Parallelization of particle-in-cell simulation modeling Hall-effect thrusters

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2005.Includes bibliographical references (p. 136-139).MIT's fully kinetic particle-in-cell Hall thruster simulation is adapted for use on parallel clusters of computers. Significant computational savings are thus realized with a predicted linear speed up efficiency for certain large-scale simulations. The MIT PIC code is further enhanced and updated with the accuracy of the potential solver, in particular, investigated in detail. With parallelization complete, the simulation is used for two novel investigations. The first examines the effect of the Hall parameter profile on simulation results. It is concluded that a constant Hall parameter throughout the entire simulation region does not fully capture the correct physics. In fact, it is found empirically that a Hall parameter structure which is instead peaked in the region of the acceleration chamber obtains much better agreement with experiment. These changes are incorporated into the evolving MIT PIC simulation. The second investigation involves the simulation of a high power, central-cathode thruster currently under development. This thruster presents a unique opportunity to study the efficiency of parallelization on a large scale, high power thruster. Through use of this thruster, we also gain the ability to explicitly simulate the cathode since the thruster was designed with an axial cathode configuration.by Justin M. Fox.S.M

A Two-dimensional Hybrid-Direct Kinetic Model of a Hall Thruster

The goal of this dissertation is to improve the state-of-the art modeling approaches available for simulating the discharge plasma in a Hall effect thruster (HET). A HET is a space propulsion device that utilizes electrical energy to ionize and accelerate propellant, generating thrust. The device features a cross-field configuration, whereby the transverse magnetic field traps electrons, and the axial electric field electrostatically accelerates ions out of the thruster channel. This configuration enables desirable thruster performance characteristics typically characterized by a relatively high specific impulse (1000-3000 s) and a high thrust density (a few Newtons per square meter). High fidelity computational models are useful to investigate the physical processes that govern the HET's performance, efficiency, and lifetime limitations. The non-equilibrium nature of the plasma transport should be resolved so that the flow can be accurately characterized. A grid-based direct kinetic (DK) simulation is capable of modeling the non-equilibrium state of plasma without the numerical noise that is inherent to particle-based methods since the velocity distribution functions (VDFs) are obtained in a deterministic manner. As the primary objective of this work, a two-dimensional, hybrid-DK simulation of the discharge plasma in a HET is developed. As a secondary objective, a plasma sheath, one of the important physical structures that form in the discharge plasma of a HET near the channel walls, is examined via a two-dimensional full DK simulation that highlights slight spatial differences in the sheath as a result of electrically disparate, adjacent wall materials. The memory storage requirements and computational load for the parallelized DK simulation grow with additional species, physical space dimensions, and velocity space dimensions. Some of these numerical limitations are encountered within this work. The hybrid-DK HET model utilizes a quasi-one-dimensional fluid electron algorithm in conjunction with a two-dimensional DK method to simulate the motion of neutral atoms and ions in a HET channel and near-field plume. Upon its development, the hybrid-DK simulation is benchmarked against results obtained from a two-dimensional hybrid-particle-in-cell (PIC) simulation with an identical fluid electron algorithm. To achieve agreement between the simulation results, a boundary condition for the DK model that satisfies particle conservation at the wall boundaries is developed, and electron model boundary conditions that provide solution stability are sought and utilized. For both high-frequency and low-frequency oscillations, the two simulations show good agreement for both time-averaged and dynamic plasma properties. Statistical noise tends to randomize plasma oscillations in the PIC simulation results, whereas the DK results exhibit coherent oscillatory behavior. Furthermore, results indicate that the DK simulation is capable of responding to small changes in electron dynamics, which is promising for future work. The DK plasma sheath simulation models a two-dimensional plasma sheath that highlights slight spatial differences inside the sheath as a result of electrically disparate, adjacent materials. To accomplish this goal, a quasi-one-dimensional sheath model is first built in a two-dimensional framework, boundary conditions are developed, and results are verified against theoretical expectations. Then, the full two-dimensional plasma sheath is modeled. The proof-of-concept model shows that two-dimensional effects are present in the vicinity of the discontinuous plasma potential at the wall, and electron and ion VDFs both clearly exhibit changes due to these effects.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/162983/1/astridr_1.pd

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

Development of Grid-Based Direct Kinetic Method and Hybrid Kinetic-Continuum Modeling of Hall Thruster Discharge Plasmas.

Novel computational methods were developed and used to characterize plasma flows and improve the efficiency of electric propulsion devices. The focus of this doctoral research is on developing a grid-based direct kinetic (DK) simulation method that is an alternative to particle-based kinetic methods. The first part of this dissertation describes development of the grid-based direct kinetic method through verification and benchmarking. The test cases include a plasma-sheath with and without secondary electron emission from a plasma-immersed material as well as trapped particle bunching instability in nonlinear plasma waves. Using a hybrid kinetic-continuum method for the discharge plasma in a Hall effect thruster, the grid-based DK simulation and a standard particle-in-cell (PIC) method are compared. It was found that ionization events and hence ionization oscillations are captured without any statistical noise in the DK simulation in comparison to a particle simulation. In the second part, mode transition of the discharge oscillations in Hall effect thrusters, which are known to affect thruster performance, is investigated using the hybrid-DK method, in which the DK method is used for ions and a continuum method is used for electrons. The numerical simulations show good agreement with experimental data. In addition, a linear perturbation theory of ionization oscillations is derived. It is found that electron transport and temperature play an important role in such discharge oscillations whereas the common understanding in the community was that the heavy species are the main contributors. In addition, a two-dimensional simulation is developed to investigate the multidimensional ionization oscillation phenomena in the Hall effect thrusters. The effect of ion magnetization due to the magnetic field is included, showing a swirling effect of accelerated ions. Local ionization oscillations in the azimuthal direction are observed.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111379/1/kenhara_1.pd

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

Fully kinetic modeling of a divergent cusped-field thruster

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 63-55).A fully kinetic, particle-in-cell plasma simulation tool has been incrementally developed by members of the Massachusetts Institute of Technology Space Propulsion Laboratory. Adapting this model to simulate the performance and plasma dynamics of a divergent cusped-field thruster is discussed. Strong magnetic fields in the cusps (B0.5 T) necessitate using a time step on the order of a picosecond in order to resolve electron cyclotron trajectories. As a result, successfully completing a divergent cusped-field thruster simulation with the full magnetic field strength has yet to be accomplished. As an intermediate step, simulation results of a divergent cusped-field thruster with the magnetic field at 1/5 the actual value are presented, including performance parameters and internal plasma structure details. Evidence suggests that even at 1/5 the magnetic field strength, ions are fully magnetized within certain regions of the divergent cusped-field thruster. This has strong implications concerning the basic operating principles of the thruster because the Hall effect does not result in a net flow of current in regions where ions are fully magnetized. Further modifications that may lead to successful simulations of divergent cusped-field thrusters at full magnetic field strength are also outlined, which may allow for more detailed studies of the plasma structure and performance of the cusped-field thruster.by Stephen R. Gildea.S.M

14-moment maximum-entropy modelling of collisionless ions for Hall thruster discharges

Ions in Hall thruster devices are often characterized by a low collisionality. In the presence of acceleration fields and azimuthal electric field waves, this results in strong deviations from thermodynamic equilibrium, introducing kinetic effects. This work investigates the application of the 14-moment maximum-entropy model to this problem. This method consists in a set of 14 PDEs for the density, momentum, pressure tensor components, heat flux and fourth-order moment associated to the particle velocity distribution function. The model is applied to the study of collisionless ion dynamics in a Hall thruster-like configuration, and its accuracy is assessed against different models, including the kinetic solution. Three test cases are considered: a purely axial acceleration problem, the problem of ion-wave trapping and finally the evolution of ions in the axial-azimuthal plane. Most of this work considers ions only, and the coupling with electrons is removed by prescribing reasonable values of the electric field. This allows us to obtain a direct comparison among different ion models. However, the possibility to run self-consistent plasma simulations is also briefly discussed, considering quasi-neutral or multi-fluid models. The maximum-entropy system appears to be a robust and accurate option for the considered test cases. The accuracy is improved over the simpler pressureless gas model (cold ions) and the Euler equations for gas dynamics, while the computational cost shows to remain much lower than direct kinetic simulations

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