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NASA NTRS1993

Coronal heating by the resonant absorption of Alfven waves - Importance of the global mode and scaling laws

Numerical simulations of the MHD equations for a fully compressible, low-beta, resistive plasma are used to study the resonance absorption process for the heating of coronal active region loops. Comparisons with more approximate analytic models show that the major predictions of the analytic theories are, to a large extent, confirmed by the numerical computations. The simulations demonstrate that the dissipation occurs primarily in a thin resonance layer. Some of the analytically predicted features verified by the simulations are (a) the position of the resonance layer within the initial inhomogeneity; (b) the importance of the global mode for a large range of loop densities; (c) the dependence of the resonance layer thickness and the steady-state heating rate on the dissipation coefficient; and (d) the time required for the resonance layer to form. In contrast with some previous analytic and simulation results, the time for the loop to reach a steady state is found to be the phase-mixing time rather than a dissipation time. This disagreement is shown to result from neglect of the existence of the global mode in some of the earlier analyses. The resonant absorption process is also shown to behave similar to a classical driven harmonic oscillator.

Steinolfson, Richard S.↗

NASA NTRSDate not supplied

Recent Progress in the International Laser Ranging Service (ILRS)

The International Laser Ranging Service (ILRS) provides Satellite Laser Ranging (SLR) and Lunar Laser Ranging (LLR) observations and data products with a focus on Earth and Lunar science and engineering applications. The basic observables are the precise two-way time-of-flight of ultra-short laser pulses from ground stations to retroreflector arrays on satellites and the Moon and the one-way time-of-flight measurements to space-borne receivers (transponders). SLR is one of the four space geodetic techniques (along with VLBI, GNSS, and DORIS). The International Terrestrial Reference Frame (ITRF) development, maintained by IERS, is based on these geodetic observations. Fundamental data products include accurate satellite ephemerides, Earth orientation parameters, three dimensional coordinates and velocities of the ILRS tracking stations, time-varying geocenter coordinates, static and time-varying coefficients of the Earth’s gravity field, fundamental physical constants, lunar ephemerides and librations, and lunar orientation parameters. The ILRS continues to expand spatial and temporal coverage of SLR observations. New stations with new technologies are being deployed; existing stations are being upgraded. Some of these stations are multi-technique Core Sites. New satellites are expanding applications and strengthening the ILRS contribution to the reference frame. New analysis, modeling, and data processing techniques are improving data products. New campaigns are expanding our applications into relativity and the study of non-gravitational forces. New activities are underway on Lunar Laser Ranging, Time Transfer, and Space Debris Tracking, helping to expand laser ranging applications. This talk will give an update on the current ILRS activities and their impact on ILRS data products.

Report on the ILRS activities↗

NASA NTRS1971

Dynamic upper atmospheric force model on stabilized vehicles for a high-precision trajectory computer program

The upper atmosphere model draws heavily on the behavior of the earth's upper atmosphere which exhibits cyclic as well as irregular variations in density profile, temperature, pressure, and composition in unison with solar activities as deduced from the more recent land-based and satellite observations. The lift and drag model is designed specifically for inertially stabilized vehicles of the Mariner class, with possible extension to gravity gradient stabilized vehicles of the GEOS class. The model considers operation in the free molecular flow regimes with large Knudsen numbers. The vehicle is considered a composite structure with basic components having well-defined shapes, each with its own surface characteristics in terms of temperature, reflectivity, and accommodation of free stream molecules. The model takes into account both the calculation of precise aerodynamic force coefficients in terms of expansion of modified Bessel functions in speed ratios and angle of attack, and approximate force coefficients when the speed ratios approach infinity. Other considerations include specular and diffused reflectivity, shielding, and shadow effects.

Khatib, A. R.↗

NASA NTRS1971

Techniques of orbital decay and long-term ephemeris prediction for satellites in earth orbit

In the special perturbation method, Cowell and variation-of-parameters formulations of the motion equations are implemented and numerically integrated. Variations in the orbital elements due to drag are computed using the 1970 Jacchia atmospheric density model, which includes the effects of semiannual variations, diurnal bulge, solar activity, and geomagnetic activity. In the general perturbation method, two-variable asymptotic series and automated manipulation capabilities are used to obtain analytical solutions to the variation-of-parameters equations. Solutions are obtained considering the effect of oblateness only and the combined effects of oblateness and drag. These solutions are then numerically evaluated by means of a FORTRAN program in which an updating scheme is used to maintain accurate epoch values of the elements. The atmospheric density function is approximated by a Fourier series in true anomaly, and the 1970 Jacchia model is used to periodically update the Fourier coefficients. The accuracy of both methods is demonstrated by comparing computed orbital elements to actual elements over time spans of up to 8 days for the special perturbation method and up to 356 days for the general perturbation method.

Barry, B. F.↗

NASA NTRS1992

Time simulation of flutter with large stiffness changes

Time simulation of flutter, involving large local structural changes, is formulated with a state-space model that is based on a relatively small number of generalized coordinates. Free-free vibration modes are first calculated for a nominal finite-element model with relatively large fictitious masses located at the area of structural changes. A low-frequency subset of these modes is then transformed into a set of structural modal coordinates with which the entire simulation is performed. These generalized coordinates and the associated oscillatory aerodynamic force coefficient matrices are used to construct an efficient time-domain, state-space model for a basic aeroelastic case. The time simulation can then be performed by simply changing the mass, stiffness, and damping coupling terms when structural changes occur. It is shown that the size of the aeroelastic model required for time simulation with large structural changes at a few apriori known locations is similar to that required for direct analysis of a single structural case. The method is applied to the simulation of an aeroelastic wind-tunnel model. The diverging oscillations are followed by the activation of a tip-ballast decoupling mechanism that stabilizes the system but may cause significant transient overshoots.

Karpel, Mordechay↗

NASA NTRS1992

Time simulation of flutter with large stiffness changes

Time simulation of flutter, involving large local structural changes, is formulated with a state-space model that is based on a relatively small number of generalized coordinates. Free-free vibration modes are first calculated for a nominal finite-element model with relatively large fictitious masses located at the area of structural changes. A low-frequency subset of these modes is then transformed into a set of structural modal coordinates with which the entire simulation is performed. These generalized coordinates and the associated oscillatory aerodynamic force coefficient matrices are used to construct an efficient time-domain, state-space model for basic aeroelastic case. The time simulation can then be performed by simply changing the mass, stiffness and damping coupling terms when structural changes occur. It is shown that the size of the aeroelastic model required for time simulation with large structural changes at a few a priori known locations is similar to that required for direct analysis of a single structural case. The method is applied to the simulation of an aeroelastic wind-tunnel model. The diverging oscillations are followed by the activation of a tip-ballast decoupling mechanism that stabilizes the system but may cause significant transient overshoots.

Karpel, M.↗

NASA NTRS2001

Implementing a Nitrogen-Based Model for Autotrophic Respiration Using Satellite and Field Observations

The rate of carbon accumulation by terrestrial plant communities in a process-level, mechanistic modeling is the difference of the rate of gross photosynthesis by a canopy (A(sub g)) and autotrophic respiration (R) of the stand. Observations for different biomes often show that R to be a large and variable fraction of A(sub g), ca. 35% to 75%, although other studies suggest the ratio of R and A(sub g) to be less variable. Here, R has been calculated according to the two compartment model as being the sum of maintenance and growth components. The maintenance respiration of foliage and living fine roots for different biomes has been determined objectively from observed nitrogen content of these organs. The sapwood maintenance respiration is based on pipe theory, and checked against an independently derived equation considering sapwood biomass and its maintenance coefficient. The growth respiration has been calculated from the difference of A(sub g) and maintenance respiration. The A(sub g) is obtained as the product of biome-specific radiation use efficiency for gross photosynthesis under unstressed conditions and intercepted photosynthetically active radiation, and adjusted for stress. Calculations have been done using satellite and ground observations for 36 consecutive months (1987-1989) over large contiguous areas (ca. 10(exp 5) sq km) of boreal forests, crop land, temperate deciduous forest, temperate grassland, tropical deciduous forest, tropical evergreen forest, tropical savanna, and tundra. The ratio of annual respiration and gross photosynthesis, (R/A(sub g)), is found to be 0.5-0.6 for temperate and cold adopted biome areas, but somewhat higher for tropical biome areas (0.6-0.7). Interannual variation of the fluxes is found to be generally less than 15%. Calculated fluxes are compared with observations and several previous estimates. Results of sensitivity analysis are presented for uncertainties in parameterization and input data. It is found that uncertainty in determining maintenance respiration for tropical biomes is such that R/A(sub g) for these biomes could be similar to that for temperate biomes.

Choudhury, Bhaskar J.↗

NASA NTRS1991

Physically weighted approximations of unsteady aerodynamic forces using the minimum-state method

The Minimum-State Method for rational approximation of unsteady aerodynamic force coefficient matrices, modified to allow physical weighting of the tabulated aerodynamic data, is presented. The approximation formula and the associated time-domain, state-space, open-loop equations of motion are given, and the numerical procedure for calculating the approximation matrices, with weighted data and with various equality constraints are described. Two data weighting options are presented. The first weighting is for normalizing the aerodynamic data to maximum unit value of each aerodynamic coefficient. The second weighting is one in which each tabulated coefficient, at each reduced frequency value, is weighted according to the effect of an incremental error of this coefficient on aeroelastic characteristics of the system. This weighting yields a better fit of the more important terms, at the expense of less important ones. The resulting approximate yields a relatively low number of aerodynamic lag states in the subsequent state-space model. The formulation forms the basis of the MIST computer program which is written in FORTRAN for use on the MicroVAX computer and interfaces with NASA's Interaction of Structures, Aerodynamics and Controls (ISAC) computer program. The program structure, capabilities and interfaces are outlined in the appendices, and a numerical example which utilizes Rockwell's Active Flexible Wing (AFW) model is given and discussed.

Karpel, Mordechay↗

NASA NTRS1998

Thermal Effects Modeling Developed for Smart Structures

Applying smart materials in aeropropulsion systems may improve the performance of aircraft engines through a variety of vibration, noise, and shape-control applications. To facilitate the experimental characterization of these smart structures, researchers have been focusing on developing analytical models to account for the coupled mechanical, electrical, and thermal response of these materials. One focus of current research efforts has been directed toward incorporating a comprehensive thermal analysis modeling capability. Typically, temperature affects the behavior of smart materials by three distinct mechanisms: Induction of thermal strains because of coefficient of thermal expansion mismatch 1. Pyroelectric effects on the piezoelectric elements; 2. Temperature-dependent changes in material properties; and 3. Previous analytical models only investigated the first two thermal effects mechanisms. However, since the material properties of piezoelectric materials generally vary greatly with temperature (see the graph), incorporating temperature-dependent material properties will significantly affect the structural deflections, sensory voltages, and stresses. Thus, the current analytical model captures thermal effects arising from all three mechanisms through thermopiezoelectric constitutive equations. These constitutive equations were incorporated into a layerwise laminate theory with the inherent capability to model both the active and sensory response of smart structures in thermal environments. Corresponding finite element equations were formulated and implemented for both the beam and plate elements to provide a comprehensive thermal effects modeling capability.

Lee, Ho-Jun↗

NASA NTRS2014

Badhwar-O'Neill 2011 Galactic Cosmic Ray Model Update and Future Improvements

The Badhwar-O'Neill Galactic Cosmic Ray (GCR) Model based on actual GCR measurements is used by deep space mission planners for the certification of microelectronic systems and the analysis of radiation health risks to astronauts in space missions. The BO GCR Model provides GCR flux in deep space (outside the earth's magnetosphere) for any given time from 1645 to present. The energy spectrum from 50 MeV/n - 20 GeV/n is provided for ions from hydrogen to uranium. This work describes the most recent version of the BO GCR model (BO'11). BO'11 determined the GCR flux at a given time applying an emperical time delay function to past sunspot activity. We describe the GCR measurement data used in the BO'11 update - modern data from BESS, PAMELA, CAPRICE, and ACE emphasized more than the older balloon data used for the previous BO model (BO'10). We look at the GCR flux for the last 24 solar minima and show how much greater the flux was for the cycle 24 minimum in 2010. The BO'11 Model uses the traditional, steady-state Fokker-Planck differential equation to account for particle transport in the heliosphere due to diffusion, convection, and adiabatic deceleration. It assumes a radially symmetrical diffusion coefficient derived from magnetic disturbances caused by sunspots carried outward by a constant solar wind. A more complex differential equation is now being tested to account for particle transport in the heliosphere in the next generation BO model. This new model is time-dependent (no longer a steady state model). In the new model, the dynamics and anti-symmetrical features of the actual heliosphere are accounted for so emperical time delay functions will no longer be required. The new model will be capable of simulating the more subtle features of modulation - such as the Sun's polarity and modulation dependence on gradient and curvature drift. This improvement is expected to significantly improve the fidelity of the BO GCR model. Preliminary results of its performance will be presented.

O'Neill, Pat M.↗

NASA NTRS2014

Badhwar-O'Neill 2011 Galactic Cosmic Ray Model Update and Future Improvements

The Badhwar-O'Neill Galactic Cosmic Ray (GCR) Model based on actual GR measurements is used by deep space mission planners for the certification of micro-electronic systems and the analysis of radiation health risks to astronauts in space missions. The BO GCR Model provides GCR flux in deep space (outside the earth's magnetosphere) for any given time from 1645 to present. The energy spectrum from 50 MeV/n-20 GeV/n is provided for ions from hydrogen to uranium. This work describes the most recent version of the BO GCR model (BO'11). BO'11 determines the GCR flux at a given time applying an empirical time delay function to past sunspot activity. We describe the GCR measurement data used in the BO'11 update - modern data from BESS, PAMELA, CAPRICE, and ACE emphasized for than the older balloon data used for the previous BO model (BO'10). We look at the GCR flux for the last 24 solar minima and show how much greater the flux was for the cycle 24 minimum in 2010. The BO'11 Model uses the traditional, steady-state Fokker-Planck differential equation to account for particle transport in the heliosphere due to diffusion, convection, and adiabatic deceleration. It assumes a radially symmetrical diffusion coefficient derived from magnetic disturbances caused by sunspots carried onward by a constant solar wind. A more complex differential equation is now being tested to account for particle transport in the heliosphere in the next generation BO model. This new model is time-dependent (no longer a steady state model). In the new model, the dynamics and anti-symmetrical features of the actual heliosphere are accounted for so empirical time delay functions will no longer be required. The new model will be capable of simulating the more subtle features of modulation - such as the Sun's polarity and modulation dependence on the gradient and curvature drift. This improvement is expected to significantly improve the fidelity of the BO GCR model. Preliminary results of its performance will be presented.

O'Neill, Pat M.↗

NASA NTRSDate not supplied

Satellite-Assisted Particulate Matter (SAPM) for the Models, In situ, and Remote Sensing of Aerosols (MIRA) Working Group

Models, In situ, and Remote sensing of Aerosols (MIRA) is an international working group that provides a forum for collaborations amongst these three atmospheric aerosol communities. MIRA consists of a collection of interdisciplinary and independently funded Topic/Project groups with clear goals and generally characterized by requests for additional scientific data. The Satellite-Assisted Particulate Matter (SAPM) Topic group focuses on the study of fine particulate matter (PM2.5), as it is a major contributor to air pollution and negatively impacts human health. Our group aims to provide intercomparisons of various methods and techniques for estimating surface PM2.5 assisted by satellite remote sensors (passive and active), global aerosol models, and in situ aerosol measurements. The overall motivation of our work is to enhance PM2.5 coverage beyond in situ ground stations, which can be limited. In this presentation, we provide an overview of various PM2.5 estimation approaches by current SAPM team members, as each approach has its own strengths and limitations. One approach uses near-surface aerosol extinction retrievals from the spaceborne Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) and an assumed value of mass extinction efficiency to derive PM2.5 concentrations (Toth et al 2019). A study using this method found a promising agreement (R=0.60; slope=0.89) with U.S. Environmental Protection Agency (EPA) in situ PM2.5 measurements over the contiguous United States (CONUS) for a 12-year (2007-2018) period (Toth et al 2022). In a different approach combining spaceborne lidar and a model, the Cloud Aerosol Transport System (CATS) lidar and Goddard Earth Observing System (GEOS) model are blended in an ensemble variational assimilation scheme to retrieve aerosol extinction and convert speciated mass concentrations to total PM2.5. A recent study (Matus et al in prep.) found agreement within 2 μg/m3 over the CONUS on the 2016 annual mean when compared to EPA ground-based measurements. Another study explored trends in city aerosol optical depth (AOD) from a spaceborne passive remote sensor, Moderate Resolution Imaging Spectroradiometer (MODIS), and found that these trends agree well with trends in city surface PM2.5, which provides confidence in the use of city AOD for city PM2.5 trend studies (Vohra et al 2021). In a follow-on study, steep and significant trends (~2.5 to 7.8% a-1) in AOD are found for several South Asian cities (e.g., Bangalore and Hyderabad), suggesting rapid growth in PM2.5 (Vohra et al 2022). Also in this presentation, we report results on our current collective SAPM study of India, a country that exhibits high levels of PM2.5 pollution. We show the temporal (i.e., seasonal) and spatial variability of PM2.5 over India using the CALIOP and CATS+model approaches, comparisons between the estimated PM2.5 from the retrieval schemes, and validation with in situ PM2.5 ground-based observations from the Central Pollution Control Board in India. This region provides us with an excellent case study to test our PM2.5 retrievals in heavily polluted scenes and over a complex and varying topography. The SAPM Topic group actively seeks international participants/collaborators in our group, including those working with in situ aerosol measurements (e.g., ACTRIS). We are interested in aerosol datasets in order to either improve our PM2.5 estimates from various approaches (e.g., using in situ mass scattering/absorption coefficient and aerosol hygroscopic properties for various aerosol species) and/or validate the PM2.5 estimates (e.g., using in situ ground-based PM2.5 concentrations).

Travis D Toth↗

NASA NTRS1989

Dynamics of the middle atmosphere in winter (Dynamics). Interrelation between the different variations of turbulent diffusion and ionospheric absorption originating in the middle atmosphere

The turbulent diffusion coefficient was computed from the parameters of sporadic E layers using the wind shear theory of midlatitude sporadic E and models of the ionosphere as well as that of the neutral upper atmosphere. The turbulent diffusion coefficient obtained for the period of circulation disturbances associated with stratospheric warmings and for the intervals of the winter anomaly indicate changes similar to the ionospheric absorption of radio waves, in the former case decreased, in the latter case increased values. This may hit at the role of turbulent transport in the formation of these anomalies. On the basis of these findings, a seasonal variation of the turbulent diffusion coefficient having a minimum in summer and an increase of this parameter with increasing geomagnetic activity are anticipated.

Bencze, P.↗

NASA NTRS2023

Developing a Radar Signal Simulator for the Community Radiative Transfer Model

Active radar instruments provide vertically resolved clouds and precipitation measurements that cannot be provided by the passive instruments. These active measurements are not conventionally assimilated into the data assimilation systems because of the lack of fast forward radiative transfer models and also difficulties in the error modelling of the measurements. This paper describes the development, evaluation, and sensitivity analysis for a forward radar model implemented in the Community Radiative Transfer Model (CRTM). The scattering properties required by the forward model are provided by the hydrometeor lookup tables that were generated using the discrete dipole approximation. The model is able to calculate both the reflectivity and the attenuated reflectivity for any given radar instrument at any given zenith angles as long as CRTM instrument specific coefficients are available. The evaluation using CloudSat measurements shows a very good agreement between the simulations and measurements as long as the input profiles of hydrometeors are consistent with the measured reflectivity profiles. Major sources contributing to the differences between the measured and simulated reflectivities are input hydrometeor profiles, scattering lookup tables, lack of melting layer in the forward model, CRTM scattering solvers, and attenuation calculations. In addition to the forward model, both Tangent Linear and Adjoint of the model are also implemented and tested within CRTM. These components may be required by some data assimilation systems for the assimilation of radar measurements.

radar↗

NASA NTRS2015

CFD Modeling of the Multipurpose Hydrogen Test Bed (MHTB) Self-Pressurization and Spray Bar Mixing Experiments in Normal Gravity: Effect of the Accommodation Coefficient on the Tank Pressure

A CFD model for simulating the self-pressurization of a large scale liquid hydrogen storage tank is utilized in this paper to model the MHTB self-pressurization experiment. The kinetics-based Schrage equation is used to account for the evaporative and condensi ng interfacial mass flows in this model. The effect of the accommodation coefficient for calculating the interfacial mass transfer rate on the tank pressure during tank selfpressurization is studied. The values of the accommodation coefficient which were considered in this study vary from 1.0e-3 to 1.0e-1 for the explicit VOF model and from 1.0e-4 to 1.0e-3 for the implicit VOF model. The ullage pressure evolutions are compared against experimental data. A CFD model for controlling pressure in cryogenic storage tanks by spraying cold liquid into the ullage is also presented. The Euler-Lagrange approach is utilized for tracking the spray droplets and for modeling the interaction between the droplets and the continuous phase (ullage). The spray model is coupled with the VOF model by performing particle tracking in the ullage, removing particles from the ullage when they reach the interface, and then adding their contributions to the liquid. Droplet-ullage heat and mass transfer are modeled. The flow, temperature, and interfacial mass flux, as well as droplets trajectories, size distribution and temperatures predicted by the model are presented. The ul lage pressure and vapor temperature evolutions are compared with experimental data obtained from the MHTB spray bar mixing experiment. The effect of the accommodation coefficient for calculating the interfacial and droplet mass transfer rates on the tank pressure during mixing of the vapor using spray is studied. The values used for the accommodation coefficient at the interface vary from 1.0e-5 to 1.0e-2. The droplet accommodation coefficient values vary from 2.0e-6 to 1.0e-4.

cryogenic fluid storage↗

NASA NTRS1998

Feature Extraction of Event-Related Potentials Using Wavelets: An Application to Human Performance Monitoring

This report describes the development and evaluation of mathematical models for predicting human performance from discrete wavelet transforms (DWT) of event-related potentials (ERP) elicited by task-relevant stimuli. The DWT was compared to principal components analysis (PCA) for representation of ERPs in linear regression and neural network models developed to predict a composite measure of human signal detection performance. Linear regression models based on coefficients of the decimated DWT predicted signal detection performance with half as many f ree parameters as comparable models based on PCA scores. In addition, the DWT-based models were more resistant to model degradation due to over-fitting than PCA-based models. Feed-forward neural networks were trained using the backpropagation,-, algorithm to predict signal detection performance based on raw ERPs, PCA scores, or high-power coefficients of the DWT. Neural networks based on high-power DWT coefficients trained with fewer iterations, generalized to new data better, and were more resistant to overfitting than networks based on raw ERPs. Networks based on PCA scores did not generalize to new data as well as either the DWT network or the raw ERP network. The results show that wavelet expansions represent the ERP efficiently and extract behaviorally important features for use in linear regression or neural network models of human performance. The efficiency of the DWT is discussed in terms of its decorrelation and energy compaction properties. In addition, the DWT models provided evidence that a pattern of low-frequency activity (1 to 3.5 Hz) occurring at specific times and scalp locations is a reliable correlate of human signal detection performance.

Trejo, Leonard J.↗

NASA NTRS1999

Feature extraction of event-related potentials using wavelets: an application to human performance monitoring

This report describes the development and evaluation of mathematical models for predicting human performance from discrete wavelet transforms (DWT) of event-related potentials (ERP) elicited by task-relevant stimuli. The DWT was compared to principal components analysis (PCA) for representation of ERPs in linear regression and neural network models developed to predict a composite measure of human signal detection performance. Linear regression models based on coefficients of the decimated DWT predicted signal detection performance with half as many free parameters as comparable models based on PCA scores. In addition, the DWT-based models were more resistant to model degradation due to over-fitting than PCA-based models. Feed-forward neural networks were trained using the backpropagation algorithm to predict signal detection performance based on raw ERPs, PCA scores, or high-power coefficients of the DWT. Neural networks based on high-power DWT coefficients trained with fewer iterations, generalized to new data better, and were more resistant to overfitting than networks based on raw ERPs. Networks based on PCA scores did not generalize to new data as well as either the DWT network or the raw ERP network. The results show that wavelet expansions represent the ERP efficiently and extract behaviorally important features for use in linear regression or neural network models of human performance. The efficiency of the DWT is discussed in terms of its decorrelation and energy compaction properties. In addition, the DWT models provided evidence that a pattern of low-frequency activity (1 to 3.5 Hz) occurring at specific times and scalp locations is a reliable correlate of human signal detection performance. Copyright 1999 Academic Press.

Evoked Potentials↗

NASA NTRS1991

Molecular hydrogen formation by excited atom radiative association

The results from a semiclassical calculation of the thermal rate coefficient for the radiative association process H(n = 2) + H(n = 1) - H2 + hv are presented (n is the principal quantum number of the separated hydrogen atoms). The relative importance of this reaction in various environments is briefly discussed. Models of the early universe around the epoch of recombination and protostellar winds have been calculated which include the excited atom process. Not surprisingly, it is shown that the excited atom process will not be important in the general interstellar medium, except possibly in environments where the amount of Ly-alpha photon trapping is large. Examples may be the material surrounding quasars, active galactic nuclei, and bright H II regions. The most likely application of this process might be within rapidly evolving systems where a large transient n = 2 population of neutral hydrogen could result in a burst of molecular hydrogen formation.

Latter, William B.↗