Cesium vapor thermionic converters are an attractive method of converting high-temperature heat directly to electricity, but theoretical descriptions of the systems have been difficult due to the multi-step ionization of Cs through inelastic electron–neutral collisions. This work presents particle-in-cell simulations of these converters, using a direct simulation Monte Carlo collision model to track 52 excited states of Cs. Here, these simulations show the dominant role of multi-step ionization, which also varies significantly based on both the applied voltage bias and pressure. The electron energy distribution functions are shown to be highly non-Maxwellian in the cases analyzed here. A comparison with previous approaches is presented, and large differences are found in ionization rates due especially to the fact that previous approaches have assumed Maxwellian electron distributions. Finally, an open question regarding the nature of the plasma sheaths in the obstructed regime is discussed. The one-dimensional simulations did not produce stable obstructed regime operation and thereby do not support the double-sheath hypothesis.
Single particle aerosol mass spectrometry (SPAMS), an analytical technique for measuring the size and composition of individual micron-scale particles, is capable of analyzing atmospheric pollutants and bioaerosols much more efficiently and with more detail than conventional methods which require the collection of particles onto filters for analysis in the laboratory. Despite SPAMS’ demonstrated capabilities, the primary mechanisms of ionization are not fully understood, which creates challenges in optimizing and interpreting SPAMS signals. In this paper, we present a well-stirred reactor model for the reactions involved with the laser-induced vaporization and ionization of an individual particle. The SPAMS conditions modeled in this paper include a 248 nm laser which is pulsed for 8 ns to vaporize and ionize each particle in vacuum. The ionization of 1 μm, spherical Al particles was studied by approximating them with a 0-dimensional plasma chemistry model. The primary mechanism of absorption of the 248 nm photons was pressure-broadened direct photoexcitation to Al(y2D). Atoms in this highly excited state then undergo superelastic collisions with electrons, heating the electrons and populating the lower energy excited states. We found that the primary ionization mechanism is electron impact ionization of various excited state Al atoms, especially Al(y2D). Because the gas expands rapidly into vacuum, its temperature decreases rapidly. The rate of three-body recombination (e- + e- + Al+ → Al + e-) increases at low temperature, and most of the electrons and ions produced recombine within several μs of the laser pulse. The importance of the direct photoexcitation indicates that the relative peak heights of different elements in SPAMS mass spectra may be sensitive to the available photoexcitation transitions. We also discuss the effects of laser intensity, particle diameter, and expansion dynamics.
Cathode-directed streamer evolution in near atmospheric air is modeled in 3D pin-to-plane geometries using a 3D kinetic Particle-In-Cell (PIC) code that simulates particle-particle collisions via the Direct Simulation Monte Carlo (DSMC) method. Due to the computational challenges associated with a complete 360° volumetric domain, a practical alternative was achieved using a wedge domain and a range of azimuthal angles was explored (5°, 15°, 30°, and 45°) to study possible effects on the streamer growth and propagation due to the finite wedge angle. A DC voltage of 6 kV is administered to a hemispherical anode of radius 100 μm, with a planar cathode held at ground potential, generating an over-volted state with an electric field of 4 MV/m across a 1500 μm gap. The domain is seeded with an initial ion and electron density of 1018 m-3 at 1 eV temperature confined to a spherical region of radius 100 μm centered at the tip of the anode. The air chemistry model [1] includes standard Townsend breakdown mechanisms (electron-neutral elastic, excitation, ionization, attachment, and detachment collision chemistry and secondary electron emission) as well as streamer mechanisms (photoionization and ion-neutral collisions) via tracking excited state neutrals which can then either quench via collisions or spontaneously emit a photon based on specific Einstein-A coefficients [2, 3]. In this work, positive streamer dynamics are formally quantified for each wedge angle in terms of electron velocity and density as temporal functions of coordinates r, Φ, and z. Applying a random plasma seed for each simulation, particles of interest are tracked with near femtosecond temporal resolution out to 1.4 ns and spatially binned. This process is repeated six times and results are averaged. Prior 2D studies have shown that the reduced electric field, E/n, can significantly impact streamer evolution [4]. We extend the analysis to 3D wedge geometries, to limit computational costs, and examine the wedge angle’s effect on streamer branching, propagation, and velocity. Results indicate that the smallest wedge angle that produced an acceptably converged solution is 30°. The potential effects that a mesh, when under-resolved with respect to the Debye length, can impart on streamer dynamics and numerical heating were not investigated, and we explicitly state here that the smallest cell size was approximately 10 times the minimum λD in the streamer channel at late times. This constraint on cell size was the result of computational limitations on total mesh count.
Particle-in-cell simulations are used to study how neutral pressure influences plasma properties at the sheath edge. The high rate of ion–neutral collisions at pressures above several mTorr are found to cause a decrease in the ion velocity at the sheath edge (collisional Bohm criterion), a decrease in the edge-to-center density ratio (hl factor), and an increase in the sheath width and sheath potential drop. A comparison with existing analytic models generally indicates favorable agreement, but with some distinctions. One is that models for the hl factor need to be made consistent with the collisional Bohm criterion. With this and similar corrections, a comprehensive fluid-based model of the plasma boundary transition is constructed that compares well with the simulation results.
Brooks, William B.; Clark, Raimi C.; Young, Jacob K.; Hopkins, Matthew M.; Dickens, James D.; Neuber, Andreas N.
Surface flashover in vacuum imposes a substantial physical limit on modern, large-scale pulsed power. One of the ramifications is a minimum size requirement for new machines, which in itself becomes a hard barrier to the modernization and improvement of existing infrastructure. Pulsed power topologies require the physical mechanisms of both anode- and cathode-initiated flashover to be considered. Originally, the geometrical implications of field emission at the cathode triple junction (CTJ) motivated the usage of configurations that avoid electrons impinging on the insulating material. This will largely suppress the cathode-initiated flashover, which is best described by the secondary electron avalanche mechanism, gas desorption, and final breakdown in the desorbed gas. It depends on the cascade growth of a conducting plasma along the length of the insulator from the cathode. Mitigating the cathode-initiated flashover typically comes at the cost of a significant field enhancement at the anode triple junction (ATJ). In a typical implementation, the anode field may be three times higher than the cathode field for a given voltage, making the corresponding anode-initiated flashover much more common than otherwise. In the case of pulsed, anode-initiated flashover, experimental evidence suggests that charge is directly extracted from the insulator resulting in the insulator taking on a net positive charge advancing the anode potential. Furthermore, along with accompanying gas desorption from the surface, the potential will then propagate from the anode toward the cathode until the effective length of the gap is sufficiently reduced to support flashover. The underlying physical mechanisms of cathode- and anode-directed flashover are discussed in light of previously gathered experimental data and recent experiments with pulsed, high-gradient, anode-initiated flashover.
Plasma etching of semiconductors is an essential process in the production of microchips which enable nearly every aspect of modern life. Two frequencies of applied voltage are often used to provide control of both the ion fluxes and energy distribution.
Structural disorder causes materials’ surface electronic properties, e.g., work function ([Formula: see text]), to vary spatially, yet it is challenging to prove exact causal relationships to underlying ensemble disorder, e.g., roughness or granularity. For polycrystalline Pt, nanoscale resolution photoemission threshold mapping reveals a spatially varying [Formula: see text] eV over a distribution of (111) vicinal grain surfaces prepared by sputter deposition and annealing. With regard to field emission and related phenomena, e.g., vacuum arc initiation, a salient feature of the [Formula: see text] distribution is that it is skewed with a long tail to values down to 5.4 eV, i.e., far below the mean, which is exponentially impactful to field emission via the Fowler–Nordheim relation. We show that the [Formula: see text] spatial variation and distribution can be explained by ensemble variations of granular tilts and surface slopes via a Smoluchowski smoothing model wherein local [Formula: see text] variations result from spatially varying densities of electric dipole moments, intrinsic to atomic steps, that locally modify [Formula: see text]. Atomic step-terrace structure is confirmed with scanning tunneling microscopy (STM) at several locations on our surfaces, and prior works showed STM evidence for atomic step dipoles at various metal surfaces. From our model, we find an atomic step edge dipole [Formula: see text] D/edge atom, which is comparable to values reported in studies that utilized other methods and materials. Our results elucidate a connection between macroscopic [Formula: see text] and the nanostructure that may contribute to the spread of reported [Formula: see text] for Pt and other surfaces and may be useful toward more complete descriptions of polycrystalline metals in the models of field emission and other related vacuum electronics phenomena, e.g., arc initiation.
Particle-in-cell, direct simulation Monte Carlo simulations reveal that ion-acoustic instabilities excited in presheaths can cause significant ion heating. Ion-acoustic instabilities are excited by the ion flow toward a sheath when the neutral gas pressure is small enough and the electron temperature is large enough. A series of 1D simulations were conducted in which neutral plasma (electrons and ions) was uniformly sourced with an ion temperature of 0.026 eV and different electron temperatures (0.1 eV-50 eV). Ion heating was observed when the electron-to-ion temperature ratio exceeded the minimum value predicted by linear response theory to excite ion-acoustic instabilities at the sheath edge (T e / T i ≈ 28). When this threshold was exceeded, the temperature equilibration rate between ions and electrons rapidly increased near the sheath so that the local temperature ratio did not significantly exceed the threshold for instability. This resulted in significant ion heating near the sheath edge, which also extended back into the bulk plasma; presumably due to wave reflection from the sheath. This ion-acoustic wave heating mechanism was found to decrease for higher neutral pressures, where ion-neutral collisions damp the ion-acoustic waves and ion heating is instead dominated by inelastic collisions in the presheath.
Understanding the role of physical processes contributing to breakdown is critical for many applications in which breakdown is undesirable, such as capacitors, and applications in which controlled breakdown is intended, such as plasma medicine, lightning protection, and materials processing. The electron emission from the cathode is a critical source of electrons which then undergo impact ionization to produce electrical breakdown. In this study, the role of secondary electron yields due to photons (γ ph) and ions (γ i) in direct current breakdown is investigated using a particle-in-cell direct simulation Monte Carlo model. The plasma studied is a one-dimensional discharge in 50 Torr of pure helium with a platinum cathode, gap size of 1.15 cm, and voltages of 1.2-1.8 kV. The current traces are compared with experimental measurements. Larger values of γ ph generally result in a faster breakdown, while larger values of γ i result in a larger maximum current. The 58.4 nm photons emitted from He(21P) are the primary source of electrons at the cathode before the cathode fall is developed. Of the values of γ ph and γ i investigated, those which provide the best agreement with the experimental current measurements are γ ph = 0.005 and γ i = 0.01. These values are significantly lower than those in the literature for pristine platinum or for a graphitic carbon film which we speculate may cover the platinum. This difference is in part due to the limitations of a one-dimensional model but may also indicate surface conditions and exposure to a plasma can have a significant effect on the secondary electron yields. The effects of applied voltage and the current produced by a UV diode which was used to initiate the discharge, are also discussed.
Abstract: This paper describes the verification and validation (V&V) framework developed for the stochastic Particle-in-Cell, Direct Simulation Monte Carlo code Aleph. An ideal framework for V&V from the viewpoint of the authors is described where a physics problem is defined, and relevant physics models and parameters to the defined problem are assessed and captured in a Phenomena Identification and Ranking Table (PIRT). Numerous V&V examples guided by the PIRT for a simple gas discharge are shown to demonstrate the V&V process applied to a real-world simulation tool with the overall goal to demonstrably increase the confidence in the results for the simulation tool and its predictive capability. Although many examples are provided here to demonstrate elements of the framework, the primary goal of this work is to introduce this framework and not to provide a fully complete implementation, which would be a much longer document. Comparisons and contrasts are made to more usual approaches to V&V, and techniques new to the low-temperature plasma community are introduced. Specific challenges relating to the sufficiency of available data (e.g., cross sections), the limits of ad hoc validation approaches, the additional difficulty of utilizing a stochastic simulation tool, and the extreme cost of formal validation are discussed. Graphic Abstract: [Figure not available: see fulltext.]
Carbone, Emile; Graef, Wouter; Hagelaar, Gerjan; Boer, Daan; Hopkins, Matthew M.; Stephens, Jacob C.; Yee, Benjamin T.; Pancheshnyi, Sergey; Van Dijk, Jan; Pitchford, Leanne
Technologies based on non-equilibrium, low-temperature plasmas are ubiquitous in today’s society. Plasma modeling plays an essential role in their understanding, development and optimization. An accurate description of electron and ion collisions with neutrals and their transport is required to correctly describe plasma properties as a function of external parameters. LXCat is an open-access, web-based platform for storing, exchangig and manipulating data needed for modeling the electron and ion components of non-equilibrium, low-temperature plasmas. The data types supported by LXCat are electron- and ion-scattering cross-sections with neutrals (total and differential), interaction potentials, oscillator strengths, and electron- and ion-swarm/transport parameters. Online tools allow users to identify and compare the data through plotting routines, and use the data to generate swarm parameters and reaction rates with the integrated electron Boltzmann solver. In this review, the historical evolution of the project and some perspectives on its future are discussed together with a tutorial review for using data from LXCat.
Helium is frequently used as a working medium for the generation of plasmas and is capable of energetic photon emissions. These energetic photon emissions are often attributed to the formation of helium excimer and subsequent photon emission. When the plasma device is exposed to another gas, such as nitrogen, this energetic photon emission can cause photoionization and further ionization wave penetration into the additional gas. Often ignored are the helium resonance emissions that are assumed to be radiation trapped and therefore not pertinent to photoionization. Here, experimental evidence for the presence of helium atomic emission in a pulsed discharge at ten's of Torr is shown. Simulations of a discharge in similar conditions agree with the experimental measurements. In this context, the role of atomic and molecular helium light emission on photoionization of molecular nitrogen in an ionization wave is studied using a kinetic modeling approach that accounts for radiation dynamics in a developing low-temperature plasma. Three different mixtures of helium at a total pressure of 250 Torr are studied in simulation. Photoionization of the nitrogen molecule by vacuum ultraviolet helium emission is used as the only seed source ahead of the ionization front. It is found that even though radiation trapped, the atomic helium emission lines are the significant source of photoionization of nitrogen. The significant effect of radiation trapped photon emission on ionization wave dynamics demonstrates the need to consider these radiation dynamics in plasma reactors where self-absorbed radiation is ignored.
The boundary regions of low-temperature plasmas are known to be susceptible to kinetic instabilities, which can affect the energies and fluxes of particles directed at the material boundary. For example, both the ion acoustic instability as well as an instability near the electron plasma frequency have been observed. Particle-in-cell (PIC) simulation is a tool that, alongside experiments, can capture the effects these instabilities have on the particle distribution functions. Ultimately, simulations can determine under what conditions these effects are significant by comparing to theoretical predictions and explore conditions unamenable to experiments.
Clark, Raimi; Young, Jacob; Brooks, William; Hopkins, Matthew M.; Mankowski, John; Stephens, Jacob; Neuber, Andreas
Early light emission provides information about the dominant mechanisms culminating in vacuum surface flashover (anode-initiated vs. cathode-initiated) for particular geometries. From experimental evidence gathered elsewhere, for the case of an insulator oriented at 45° with respect to the anode, anode-initiated flashover is believed to dominate since the field at the anode triple point is roughly three times that of the cathode. Similar to previous work performed on cathode-initiated flashover, light emission from the voltage rise through the impedance collapse is collected into two optical fibers focused on light emanating from the insulator in regions near the anode and cathode. The optical fibers are either connected to PMTs for spectrally integrated localized light intensity information or to a spectrograph used in conjunction with an ICCD camera. Challenges associated with localizing the flashover for optical diagnostics and incorporating the optical diagnostics into the high-field environment are discussed. Initial results for cross-linked polystyrene (Rexolite 1422) support the premise that flashover is initiated from the anode for these geometries, as early light from the anode leads cathode light up to photocathode saturation. Early spectroscopy results show promise for future characterization of the spatio-temporal development of emission from desorbed gas species across the insulator surface and identification of bulk insulator involvement if it occurs.
PIC MCC simulation results on the breakdown in the pulse discharge in helium at pressure of 100 Torr and voltage of U=3.25 kV are presented. The delay of the breakdown development is studied with different initial densities of plasma and excited helium atoms, which corresponds to various discharge operation frequencies. It is shown that for high concentration of excited atoms the photoemission determines the breakdown delay time. In opposite case of low excited atoms density, the ion-electron emission plays a key role in the breakdown development. The photoemission from the cathode is set with a flux of the photons with Doppler shift over the frequency. These photons are generated in reactions between exited atoms and fast atoms. A wide distribution of breakdown delay time was observed in different runs and analyzed.
Modern computational validation efforts rely on comparison of known experimental quantities such as current, voltage, particle densities, and other plasma properties with the same values determined through simulation. A discrete photon approach for radiation transport was recently incorporated into a particle-in-cell/direct simulation Monte Carlo code. As a result, spatially and temporally resolved synthetic spectra may be generated even for non-equilibrium plasmas. The generation of this synthetic spectra lends itself to potentially new validation opportunities. In this work, initial comparisons of synthetic spectra are made with experimentally gathered optical emission spectroscopy. A custom test apparatus was constructed that contains a 0.5 cm gap distance parallel plane discharge in ultra high purity helium gas (99.9999%) at a pressure of 75 Torr. Plasma generation is initiated with the application of a fast rise-time, 100 ns full-width half maximum, 2.0 kV voltage pulse. Transient electrical diagnostics are captured along with time-resolved emission spectra. A one-dimensional simulation is run under the same conditions and compared against the experiment to determine if sufficient physics are included to model the discharge. To sync the current measurements from experiment and simulation, significant effort was undertaken to understand the kinetic scheme required to reproduce the observed features. Additionally, the role of the helium molecule excimer emission and atomic helium resonance emission on photocurrent from the cathode are studied to understand which effect dominates photo-feedback processes. Results indicate that during discharge development, atomic helium resonance emission dominates the photo-flux at the cathode even though it is strongly self-absorbed. A comparison between the experiment and simulation demonstrates that the simulation reproduces observed features in the experimental discharge current waveform. Furthermore, the synthesized spectra from the kinetic method produces more favorable agreement with the experimental data than a simple local thermodynamic equilibrium calculation and is a first step towards using spectra generated from a kinetic method in validation procedures. The results of this study produced a detailed compilation of important helium plasma chemistry reactions for simulating transient helium plasma discharges.
The influence of different quantum yields for photons and secondary emission yields for ions striking a surface is investigated. Using a one-dimensional particle-in-cell simulation, these secondary emission coefficients are varied to observe the impact on discharge current. The discharge is assumed to occur in pure helium gas at a pressure of 75 torr. To handle binary particle interactions, the Direct Simulation Monte Carlo (DSMC) method is utilized. The model includes electron-neutral interactions, neutral-neutral interactions, and photon-neutral interactions. It is observed that the discharge current in the early stages of discharge is heavily dependent upon the quantum yield due to photon impact. In the later stages of discharge, the current depends on both the quantum yield and secondary emission coefficient for ion impact.
In most models of vacuum breakdown, there is some initial emission of electrons from the cathodic surface, usually employing some form of Fowler-Nordheim emission. While this may be correct for 'textbook' surfaces, it is generally unreliable for real surfaces and fitted parameters are often used. For example, the beta employed is generally unphysical based on usual definitions (e.g., it incorporates more, but unexplained, physics than just a geometry-based field concentration effect). In this work, we describe experimental efforts to better characterize which surface structure parameters influence the vacuum field emission current.
A fully resolved kinetic model (particle-in-cell and direct simulation Monte Carlo for particle/photon collisions) of a near atmospheric pressure ionization wave is presented here. Fully resolving the required numerical spatial (sub-μm) and temporal scales (tens of fs) for atmospheric pressure discharges in three-dimensions is still a challenging task on modern super computers. To keep the overall problem tractable, the total number of elements are reduced by only simulating a 10° wedge rather than a full 360° geometry. The ionization wave is generated in a needle-plane configuration with a gap size of 250 μm and a background of nitrogen and helium gas. A voltage of 1500 V is applied to the anode and an initial electron and ion density of 109 cm-3 is seeded in a region near the anode electrode tip and extending towards the cathode. As these initial electrons are swept away, photoionization and photoemission create new electrons and allow the ionization front to propagate towards the cathode. Results from the 90% N2, 10% He discharge indicate that photoionization has minimal impact on plasma formation processes and cathode photoemission is the dominant mechanism for new electrons. In the 90% He, 10% N2 discharge case, however, photoionization likely has an impact as the observed locations of photoionization occur far enough away from the ionization front to allow for sufficient avalanche processes that contribute to the propagation of the ionization wave. Additionally, the electron energy distribution functions in the 90% He, 10% N2 case indicate that there is less energy loss to the low lying molecular N2 electronic states as well as the vibrational and rotational modes. This leads to higher electron energies and faster plasma development times of ∼0.4 ns for the 90% He, 10% N2 case, and ∼1.5 ns for the 90% N2, 10% He case. In addition to analysis of the ionization wave results, the overall challenges associated with simulations near atmospheric pressure discharges in three-dimensions are discussed, including the limitations of the 10° wedge that produces, at least qualitatively, minimal 3D effects.
When electrodes are biased above the plasma potential, electrons accelerated through the associated electron sheath can dramatically increase the ionization rate of neutrals near the electrode surface. It has previously been observed that if the ionization rate is great enough, a double layer separates a luminous high-potential plasma attached to the electrode surface (called an anode spot or fireball) from the bulk plasma. Here, results of the first 2D particle-in-cell simulations of anode spot formation are presented along with a theoretical model describing the formation process. It is found that ionization leads to the build-up of an ion-rich layer adjacent to the electrode, forming a narrow potential well near the electrode surface that traps electrons born from ionization. It is shown that anode spot onset occurs when a quasineutral region is established in the potential well and the density in this region becomes large enough to violate the steady-state Langmuir condition, which is a balance between electron and ion fluxes across the double layer. A model for steady-state properties of the anode spot is also presented, which predicts values for the anode spot size, double layer potential drop, and form of the sheath at the electrode by considering particle, power, and current balance. These predictions are found to be consistent with the presented simulation and previous experiments.
A kinetic description for electronic excitation of helium for principal quantum number n 4 has been included into a particle-in-cell (PIC) simulation utilizing direct simulation Monte Carlo (DSMC) for electron-neutral interactions. The excited electronic levels radiate state-dependent photons with wavelengths from the extreme ultraviolet (EUV) to visible regimes. Photon wavelengths are chosen according to a Voigt distribution accounting for the natural, pressure, and Doppler broadened linewidths. This method allows for reconstruction of the emission spectrum for a non-thermalized electron energy distribution function (EEDF) and investigation of high energy photon effects on surfaces, specifically photoemission. A parallel plate discharge with a fixed field (i.e. space charge neglected) is used to investigate the effects of including photoemission for a Townsend discharge. When operating at a voltage near the self-sustaining discharge threshold, it is observed that the electron current into the anode is higher when including photoemission from the cathode than without even when accounting for self-absorption from ground state atoms. The photocurrent has been observed to account for as much as 20% of the total current from the cathode under steady-state conditions.
The temporal evolution of spectral lines from microplasma devices (MD) was studied, including impurity transitions. Long-wavelength emission diminishes more rapidly than deep UV with decreasing pulse width and RF operation. Thus, switching from DC to short pulsed or RF operation, UV emissions can be suppressed, allowing for real-time tuning of the ionization energy of a microplasma photo-ionization source, which is useful for chemical and atomic physics. Scaling allows MD to operate near atmospheric pressure where excimer states are efficiently created and emit down to 65 nm; laser emissions fall off below 200 nm, making MD light sources attractive for deep UV use. A first fully-kinetic three-dimensional model was developed that explicitly calculates electron-energy distribution function. This, and non-continuum effects, were studied with the model and how they are impacted by geometry and transient or DC operation. Finally, a global non-dimensional model was developed to help explain general trends MD physics.
The form of a sheath near a small electrode, with bias changing from below to above the plasma potential, is studied using 2D particle-in-cell simulations. When the electrode is biased within Te/2e below the plasma potential, the electron velocity distribution functions (EVDFs) exhibit a loss-cone type truncation due to fast electrons overcoming the small potential difference between the electrode and plasma. No sheath is present in this regime, and the plasma remains quasineutral up to the electrode. The EVDF truncation leads to a presheath-like density and flow velocity gradients. Once the bias exceeds the plasma potential, an electron sheath is present. In this case, the truncation driven behavior persists, but is accompanied by a shift in the maximum value of the EVDF that is not present in the negative bias cases. The flow moment has significant contributions from both the flow shift of the EVDF maximum, and the loss-cone truncation.
In this paper, we provide insight into the role and impact that a positively biased electrode (anode) has on bulk plasma potential. Using two-dimensional Particle-in-Cell simulations, we investigate the plasma potential as an anode transitions from very small ("probe" mode) to large ("locking" mode). Prior theory provides some guidance on when and how this transition takes place. Initial experimental results are also compared. The simulations demonstrate that as the surface area of the anode is increased transitions in plasma potential and sheath polarity occur, consistent with experimental observations and theoretical predictions. It is expected that understanding this basic plasma behavior will be of interest to basic plasma physics communities, diagnostic developers, and plasma processing devices where control of bulk plasma potential is important.
Electron sheaths are commonly found near Langmuir probes collecting the electron saturation current. The common assumption is that the probe collects the random flux of electrons incident on the sheath, which tacitly implies that there is no electron presheath and that the flux collected is due to a velocity space truncation of the electron velocity distribution function (EVDF). This work provides a dedicated theory of electron sheaths, which suggests that they are not so simple. Motivated by EVDFs observed in particle-in-cell (PIC) simulations, a 1D model for the electron sheath and presheath is developed. In the model, under low temperature plasma conditions (Te 蠑 Ti), an electron pressure gradient accelerates electrons in the presheath to a flow velocity that exceeds the electron thermal speed at the sheath edge. This pressure gradient generates large flow velocities compared to what would be generated by ballistic motion in response to the electric field. It is found that in many situations, under common plasma conditions, the electron presheath extends much further into the plasma than an analogous ion presheath. PIC simulations reveal that the ion density in the electron presheath is determined by a flow around the electron sheath and that this flow is due to 2D aspects of the sheath geometry. Simulations also indicate the presence of ion acoustic instabilities excited by the differential flow between electrons and ions in the presheath, which result in sheath edge fluctuations. The 1D model and time averaged PIC simulations are compared and it is shown that the model provides a good description of the electron sheath and presheath.
This document describes the form and use of three supplemental capabilities added to Goma during 1998 -- augmenting conditions, automatic continuation and linear stability analysis. Augmenting conditions allow the addition of constraints and auxiliary conditions which describe the relationship between unknowns, boundary conditions, material properties and post-processing extracted quantities. Automatic continuation refers to a family of algorithms (zeroth and first order here, single and multi-parameter) that allow tracking steady-state solution paths as material parameters or boundary conditions are varied. The stability analysis capability in Goma uses the method of small disturbances and superposition of normal modes to test the stability of a steady- state flow, i.e., it determines if the disturbance grows or decays in time.
We present an error estimation method for immersed interface solutions of elliptic boundary value problems. As opposed to an asymptotic rate that indicates how the errors in the numerical method converge to zero, we seek a posteriori estimates of the errors, and their spatial distribution, for a given solution. Our estimate is based upon the classical idea of defect corrections, which requires the application of a higher-order discretization operator to a solution achieved with a lower-order discretization. Our model problem will be an elliptic boundary value problem in which the coefficients are discontinuous across an internal boundary.
Multilayer coextrusion has become a popular commercial process for producing complex polymeric products from soda bottles to reflective coatings. A numerical model of a multilayer coextrusion process is developed based on a finite element discretization and two different free-surface methods, an arbitrary-Lagrangian-Eulerian (ALE) moving mesh implementation and an Eulerian level set method, to understand the moving boundary problem associated with the polymer-polymer interface. The goal of this work is to have a numerical capability suitable for optimizing and troubleshooting the coextrusion process, circumventing flow instabilities such as ribbing and barring, and reducing variability in layer thickness. Though these instabilities can be both viscous and elastic in nature, for this work a generalized Newtonian description of the fluid is used. Models of varying degrees of complexity are investigated including stability analysis and direct three-dimensional finite element free surface approaches. The results of this work show how critical modeling can be to reduce build test cycles, improve material choices, and guide mold design.
This report summarizes the work completed during FY2007 and FY2008 for the LDRD project ''Hybrid Plasma Modeling''. The goal of this project was to develop hybrid methods to model plasmas across the non-continuum-to-continuum collisionality spectrum. The primary methodology to span these regimes was to couple a kinetic method (e.g., Particle-In-Cell) in the non-continuum regions to a continuum PDE-based method (e.g., finite differences) in continuum regions. The interface between the two would be adjusted dynamically ased on statistical sampling of the kinetic results. Although originally a three-year project, it became clear during the second year (FY2008) that there were not sufficient resources to complete the project and it was terminated mid-year.
Many current and future modeling applications at Sandia including ASC milestones will critically depend on the simultaneous solution of vastly different physical phenomena. Issues due to code coupling are often not addressed, understood, or even recognized. The objectives of the LDRD has been both in theory and in code development. We will show that we have provided a fundamental analysis of coupling, i.e., when strong coupling vs. a successive substitution strategy is needed. We have enabled the implementation of tighter coupling strategies through additions to the NOX and Sierra code suites to make coupling strategies available now. We have leveraged existing functionality to do this. Specifically, we have built into NOX the capability to handle fully coupled simulations from multiple codes, and we have also built into NOX the capability to handle Jacobi Free Newton Krylov simulations that link multiple applications. We show how this capability may be accessed from within the Sierra Framework as well as from outside of Sierra. The critical impact from this LDRD is that we have shown how and have delivered strategies for enabling strong Newton-based coupling while respecting the modularity of existing codes. This will facilitate the use of these codes in a coupled manner to solve multi-physic applications.
As part of an effort to reduce costs and improve quality control in encapsulation and potting processes the Technology Initiative Project ''Defect Free Manufacturing and Assembly'' has completed a computational modeling study of flows representative of those seen in these processes. Flow solutions are obtained using a coupled, finite-element-based, numerical method based on the GOMA/ARIA suite of Sandia flow solvers. The evolution of the free surface is solved with an advanced level set algorithm. This approach incorporates novel methods for representing surface tension and wetting forces that affect the evolution of the free surface. In addition, two commercially available codes, ProCAST and MOLDFLOW, are also used on geometries representing encapsulation processes at the Kansas City Plant. Visual observations of the flow in several geometries are recorded in the laboratory and compared to the models. Wetting properties for the materials in these experiments are measured using a unique flowthrough goniometer.
Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes the incompressible Navier-Stokes equations, energy transport equation, species transport equations, nonlinear elastic solid mechanics, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods, fully-coupled Picard's method, and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h-adaptivity and dynamic load balancing are some of Aria's more advanced capabilities. Aria is based on the Sierra Framework.
To reduce costs and hazardous wastes associated with the production of lead-based active ceramic components, an injection molding process is being investigated to replace the current machining process. Here, lead zirconate titanate (PZT) ceramic particles are suspended in a thermoplastic resin and are injected into a mold and allowed to cool. The part is then bisque fired and sintered to complete the densification process. To help design this new process we use a finite element model to describe the injection molding of the ceramic paste. Flow solutions are obtained using a coupled, finite-element based, Newton-Raphson numerical method based on the GOMA/ARIA suite of Sandia flow solvers. The evolution of the free surface is solved with an advanced level set algorithm. This approach incorporates novel methods for representing surface tension and wetting forces that affect the evolution of the free surface. Thermal, rheological, and wetting properties of the PZT paste are measured for use as input to the model. The viscosity of the PZT is highly dependent both on temperature and shear rate. One challenge in modeling the injection process is coming up with appropriate constitutive equations that capture relevant phenomenology without being too computationally complex. For this reason we model the material as a Carreau fluid and a WLF temperature dependence. Two-dimensional (2D) modeling is performed to explore the effects of the shear in isothermal conditions. Results indicate that very low viscosity regions exist near walls and that these results look similar in terms of meniscus shape and fill times to a simple Newtonian constitutive equation at the shear-thinned viscosity for the paste. These results allow us to pick a representative viscosity to use in fully three-dimensional (3D) simulation, which because of numerical complexities are restricted to using a Newtonian constitutive equation. Further 2D modeling at nonisothermal conditions shows that the choice of representative Newtonian viscosity is dependent on the amount of heating of the initially room temperature mold. An early 3D transient model shows that the initial design of the distributor is sub-optimal. However, these simulations take several months to run on 4 processors of an HP workstation using a preconditioner/solver combination of ILUT/GMRES with fill factors of 3 and PSPG stabilization. Therefore, several modifications to the distributor geometry and orientations of the vents and molds have been investigated using much faster 3D steady-state simulations. The pressure distribution for these steady-state calculations is examined for three different distributor designs to see if this can indicate which geometry has the superior design. The second modification, with a longer distributor, is shown to have flatter, more monotonic isobars perpendicular to the flow direction indicating a better filling process. The effects of the distributor modifications, as well as effects of the mold orientation, have also been examined with laboratory experiments in which the flow of a viscous Newtonian oil entering transparent molds is recorded visually. Here, the flow front is flatter and voids are reduced for the second geometry compared to the original geometry. A horizontal orientation, as opposed to the planned vertical orientation, results in fewer voids. Recently, the Navier-Stokes equations have been stabilized with the Dohrman-Bochev PSPP stabilization method, allowing us to calculate transient 3D simulations with computational times on the order of days instead of months. Validation simulations are performed and compared to the experiments. Many of the trends of the experiments are captured by the level set modeling, though quantitative agreement is lacking mainly due to the high value of the gas phase viscosity necessary for numerical stability, though physically unrealistic. More correct trends are predicted for the vertical model than the horizontal model, which is serendipitous as the actual mold is held in a vertical geometry. The full, transient mold filling calculations indicate that the flow front is flatter and voids may be reduced for the second geometry compared to the original geometry. The validated model is used to predict mold filling for the actual process with the material properties for the PZT paste, the original distributor geometry, and the mold in a vertical orientation. This calculation shows that voids may be trapped at the four corners of the mold opposite the distributor.
This report documents the results for an FY06 ASC Algorithms Level 2 milestone combining error estimation and adaptivity, uncertainty quantification, and probabilistic design capabilities applied to the analysis and design of bistable MEMS. Through the use of error estimation and adaptive mesh refinement, solution verification can be performed in an automated and parameter-adaptive manner. The resulting uncertainty analysis and probabilistic design studies are shown to be more accurate, efficient, reliable, and convenient.
This report contains the summary of the 'Magnetophoretic Bead Trapping in a High-Flowrate Biological Detection System' LDRD project 74795. The objective of this project is to develop a novel biodetection system for high-throughput sample analysis. The chief application of this system is in detection of very low concentrations of target molecules from a complex liquid solution containing many different constituents--some of which may interfere with identification of the target molecule. The system is also designed to handle air sampling by using an aerosol system (for instance a WESP - Wet Electro-Static Precipitator, or an impact spray system) to get air sample constituents into the liquid volume. The system described herein automatically takes the raw liquid sample, whether air converted or initially liquid matrix, and mixes in magnetic detector beads that capture the targets of interest and then performs the sample cleanup function, allowing increased sensitivity and eliminating most false positives and false negatives at a downstream detector. The surfaces of the beads can be functionalized in a variety of ways in order to maximize the number of targets to be captured and concentrated. Bacteria and viruses are captured using antibodies to surface proteins on bacterial cell walls or viral particle coats. In combination with a cell lysis or PCR (Polymerase Chain Reaction), the beads can be used as a DNA or RNA probe to capture nucleic acid patterns of interest. The sample cleanup capability of this system would allow different raw biological samples, such as blood or saliva to be analyzed for the presence of different infectious agents (e.g. smallpox or SARS). For future studies, we envision functionalizing bead surfaces to bind to chemical weapons agents, radio-isotopes, and explosives. The two main objectives of this project were to explore methods for enhancing the mixing of the capture microspheres in the sample, and to develop a novel high-throughput magnetic microsphere trap. We have developed a novel technique using the magnetic capture microspheres as 'stirrer bars' in a fluid sample to enhance target binding to the microsphere surfaces. We have also made progress in developing a polymer-MEMS electromagnet for trapping magnetic spheres in a high-flowrate fluid format.
This report documents the strategies for verification and validation of the codes LSP and ICARUS used for simulating the operation of the neutron tubes used in all modern nuclear weapons. The codes will be used to assist in the design of next generation neutron generators and help resolve manufacturing issues for current and future production of neutron devices. Customers for the software are identified, tube phenomena are identified and ranked, software quality strategies are given, and the validation plan is set forth.