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

H- ion source for CERN's Linac4 accelerator:simulation, experimental validation and optimization of the hydrogen plasma

Linac4 is the new negative hydrogen ion (H-) linear accelerator of the European Organization for Nuclear Research (CERN). Its ion source operates on the principle of Radio-Frequency Inductively Coupled Plasma (RF-ICP) and it is required to provide 50 mA of H- beam in pulses of 600 us with a repetition rate up to 2 Hz and within an RMS emittance of 0.25 pi mm mrad in order to fullfil the requirements of the accelerator. This thesis is dedicated to the characterization of the hydrogen plasma in the Linac4 H- ion source. We have developed a Particle-In-Cell Monte Carlo Collision (PIC-MCC) code to simulate the RF-ICP heating mechanism and performed measurements to benchmark the fraction of the simulation outputs that can be experimentally accessed. The code solves self-consistently the interaction between the electromagnetic field generated by the RF coil and the resulting plasma response, including a kinetic description of charged and neutral species. A fully-implicit implementation allowed to simulate the high density regime of the Linac4 H- ion source, ensuring the energy conservation while maintaining the computational resources tractable. We studied the capacitive to inductive transition characteristic of the initial phase of the pulsed discharge. The simulation results were confirmed by time-resolved photometry measurements and allowed quantifying the effect of the hydrogen pressure and of the external magnetic cusp field on the transition dynamics. This provided insights into possible modifications to the magnetic cusp field configuration to maximize the power deposited to the plasma. The optimal ion source configuration maximizes the density of volume produced H-, the flux of H0 atoms onto the cesiated molybdenum plasma electrode surface at the origin of H- emission, and minimizes the electron density and energy in the beam formation region. We simulated the high-density regime (10^19 m-3) representative of the nominal operation of the Linac4 ion source during beam extraction. We performed a parametric study of the RF current, hydrogen pressure and magnetic configuration (cusp and filter) to assess their impact on the plasma parameters. The simulation results allowed assessment of these parameters and provided guidelines for the optimization of the ion source operational and design parameters. The simulation results of electron density, electron energy and hydrogen dissociation degree showed excellent agreement with optical emission spectroscopy measurements both as a function of RF coil current and magnetic configuration. The outputs of these simulations provide crucial inputs to beam formation and extraction physics models. Dedicated PIC software packages are being developed that will eventually shed insight into essential beam parameters such as the intensity and emittance of the H° beam and the intensity of the co-extracted electrons

Particle-in-cell simulations of electron dynamics in low pressure discharges with magnetic fields

In modern low pressure plasma discharges, the electron mean free path often exceeds the device dimensions. Under such conditions the electron velocity distribution function may significantly deviate from Maxwellian, which strongly affects the discharge properties. The description of such plasmas has to be kinetic and often requires the use of numerical methods. This thesis presents the study of kinetic effects in inductively coupled plasmas and Hall thrusters carried out by means of particle-in-cell simulations. The important result and the essential part of the research is the development of particle-in-cell codes. An advective electromagnetic 1d3v particle-in-cell code is developed for modelling the inductively coupled plasmas. An electrostatic direct implicit 1d3v particle-in-cell code EDIPIC is developed for plane geometry simulations of Hall thruster plasmas. The EDIPIC code includes several physical effects important for Hall thrusters: collisions with neutral atoms, turbulence, and secondary electron emission. In addition, the narrow sheath regions crucial for plasma-wall interaction are resolved in simulations. The code is parallelized to achieve fast run times. Inductively coupled plasmas sustained by the external RF electromagnetic field are widely used in material processing reactors and electrodeless lighting sources. In a low pressure inductive discharge, the collisionless electron motion strongly affects the absorption of the external electromagnetic waves and, via the ponderomotive force, the density profile. The linear theory of the anomalous skin effect based on the linear electron trajectories predicts a strong decrease of the ponderomotive force for warm plasmas. Particle-in-cell simulations show that the nonlinear modification of electron trajectories by the RF magnetic field partially compensates the effects of electron thermal motion. As a result, the ponderomotive force in warm collisionless plasmas is stronger than predicted by linear kinetic theory. Hall thrusters, where plasma is maintained by the DC electric field crossed with the stationary magnetic field, are efficient low-thrust devices for spacecraft propulsion. The energy exchange between the plasma and the wall in Hall thrusters is enhanced by the secondary electron emission, which strongly affects electron temperature and, subsequently, thruster operation. Particle-in-cell simulations show that the effect of secondary electron emission on electron cooling in Hall thrusters is quite different from predictions of previous fluid studies. Collisionless electron motion results in a strongly anisotropic, nonmonotonic electron velocity distribution function, which is depleted in the loss cone, subsequently reducing the electron wall losses compared to Maxwellian plasmas. Secondary electrons form two beams propagating between the walls of a thruster channel in opposite radial directions. The secondary electron beams acquire additional energy in the crossed external electric and magnetic fields. The energy increment depends on both the field magnitudes and the electron flight time between the walls. A new model of secondary electron emission in a bounded plasma slab, allowing for emission due to the counter-propagating secondary electron beams, is developed. It is shown that in bounded plasmas the average energy of plasma bulk electrons is far less important for the space charge saturation of the sheath than it is in purely Maxwellian plasmas. A new regime with relaxation oscillations of the sheath has been identified in simulations. Recent experimental studies of Hall thrusters indirectly support the simulation results with respect to the electron temperature saturation and the channel width effect on the thruster discharge

Control of Plasma Kinetics for Microelectronics Fabrication.

The fluxes of radicals and ions to the wafer during plasma processing of microelectronics devices determine the quality of the etch or deposition. These fluxes are largely controlled by controlling the electron energy distribution (EED) which determines the dissociation patterns of feedstock gases. Also, the quality of the process is in large part determined by the ability to control the ion energy distribution (IED) onto the wafer. In this thesis, the possibilities of controlling EED and IED are modeled using a two-dimensional plasma equipment model. The techniques to control the EED include a magnetic field, beam electrons and a pulsed power source. Due to the magnetic confinement, the EED varies with position of the chamber depending on the pressure and power. Using beam electrons also provides a possibility to customize EED by delivering the energy to the bulk electrons through the e-e collisions. In dual frequency capacitively coupled plasmas (DF-CCP), the pulsed power is one technique being investigated to provide additional degrees of freedom to control the EED and IED. By using pulsed power, electron sources and sinks do not need to instantaneously balance – they only need to balance over the longer pulse period. This provides additional leverage to customize EED and IED. As an application, the etching properties were also investigated in the DF-CCP using pulsed power. In the pulsed operation, there are typically two phases; deposition and etching. As a result, using pulse power provides one with the ability to control the balance between the etching and deposition, which enables us to manipulate the etching profile. It was found that sidewall bowing can be suppressed by pulsing.PHDNuclear Engineering & Radiological SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/108809/1/ssongs_1.pd

Modeling of very high frequency large-electrode capacitively coupled plasmas with a fully electromagnetic particle-in-cell code

Phenomena taking place in capacitively coupled plasmas with large electrodes and driven at very high frequencies are studied numerically utilizing a novel energy- and charge-conserving implicit fully electromagnetic particle-in-cell / Monte Carlo code ECCOPIC2M. The code shows a good agreement with different cases having various collisionality and absorbed power. Although some aspects of the underlying physics were demonstrated in the previous literature with other models, the particle-in-cell method is advantageous for the predictive modeling due to a complex interplay between the surface mode excitations and the nonlocal physics of the corresponding type of plasma discharges operated at low pressures, which is hard to reproduce in other models realistically

Electron dynamics in planar radio frequency magnetron plasmas: II. Heating and energization mechanisms studied via a 2d3v particle-in-cell/Monte Carlo code

The present work investigates electron transport and heating mechanisms using an (r, z) particle-in-cell (PIC) simulation of a typical rf-driven axisymmetric magnetron discharge with a conducting target. It is shown that for the considered magnetic field topology the electron current flows through different channels in the (r, z) plane: a ``transverse'' one, which involves current flow through the electrons' magnetic confinement region (EMCR) above the racetrack, and two ''longitudinal'' ones. Electrons gain energy from the electric field along these channels following various mechanisms, which are rather distinct from those sustaining dc-powered magnetrons. The longitudinal power absorption involves mirror-effect heating (MEH), nonlinear electron resonance heating (NERH), magnetized bounce heating (MBH), and the heating by the ambipolar field at the sheath-presheath interface. The MEH and MBH represent two new mechanisms missing from the previous literature. The MEH is caused by a reversed electric field needed to overcome the mirror force generated in a nonuniform magnetic field to ensure sufficient flux of electrons to the powered electrode, and the MBH is related to a possibility for an electron to undergo multiple reflections from the expanding sheath in the longitudinal channels connected by the arc-like magnetic field. The electron heating in the transverse channel is caused mostly by the essentially collisionless Hall heating in the EMCR above the racetrack, generating a strong ExB azimuthal drift velocity. The latter mechanism results in an efficient electron energization, i.e., energy transfer from the electric field to electrons in the inelastic range. Since the main electron population energized by this mechanism remains confined within the discharge for a long time, its contribution to the ionization processes is dominant

The physics of streamer discharge phenomena

In this review we describe a transient type of gas discharge which is commonly called a streamer discharge, as well as a few related phenomena in pulsed discharges. Streamers are propagating ionization fronts with self-organized field enhancement at their tips that can appear in gases at (or close to) atmospheric pressure. They are the precursors of other discharges like sparks and lightning, but they also occur in for example corona reactors or plasma jets which are used for a variety of plasma chemical purposes. When enough space is available, streamers can also form at much lower pressures, like in the case of sprite discharges high up in the atmosphere. We explain the structure and basic underlying physics of streamer discharges, and how they scale with gas density. We discuss the chemistry and applications of streamers, and describe their two main stages in detail: inception and propagation. We also look at some other topics, like interaction with flow and heat, related pulsed discharges, and electron runaway and high energy radiation. Finally, we discuss streamer simulations and diagnostics in quite some detail. This review is written with two purposes in mind: First, we describe recent results on the physics of streamer discharges, with a focus on the work performed in our groups. We also describe recent developments in diagnostics and simulations of streamers. Second, we provide background information on the above-mentioned aspects of streamers. This review can therefore be used as a tutorial by researchers starting to work in the field of streamer physics.Comment: 89 pages, 29 figure

Controlling Photon and Ion Fluxes in Low Pressure Low Temperature Plasmas

Low temperature plasmas are widely used in both industry and everyday life, from fluorescent lighting, water purification to important processes in semiconductor industry fabricating electronic devices. In most of these applications, the flux of various energetic species generated by low temperature plasmas are the main promoter of necessary reactions facilitating the applications, by efficiently delivering energy for chemical reactions at molecular level. For example, in the process of plasma etching for semiconductor material processing, fluxes of radicals and ions can selectively react with material on the surface of the wafer, creating surface structures on the order of 10s of nm over the surface area of 103 cm-3. In the work of this thesis, the possibility of gaining a better understanding at controlling those fluxes is explored numerically using a two-dimensional plasma equipment model. In semiconductor industry, control of ion fluxes and ion energy distribution is critical to optimizing fabrication process and pushing the limit of Moore’s law. In this thesis, a unconventional tri-frequency capacitively coupled plasma (CCP) is investigated for scaling of ion fluxes and energy over power of individual frequencies. Compared with the conventional single-frequency and state-of-the-art dual-frequency CCP, we discovered that additional control of ion energy distribution can be achieved by the power of two lower frequencies. Ion fluxes scale positively with increasing power at all frequencies, and are more sensitive to low frequency power. Vacuum-Ultra-Violet (VUV) photon fluxes are also discovered to have important effect during plasma etching, such that controlling of VUV photon fluxes could potentially benefit to process optimization. This work studied dynamics of a low pressure inductively coupled plasma (ICP), trying to develop approaches of separate controlling VUV and ion fluxes. It was discovered that the ratio of VUV and ion flux, β, can be controlled by pressure, gas mixture and even surface conditions of the reactor wall. β can also be a function of duty cycle in pulsed ICP, caused by the customized electron energy distribution facilitated by the pulse power. Pulsed ICP has been widely studied for its unique tunability of electron energy distribution. Normally operating in radio frequency, power delivery of ICP can be sensitive to the matching circuit of the system. In this thesis, the dynamics of a pulsed ICP is investigated against the matching network. Instead of considering power mismatch as limiting factor, a deliberately tuned off-match condition is used to control the plasma density of a pulsed ICP. Both experimental and computational results are reported to observe instantaneous match time changes with configuration of matching circuit. Pulsed ICP that matches at a later time exhibits delayed density rise time with a larger final density. Low temperature plasma source are also investigated as a device for chemical analysis. A microwave excited microplasma, operated at several watts, is generated in dielectric cavities of hundreds of microns as ionization source for a novel concept of mass spectrometer. VUV photon fluxes produced from such microplasma source are then used to ionize samples for spectrometry. Result shows that the power efficiency of VUV emission is less than 1% and saturates as power increases. The VUV spectra can be individually tuned by adding Penning gas in the mixtures.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144041/1/tianpeng_1.pd

Pitfalls in Modeling Walls and Neutrals Physics in Gas Discharges Using Parallel Particle-in-Cell Monte Carlo Collision Algorithms

Owing to their ability to model the physics of low-pressure plasmas away from thermodynamical equilibrium, particle-in-cell (PIC) techniques have become one of the tools of choice to simulate the operation of many plasma devices. This trend is reinforced by the growing access to parallel computing resources which enables tackling problems that were previously intractable with PIC techniques. However, accurate modeling of these plasmas often depends critically on the detailed description of a variety of physical phenomena ranging from microscopic to macroscopic scale and from electrons' to neutral particles' timescale. Among those are coupling phenomena between charged particles and neutrals. We illustrate here how the implementation of simplified models for scattering kinematics, neutrals dynamics and particle-wall interaction can affect simulation results. Until the full breadth of these effects can be captured in models, these results underline the importance of using extensive parametric scans to assess the importance of these effects