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

Spacecraft-plasma-debris interaction in an ion beam shepherd mission

This paper presents a study of the interaction between a spacecraft, a plasma thruster plume and a free floating object, in the context of an active space debris removal mission based on the ion beam shepherd concept. The analysis is performed with the EP2PLUS hybrid code and includes the evaluation of the transferred force and torque to the target debris, its surface sputtering due to the impinging hypersonic ions, and the equivalent electric circuit of the spacecraft-plasma-debris interaction. The electric potential difference that builds up between the spacecraft and the debris, the ion backscattering and the backsputtering contamination of the shepherd satellite are evaluated for a nominal scenario. A sensitivity analysis is carried out to evaluate quantitatively the effects of electron thermodynamics, ambient plasma, heavy species collisions, and debris position

Three-dimensional geomagnetic field effects on a plasma thruster plume expansion

A 3D hybrid particle-in-cell code with a partially-magnetized fluid electron model is presented and applied to study the effects of a uniform external geomagnetic field on an expanding plasma thruster plume at three different angles. Electron currents are governed by both the magnetic field and collisional effects with the heavy ions and neutrals. While an axial magnetic field (parallel to the plume axis) induces azimuthal electric currents and an observable plume channeling, an oblique field produces non-trivial asymmetric deformations of the plume cross-section, and induces axial-radial electric current loops. A center of mass analysis of the plasma plume demonstrates that the electron response produces an electric field that balances the Lorentz force deflection on the ions, so that no net plume momentum deflection is observed.The primary funder of this research was the Comunidad de Madrid (Spain), under PROMETEO-CM project, with grant number Y2018/NMT-4750. Initial support was provided by the Ministerio de Economía y Competitividad (Spain), under project ESP2016-75887-

Coupling plasma physics and chemistry in the PIC model of electric propulsion: Application to an air-breathing, low-power Hall thruster

This work represents a first attempt to include the complex variety of electron-molecule processes in a full kinetic particle-in-cell/test particle Monte Carlo model for the plasma and neutral gas phase in a Hall thruster. Particular emphasis has been placed on Earth's atmosphere species for the air-breathing concept. The coupling between the plasma and the gas phase is self-consistently captured by assuming the cold gas approximation and considering gas-wall and gas recycling from the walls due to ion neutralization. The results showed that, with air molecular propellants, all the most relevant thruster performance figures degraded relative to the nominal case using Xe propellant. The main reasons can be ascribed to a reduced ionization cross-section, a larger gas ionization mean free path due to lighter mass air species, and additional electron collisional power losses. While vibrational excitations power losses are negligible, dissociation and electronic excitations compete with the ionization channel. In addition, for molecular oxygen, the large dissociation leads to even faster atoms, further reducing their transit time inside the discharge channel. Future studies are needed to investigate the role of non-equilibrium vibrational kinetics and metastable states for stepwise ionization

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

Formation and neutralization of electric charge and current of an ion thruster plume

A 3D hybrid model is introduced and applied to the simulation of the xenon plasma plume extraction, formation, and neutralization in a gridded ion thruster. The acceleration voltage is 1100 V and the inflow Xe+ per hole ranges from 0.07 to 0.92 μg s−1. While ions and neutrals are treated with a particle-in-cell formulation, electrons are modeled as two independent isothermal populations: one inside the discharge chamber and one in the plume. The definition of a thermalized potential allows to solve the electron currents in the high-conductivity limit of the Ohm's law. The space charge neutralization distance is observed to be short and thus essentially independent of the acceleration grid-neutralizer distance, which is varied from 10 to 25 mm axially. However, this position strongly affects the electric current neutralization paths in the near plume for each ion beamlet. Electron inertial forces are shown to be comparable to collisional forces in certain plasma regions. A semi-analytical 1D fluid model of the plume, matched to the hybrid model, allows to complete the far plume expansion down to infinity. Grids with an infinite and finite number of apertures are simulated and compared with each other and with the 1D model. The numerically obtained divergence angle of the ion plume is compared with experimental measurements, observing relative errors of around 7% in the position of the optimal perveance, and smaller than 4% in the divergence angle average value.This work has been supported by the ESPEOS project, funded by the Agencia Estatal de Investigación (Spanish National Research Agency), under Grant No. PID2019-108034RB-I00/AEI/10.13039/501100011033

Determination of the force transmitted by an ion thruster plasma plume to an orbital object

An approach to determine the force transmitted by the plasma plume of an ion thruster to an orbital object immersed in it using its central projection on a selected plane is proposed. A photo camera is used to obtain the image of the object central projection. The algorithms for the calculation of the transmission of momentum by the impacting ion beam are developed including the determination of the object contour and the correction of the error due to a camera offset from the ion beam axis, and the computation of the fraction of the ion beam that impinges on the object surface.The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement n°607457

On heavy particle-wall interaction in axisymmetric plasma discharges

The effects of heavy particle-wall interaction on a cylindrical plasma source discharge are investigated, through hybrid particle-in-cell/fluid simulations. The bulk plasma is considered quasineutral with isothermal electrons, and with no secondary electron emission from the walls. The neutral gas wall reflection model is shown to play a major role in determining the conditions for a self-sustained and stationary plasma discharge. A hysteresis cycle on the injection mass flow rate is found when neutrals deviate from a purely diffuse reflection at the walls, with the mass utilization efficiency changing up to 20% between purely specular and diffuse scenarios. However, as the ratio of ionization mean free path to macroscopic length is decreased, the neutral-wall reflection model becomes irrelevant. Finally, even small deviations from unity of the ion energy accommodation coefficient at the walls are seen to have a major impact on both the ion and neutral distribution functions, and ultimately the mass utilization efficiency. This behavior stresses out the importance of a precise experimental determination of this parameter for accurate simulations.This paper has been funded mainly by Comunidad de Madrid/FEDER/FSE, through the PROMETEO-CM project, Grant No. Y2018/NMT-4750. Additional support came from the ESPEOS project, funded by the Agencia Estatal de Investigación (Spanish National Research Agency), under Grant No. PID2019-108034RB-I00/AEI/10.13039/501100011033

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

Electric propulsion subsystem optimization for "Ion Beam Shepherd" missions

The ion beam shepherd is an innovative contactless technique for space debris removal in which an impulse transfer thruster pushes the debris object through the action of a plasma plume and an impulse compensation thruster maintains formation flying. The optimal operational point of both thrusters strongly depends on their characteristics and on the physics of the plasma plume expansion into vacuum. With the use of dedicated thruster performance models, complemented with simplified plume expansion and plasma-debris interaction models, a system-level optimization study of the impulse transfer thruster alone and of the overall electric propulsion subsystem is presented for an ion beam shepherd mission example. An optimum design point is found for minimum overall power consumption in both cases.The research leading to the results of this paper was carried out within the LEOSWEEP project and received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement number 607457. Additional funding was received by Spain's Research and Development National Plan, grant ESP2013-4105