A Three-dimensional Particle-in-Cell Methodology on Unstructured Voronoi Grids with Applications to Plasma Microdevices

The development and numerical implementation of a three-dimensional Particle-In-Cell (PIC) methodology on unstructured Voronoi-Delauney tetrahedral grids is presented. Charge assignment and field interpolation weighting schemes of zero- and first-order are formulated based on the theory of long-range constraints for three-dimensional unstructured grids. The algorithms for particle motion, particle tracing, particle injection, and loading are discussed. Solution to Poisson\u27s equation is based on a finite-volume formulation that takes advantage of the Voronoi-Delauney dual. The PIC methodology and code are validated by application to the problem of current collection by cylindrical Langmuir probes in stationary and moving collisionless plasmas. Numerical results are compared favorably with previous numerical and analytical solutions for a wide range of probe radius to Debye length ratios, probe potentials, and electron to ion temperature ratios. A methodology for evaluation of the heating, slowing-down and deflection times in 3D PIC simulations is presented. An extensive parametric evaluation is performed and the effects of the number of computational particles per cell, the ratio of cell-edge to Debye length, and timestep are investigated. The unstructured PIC code is applied to the simulation of Field Emission Array (FEA) cathodes. Electron injection conditions are obtained from a Field Emission microtip model and the simulation domain includes the FEA cathode and anode. Currents collected by the electrodes are compared to theoretical values. Simulations show the formation of the virtual cathode and three-dimensional effects under certain injection conditions. The unstructured PIC code is also applied to the simulation of a micro-Retarding Potential Analyzer. For simple cases the current at the collector plate is compared favorably with theoretical predictions. The simulations show the complex structure of the potential inside the segmented microchannel, the phase space of plasma species and the space-charge effects not captured by the theory

3D Simulation of Plume Flows from a Cluster of Plasma Thrusters

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77194/1/AIAA-2005-4662-529.pd

Verified modeling of a low pressure hydrogen plasma generated by electron cyclotron resonance

A self-consistent fluid model has been successfully developed and employed to model an electron cyclotron resonance driven hydrogen plasma at low pressure. This model has enabled key insights to be made on the mutual interaction of microwave propagation, power density, plasma generation, and species transport at conditions where the critical plasma density is exceeded. The model has been verified by two experimental methods. Good agreement with the ion current density and floating potential—as measured by a retarding energy field analyzer—and excellent agreement with the atomic hydrogen density—as measured by two-photon absorption laser induced fluorescence—enables a high level of confidence in the validity of the simulation

Experimental and theoretical characterization of a Hall thruster plume

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2007.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Page 230 blank.Includes bibliographical references (p. 201-206).Despite the considerable flight heritage of the Hall thruster, the interaction of its plume with the spacecraft remains an important integration issue. Because in-flight data fully characterizing the plume in the space environment are currently unavailable, laboratory measurements are often used to understand plasma expansion and thereby minimize adverse plume-spacecraft interactions. However, experimental measurements obtained in ground facilities do not properly capture the wide angle plume effects most important for plume-spacecraft interactions because of the high background pressure of the laboratory environment. This research describes a method to determine the in-orbit plume divergence of a Hall thruster from laboratory measurements and characterizes the plasma properties of the in-orbit plume. Plume measurements were taken with a Faraday probe and a Retarding Potential Analyzer at various background pressures to correlate changes in current density and ion energy distribution with changes in pressure. Results showed that current density increases linearly with background pressure at any given angle. This linear relationship was used to extrapolate laboratory measurements to zero background pressure, the in-orbit condition. Measurements from the Faraday probe and the Retarding Potential Analyzer were compared to ensure consistency. The effect of discharge voltage on plume divergence was also investigated. Measurements from both probes revealed that plume divergence decreases with an increase in discharge voltage. Hall thruster plume expansion was also characterized using a numerical plume simulation. Comparison of plume simulation results for in-orbit conditions to extrapolated current density at zero pressure demonstrated good agreement.(cont.) However, comparison of plume simulation and experimental results at a non-zero background pressure showed deficiencies in the collision model of the plume simulation. An analytical expression for current density obtained using a elf-similar plume model was compared to extrapolated current density at zero pressure and showed good agreement. In addition, an analytical model derived for current density of source ion collisions with neutrals was consistent with experimental measurements and confirms the deficiencies in the simulation's collision model. In summary, experimental, numerical and analytical results indicate that the method of determining in-orbit plume divergence from laboratory measurements is valid and can be used to integrate Hall thrusters with the spacecraft.by Yassir Azziz.Ph.D

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

Development and Implementation of Diagnostics for Unsteady Small-scale Plasma Plumes

This research seeks to increase the applicable range and sensitivity of Triple Langmuir Probes (TLPs) and Retarding Potential Analyzers (RPAs) in the characterization of sub-centimeter scale, unsteady plasmas found in micropropulsion and other non-propulsive applications. The validation of these plasma diagnostics is accomplished by their implementation in the plume of a Micro Liquid-fed Pulsed Thruster (MiLiPulT) prototype developed and MEMS fabricated by the Johns Hopkins University Applied Physics Laboratory. A current-mode TLP (CM-TLP) theory of operation for the thin-sheath and the transitional regimes is expanded to include the Orbital Motion Limited regime applicable to low density plasmas. An optimized CM-TLP bias circuit employing operational amplifiers in both a differential amplifier configuration as well as a voltage follower configuration has been developed to adequately amplify current signals in instances where traditional current measuring techniques are no longer valid. This research also encompasses novel sub-microampere signal amplification in the presence of substantial common-mode noise as well as several a priori electromagnetic interference elimination and filtering techniques. The CM-TLP wires used in the experiments were designed with a radius of 37.5 micron and a length of 5 mm. Measurements were taken in the plume of the MiLiPulT at 2.0 cm, 6.0 cm and 10.0 cm downstream of the exit using a linear translation stage. Reduced electron temperature and electron number density profiles for a set of filtered CM-TLP raw currents are presented. The results indicate increased accuracy due to successful amplification of CM-TLP current signals at the risk of op-amp saturation due to inherent electrical noise of the plasma source. This research also includes the experimental validation of two new and distinct collimating RPA design types. Specifically, these design improvements include a 406 micron diameter single channel bore and a multi-channel plate (MCP) consisting of sixty-four 2 micron diameter bores, respectively. Both of these collimators relax the Debye length constraints within the electrode series and increase the instrument\u27s range while minimizing the presence of space charge limitations. The single channel needle also has the added advantage of providing a relatively small cross-section to the incident plasma, thus minimizing pressure gradients and shock effects inherent to bulkier instrumentation. Experimental results obtained in the plume of the MiLiPulT are benchmarked against those of a traditional gridded RPA (having a 650 micron grid wire gap) and are reduced using an iterative fuzzy logic algorithm. Modifications to the classical RPA current collection theory include a thorough treatment of geometrical flux limitations due to an electrically floating cylindrical channel of high diameter to length aspect ratio. The differences between true and effective RPA collimating channel transparencies in the presence of a Maxwellian plasma are also addressed

3D plume modeling of SPT-100

Hall thrusters are a spacecraft propulsion device for orbit maintenance and north-south station keeping. One of the concerns about Hall thrusters is the sputtering of high energy ions which could result in the erosion of sensitive surface coatings used for solar cell elements and thermal control. In this thesis, a 3D DSMC-PIC hybrid kinetic simulation of a well known, stationary plasma thruster SPT-100 plume modeling was performed using a hybrid MPI-GPU AMR code CHAOS. Xe atoms, Xe+, and Xe+2 ions are modeled using a kinetic approach. Modeling electrons using a kinetic approach is not feasible in today's computational power for a Hall thruster plume. Thus three different models are used to compute the plasma potential. First, Boltzmann and polytropic models are used for electric potential calculations. Current density values obtained from both electron models are compared with previous experimental measurements and simulations in the literature. It was seen that the polytropic model shows better agreement with the experimental measurements than the Boltzmann model and previous studies. In order to implement more detailed models, an electron fluid model is implemented and is solved on an AMR octree grid using the preconditioned conjugate gradient method. Current density comparisons of the electron fluid model with the experimental measurements showed a worse comparison than the polytropic model for the selected parameters. The implemented electron fluid model is then compared with ion energy distributions from flight measurements and previous simulations and showed good agreement for the chosen parameters. In order to investigate the influence of solar panel voltage on a spacecraft plume, simulations using the electron fluid and the polytropic models were compared. It was seen that the spatial distribution of ions in the core plume and in the backflow region are similar for both electron models. Finally, sputtering calculations were performed and it was seen that the energies of ions that hit the solar panel are smaller than the threshold energy of aluminum, and so that there would be insignificant sputtering. This is because neutralized particles in the vicinity of the solar panel create a shield that protects the solar panel from the high energy CEX ions

Computational modeling of a Hall thruster plasma plume in a vacuum tank

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2002.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 169-171).Hall thrusters have become a tempting alternative to traditional chemical propulsion systems due to the great mass savings they provide through high specific impulses. However, a major stumbling block to their widespread integration is uncertainty about the thruster plume's interaction with spacecraft components. While in-space data is difficult to collect, much experimental data from vacuum tank tests is readily available. Effectively taking advantage of this wealth requires understanding of the effects from imperfect ground test conditions. A previous plume model, Qasi3, has been upgraded to better simulate the vacuum tank environment primarily through improvements to the source model, the collision method, and the sputtering method. The code is now more accurate and provides insight into phenomena such as background pressure consequences. sputtering and sputtered material deposition.by Shannon Yun-Ming Cheng.S.M

Development of the plasma thruster particle-in-cell simulator to complement empirical studies of a low-power cusped-field thruster

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, February 2013.This electronic version was submitted and approved by the author's academic department as part of an electronic thesis pilot project. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from department-submitted PDF version of thesis.Includes bibliographical references (p. 273-285).Cusped-field plasma thrusters are an electric propulsion concept being investigated by several laboratories in the United States and Europe. This technology was implemented as a low-power prototype in 2007 to ascertain if durability and performance improvements over comparable Hall thruster designs could be provided by the distinct magnetic topologies inherent to these devices. The first device tested at low-powers was eventually designated the "diverging cusped- field thruster" (DCFT) and demonstrated performance capabilities similar to state-of-the-art Hall thrusters. The research presented herein is a continuation of these initial studies, geared toward identifying significant operational characteristics of the thruster using experiments and numerical simulations. After a review of hybrid, fluid, and particle-in-cell Hall thruster models, experimental contributions from this work are presented. Anode current waveform measurements provide the first evidence of the distinct time-dependent characteristics of the two main modes of DCFT operation. The previously named "high-current" mode exhibits oscillation amplitudes several factors larger than mean current values, while magnitudes in "low-current" mode are at least a full order smaller. Results from a long-duration test, exceeding 200 hours of high-current mode operation, demonstrate lifetime-limiting erosion rates about 50% lower than those observed in comparable Hall thrusters. Concurrently, the plasma thruster particle-in-cell (PTpic) simulator was developed by upgrading numerous aspects of a preexisting Hall thruster model. Improvements in performance and accuracy have been achieved through modifications of the particle moving and electrostatic potential solving algorithms. Data from simulations representing both modes of operation are presented. In both cases, despite being unable to predict the correct location of the main potential drop in the thruster chamber, the model successfully reproduces the hollow conical jet of fast ions in the near plume region. The influences guiding the formation of the simulated beam in low-current mode are described in detail. A module for predicting erosion rates on dielectric surfaces has also been incorporated into PTpic and applied to simulations of both DCFT operational modes. Two data sets from highcurrent mode simulations successfully reproduce elevated erosion profiles in each of the three magnetic ring-cusps present in the DCFT. Discrepancies between the simulated and experimental data do exist, however, and are once again attributable to the misplacement of the primary acceleration region of the thruster. Having successfully captured the most significant erosion profile features observed in high-current mode, a simulation of erosion in low-current mode indicates substantially reduced erosion in comparison to the more oscillatory mode. These findings further motivate the completion of low-current mode erosion measurements, and continued numerical studies of the DCFT. Additionally, PTpic has proven to be a useful simulation tool for this project, and has been developed with adaptability in mind to facilitate its application to a variety of thruster designs -- including Hall thrusters.by Stephen Robert Gildea.Ph.D