Semi-Analytic Functions to Calculate the Deposition Coefficients for Ice Crystal Vapor Growth in Bin and Bulk Microphysical Models.
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More recently, reactor core simulators for core designs associated with commercial nuclear power plants that utilize what is believed to be higher fidelity models have been developed. Features such as neutronics models that utilize transport equation solvers with fine spatial meshes and many energy-groups, thermal-hydraulic models that utilize sub-channel solvers with fine spatial mesh and capable of treating a wide range of fluid conditions, and fuel-coolant chemistry interaction models capable of treating CRUD deposition are to be found in these higher fidelity core simulators. These reactor core simulators require access to higher performance computers, characterized by many processors, cores and large memory. So associated with utilization of these simulators is access to high performance computers and ability to accommodate in one’s workflow longer execution times. By contrast, currently used core simulators by the nuclear industry can execute on engineering workstations and have execution times of seconds to minutes. The desirability for having short execution times is not only desired for support of time critical tasks but supports the mental process of decision making by engineers. The goal of the work reported upon here has the objective of retaining the fidelity of higher fidelity models while retaining the ability to utilize engineering workstations. Beyond the core simulator goal, additional goals of this work include incorporating the just described core simulator capability into a Nuclear Steam Supply System (NSSS) simulator, and to incorporate the resulting capability into an environment supportive of design and operational decision making associated with nuclear power stations. The model selected for the core neutronics model is the NESTLE code, for the core thermal-hydraulic model is the CTF code utilizing coarse mesh, and for the NSSS model is the RELAP5-3D code. WSC’s proprietary 3KEYMASTERTM platform is being used to provide software coupling, user interface, visualization, and reporting. The NESTLE core neutronics simulator was first integrated with the CTF core thermal-hydraulic simulator using CTF developed communication commands which are also used for CTF to communicate with RELAP5-3D under WSC’s proprietary 3KEYMASTERTM platform. To assure NESTLE prediction consistency with higher fidelity core neutronic simulators, buffer codes have been created to automatically generate from output files written by the VERA core simulator the NESTLE nodal neutronic parameter’ library, geometry, and pin-power reconstruction input files, thereby avoiding a number of challenges associated with utilizing lattice physics codes and providing consistency with VERA predictions. To treat absorber rod effects a multi-set library is utilized, where a set refers to a specific absorber rod fully inserted pattern. A coarse spatial mesh CTF model was developed with features added that support using CTF as envisioned in the engineering quality simulator. A hybrid meshing approach was implemented to allow for automated construction of models with mixed levels of refinement. Specifically, a core model could resolve some assemblies at a nodal level (4 subchannels per assembly) and others at a pin-resolution (one subchannel per coolant subchannel in the assembly). The intention is that this will allow for better resolution of limiting conditions such as DNBR and PCT, which are based on local rod and subchannel conditions. Further development was done of features that enhance the capabilities for the envisioned engineering quality simulator that has been developed, but now for RELAP-3D. The RELAP5-3D code development includes ability to model more than 999 components and the addition of the cross-channels turbulence mixing model and the void drift model that are implemented in CTF, aiming to achieve closer prediction agreement of the two codes for transient simulations, specifically, more accurate matches of the overall mass, momentum, and energy exchanges of both the liquid and gas phases between the neighboring core assemblies. Graphics were also developed for the Instructor Station for this project under WSC’s proprietary 3KEYMASTERTM platform to facilitate design and operational decision making.
We have developed a general theoretical model for the interaction of ionizing radiation with chromatin. Chromatin is modeled as a 30-nm-diameter solenoidal fiber comprised of 20 turns of nucleosomes, 6 nucleosomes per turn. Charged-particle tracks are modeled by partitioning the energy deposition between primary track core, resulting from glancing collisions with 100 eV or less per event, and delta rays due to knock-on collisions involving energy transfers >100 eV. A Monte Carlo simulation incorporates damages due to the following molecular mechanisms: (1) ionization of water molecules leading to the formation of OH, H, eaq, etc.; (2) OH attack on sugar molecules leading to strand breaks: (3) OH attack on bases; (4) direct ionization of the sugar molecules leading to strand breaks; (5) direct ionization of the bases. Our calculations predict significant clustering of damage both locally, over regions up to 40 bp and over regions extending to several kilobase pairs. A characteristic feature of the regional damage predicted by our model is the production of short fragments of DNA associated with multiple nearby strand breaks. The shapes of the spectra of DNA fragment lengths depend on the symmetries or approximate symmetries of the chromatin structure. Such fragments have subsequently been detected experimentally and are reported in an accompanying paper (B. Rydberg, Radiat, Res. 145, 200-209, 1996) after exposure to both high- and low-LET radiation. The overall measured yields agree well quantitatively with the theoretical predictions. Our theoretical results predict the existence of a strong peak at about 85 bp, which represents the revolution period about the nucleosome. Other peaks at multiples of about 1,000 bp correspond to the periodicity of the particular solenoid model of chromatin used in these calculations. Theoretical results in combination with experimental data on fragmentation spectra may help determine the consensus or average structure of the chromatin fibers in mammalian DNA.
To adequately constrain the frequency of energy deposition in active region cores in the solar corona, systematic comparisons between detailed models and observational data are needed. In this paper, we describe a pipeline for forward modeling active region emission using magnetic field extrapolations and field-aligned hydrodynamic models. We use this pipeline to predict time-dependent emission from active region NOAA 1158 for low-, intermediate-, and high-frequency nanoflares. In each pixel of our predicted multi-wavelength, time-dependent images, we compute two commonly used diagnostics: the emission measure slope and the time lag. We find that signatures of the heating frequency persist in both of these diagnostics. In particular, our results show that the distribution of emission measure slopes narrows and the mean decreases with decreasing heating frequency and that the range of emission measure slopes is consistent with past observational and modeling work. Furthermore, we find that the time lag becomes increasingly spatially coherent with decreasing heating frequency while the distribution of time lags across the whole active region becomes more broad with increasing heating frequency. In a follow-up paper, we train a random forest classifier on these predicted diagnostics and use this model to classify real observations of NOAA 1158 in terms of the underlying heating frequency.
This study develops more computationally efficient versions of the TwO-Moment Aerosol Sectional (TOMAS) microphysics algorithms, collectively called Fast TOMAS. Several methods for speeding up the algorithm were attempted, but only reducing the number of size sections was adopted. Fast TOMAS models, coupled to the GISS GCM II-prime, require a new coagulation algorithm with less restrictive size resolution assumptions but only minor changes in other processes. Fast TOMAS models have been evaluated in a box model against analytical solutions of coagulation and condensation and in a 3-D model against the original TOMAS (TOMAS-30) model. Condensation and coagulation in the Fast TOMAS models agree well with the analytical solution but show slightly more bias than the TOMAS-30 box model. In the 3-D model, errors resulting from decreased size resolution in each process (i.e., emissions, cloud processing wet deposition, microphysics) are quantified in a series of model sensitivity simulations. Errors resulting from lower size resolution in condensation and coagulation, defined as the microphysics error, affect number and mass concentrations by only a few percent. The microphysics error in CN70CN100 (number concentrations of particles larger than 70100 nm diameter), proxies for cloud condensation nuclei, range from 5 to 5 in most regions. The largest errors are associated with decreasing the size resolution in the cloud processing wet deposition calculations, defined as cloud-processing error, and range from 20 to 15 in most regions for CN70CN100 concentrations. Overall, the Fast TOMAS models increase the computational speed by 2 to 3 times with only small numerical errors stemming from condensation and coagulation calculations when compared to TOMAS-30. The faster versions of the TOMAS model allow for the longer, multi-year simulations required to assess aerosol effects on cloud lifetime and precipitation.
The rare earth elements (REE) are important metals used increasingly in advanced technologies. Within the crust, the elements Ce and Y are commonly more abundant compared to other lanthanides and comprise important end-member constituents of REE-bearing minerals. Specifically, Ce is part of the light (L) REE which have larger ionic radii than the heavy (H) REE, which are grouped together with Y. These differences in ionic radius can lead to important physico-chemical trends within the lanthanide group. Despite a recent increase in experimental and thermodynamic data for the REE at high temperature and pressure, there is still a significant lack of these data at supercritical conditions. In this study we conducted batch-type experiments to measure the solubility of REE phosphates (CePO 4 and YPO 4 ) at varying starting pH (1.5–10), and salinity (0.01–1.4 mol/kg NaCl) at 350 and P sat , and from 400 to 450 °C at 700 bar. Results show that the solubility of Ce (33–0.14 ppb) is generally higher than Y (13–0.13 ppb) and that Ce complexes more strongly with both chloride and hydroxyl ligands compared to Y. The solubilities of both REE phosphates are highly pH-dependent and, to a lesser extent, depend on salinity at the studied conditions. The solubility data from this study were implemented into the GEMSFITS program to optimize the thermodynamic properties of Ce and Y hydroxyl and chloride species. The updated standard partial molal Gibbs energies of formation (Δ f G 0 T,P ) are used within the experimental temperature and pressure range to accurately predict the CePO 4 and YPO 4 solubility and Ce and Y speciation behavior. Based on the updated thermodynamic properties we also provide formation constants (log β n Cl,OH ) for Ce and Y hydroxyl and chloride species. Updated thermodynamic properties are applied to model REE-apatite dissolution and REE mobility based on the Pea Ridge iron oxide apatite deposit in Missouri, USA. The apatite dissolution model replicates natural observations including the replacement of monazite and xenotime after apatite and is an example of the utility of the new thermodynamic constants applied to supercritical crustal fluids. Furthermore, the findings of this study advance the predictive capabilities of geochemical models, our understanding of the behavior of individual REE, and permit modeling the overarching fractionation trends between LREE and HREE in supercritical crustal fluids.
Recent analyses of SeaWiFS data have shown that global ocean chlorophyll has increased more than 4% since 1998. The North Pacific ocean basin has increased nearly 19%. These trend analyses follow earlier results showing decadal declines in global ocean chlorophyll and primary production. To understand the causes of these changes and trends we have applied the newly developed NASA Ocean Biogeochemical Assimilation Model (OBAM), which is driven in mechanistic fashion by surface winds, sea surface temperature, atmospheric iron deposition, sea ice, and surface irradiance. The model utilizes chlorophyll from SeaWiFS in a daily assimilation. The model has in place many of the climatic variables that can be expected to produce the changes observed in SeaWiFS data. This enables us to diagnose the model performance, the assimilation performance, and possible causes for the increase in chlorophyll. A full discussion of the changes and trends, possible causes, modeling approaches, and data assimilation will be the focus of the seminar.
The deposition of NOx and HCl in the stratosphere from the space shuttle solid rocket motors (SRM) and exhaust plume is discussed. A detailed comparison between stratospheric deposition rates using the baseline SRM propellant and an alternate propellant, which replaces ammonium perchlorate by ammonium nitrate, shows the total NOx deposition rate to be approximately the same for each propellant. For both propellants the ratio of the deposition rates of NOx to total chlorine-containing species is negligibly small. Rocket exhaust ground cloud transport processes in the troposphere are also examined. A brief critique of the multilayer diffusion models (presently used for predicting pollutant deposition in the troposphere) is presented, and some detailed cloud rise calculations are compared with data for Titan 3C launches. The results show that, when launch time meteorological data are used as input, the model can reasonably predict measured cloud stabilization heights.
The lithium tokamak experiment (LTX) is a spherical torus designed to investigate a low-recycling wall regime for magnetically confined plasmas. Traditional measurements of recycling using Dα emission are not feasible in LTX due to reflections off the plasma-facing-components: stainless-steel shell, liquid lithium layer, and molybdenum limiters. Since lithium has low VUV reflectivity, LTX will use Lyman-α emission to measure particle recycling. LTX will use 10- and 20-channel AXUV diode arrays with Lyman-α filters to view recycling off the inboard and outboard shells. A single detector views recycling off a limiter. Measurements will be used with neutral modeling to calculate recycling and neutral deposition. To investigate the performance of an AXUV diode with directly-deposited filter, measurements were obtained with this detector and a visible detector viewing a calibration plasma then compared with emission calculated using a collisional-radiative model.
We address compositional evolution in planetary ring systems subsequent to meteoroid bombardment. The huge surface area to mass ratio of planetary rings ensures the importance of this process, given currently expected values of meteoroid flux. We developed a model which includes both direct deposition of extrinsic meteoritic 'pollutants', and ballistic transport of the increasingly polluted ring material as impact ejecta. Certain aspects of the observed regional variations in ring color and albedo can be understood in terms of such a process. We conclude that the regional scale color and albedo differences between the C ring and B ring can be understood if all ring material began with the same composition (primarily water ice, based on other data, but colored by tiny amounts of non-icy, reddish absorber) and then evolved entirely by addition and mixing of extrinsic, neutrally colored, highly absorbing material. This conclusion is readily extended to the Cassini Division and its surroundings as well. Typical silicates are unable to satisfy the ring color, spectroscopic, and microwave absorption constraints either as intrinsic or extrinsic non-icy constituents. However, 'Titan Tholin' provides a satisfactory match for the inferred refractive indices of the 'pre-pollution' nonicy ring material. The extrinsic bombarding material is compatible with the properties of Halley or Chiron, but not with the properties of other 'red' primitive objects such as Pholus. We further demonstrate that the detailed radial profile of color across the abrupt B ring - C ring boundary is quite compatible with such a 'pollution transport' process, and that the shape of the profile can constrain key parameters in the model. We use the model to estimate the 'exposure age' of Saturn's rings to extrinsic meteoroid flux. We obtain a geologically young 'age' which is compatible with timescales estimated independently based on the evolution of ring structure due to ballistic transport, and also with other 'short timescales' estimated on the grounds of gravitational torques.
The objective of this project is to develop a novel numerical approach based on the extended finite element method (XFEM) for modeling moving boundaries of material deposited in additive manufacturing (AM) process with improved accuracy and reduced computational cost. One of the major challenges in simulating AM processes is that the boundaries of the computational domain need to change as material is deposited. Previous approaches have achieved this by activating new finite elements, but this requires a high level of mesh refinement to capture small movement of the boundary. XFEM allows the solution boundary to move independently of the mesh, permitting smooth representation of the evolution of the boundary as material is deposited. As a result, this new method will significantly improve the simulation accuracy while reducing the computational cost compared with existing approaches. Furthermore, this project will bring significant improvements for the design and AM process optimization in an iterative fashion among numerical simuation, parameter optimization, and experimental validation. Specifically, this project will support the protonic ceramic electrochemical cells (PCEC) stack development at INL by providing insights into the density, residual stress, thermal and mechanical properties of the PCEC manifold and interconnect, which is critical in enhancing the system lifetime and reducing the overall cost. Upon the success of proposed development and validation of the proposed approach, simulation will be applied to determine an optimal set of AM process parameters for the PCEC manifold production. This project will consolidate Idaho National Laboratory (INL)’s simulation capabilities provided by the MOOSE framework and the Valhalla AM simulation application, with encouraging expansion to emerging PCEC applications and AM technologies at INL and beyond.
When the local heat flux exceeds specified flux limit, tungsten PFC surfaces can be damaged, which is not acceptable for a reliable reactor operations. The divertor PFCs are typically designed for a specific heat flux limit usually assuming an average steady-state heat flux which is typically 5–10 MW/m 2 . However, in addition to steady-state heat flux, fusion reactor divertor PFCs could experience transient heat fluxes such as ELMs and/or other magnetic reconnection events which can deposit large transient heat fluxes onto the divertor PFCs. The transient divertor heat flux could be significantly larger than the steady-state heat flux which could damage the solid PFC surfaces. The divertor heat flux can be subjected to additional complications such as the uncertainties in the the divertor strike point heat flux projection. Moreover, there are additional experimental observations of non-axisymmetric power flux which can occur under non-axisymmetric magnetic perturbations. The liquid lithium (LL) PFCs is more resilient against such transient heat fluxes as they could evaporate LL as needed and the lost LL can be then replenished afterward. In this paper, we analyze a case for a transient divertor heat pulse of 1 MJ in 10 ms for a ITER-size reactor. This is a small perturbation (~ 0.1%) to the expected plasma stored energy compared to the previously analyzed case of 20 MJ heat pulse. Even with this relatively modest heat pulse, the LL surface undergoes ~ 100 °C temperature rise. However, the resulting LL surface heating without rapid cooldown mechanism could lead to excessive LL evaporation continuing well after the transient heat flux resulting in a significant Li injection of ~ 0.6 mol in about a 200 ms period. This amount of Li injection could cause plasma dilution and performance degradation. On the other hand, an active Li injection capability if optimized could prevent the LL surface temperature rise and thus reducing subsequent Li evaporation into the plasma by a factor of 7 compared to the passive LL PFC case. A crucial tool of active Li injection is a rapid response pellet injector which could inject light impurity pellets before the excessive heat flux could reach the divertor plate causing serious damage. A simple pellet ablation model suggests a favorable pellet deposition profile for smaller ~ 0.1 mm radius pellet with ~ 10–20 m/s velocity. Moreover, if it is possible to inject from the private flux region, the pellet injection efficiency into the high heat flux strike point region can be as high as 80% compared to ~ 50% for the injection from outer radius region. The pellet deposition efficiency can be further improved by designing a shell-pellet which can burst when a certain ablation fraction is reached. Finally, a possible implementation technique using an inductive pellet injector with a rapid time response of a few msec is proposed here which can be tested in NSTX-U.
The flash of thermal radiation produced as part of the impact-crater forming process can be used to determine the energy of the impact if the luminous efficiency is known. From this energy the mass and, ultimately, the mass flux of similar impactors can be deduced. The luminous efficiency, Eta is a unique function of velocity with an extremely large variation in the laboratory range of under 8 km/s but a necessarily small variation with velocity in the meteoric range of 20 to 70 km/s. Impacts into granular or powdery regolith, such as that on the moon, differ from impacts into solid materials in that the energy is deposited via a serial impact process which affects the rate of deposition of internal (thermal) energy. An exponential model of the process is developed which differs from the usual polynomial models of crater formation. The model is valid for the early time portion of the process and focuses on the deposition of internal energy into the regolith. The model is successfully compared with experimental luminous efficiency data from laboratory impacts and from astronomical determinations and scaling factors are estimated. Further work is proposed to clarify the effects of mass and density upon the luminous efficiency scaling factors
The flash of thermal radiation produced as part of the impact-crater forming process can be used to determine the energy of the impact if the luminous efficiency is known. From this energy the mass and, ultimately, the mass flux of similar impactors can be deduced. The luminous efficiency, eta, is a unique function of velocity with an extremely large variation in the laboratory range of under 6 km/s but a necessarily small variation with velocity in the meteoric range of 20 to 70 km/s. Impacts into granular or powdery regolith, such as that on the moon, differ from impacts into solid materials in that the energy is deposited via a serial impact process which affects the rate of deposition of internal (thermal) energy. An exponential model of the process is developed which differs from the usual polynomial models of crater formation. The model is valid for the early time portion of the process and focuses on the deposition of internal energy into the regolith. The model is successfully compared with experimental luminous efficiency data from both laboratory impacts and from lunar impact observations. Further work is proposed to clarify the effects of mass and density upon the luminous efficiency scaling factors. Keywords hypervelocity impact impact flash luminous efficiency lunar impact meteoroid 1
The simulation of radiation effects in materials broadly falls into two categories. At short time and length scales lies the modeling of primary radiation damage, such as point defect creation, energy deposition, and ballistic mixing. This is followed by the modeling at longer time scales of thermally activated microstructure evolution and defect reactions, such as recombination, clustering, and coarsening. The binary collision Monte Carlo method is an established, numerically efficient method for the computation of primary radiation damage. Conversely, the phase field method is a state of the art method for microstructure evolution on longer time and length scales. Here we present a concurrent coupling of these two methods, overcoming the difference between the discrete object Monte Carlo paradigm for primary radiation damage and the continuum field variable approach for microstructure evolution. The coupling is bidirectional, in which the microstructure evolution in the MOOSE finite element frame- work provides the spatial scattering data set for the charged particle trans- port and receives point defect, mass transport, and heat source terms from the simulated collision cascades that contribute to the field variable evolution. The concurrent coupling scheme is implemented in the code Magpie and demonstrated by investigating patterning for a model irradiated immiscible binary alloy. The results from the coupled binary collision Monte Carlo/phase field simulations reproduce the results of analytical models for phase separation, phase mixing, and patterning, supporting the approach and indicating its utility for modeling real materials systems.
The Mars Science Laboratory Rover Curiosity is commencing a two-year investigation of Gale crater and Mt. Sharp, the craters prominent central mound. Gale is a 155 km, late Noachian/early Hesperian impact crater located near the dichotomy boundary separating the southern highlands from the northern plains. The central mound is composed of layered sedimentary rock, with upper and lower mound units separated by a prominent erosional unconformity. The lower mound is of particular interest, as it contains secondary minerals indicative of a striking shift from water-rich to water-poor conditions on early Mars. A key unknown in the history of Gale is the relationship between the sedimentary units in the mound and sedimentary sequences in the surrounding region. We employed orbital remote sensing data to determine if areas within a 1,000 km radius of Gale match the characteristics of sedimentary units in Mt. Sharp. Regions of interest were defined based on: the mound s inferred age, altitude range, and THEMIS nighttime brightness (a proxy for thermal inertia). Using orbital CTX, MOC and HiRISE images we examined all areas within our regions of interest for analogous geomorphic units in the same altitude ranges as the corresponding units in Mt. Sharp. The results are consistent with the hypothesis that sedimentary units in both the upper and lower sections of the Gale mound are related to nearby regional units located along the dichotomy boundary. This relationship supports an inferred geologic history that includes several episodes of widespread sedimentary deposition and erosion in the martian mid-latitudes. In this model Mt. Sharp is the remnant of regional sedimentary deposits that partially or completely filled the crater, became lithified, and were subsequently deeply eroded. Key questions that will be addressed by Curiosity include the compositions of the sediments, the modes of deposition, the mechanisms of lithification, and the nature of the erosion.
Two NASA microwave radiometers, the satellite-borne GPM (Global Precipitation Measurement) Microwave Imager (GMI) and the aircraft-borne CoSMIR (the Conical Scanning Millimeter-wave Imaging Radiometer), measure vertically- and horizontally-polarized microwaves emitted by cloud particles and the Earth below, providing unique information on ice crystal properties in clouds. Their data reveal that non-spherical ice crystals are common and they fall in a preferred horizontally aligned orientation in convective and optically thick clouds especially near cloud top. A bin (particle-size-resolving) microphysical model with an ice crystal shape representation is developed to simulate the evolution of ice crystal properties (i.e., size, shape and orientation), where the radiation effect on microphysics (REM) is taken into account. Since REM represents the effect of all (e.g., both infrared and solar) radiation on ice crystal temperature, it relies upon the ice crystal proprieties that determine how an ice crystal receives radiation. Definitely, REM is different from the radiative effects that cause sensitivity at the microwave frequencies in the GPM and CoSMIR observations. Model results show that horizontally-oriented ice crystals grow faster than vertically-oriented (or spherical) ones due to REM. When both horizontally- and vertically-oriented ice crystals coexist in an air parcel, the model results show that the former grow by vapor deposition whereas the latter shrink by sublimation and disappear eventually. These modeling results are supported by the GMI data and the CoSMIR observations from MC3E (Midlatitude Continental Convective Clouds Experiment) and OLYMPEX (Olympic Mountains Experiment) on the prevalence of horizontally-oriented ice crystals. Moreover, the REM-induced precipitation explains the CloudSat observations of rare thin clouds in the tropical mid-troposphere as well as the common diamond dust in the high latitudes.
Thin-film deposition from chemically reactive multi-component plasmas is complex, and the lack of electron collision cross-sections for even the most common metalorganic precursors and their fragments complicates their modeling based on fundamental plasma physics. This study focuses on understanding the plasma physics and chemistry in argon (Ar) plasmas containing lithium bis (trimethylsilyl) amide used to deposit Li x Si y thin films. These films are emerging as potential solid electrolytes for lithium-ion batteries, and the Li-to-Si ratio is a crucial parameter to enhance their ionic conductivity. We deposited Li x Si y films in an axial flow-through plasma reactor and studied the factors that determine the variation of the Li-to-Si ratio in films deposited at various points on a substrate spanning the entire reactor axis. While the Li-to-Si ratio is 1:2 in the precursor, the Li-to-Si ratio is as high as 3:1 in films deposited near the plasma entrance and decreases to 1:1 for films deposited downstream. Optical emission from the plasma is dominated by Li emission near the entrance, but Li emission disappears downstream, which we attribute to the complete consumption of the precursor. We hypothesized that the axially decreasing precursor concentration affects the electron energy distribution function in a way that causes different dissociation efficiencies for the production of Li and Si. We used Li line intensities to estimate the local precursor concentration and Ar line ratios to estimate the local reduced electric field to test this hypothesis. This analysis suggests that the mean electron energy increases along the reactor axis with decreasing precursor concentration. As a result, the decreasing Li-to-Si ratio with axially decreasing precursor concentration may be explained by Li release from the precursor having lower threshold energy than Si release.