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At least 829 records · Page 46

Advancing Multiscale Simulation of Plasma-Surface Interfaces

We report the development of an atomistic-informed, surface-state-dependent predictive model for particle exchange in a carbon-tungsten plasma-surface interface. The predictive model uses machine learning (ML) techniques to learn the energy and angular distributions for particle exchange and rate functions for surface state evolution from molecular dynamics simulations of cumulative bombardment of tungsten by energetic carbon ions. Each predictive component is sensitive to the energy and trajectory of incident plasma species and the surface state. The surface state is represented by a set of surface state descriptors, which were derived from the atomistic surface state for each independent carbon bombardment event. These descriptors are representative of the composition and degree of amorphization of the outermost angstrom of surface material and were chosen to optimize predictive performance for particle exchange at the interface. The distributions for particle exchange (reflection/sputtering) are demonstrated to vary with each surface state descriptor, motivating the development of surface-state-dependent particle exchange models for plasma simulations. The performance of various ML methods was compared, including polynomial quantile regression, artificial neural networks, k-nearest neighbors, and random forest algorithms, with polynomial regression performing the best for interpolation and extrapolation of learned relationships. In addition to the particle exchange model, a neutral network was developed and used to identify data sufficiency throughout surface descriptor space, which will enable real-time feedback during future data production to ensure data is produced where it is most needed, and we provide commentary on improvements to the data production workflow for future endeavors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Demonstration of Capability to Simulate Particle Irregular Shape and Poly-Disperse Mixtures Within Lunar Lander Plume-Surface Interaction

Plume-Surface Interaction (PSI) between lander engine plumes and regolith soil creates hazards in obscuration and contamination by particle clouds, high-energy ejecta streams, and landing area cratering damage. The MSFC Fluid Dynamics Branch is developing simulation tools to offer a predictive PSI capability to NASA customers such as the Human Lander System (HLS) and Commercial Lunar Payload Services (CLPS). The Gas-Granular Flow Solver (GGFS) is the main application tool for coupled gas-particle two-phase flow simulations to predict the range of PSI effects from onset of surface erosion to deep crater formation. GGFS features an Eulerian-Eulerian modeling approach, treating both gas and granular material as interacting continuum phases. Modeling the lunar regolith granular material fluidic characteristics poses special challenges due to complex particle shapes and mixture composition. The lunar regolith is poorly sorted with broad particle size distributions and large fines content. It has significant cohesion, due to interlocking jagged particle shapes. Eulerian granular material flow modeling requires closure formulations for the granular material constitutive models (stress, friction, collisional and kinetic energy dissipation, drag, etc.). While closure models for spherical particles are available from particle kinetic theory, closure models for realistic non-spherical particles must be extracted from unit physics Discrete Element Model (DEM) particle interaction simulations and provided in the form of tabular datasets. The effects of particle irregular shape (non-spherical shape factors, angular particle surface roughness, and interlocking features) are simulated by approximating the particle features in the form of grouped elemental spheres to form composite particles in the DEM simulations. The effects of the wide range of regolith mixture particle sizes and the strong effects of the presence of the small particle sizes results in high cohesion and low porosity of the regolith mixture. The range of particle sizes is simulated by binning the particle sizes into an appropriate finite number of particle-size species and solving the problem as a species mixture. Combining these two modeling approaches enables simulations to capture both, the contributions of the irregular particle shape and the particle size distribution. The integration and maturation of the DEM-based constitutive model database generation process and poly-disperse mixture binning approach into the GGFS simulation framework are proceeding under funding by the NASA Game Changing Development program. The status of current capabilities will be presented in comparisons of crater characteristics resulting for spherical and irregular shape particles, and for mono-, bi-, and tri-disperse mixture simulations of Apollo LM plume-surface interaction. The computational results confirm the significance of including the particle shape and mixture effects. Going forward plans for the full implementation of the general poly-disperse regolith modeling capability and maturation towards NASA project application readiness under the GCD program will be presented.

Peter A Liever↗

Demonstration of Capability to Simulate Particle Irregular Shape and Poly-Disperse Mixtures Within Lunar Lander Plume-Surface Interaction

Plume-Surface Interaction (PSI) between lander engine plumes and regolith soil creates hazards in obscuration and contamination by particle clouds, high-energy ejecta streams, and landing area cratering damage. The MSFC Fluid Dynamics Branch is developing simulation tools to offer a predictive PSI capability to NASA customers such as the Human Lander System (HLS) and Commercial Lunar Payload Services (CLPS). The Gas-Granular Flow Solver (GGFS) is the main application tool for coupled gas-particle two-phase flow simulations to predict the range of PSI effects from onset of surface erosion to deep crater formation. GGFS features an Eulerian-Eulerian modeling approach, treating both gas and granular material as interacting continuum phases. Modeling the lunar regolith granular material fluidic characteristics poses special challenges due to complex particle shapes and mixture composition. The lunar regolith is poorly sorted with broad particle size distributions and large fines content. It has significant cohesion, due to interlocking jagged particle shapes. Eulerian granular material flow modeling requires closure formulations for the granular material constitutive models (stress, friction, collisional and kinetic energy dissipation, drag, etc.). While closure models for spherical particles are available from particle kinetic theory, closure models for realistic non-spherical particles must be extracted from unit physics Discrete Element Model (DEM) particle interaction simulations and provided in the form of tabular datasets. The effects of particle irregular shape (non-spherical shape factors, angular particle surface roughness, and interlocking features) are simulated by approximating the particle features in the form of grouped elemental spheres to form composite particles in the DEM simulations. The effects of the wide range of regolith mixture particle sizes and the strong effects of the presence of the small particle sizes results in high cohesion and low porosity of the regolith mixture. The range of particle sizes is simulated by binning the particle sizes into an appropriate finite number of particle-size species and solving the problem as a species mixture. Combining these two modeling approaches enables simulations to capture both, the contributions of the irregular particle shape and the particle size distribution. The integration and maturation of the DEM-based constitutive model database generation process and poly-disperse mixture binning approach into the GGFS simulation framework are proceeding under funding by the NASA Game Changing Development program. The status of current capabilities will be presented in comparisons of crater characteristics resulting for spherical and irregular shape particles, and for mono-, bi-, and tri-disperse mixture simulations of Apollo LM plume-surface interaction. The computational results confirm the significance of including the particle shape and mixture effects. Going forward plans for the full implementation of the general poly-disperse regolith modeling capability and maturation towards NASA project application readiness under the GCD program will be presented.

Peter A. Liever↗

Simulation of the Aerosol Size Distribution Using a Neural Network Surrogate for the Modal Aerosol Module (MAM7)

One objective of atmospheric simulations is to quantify the distribution of aerosols and their properties. Accurate parameterizations of the processes governing aerosol mass, particle number, and particle size distribution are important for predicting the Earth’s net radiative balance and aerosol-cloud interactions. The Modal Aerosol Module (MAM7) is a two-moment aerosol model that simulates mass, number, and size distribution of seven modes comprised of internally mixed aerosol species. The two-moment scheme adds significant computational expense but allows for the prediction of varying particle size distribution relative to the bulk method which predicts only total mass. In this work, we developed a neural network surrogate model for MAM7 (MAMnet) to predict the aerosol number concentration in NASA’s Global Earth Observing System (GEOS) without adding prohibitive computational expense. MAMnet, can be driven by output from a single moment, mass-based, aerosol scheme (Goddard Chemistry Aerosol and Radiation model (GOCART)) or from reanalysis products (Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2)). MAMnet was trained using number concentrations from a 5-year GEOS/MAM7 simulation at 1-degree horizontal resolution and using the total mass calculated across modes as inputs, as well as temperature and air density. The model architecture for MAMnet was based on AlexNet, the 2012 winner of the ImageNet Large Scale Visual Recognition Challenge. While some modifications were necessary to accommodate our problem, important aspects of the network were preserved. MAMnet was able to reproduce zonal dynamics and spatial distributions of the aerosol number concentration however predictability in the upper troposphere was poor.

Katherine H Breen↗

Microtomographic Measurements of Total Air‐Water Interfacial Areas for Soils

Abstract Synchrotron X‐ray microtomography (XMT) was used to measure total air‐water interfacial areas (A aw ) as a function of water saturation (S w ) for several soils that comprise a range of physical and geochemical properties. Measurements were also conducted for glass beads and quartz sands for comparison. Apparent near‐linearA aw ‐S w relationships are observed for the three sands and the three sandy soils. In contrast, the measured interfacial areas for two soils that contain greater proportions of silt and clay are strongly nonlinear functions of water saturation. The greater degree of nonlinearity observed for these two soils is due to their much greater particle‐size distributions (i.e., uniformity coefficients) and their concomitant greater range in pore sizes. Interfacial areas determined with the thermodynamic method were used to benchmark the XMT measurements. XMT‐measured interfacial areas compare well to the thermodynamic‐determined values for the sands and sandy soils. In contrast, the XMT‐measured interfacial areas for the two soils with larger particle‐size distributions are not fully congruent with the thermodynamic‐determined values. Both of these soils have large fractions of pore space comprising nominal pore diameters smaller than the resolution of the XMT imaging. These results suggest that air‐water interfacial area may not always be fully characterized by standard XMT for soils with large particle‐size distributions.

Environmental Sciences & Ecology↗

FY23 Update: Aerosol Sampling for the Canister Deposition Field Demonstration

This report describes the results of preliminary testing of aerosol monitoring equipment that will be used to continuously monitor the aerosol source term for the multi-year Canister Deposition Field Demonstration (CDFD). These data are required inputs for the development and validation of models for the deposition of dust and potentially corrosive salts on the surface of spent nuclear fuel (SNF) dry storage canisters. Surface salt loads correlate with the extent of corrosion damage on a metal surface, and potentially to the likelihood and timing of initiation of stress corrosion cracks. Aerosols will be monitored at the CDFD site using three instruments. A Dekati ® ELPI+ cascade impactor will be used for real-time monitoring of aerosol particle sizes. It will also collect dust in 14 size bins on impactor targets that can be chemically analyzed to determine the soluble salts present as a function of particle size. However, this instrument can only measure dried aerosols, with a diameter of <10 µm. The second instrument is a Topas laser particle size spectrometer, which provides real-time monitoring of aerosol particle sizes up to ~40 µm in size. It monitors both the ambient (potentially deliquesced) aerosol particle size distributions required for the dust deposition models and the distributions of the equivalent dried particles, allowing correlation with the Dekati ® data. However, it does not discriminate between inert dust particles and salt aerosols, and it does not retain samples of the different particle sizes for later analysis. The third instrument that will monitor aerosols at the CDFD site is a Clean Air Status and Trends Network (CASTNET) tower, which uses a multiple canister system to collect weekly samples for analysis to total suspended aerosol particle compositions and atmospheric gas concentrations. This status report describes work in FY23 to develop the capabilities for using these tools. In two training exercises, the cascade impactor and laser particle sizer were deployed in two different testing environments, one indoor and one outdoor. For the cascade impactor, the tests provided opportunities for the operators to familiarize themselves with impactor substrate preparation, and post-test sample removal and analysis. For the laser particle sizer, the tests were used to evaluate different instrument parameters, to determine the most appropriate settings for capturing transient events. Data and samples were collected for weeks to months for each test, and the results are presented here. In addition to the preliminary testing, contracts were developed with WSP Analytical Labs for sample preparation and analysis of the cascade impactor samples. The impactor tower from outdoor test was delivered to WSP and used to train the staff there in disassembly, sample extraction, sample analysis, and tower reassembly with new target substrates. These are tasks that WSP will be performing routinely for the CDFD project. The CASTNET system cannot be purchased or tested until an actual site has been selected for the CDFD test. Work for this FY has been restricted to preparation of contracts for purchasing the CASTNET tower, and for sample analysis, once the tower is in operation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Zodiacal light photography

Polarized and red- and blue-filter photographs of zodiacal light obtained by Apollo 17 are analyzed. Attempts were made to identify the cause of subtle change in the observed light and determine the dust composition of the light. A comparison of red and blue images indicates such changes may be caused by particle size distribution and range, number of particles along any given line of sight, particle surface characteristics including dielectric compared to metallic properties, and variations of the parameters as a function of distance from the sun.

Mercer, R. D.↗

Particle size and velocity measurement by laser anemometry

The use of a forward scattering Laser Anemometer system for the measurement of particle diameters larger than the fringe spacing is investigated. A systematic calibration experiment demonstrates a direct relationship between signal amplitude and particle diameter for transparent particles between 30 microns and 240 microns in diameter. A light scattering analysis confirms these measurements and indicates how the range of particles which can be measured using the peak (mean) signal depends on the optical arrangement and particle properties. On the basis of this work a real time Laser Anemometer signal processor is modified so that the peak of the mean of each signal can be measured. A method of correcting data for the effect of particles which do not go through the center of the measurement volume is derived. Good agreement is found between particle size distributions measured in sprays by using the Laser Anemometer and size distributions measured by collecting the particles on a slide and using an image analysis computer.

Yule, A. J.↗

Particle nonuniformity effects on particle cloud flames in low gravity

Experimental and analytical studies of particle cloud combustion at reduced gravity reveal the substantial roles that particle cloud nonuniformities may play in particle cloud combustion. Macroscopically uniform, quiescent particle cloud systems (at very low gravitational levels and above) sustain processes which can render them nonuniform on both macroscopic and microscopic scales. It is found that a given macroscopically uniform, quiescent particle cloud flame system can display a range of microscopically nonuniform features which lead to a range of combustion features. Microscopically nonuniform particle cloud distributions are difficult experimentally to detect and characterize. A uniformly distributed lycopodium cloud of particle-enriched microscopic nonuniformities in reduced gravity displays a range of burning velocities for any given overall stoichiometry. The range of observed and calculated burning velocities corresponds to the range of particle enriched concentrations within a characteristic microscopic nonuniformity. Sedimentation effects (even in reduced gravity) are also examined.

Berlad, A. L.↗

Parameterization of Cloud Optical Properties for a Mixture of Ice Particles for use in Atmospheric Models

Based on the single-scattering optical properties that are pre-computed using an improve geometric optics method, the bulk mass absorption coefficient, single-scattering albedo, and asymmetry factor of ice particles have been parameterized as a function of the mean effective particle size of a mixture of ice habits. The parameterization has been applied to compute fluxes for sample clouds with various particle size distributions and assumed mixtures of particle habits. Compared to the parameterization for a single habit of hexagonal column, the solar heating of clouds computed with the parameterization for a mixture of habits is smaller due to a smaller cosingle-scattering albedo. Whereas the net downward fluxes at the TOA and surface are larger due to a larger asymmetry factor. The maximum difference in the cloud heating rate is approx. 0.2 C per day, which occurs in clouds with an optical thickness greater than 3 and the solar zenith angle less than 45 degrees. Flux difference is less than 10 W per square meters for the optical thickness ranging from 0.6 to 10 and the entire range of the solar zenith angle. The maximum flux difference is approximately 3%, which occurs around an optical thickness of 1 and at high solar zenith angles.

Chou, Ming-Dah↗

Parameterization of Shortwave Cloud Optical Properties for a Mixture of Ice Particle Habits for use in Atmospheric Models

Based on the single-scattering optical properties pre-computed with an improved geometric optics method, the bulk absorption coefficient, single-scattering albedo, and asymmetry factor of ice particles have been parameterized as a function of the effective particle size of a mixture of ice habits, the ice water amount, and spectral band. The parameterization has been applied to computing fluxes for sample clouds with various particle size distributions and assumed mixtures of particle habits. It is found that flux calculations are not overly sensitive to the assumed particle habits if the definition of the effective particle size is consistent with the particle habits that the parameterization is based. Otherwise, the error in the flux calculations could reach a magnitude unacceptable for climate studies. Different from many previous studies, the parameterization requires only an effective particle size representing all ice habits in a cloud layer, but not the effective size of individual ice habits.

Chou, Ming-Dah↗

Further Characterization of Aerosols Sampled on the International Space Station

Spacecraft cabin air quality is of fundamental importance to crew health, with concerns encompassing both gaseous contaminants and airborne particles. Quantification of spacecraft indoor aerosols will increase our understanding of crew exposure and cabin cleanliness. Aerosols on the International Space Station (ISS) have been sampled and brought back to Earth for analysis to characterize the airborne particulate matter in the cabin. Microscopic analyses have been performed to determine morphology and particle size information, and Energy Dispersive X-ray Spectroscopy (EDS) provides information on the chemical elements present in the particles. With the use of IntelliSEM software for computer-controlled scanning electron microscopy (CCSEM), this data provides particle size distribution information and statistics on particle materials. Many of the particles collected were made up of multiple elements and had uncommon morphologies compared to typical indoor aerosols on Earth. These characteristics are thought to be from unique formation mechanisms in the microgravity environment. Several notable particle types are examined further in this work. Bromine-containing particles and cadmium-containing particles are discussed as they constitute a health hazard to crew members. Humans in indoor living and working spaces are typically the single largest particle emission source, and this was observed in the sampled aerosols in ISS as well.

Sampling↗

Relationship Between the Sub-Micron Fraction (SMF) and Fine-Mode Fraction (FMF) in the Context of AERONET Retrievals

The sub-micron (SM) aerosol optical depth (AOD) is an optical separation based on the fraction of particles below a specified cutoff radius of the particle size distribution (PSD) at a given particle radius. It is fundamentally different from spectrally separated FM (fine-mode) AOD. We present a simple (AOD-normalized) SM fraction versus FM fraction (SMF vs. FMF) linear equation that explains the well-recognized empirical result of SMF generally being greater than the FMF. The AERONET inversion (AERinv) products (combined inputs of spectral AOD and sky radiance) and the spectral deconvolution algorithm (SDA) products (input of AOD spectra) enable, respectively, an empirical SMF vs. FMF comparison at similar (columnar) remote sensing scales across a variety of aerosol types. SMF (AERinv-derived) vs. FMF (SDA-derived) behavior is primarily dependent on the relative truncated portion (ε c ) of the coarse-mode (CM) AOD associated with the cutoff portion of the CM PSD and, to a second order, the cutoff FM PSD and FM AOD (ε f ). The SMF vs. FMF equation largely explains the SMF vs. FMF behavior of the AERinv vs. SDA products as a function of PSD cutoff radius (“inflection point”) across an ensemble of AERONET sites and aerosol types (urban-industrial, biomass burning, dust, maritime and a mixed class of Arctic aerosols). The overarching dynamic was that the linear SMF vs. FMF relation pivots clockwise about the approximate (SMF, FMF) singularity of (1, 1) in a “linearly inverse” fashion (slope and intercept of approximately 1−ε c and ε c ) with increasing cutoff radius. SMF vs. FMF slopes and intercepts derived from AERinv and SDA retrievals confirmed the general domination of ε c over ε f in controlling that dynamic. A more general conclusion is the apparent confirmation that the optical impact of truncating modal (whole) PSD features can be detected by an SMF vs. FMF analysis.

Norman T. O'Neill↗

Spectral Power-law Formation by Sequential Particle Acceleration in Multiple Flare Magnetic Islands

We present a first-principles model of pitch-angle and energy distribution function evolution as particles are sequentially accelerated by multiple flare magnetic islands. Data from magnetohydrodynamic (MHD) simulations of an eruptive flare/coronal mass ejection provide ambient conditions for the evolving particle distributions. Magnetic islands, which are created by sporadic reconnection at the self-consistently formed flare current sheet, contract and accelerate the particles. The particle distributions are evolved using rules derived in our previous work. In this investigation, we assume that a prescribed fraction of particles sequentially "hops" to another accelerator and receives an additional boost in energy and anisotropy. This sequential process generates particle number spectra that obey an approximate power law at mid-range energies and presents low- and high-energy breaks. We analyze these spectral regions as functions of the model parameters. We also present a fully analytic method for forming and interpreting such spectra, independent of the sequential acceleration model. The method requires only a few constrained physical parameters, such as the percentage of particles transferred between accelerators, the energy gain in each accelerator, and the number of accelerators visited. Our investigation seeks to bridge the gap between MHD and kinetic regimes by combining global simulations and analytic kinetic theory. The model reproduces and explains key characteristics of observed flare hard X-ray spectra as well as the underlying properties of the accelerated particles. Our analytic model provides tools to interpret high-energy observations for missions and telescopes, such as RHESSI, FOXSI, NuSTAR, Solar Orbiter, EOVSA, and future high-energy missions.

magnetic reconnection↗

Influence of gradation on shear behavior and pore water response of sand

Here, this paper examines the influence of particle size distribution (PSD) on the shearing behavior of sand using axisymmetric triaxial compression (ATC) testing in conjunction with 3D imaging using synchrotron micro-computed tomography (SMT). Angular sand was sieved to obtain a narrow gradation (uniform) and a wide gradation (non-uniform) with uniformity coefficients (C u ) of 1.2 and 3.0, respectively. Experiments were conducted under drained conditions and a constant effective cell pressure (σ$^{'}_3$) of 50 kPa at low and high back pressures (BP). Results of paired ATC-SMT were analyzed in terms of global constitutive behavior, strain localization, and localized flow characteristics. A new particle tracking algorithm is developed to expose strain localization. Relative particle translation gradient (RPTG) results revealed that gradation affects how early the shear band develops and a tendency for narrow gradation to exhibit varying degrees of diffused shear band at high axial strain (ε 1 ) even though a clear single shear band was observed at the peak strength. Geometric tortuosity (τ) is used as a quantitative parameter to assess flow changes and the efficiency of the flow path. Representative elementary volumes (REVs) inside and outside the shear band were analyzed and the results showed a variation in flow path characteristics where wide gradation specimens had preferential flow paths.

Computed tomography↗

238 PuO 2 In Vitro Lung Dissolution Rate and Particle Size Determination for Material Involved in the June 8, 2020 Incident at the Los Alamos National Laboratory PF-4 Facility

As part of the LANL response to the June 8, 2020 238 PuO 2 inhalation exposure incident in PF-4, the Nuclear and Radiochemistry Group (C-NR) was asked to assist in determining the lung dissolution rate and particle size distribution of the airborne material. These material characteristics, along with urine and fecal bioassay data, are used by the Radiation Protection Services (RP-SVS) internal dosimetrists to refine dose estimates for exposed workers. Similar to previous studies, an in vitro lung dissolution rate study was performed to assess how fast 238 Pu is cleared from the lungs. Given that PuO 2 is a relatively insoluble material, it dissolves very slowly and requires in vitro studies of 100 or more days to estimate dissolution rates. This report details the results of a 100 day in vitro dissolution rate study and the particle size characteristics of 238 PuO 2 collected on an air filters during the incident. Results show that the 238 PuO 2 involved in this incident has behavior comparable to PuO 2 from previous in vitro studies, with approximately 1% of material dissolving quickly, and 99% of the material dissolving very slowly, with a half-time of approximately 120 years. This is somewhat slower than what was determined in a previous study of LANL 238 PuO 2 , which had an experimental dissolution half-time of 3 years, but significantly faster than 3000 years measured for 239 PuO 2 . Particle size distribution measurements indicate that particle sizes range from 0.10 µm – 6 µm, with most < 2 µm, which is reasonable based on our understanding of the process history of the 238 PuO 2 . Particle size, specific surface area, calcining temperature, specific activity, and age all are known factors that can impact the dissolution rate of refractory materials, however, there are too few studies to quantify the exact influence of these parameters on a measured dissolution rate. The results of this study add to that knowledge base, and provide new insights into the dissolution rates for this LANL process-specific 238 PuO 2 material.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗

Pulsed power to control growth of silicon nanoparticles in low temperature flowing plasmas

Low-temperature plasmas have seen increasing use for synthesizing high-quality, mono-disperse nanoparticles (NPs). Recent work has highlighted that an important process in NP growth in plasmas is particle trapping—small, negatively charged nanoparticles become trapped by the positive electrostatic potential in the plasma, even if only momentarily charged. In this article, results are discussed from a computational investigation into how pulsing the power applied to an inductively coupled plasma (ICP) reactor may be used for controlling the size of NPs synthesized in the plasma. The model system is an ICP at 1 Torr to grow silicon NPs from an Ar/SiH 4 gas mixture. This system was simulated using a two-dimensional plasma hydrodynamics model coupled to a three-dimensional kinetic NP growth and trajectory tracking model. The effects of pulse frequency and pulse duty cycle are discussed. We identified separate regimes of pulsing where particles become trapped for one pulsed cycle, a few cycles, and many cycles—each having noticeable effects on particle size distributions. For the same average power, pulsing can produce a stronger trapping potential for particles when compared to continuous wave power, potentially increasing particle mono-dispersity. Pulsing may also offer a larger degree of control over particle size for the same average power. Experimental confirmation of predicted trends is discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗