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At least 847 records · Page 47

Potentials of mean force fail to describe chemical bond-breaking in solution

Many liquid phase studies assume that the potential energy surfaces of reacting molecules are the same as in the gas phase, neglecting complex solvent dynamics that can completely alter the nature of chemical reactivity. Even studies that include solvent effects typically only consider them in an average, equilibrium way as part of a potential of mean force (PMF). In this work, we use mixed quantum/classical simulations to compare how equilibrium and non-equilibrium solvent motions affect the photodissociation of a simple diatomic molecule, NaK + , in liquid tetrahydrofuran. A PMF analysis shows that as the excited-state molecule dissociates with the solvent at equilibrium, the bonding electron remains associated with K + at short bond distances but eventually localizes on Na + at the end of dissociation. When we examine non-equilibrium dynamical photodissociation trajectories, however, we find that they fall into three distinct categories: about a quarter of them have the bonding electron mainly associated with Na + , another quarter stay mainly associated with K + , and about half have the bonding electron shared roughly equally between the two ions. The results show that equilibrium PMFs cannot accurately describe the dynamics of bond-breaking chemical reactions in solution because there is insufficient time for the solvent to reach equilibrium on the time scale over which bond dissociation occurs. Furthermore, our analysis shows that the solvent coupling between the electronic energy surfaces is similar at and away from equilibrium, suggesting that other factors, such as solute velocity-driven solvent memory effects, play a more important role in explaining the failure of the equilibrium PMF to predict the non-equilibrium dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Stochastic Transport Theory for Investigating the Three-Dimensional Canopy Structure from Space Measurements

Radiation reflected from vegetation canopies exhibits high spatial variation. Satellite-borne sensors measure the mean intensities emanating from heterogeneous vegetated pixels. The theory of radiative transfer in stochastic media provides the most logical linkage between satellite observations and the three-dimensional canopy structure through a closed system of simple equations which contains the mean intensity and higher statistical moments directly as its unknowns. Although this theory has been a highly active research field in recent years, its potential for satellite remote sensing of vegetated surfaces has not been fully realized because of the lack of models of a canopy pair-correlation function that the stochastic radiative transfer equations require. The pair correlation function is defined as the probability of finding simultaneously phytoelements at two points. This paper presents analytical and Monte Carlo generated pair correlation functions. Theoretical and numerical analyses show that the spatial correlation between phytoelements is primarily responsible for the effects of the three-dimensional canopy structure on canopy reflective and absorptive properties. The pair correlation function, therefore, is the most natural and physically meaningful measure of the canopy structure over a wide range of scales. The stochastic radiative transfer equations naturally admit this measure and thus provide a powerful means to investigate the three-dimensional canopy structure from space. Canopy reflectances predicted by the stochastic equations are assessed by comparisons with the PARABOLA measurements from coniferous and broadleaf forest stands in the BOREAS Southern Study Areas. The pair correlation functions are derived from data on tree structural parameters collected during field campaigns conducted at these sites. The simulated canopy reflectances compare well with the PARABOLA data.

Huang, Dong↗

Advances in constraining intrinsic alignment models with hydrodynamic simulations

We use galaxies from the illustristng, massiveblack-ii, and illustris-1 hydrodynamic simulations to investigate the behaviour of large scale galaxy intrinsic alignments. Our analysis spans four redshift slices over the approximate range of contemporary lensing surveys z = 0–1. We construct comparable weighted samples from the three simulations, which we then analyse using an alignment model that includes both linear and quadratic alignment contributions. Our data vector includes galaxy–galaxy, galaxy–shape, and shape–shape projected correlations, with the joint covariance matrix estimated analytically. In all of the simulations, we report non-zero IAs at the level of several σ. For a fixed lower mass threshold, we find a relatively strong redshift dependence in all three simulations, with the linear IA amplitude increasing by a factor of ~2 between redshifts z = 0 and z = 1. We report no significant evidence for non-zero values of the tidal torquing amplitude, A 2 , in TNG, above statistical uncertainties, although MBII favours a moderately negative A 2 ~ –2. Examining the properties of the TATT model as a function of colour, luminosity and galaxy type (satellite or central), our findings are consistent with the most recent measurements on real data. We also outline a novel method for constraining the TATT model parameters directly from the pixelized tidal field, alongside a proof-of-concept exercise using TNG. This technique is shown to be promising, although comparison with previous results obtained via other methods is non-trivial.

79 ASTRONOMY AND ASTROPHYSICS↗

The good, the bad, and the ugly: Data-driven load profile discord identification in a large building portfolio

Reducing the overall energy consumption and associated greenhouse gas emissions in the building sector is essential for meeting our future sustainability goals. Recently, smart energy metering facilities have been deployed to enable monitoring of energy consumption data with hourly or subhourly temporal resolution. This unprecedented data collection has created various opportunities for advanced data analytics involving load profiles (e.g., building energy benchmarking programs, building-to-grid integration, and calibration of urban-scale energy models). These applications often need preprocessing steps to detect daily load profile discords, such as: 1) outliers due to system malfunctions (the bad) and 2) irregular energy consumption patterns, such as those resulting from holidays (the ugly) compared to normal consumption patterns (the good). However, current preprocessing methods predominantly focus on filtering using statistical threshold values, which fail to capture the contextual discords of daily profiles. In addition, discord detection algorithms in building research are often aimed at finding individual building-level discords, which are not suitable at a large scale. Thus, here, we develop a method for automated load profile discord identification (ALDI) in a large portfolio of buildings (more than 100 buildings). Specifically, ALDI 1) uses the matrix profile (MP) method to quantify the similarities of daily subsequences in time series meter data, 2) compares daily MP values with typical-day MP distributions using the Kolmogorov-Smirnov test, and 3) identifies daily load profile discords in a large building portfolio. We evaluate ALDI using the metering data of both an academic campus and a residential neighborhood. Our results demonstrate that ALDI efficiently discovers measurement errors by system malfunctions and low energy consumption days in the academic campus portfolio, and it detects unique load shape patterns likely driven by occupant behavior and extreme weather conditions in the residential neighborhood.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Accelerating the rate of discovery: toward high-repetition-rate HED science

As high-intensity short-pulse lasers that can operate at high-repetition-rate (HRR) (>10 H z ) come online around the world, the high energy density (HED) science they enable will experience a radical paradigm shift. The >10 3 increase in shot rate over today's shot-per-hour drivers translates into dramatically faster data acquisition, more experiments, and the ability to exploit machine learning, and thus the potential to significantly accelerate the advancement of HED science. A wide range of HED experiments, from opacity investigations to secondary source generation to plasma nuclear physics, will benefit from the increased statistics, precision, and exploration of phase space. Besides increasing the rate at which scientific experiments can be performed, HRR also allows for the rapid delivery of optimal experiments supported by simulations and modeling augmented by close coupling to empirical data. To fully realize such an HRR framework, numerous subsystems must be developed and brought together, including feedback laser control loops, high-throughput targetry and diagnostics, cognitive simulation, enhanced HED codes, and advanced data analytics. This paper describes the vision for an integrated HRR laser experimental HED system and outlines some of the major considerations and challenges for realizing it.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Pathway-based analyses of gene expression profiles at low doses of ionizing radiation

Radiation exposure poses a significant threat to human health. Emerging research indicates that even low-dose radiation once believed to be safe, may have harmful effects. This perception has spurred a growing interest in investigating the potential risks associated with low-dose radiation exposure across various scenarios. To comprehensively explore the health consequences of low-dose radiation, our study employs a robust statistical framework that examines whether specific groups of genes, belonging to known pathways, exhibit coordinated expression patterns that align with the radiation levels. Notably, our findings reveal the existence of intricate yet consistent signatures that reflect the molecular response to radiation exposure, distinguishing between low-dose and high-dose radiation. Moreover, we leverage a pathway-constrained variational autoencoder to capture the nonlinear interactions within gene expression data. By comparing these two analytical approaches, our study aims to gain valuable insights into the impact of low-dose radiation on gene expression patterns, identify pathways that are differentially affected, and harness the potential of machine learning to uncover hidden activity within biological networks. This comparative analysis contributes to a deeper understanding of the molecular consequences of low-dose radiation exposure.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗

APMS: An Integrated Set of Tools for Measuring Safety

This is a report of work in progress. In it, I summarize the status of the research and development of the Aviation Performance Measuring System (APMS) for managing, processing, and analyzing digital flight-recorded data. The objectives of the NASA-FAA APMS research project are to establish a sound scientific and technological basis for flight-data analysis, to define an open and flexible architecture for flight-data-analysis systems, and to articulate guidelines for a standardized database structure on which to continue to build future flight-data-analysis extensions. APMS will offer to the air transport community an open, voluntary standard for flight-data-analysis software, a standard that will help to ensure suitable functionality, and data interchangeability, among competing software programs. APMS will develop and document the methodologies, algorithms, and procedures for data management and analyses to enable users to easily interpret the implications regarding safety and efficiency of operations. APMS does not entail the implementation of a nationwide flight-data-collection system. It is intended to provide technical tools to ease the large-scale implementation of flight-data analyses at both the air-carrier and the national-airspace levels in support of their Flight Operations and Quality Assurance (FOQA) Programs and Advanced Qualifications Programs (AQP). APMS cannot meet its objectives unless it develops tools that go substantially beyond the capabilities of the current commercially available software and supporting analytic methods that are mainly designed to count special events. These existing capabilities, while of proven value, were created primarily with the needs of air crews in mind. APMS tools must serve the needs of the government and air carriers, as well as air crews, to fully support the FOQA and AQP programs. They must be able to derive knowledge not only through the analysis of single flights (special-event detection), but through statistical evaluation of the performance of large groups of flights. This paper describes the integrated suite of tools that will assist analysts in evaluating the operational performance and safety of the national air transport system, the air carrier, and the air crew.

Statler, Irving C.↗

APMS: An Integrated Suite of Tools for Measuring Performance and Safety

This is a report of work in progress. In it, I summarize the status of the research and development of the Aviation Performance Measuring System (APMS) for managing, processing, and analyzing digital flight-recorded data. The objectives of the NASA-FAA APMS research project are to establish a sound scientific and technological basis for flight-data analysis, to define an open and flexible architecture for flight-data-analysis systems, and to articulate guidelines for a standardized database structure on which to continue to build future flight-data-analysis extensions . APMS will offer to the air transport community an open, voluntary standard for flight-data-analysis software, a standard that will help to ensure suitable functionality, and data interchangeability, among competing software programs. APMS will develop and document the methodologies, algorithms, and procedures for data management and analyses to enable users to easily interpret the implications regarding safety and efficiency of operations. APMS does not entail the implementation of a nationwide flight-data-collection system. It is intended to provide technical tools to ease the large-scale implementation of flight-data analyses at both the air-carrier and the national-airspace levels in support of their Flight Operations and Quality Assurance (FOQA) Programs and Advanced Qualifications Programs (AQP). APMS cannot meet its objectives unless it develops tools that go substantially beyond the capabilities of the current commercially available software and supporting analytic methods that are mainly designed to count special events. These existing capabilities, while of proven value, were created primarily with the needs of air crews in mind. APMS tools must serve the needs of the government and air carriers, as well as air crews, to fully support the FOQA and AQP programs. They must be able to derive knowledge not only through the analysis of single flights (special-event detection), but through statistical evaluation of the performance of large groups of flights. This paper describes the integrated suite of tools that will assist analysts in evaluating the operational performance and safety of the national air transport system, the air carrier, and the air crew.

Statler, Irving C.↗

APMS: An Integrated Suite of Tools for Measuring Performance and Safety

This is a report of work in progress. In it, I summarize the status of the research and development of the Aviation Performance Measuring System (APMS) for managing, processing, and analyzing digital flight-recorded data. The objectives of the NASA-FAA APMS research project are to establish a sound scientific and technological basis for flight-data analysis, to define an open and flexible architecture for flight-data-analysis systems, and to articulate guidelines for a standardized database structure on which to continue to build future flight-data-analysis extensions. APMS will offer to the air transport community an open, voluntary standard for flight-data-analysis software, a standard that will help to ensure suitable functionality, and data interchangeability, among competing software programs. APMS will develop and document the methodologies, algorithms, and procedures for data management and analyses to enable users to easily interpret the implications regarding safety and efficiency of operations. APMS does not entail the implementation of a nationwide flight-data-collection system. It is intended to provide technical tools to ease the large-scale implementation of flight-data analyses at both the air-carrier and the national-airspace levels in support of their Flight Operations and Quality Assurance (FOQA) Programs and Advanced Qualifications Programs (AQP). APMS cannot meet its objectives unless it develops tools that go substantially beyond the capabilities of the current commercially available software and supporting analytic methods that are mainly designed to count special events. These existing capabilities, while of proven value, were created primarily with the needs of air crews in mind. APMS tools must serve the needs of the government and air carriers, as well as air crews, to fully support the FOQA and AQP programs. They must be able to derive knowledge not only through the analysis of single flights (special-event detection), but through statistical evaluation of the performance of large groups of flights. This paper describes the integrated suite of tools that will assist analysts in evaluating the operational performance and safety of the national air transport system, the air carrier, and the air crew.

Statler, Irving C.↗

The Aviation Performance Measuring System (APMS): An Integrated Suite of Tools for Measuring Performance and Safety

This is a report of work in progress. In it, I summarize the status of the research and development of the Aviation Performance Measuring System (APMS) for managing, processing, and analyzing digital flight-recorded data, The objectives of the NASA-FAA APMS research project are to establish a sound scientific and technological basis for flight-data analysis, to define an open and flexible architecture for flight-data analysis systems, and to articulate guidelines for a standardized database structure on which to continue to build future flight-data-analysis extensions. APMS offers to the air transport community an open, voluntary standard for flight-data-analysis software; a standard that will help to ensure suitable functionality and data interchangeability among competing software programs. APMS will develop and document the methodologies, algorithms, and procedures for data management and analyses to enable users to easily interpret the implications regarding safety and efficiency of operations. APMS does not entail the implementation of a nationwide flight-data-collection system. It is intended to provide technical tools to ease the large-scale implementation of flight-data analyses at both the air-carrier and the national-airspace levels in support of their Flight Operations and Quality Assurance (FOQA) Programs and Advanced Qualifications Programs (AQP). APMS cannot meet its objectives unless it develops tools that go substantially beyond the capabilities of the current commercially available software and supporting analytic methods that are mainly designed to count special events. These existing capabilities, while of proven value, were created primarily with the needs-of aircrews in mind. APMS tools must serve the needs of the government and air carriers, as well as aircrews, to fully support the FOQA and AQP programs. They must be able to derive knowledge not only through the analysis of single flights (special-event detection), but also through statistical evaluation of the performance of large groups of flights. This paper describes the integrated suite of tools that will assist analysts in evaluating the operational performance and safety of the national air transport system, the air carrier, and the aircrew.

Statler, Irving C.↗

Quantifying the Variation in the Number of Donors in Quantum Dots Created Using Atomic Precision Advanced Manufacturing

Atomic-precision advanced manufacturing enables unique silicon quantum electronics built on quantum dots fabricated from small numbers of phosphorus dopants. The number of dopant atoms comprising a dot plays a central role in determining the behavior of charge and spin confined to the dots and thus overall device performance. Here in this work, we use both theoretical and experimental techniques to explore the combined impact of lithographic variation and stochastic kinetics on the number of P incorporations in quantum dots made using these techniques and how this variation changes as a function of the size of the dot. Using a kinetic model of PH3 dissociation augmented with novel reaction barriers, we demonstrate that for a 2 × 3 silicon dimer window the probability that no donor incorporates goes to zero, allowing for certainty in the placement of at least one donor. However, this still comes with some uncertainty in the precise number of incorporated donors (either one or two), and this variability may still impact certain applications. We also examine the impact of the size of the initial lithographic window, finding that the incorporation fraction saturates to δ-layer-like coverage as the circumference-to-area ratio decreases. We predict that this incorporation fraction depends strongly on the dosage of the precursor and that the standard deviation of the number of incorporations scales as ~√n, as would be expected for a sequence of largely independent incorporation events. Finally, we characterize an array of 36 experimentally prepared multidonor 3 × 3 nm lithographic windows with scanning tunneling microscopy, measuring the fidelity of the lithography to the desired array and the final location of PH x fragments within these lithographic windows. We use our kinetic model to examine the expected variability due to the observed lithographic error, predicting a negligible impact on incorporation statistics. We find good agreement between our model and the inferred incorporation locations in these windows from scanning tunneling microscope measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Path Integrals for Nonadiabatic Dynamics: Multistate Ring Polymer Molecular Dynamics

This review focuses on a recent class of path-integral-based methods for the simulation of nonadiabatic dynamics in the condensed phase using only classical molecular dynamics trajectories in an extended phase space. Specifically, a semiclassical mapping protocol is used to derive an exact, continuous, Cartesian variable path-integral representation for the canonical partition function of a system in which multiple electronic states are coupled to nuclear degrees of freedom. Building on this exact statistical foundation, multistate ring polymer molecular dynamics methods are developed for the approximate calculation of real-time thermal correlation functions. As a result, the remarkable promise of these multistate ring polymer methods, their successful applications, and their limitations are discussed in detail.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Rapid monitoring of fermentations: a feasibility study on biological 2,3-butanediol production

2,3-butanediol (2,3-BDO) is an economically important platform chemical that can be produced by the fermentation of sugars using an engineered strain of Zymomonas mobilis . These fermentations require continuous monitoring and modification of fermentation conditions to maximize 2,3-BDO yields and minimize the production of the undesired coproducts glycerol and acetoin. Because of the time required for sampling and off-line chromatographic measurement of fermentation samples, the ability of fermentation scientists to modify fermentation conditions in a timely manner is limited. The goal of this study was to test if near-infrared spectroscopy (NIRS) along with multivariate statistics could reduce the time needed for this analysis and enable real-time monitoring and control of the fermentation. In this work we developed partial least squares (PLS) calibration models to predict the concentrations of glucose, xylose, 2,3-BDO, acetoin, and glycerol in fermentations via NIRS using two different spectrometers and two different spectroscopy modalities. We first evaluated the feasibility of rapid NIRS monitoring through experiments where we measured the signals from each analyte of interest and built NIRS-based PLS models using spectra from synthetic samples containing uncorrelated concentrations of these analytes. All analytes showed unique spectral signatures, and this initial modeling showed that all analytes could be detected simultaneously. We then began work with samples from laboratory fermentation experiments and tested the feasibility of regression model development across two spectral collection modalities (at-line and on-line) and two instruments: a laboratory-grade instrument and a low-cost instrument with a more limited spectral range. All modalities showed promise in the ability to monitor Z. mobilis fermentations of glucose and xylose to 2,3-BDO. The low-cost instrument displayed a lower signal-to-noise ratio than the laboratory-grade instrument, which led to comparatively lower performance overall, but still provided sufficient accuracy to monitor fermentation trends. While the ease of use of on-line monitoring systems was favored as compared to at-line systems due to the lack of sampling required and potential for automated process control, we observed some decrease in performance due to the additional complexity of the sample matrix. We have demonstrated that NIRS combined with multivariate analysis can be used for at-line and on-line monitoring of the concentrations of glucose, xylose, 2,3-BDO, acetoin, and glycerol during Z. mobilis fermentations. The decrease in signal-to-noise ratio when using a low-cost spectrometer led to greater prediction error than the laboratory-grade spectrometer for at-line monitoring. The on-line monitoring modality showed great promise for real time process control via NIRS.

09 BIOMASS FUELS↗

Phasor-Measurement-Unit-Based Data Analytics Using Digital Twin and PhasorAnalytics Software

A major objective of this project was to apply GE’s commercial machine learning and data analytics toolsets to large-scale, real-world, anonymized Phasor Measurement Unit (PMU) datasets in order to extract signatures, correlated and/or causal factors, and precursor patterns associated with significant power system phenomena. The project had a particular emphasis on extraction of insights relevant to asset health monitoring, real-time load modeling and cybersecurity monitoring. Additionally, the team was directed to undertake a comprehensive data quality analysis for the provided datasets and encouraged to estimate the ‘machine-learning readiness’ of the datasets by documenting any major obstacles to the application of commercial machine learning algorithms. To accomplish the aforementioned objectives, the project team’s work centered around the identification of key event signatures and application of the identified event signatures for event detection and event classification. The industry-validated, semi-supervised machine learning strategy employed for event signature identification involved several major tasks, including data-preprocessing, generation of an overabundance of features, normal data identification, normality modeling, and event signature identification through a methodical, quantitative ranking of features in order of relevance to each studied event type. Throughout the project, data quality issues and mitigation techniques were investigated. In this report, insights are provided regarding the readiness of the provided synchrophasor datasets for application of machine learning and data analytics. The methodologies employed for this technical strategy are summarized in this report. With regards to data preprocessing and feature generation, the provided Training and Test Datasets were ingested into GE’s big data environment. Subsequently, the team applied bad data cleansing and data imputation scripts, event detection scripts, and application programming interfaces (APIs) to the datasets for convenient data access. The project team completed development and validation of dozens of physics-based, statistics-based and transformation-based feature functions used for the extraction of over 60 synchrophasor features. Using a new parallel feature generation technology developed on this project, over 60 features have been rapidly generated for the full two years’ worth of Training and Test Dataset data associated with both the Eastern and Western interconnects. Even accommodating for temporal down-sampling inherent to the feature extraction procedure, this parallel feature generation activity resulted in a massive feature set with a storage requirement approximately equal to that of the raw training dataset itself. With regards to normal data identification and normality modeling, a normality model was built using the feature data extracted from the Training Dataset and iteratively refined subsequent to incremental adjustments and expansions of the Training Dataset feature data. With respect to event characterization and signature identification, an event signature identification pipeline was developed and used in conjunction with the normality model to identify over 15 event signatures for key event categories within the Training Dataset. The identified event signatures were used to characterize hundreds of key events in terms of relative severity, duration, and location of the event. An investigation was undertaken to identify correlated and causal factors involved in transformer events. A separate investigation into temporal trends in ring-down analysis results was undertaken to determine possible associations between system dynamics and various other factors such as loading, season or year. To validate the identified event signatures, additional work was undertaken to develop signature-based anomaly detection and classification tools suitable for convenient application to the synchrophasor datasets. The anomaly detection and classification tools, suitable for online application, were then applied to the entirety of the Eastern Interconnect Training and Test Datasets. Performance of the event detection and classification tools was evaluated upon receipt of the Test Dataset event logs (i.e., the labels for events contained in the Test Dataset), and promising results were obtained despite several challenges (documented herein) associated with application of supervised or semi-supervised machine learning methods to large-scale, anonymized datasets. Finally, the detection and classification tools were used to detect, classify, and characterize thousands of new events not included in the original event logs provided by the DOE within both the Training and Test Datasets.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Considerations in the design of large space structures

Several analytical studies of topics relevant to the design of large space structures are presented. Topics covered are: the types and quantitative evaluation of the disturbances to which large Earth-oriented microwave reflectors would be subjected and the resulting attitude errors of such spacecraft; the influence of errors in the structural geometry of the performance of radiofrequency antennas; the effect of creasing on the flatness of tensioned reflector membrane surface; and an analysis of the statistics of damage to truss-type structures due to meteoroids.

Hedgepeth, J. M.↗

Sea surface temperature anomalies, planetary waves, and air-sea feedback in the middle latitudes

Current analytical models for large-scale air-sea interactions in the middle latitudes are reviewed in terms of known sea-surface temperature (SST) anomalies. The scales and strength of different atmospheric forcing mechanisms are discussed, along with the damping and feedback processes controlling the evolution of the SST. Difficulties with effective SST modeling are described in terms of the techniques and results of case studies, numerical simulations of mixed-layer variability and statistical modeling. The relationship between SST and diabatic heating anomalies is considered and a linear model is developed for the response of the stationary atmosphere to the air-sea feedback. The results obtained with linear wave models are compared with the linear model results. Finally, sample data are presented from experiments with general circulation models into which specific SST anomaly data for the middle latitudes were introduced.

Frankignoul, C.↗

Energy loss of fast nonthermal electrons in plasmas

Simple analytical expressions for equilibration times of nonrelativistic monoenergetic electrons in plasmas are evaluated in the 'weak'-beam approximation when the density of the monoenergetic electrons is much smaller than the plasma density. The equilibration time is defined as the time needed by the beam of monenergetic electrons to lose most of its energy as a result of collisions with plasma particles having a Maxwellian energy distribution. The process of energy equilibration is treated as a statistical superposition of both elastic and inelastic collisions in the plasma. The possibility of collisionless equilibration is discussed. Comparison of the equilibration times with the Spitzer relaxation times indicates that the former times are more appropriate for an estimate of the energy loss of the 'weak' electron beams in highly ionized plasmas.

Kunc, Joseph A.↗