATRA to simulate charged particles and make SINATRA a DSMC-PIC hybrid. The electric potential is calculated through a 7-point 3D stencil on the mesh nodes and solved with a Gauss-Seidel solver. It is validated through test cases of charged particles to demonstrate the accuracy and capabilities of the model. An ambipolar diffusion test case is compared to a neutral diffusion case and the electric field is shown to stabilize the diffusion rate. A steady state flow test case shows the simulation is able to stabilize and solve the electric potential for a plume-like scenario. It includes additional features to simplify further research including a comprehensive user manual, industry-standard version control, text file inputs, GUI control, and simple parallelism of the simulation. Compilation and execution are standardized to be simple and platform independent to allow longevity of the code base. Finally, the execution bottlenecks of linking particles to cells and particle moving were removed to reduce the simulation time by 95%

CHAOS: A multi-GPU PIC-DSMC solver for modeling gas and plasma flows

Numerical modeling of gas and plasma-surface interactions is critical to understanding the complex kinetic processes that dominate the extreme environments of planetary entry and in-space propulsion. However, simulations of these systems that evolve over multiple length- and time-scales is computationally expensive. Until recently, approximations were used to keep computational costs tenable, which in turn, increased the uncertainty in predictions and offered limited insights into the micro-scale flow properties and electron kinetics that dominate the macroscale processes. The need to perform high-fidelity physics-based gas and plasma simulations has led to the development of a three-dimensional, multi-GPU, Particle-in-cell (PIC)-direct simulation Monte Carlo (DSMC) solver called Cuda-based Hybrid Approach for Octree Simulations (CHAOS) that is presented in this work. This computational tool has been applied to candidate PICA-like TPS materials that consist of an irregular porous network of fibers to allow high-temperature boundary layer gases as well as pyrolysis by-products to penetrate in and flow out of the material. Quantifying bulk transport properties of these materials is essential for accurate prediction of the macroscopic ablation rate. The second application that CHAOS is being used with is the modeling of ion thruster plumes that consist of fast beam ions and slow neutrals that undergo charge-exchange (CEX) reactions to produce slow ions and fast neutrals. These slow CEX ions are strongly influenced by the electric field induced between the ion plume and the thruster surface, resulting in a backflow of ions towards the critical solar panel and thruster surfaces. Three backflow quantities, namely, ion flux, incidence angle, and incidence energy affect the macroscopic sputtering rate of the solar panel surfaces over extended operational times and are predicted from the PIC-DSMC simulations

Improving PIC-DSMC Simulations of RF Plasmas via Event Splitting

Particle-in-Cell Direct Simulation Monte Carlo (PIC-DSMC) is a widely used method for simulation of non-equilibrium plasmas, especially when the plasma flow is rarefied, and the applicability of fluid models is questionable. However, the PIC-DSMC method is subject to stochastic noise, and depending on the process being simulated, might require extremely large computational efforts. Therefore, the improvement of accuracy of PIC-DSMC methods is a topic of active research. In the present work, a recently developed collision and boundary condition treatment scheme, dubbed 'event splitting', which aims at improving simulation of low-probability processes, is applied to ionization processes in xenon and helium plasmas, where it shown to reduce the level of stochastic noise compared to standard DSMC collision schemes

Axisymmetric plasma plume characterization with 2D and 3D particle codes

The expansion of a rarefied axisymmetric plume emitted by a plasma thruster is analyzed and compared with a 3D Cartesian-type and a 2D cylindrical-type simulation code, both based on a particle-in-cell formulation for the heavy species and a simple Boltzmann-type model for the electrons. The first part of the paper discusses the 2D code numerical challenges in the moving of particles, their generation within the cells, and the weighting to the nodes, caused by the radial non-uniformity and the singular and boundary character of the symmetry axis. The second part benchmarks the 2D code against the 3D one for a high-energy, unmagnetized plume with three major species populations (injected neutrals, singly-charged and doubly-charged ions) and three minor species populations (constituted by particles coming from collisional processes, such as the charge-exchange reactions). The excellent agreement found in the results proves that both plume codes are capable of simulating, with a reasonable noise level, heavy particle populations differing by several orders of magnitude in number density. For simulations with a comparable level of accuracy, the 2D code presents a ten-fold gain in computational cost, although the symmetry axis remains its weakest point, due to particle depletion there and the related weighting noise

Improving PIC-DSMC Simulations of Electrical Breakdown via Event Splitting

A newly developed variable-weight DSMC collision scheme for inelastic collision events is applied to PIC-DSMC modelling of electrical breakdown in 1-dimensional helium and argon-filled gaps. Application of the collision scheme to various inelastic collisional and gas-surface interaction processes (electron-impact ionization, electronic excitation, secondary electron emission) is considered. The collision scheme is shown to improve the level of noise in the computed current density compared to the commonly used approach of sampling a single process, whilst maintaining a comparable level of computational cost and providing less variance in the average number of particles per cell

Hybrid 3D model for the interaction of plasma thruster plumes with nearby objects

This paper presents a hybrid particle-in-cell (PIC) fluid approach to model the interaction of a plasma plume with a spacecraft and/or any nearby object. Ions and neutrals are modeled with a PIC approach, while electrons are treated as a fluid. After a first iteration of the code, the domain is split into quasineutral and non-neutral regions, based on non-neutrality criteria, such as the relative charge density and the Debye length-to-cell size ratio. At the material boundaries of the former quasineutral region, a dedicated algorithm ensures that the Bohm condition is met. In the latter non-neutral regions, the electron density and electric potential are obtained by solving the coupled electron momentum balance and Poisson equations. Boundary conditions for both the electric current and potential are finally obtained with a plasma sheath sub-code and an equivalent circuit model. The hybrid code is validated by applying it to a typical plasma plume-spacecraft interaction scenario, and the physics and capabilities of the model are finally discussed.The research leading to the results of this paper was initiated within the LEOSWEEP project (“Improving Low Earth Orbit Security With Enhanced Electric Propulsion”), funded by the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement N.607457. Additional funding to complete it has been received by Spain’s R&D National Plan, under grant ESP2016-75887

Plasma propulsion simulation using particles

This perspective paper deals with an overview of particle-in-cell / Monte Carlo collision models applied to different plasma-propulsion configurations and scenarios, from electrostatic (E x B and pulsed arc) devices to electromagnetic (RF inductive, helicon, electron cyclotron resonance) thrusters, with an emphasis on plasma plumes and their interaction with the satellite. The most important elements related to the modeling of plasma-wall interaction are also presented. Finally, the paper reports new progress in the particle-in-cell computational methodology, in particular regarding accelerating computational techniques for multi-dimensional simulations and plasma chemistry Monte Carlo modules for molecular and alternative propellan

Analysis of the expansion of a plasma thruster plume into vacuum

Mención Internacional en el título de doctorThe analysis of the interaction between a plasma plume and a satellite is gradually becoming a very demanded task in the space industry, given the increasing use of electric propulsion. In fact, the plasma plumes generated by the electric thrusters can damage sensitive spacecraft components, such as the solar arrays or onboard optical sensors. Moreover, plasma plumes can be used to one's benefit in the context of the ion beam shepherd technique for space debris removal, in which a shepherd spacecraft relocates a debris object to a different orbit, by directing towards it a plasma plume, at an operational distance of several meters. This thesis focuses on the numerical study of the expansion of a plasma thruster plume into vacuum and its interaction with the satellite and any downstream object. Two simulation codes have been developed. The first code, named EASYPLUME, is based on an axisymmetric two-fluid plasma plume model and allows to quickly estimate the plasma plume properties farther downstream. With this code the physics of the plume expansion has been investigated, understanding its dependence on the most important plume parameters, such as the divergence angle, the ion Mach number, and the electron cooling rate. Moreover, the code has been used in the context of the ion beam shepherd technique to estimate the force transmission to a space debris object, and optimize the overall electric propulsion subsystem of the shepherd spacecraft. The second code, named EP2PLUS, is a three-dimensional hybrid particle-incell/fluid code that simulates the complex interaction between a plasma plume, the spacecraft and other objects. The most relevant modeling novelties regard the electron model, which enables the computation of the electric currents in the plume, and the treatment of quasineutral and non-neutral plasma regions. This code has been applied to study both the satellite-plume interaction and a reference ion beam shepherd scenario. In the latter, several operational problems have been evaluated: the ion backscattering towards the shepherd satellite, the sputtering of the debris object (due to the impingement of hypersonic ions), the backsputtering contamination of the spacecraft, and the electric charging of both the satellite and the target debris. Finally, the report of an experimental campaign, carried out during my PhD visit at the “Laboratoire de Physique des Plasmas" (Paris) and aiming at characterizing the plasma plume of the PEGASES plasma thruster, completes this work.El estudio de la interacción entre el satélite y un chorro de plasma producido por un propulsor eléctrico se está convirtiendo en un análisis muy demandado en la industria espacial, debido al uso cada vez más extenso de la propulsión eléctrica. Dicho chorro puede dañar seriamente componentes sensibles del satélite, como los paneles solares o los sensores ópticos. Por otra parte, puede utilizarse activamente en el contexto de la técnica de eliminación de desechos espaciales conocida como “ion beam shepherd". Esta técnica se basa en trasladar dichos objetos a una órbita diferente, por medio de la presión producida por el impacto de los iones de un chorro de plasma dirigido hacia ellos, desde una distancia de varios metros. Esta tesis se centra en el estudio numérico de la expansión de un chorro de plasma generado por un propulsor eléctrico en el vacío, y de su interacción con otros objetos. Con este propósito, se han desarrollado dos códigos de simulación. El primero, llamado EASYPLUME, se basa sobre un modelo axial simétrico con dos fluidos (iones y electrones) y permite estimar rápidamente las propiedades del chorro de plasma a grandes distancias aguas abajo. Con este código, se ha estudiado la física de la expansión del plasma en detalle, comprendiendo la influencia de parámetros como el ángulo de divergencia, el número de Mach y la tasa de enfriamiento electrónico. Además, el código ha sido utilizado en el contexto del “ion beam shepherd" para estimar la fuerza transmitida al objeto y optimizar el sistema de propulsión eléctrica del satélite. El segundo, llamado EP2PLUS, es un código tridimensional híbrido PIC-fluido que simula la interacción compleja entre un chorro de plasma, el satélite y otros objetos. Entre las novedades más relevantes destacan el nuevo modelo electrónico, que permite estudiar las corrientes eléctricas en el plasma, y el tratamiento de regiones quasi-neutras y no neutras. Este código se ha empleado en el estudio de la interacción chorro-satélite y en el análisis de la interacción chorro-satélite-objeto en el contexto del “ion beam shepherd" para una misión de referencia. En este último estudio, diferentes problemas operacionales han sido evaluados numéricamente: el retorno de los iones lentos hacia el satélite, la emisión de partículas erosionadas desde la superficie del desecho espacial (debido al impacto de los iones hipersónicos), la contaminación por difusión de dichas partículas hacia el satélite, y la acumulación de carga eléctrica de _este y del objeto espacial. Finalmente, el informe de una campaña de caracterización experimental del chorro del motor de plasma PEGASES completa este trabajo. Dicha campaña se realizó durante mi estancia de visita al “Laboratoire de Physique des Plasmas" en París.Programa Oficial de Doctorado en Plasmas y Fusión NuclearPresidente: Victoria Lapuerta González.- Secretario: Luis Raúl Sánchez Fernández.- Vocal: Francesco Taccogn

Axisymmetric simulation codes for hall effect thrusters and plasma plumes

Mención Internacional en el título de doctorThe development of reliable and versatile plasma discharges simulation codes is becoming of central importance, given the rapidly evolving electric propulsion landscape. These tools are essential for facilitating and complementing the design of new prototypes, signiffcantly reducing development time and costs. Moreover, they can provide a deeper insight on already proven technologies, revealing optimization opportunities so as to improve the thruster performance and lifetime, and predicting the operational parameters at different regimes of interest. This Thesis is devoted to the numerical study of different plasma discharges and, in particular, the Hall effect thruster (HET) discharge. With special focus on particle-based modeling, two simulation codes have been developed. The first one, named HYPHEN, is a new two-dimensional axisymmetric hybrid, particle-in-cell (PIC)/fluid multi-thruster simulation platform. Its versatile PIC-based module for heavy species supports the simulation of inner active surfaces, mixed specular-diffuse neutral-wall reflection, and chargeexchange (CEX) collisions, thus extending the code capabilities and enabling the simulation of axisymmetric plasma plumes. Moreover, it features a new population control which monitors independently every heavy species and limits the statistical noise at a low computational cost. Furthermore, an improved version of the HET electron fluid module for the isotropic electron pressure case is presented. Three major studies have been carried out with this code. First, the simulation of an ion thruster plasma plume has permitted to benchmark HYPHEN against the 3D plasma plume code EP2PLUS. Second, an investigation on the neutral-wall interaction effects on an unmagnetized plasma discharge in a surface-dominated cylindrical channel with isothermal electrons has been performed. The discharge ignition requires different propellant injection mass ows in the diffuse and specular neutral-wall reflection cases. Third, preliminary simulations of a SPT-100 HET have been carried out to demonstrate the code capabilities and reveal its limitations. Consistent results have been obtained for different cathode locations in the near plume region and various electron turbulent transport parameter profiles. The second code corresponds to a new version of the one-dimensional radial particle model of a HET discharge, originally developed by F. Taccogna. The major improvements are an ionization controlled discharge algorithm, which enables sustaining a steady-state discharge, and an extended volumetric weighting algorithm which provides a more accurate macroscopic description of the low populated species, such as the wall-emitted secondary electrons. The radial dynamics of both the primary and secondary electron populations have been analyzed in detail, assessing the temperature anisotropy ratio of their velocity distribution functions and the asymmetries introduced by cylindrical geometry effects in the macroscopic laws of interest, thus aiming at a future improvement of the plasma-wall interaction module implemented in HYPHEN.El desarrollo de códigos fiables y versátiles para la simulación de descargas de plasma es cada vez más importante dada la rápida evolución de la propulsión espacial eléctrica. Estas herramientas son esenciales para facilitar y complementar el diseño de nuevos prototipos, reduciendo significativamente los tiempos y costes de desarrollo. Además, pueden ampliar la comprensión de las tecnologías ya establecidas, revelar vías de optimización del propulsor que permitan mejorar su rendimiento y vida útil, y predecir los parámetros de operación del mismo en diferentes regímenes de interés. Esta Tesis está dedicada al estudio numérico de diferentes descargas de plasma y, en particular, de descargas HET. Se han desarrollado dos códigos de simulación, con especial énfasis en los modelos de partículas. El primero de ellos, llamado HYPHEN, es una nueva plataforma de simulación multi-propulsor, híbrida PIC/fluida y axisimétrica. Su módulo PIC para especies pesadas permite la simulación de superficies activas inmersas en el plasma, procesos de reflexión especular-difuso de neutros en pared y colisiones CEX, extendiendo por tanto las capacidades del código y permitiendo la simulación de plumas de plasma axisimétricas. Además, incluye un nuevo control de población que monitoriza a cada especie pesada por separado limitando el ruido estadístico y el coste computacional. Por otra parte, se presenta una versión mejorada del modelo fluido de electrones isótropos para HET. Tres estudios principales se han llevado a cabo con este código. En primer lugar, la simulación de la pluma de plasma de un motor iónico ha permitido validar HYPHEN con el código de plumas 3D EP2PLUS. Por otro lado, se ha investigado el efecto de la interacción del gas neutro con la pared en una descarga no magnetizada con electrones isotermos en un canal cilíndrico esbelto. La ignición de la descarga requiere inyectar diferentes gastos másicos de propulsante en los casos de reflexión difusa y especular. En tercer lugar, se han realizado simulaciones preliminares de un motor HET de tipo SPT- 100 con el objeto de demostrar las capacidades del código y revelar sus limitaciones, obteniendo resultados consistentes para diferentes posiciones del cátodo en la región de la pluma cercana, y perfies del parámetro de turbulencia de electrones. El segundo código representa una nueva versión del modelo radial de partículas de una descarga HET desarrollado originalmente por F. Taccogna. Las principales mejoras consisten en un algoritmo de control de la descarga a través de la ionización, que permite obtener una descarga estacionaria, y un algoritmo de pesado volumétrico extendido, que proporciona una descripción macroscópica más precisa de las especies poco pobladas, como los electrones secundarios emitidos desde las paredes del motor. Para posibilitar una futura mejora del módulo de HYPHEN de interacción plasma-pared, se han analizado en detalle la dinámica radial de los electrones primarios y secundarios, la anisotropía de temperatura de sus funciones de distribución de velocidad, y las asimetrías cilíndricas en las leyes macroscópicas de interés.Programa Oficial de Doctorado en Mecánica de Fluidos por la Universidad Carlos III de Madrid; la Universidad de Jaén; la Universidad de Zaragoza; la Universidad Nacional de Educación a Distancia; la Universidad Politécnica de Madrid y la Universidad Rovira i Virgili.Presidente: Iván Calvo Rubio.- Secretario: Gonzalo Sánchez Arriaga.- Vocal: Daniela Pedrin