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NASA NTRS2016

Titan Polar Landscape Evolution

With the ongoing Cassini-era observations and studies of Titan it is clear that the intensity and distribution of surface processes (particularly fluvial erosion by methane and Aeolian transport) has changed through time. Currently however, alternate hypotheses substantially differ among specific scenarios with respect to the effects of atmospheric evolution, seasonal changes, and endogenic processes. We have studied the evolution of Titan's polar region through a combination of analysis of imaging, elevation data, and geomorphic mapping, spatially explicit simulations of landform evolution, and quantitative comparison of the simulated landscapes with corresponding Titan morphology. We have quantitatively evaluated alternate scenarios for the landform evolution of Titan's polar terrain. The investigations have been guided by recent geomorphic mapping and topographic characterization of the polar regions that are used to frame hypotheses of process interactions, which have been evaluated using simulation modeling. Topographic information about Titan's polar region is be based on SAR-Topography and altimetry archived on PDS, SAR-based stereo radar-grammetry, radar-sounding lake depth measurements, and superposition relationships between geomorphologic map units, which we will use to create a generalized topographic map.

Cassini↗

NASA NTRS2017

Daily Kilometer-Scale MODIS Satellite Maps of PM2.5 Describe Wintertime Episodes

The San Joaquin Valley (SJV) suffers from severe health-endangering episodes of PM2.5 aerosol loadings in wintertime; episodes last approximately 5 days and differ in geographical distribution and composition. PM2.5 stations are scattered; consequently the use of remote sensing to map variable regional patterns of these varying respirable aerosol concentrations is desirable. High-precision AOT retrievals can capture column particulate loading. However,PM2.5 mapping is challenging due to several reasons: particularly thin mixed layers (ML) and thus relatively low aerosol optical thickness (AOT) close to current measurement limits, variable and a typical composition of the aerosols, and complex surface bidirectional reflectance. However, the West does present some advantages in analysis. Air basins are isolated from long-distance transport, and experience predominant strong meteorological subsidence. Thus these Western basin regions have fewer problematic cases of overriding aerosol layers detached from the surface. To counter such local overriding, Chu et al. have described an approach for the Eastern US, and He et al have described a synoptic classification approach useful in Shanghai. The Bay Area Air Quality Management District (BAAQMD) expands our experience with the use of AOT, with lower PM2.5 and several isolated sub-basins. We have prepared daily maps of episodes in each region. We present also a sequence of increasingly detailed statistical models, AOT initially appears to contribute little information; however, inclusion of weather information reveals its utility. Lyapustin and Wang's MultiAngle Implementation of Atmospheric Correction (MAIAC) retrieval for AOT provided the most useful operational remote sensing information for these regions. It provides high (1-km) spatial resolution maps and a high percentage of availability. Empirical regression methods have found that random effects regression models (aka mixed effects models, ME) employing AOT provide good estimates of ground PM2.5 concentrations.Here, we attempt to extend these methods and evaluate the usefulness of AOT with greater physical analysis, based on DISCOVER-AQ4 experience.

Chatfield, Robert B.↗

DOE OSTI2021

Federal Oversight of Hydrogen Systems

The application of hydrogen as an energy carrier has been expanding into industrial and transportation sectors enabling sustainable energy resources and providing a zero-emission energy infrastructure. The hydrogen supply infrastructure includes processes from production and storage, to transportation and distribution, to end use. Each portion of the hydrogen supply infrastructure is regulated by international, federal, state, and local entities. Regulations are enforced by entities which provide guidance and updates as necessary. While energy sources such as natural gas are currently regulated via the Code of Federal Regulations and United States Code, there might be some ambiguity as to which regulations are applicable to hydrogen and where regulatory gaps may exist. This report contains an overview of the regulations that apply to hydrogen, and those that may indirectly cover hydrogen as an energy carrier participating in a sustainable zero emission global energy system. As part of this effort, the infrastructure of hydrogen systems and regulation enforcement entities are defined, and a visual map and reference table are developed. This regulatory map and table can be used to identify the boundaries of federal oversight for each component of the hydrogen supply value chain which includes production, storage, distribution, and use.

08 HYDROGEN↗

DOE OSTI2022

Mapping the Universe in hydrogen deuteride

Hydrogen deuteride (HD) is prevalent in a wide variety of astrophysical environments, and measuring its large-scale distribution at different epochs can, in principle, provide information about the properties of these environments. In this paper we explore the prospects for accessing this distribution using line-intensity mapping of emission from the lowest rotational transition in HD, focusing on observations of the epoch of reionization (z~6–10) and earlier. We find the signal from the epoch of reionization to be most promising, through cross correlations within existing [CII] intensity mapping surveys. While the signal we predict is out of reach for current-generation projects, planned future improvements should be able to detect reionization-era HD without any additional observations, and would help to constrain the properties of the star-forming galaxies thought to play a key role in reionization. We also investigate several avenues for measuring HD during “cosmic dawn” (z~10–30), a period in which HD could provide one of the only complementary observables to 21 cm intensity maps. We conclude that existing and planned facilities are poorly matched to the specifications desirable for a significant detection, though such a measurement may be achievable with sustained future effort. Finally, we explain why HD intensity mapping of the intergalactic medium during the cosmic dark ages (z≳30) appears to be out of reach of any conceivable experiment.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

State-to-State Molecular Reactions in the Ultracold Regime (Final Scientific Report)

We have achieved the proposed goal to experimentally probe the AB + CD and AB + C types of reactions with state-to-state resolution, which we also compared to advanced theoretical calculations to help elucidate the role of quantum mechanics in the processes of bond breakage and formation. Our approach uses reactants that are prepared at ultracold temperatures (< 1µK) such that the quantum effects of translational motion are an important factor. Specific example reactions, including the potassium-rubidium metathesis reaction KRb + KRb → K 2 + Rb 2 as well as the atom exchange reaction Rb + KRb → Rb2 + K, are chosen because the technology of quantum internal and motional state control of these types of molecules is particularly advanced. The results for the entire funding period are fruitful. For the majority of this grant, we have constructed a one-of-the-kind quantum degenerate gas apparatus that integrates ion detection and velocity map imaging capabilities, allowing us to explore the KRb + KRb → K 2 + Rb 2 bimolecular reaction in detail. Specifically, we first verified such a reaction indeed proceed at ultracold temperatures by direct detection of reaction products. We then mapped out the complete product state distribution, which was compared to a state-counting model based on statistical theory. Our results show an overall agreement with the statistical state counting model, but also reveal several deviating state-pairs. An exact quantum calculation for molecule-molecule collisions, that is needed to understand these deviations, is however beyond the current state-of-the-art. Beside scrutinizing the reaction products, we also directly observe the reaction intermediate complex, which was quite a surprise to us. The intermediate complexes are long-lived and can interact with the inferred light that we use to trap the ultracold gas. After molecule-molecule collisions, we then explored the more theoretically tractable Rb + KRb reaction, which is endothermic. Surprisingly, we observed an exceedingly long-lived KRb$^*_2$ collisional complexes, with our experimentally measured complex lifetime deviating from conventional theoretical calculations by five orders of magnitude. This discrepancy has motivated many explorations of possible underlying causes, though no model yet captures this phenomenon completely. In the final year and the work that continues today, we extend upon these atom-molecule collision experiments to explore the origin of the long-lived KRb$^*_2$ complex lifetime and develop means to control the outcome of the reaction complex. The 5-year funded work advanced our understanding of chemical reactions at the lowest possible temperatures and at the same time opened up many new questions that are beyond our initial imaginations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1993

AVIRIS calibration and application in coastal oceanic environments - Tracers of soluble and particulate constituents of the Tampa Bay coastal plume

AVIRIS is a testbed for future spacecraft sensors (such as HIRIS and MODIS) planned for the Earth Observing System. Model-derived absorption coefficients at 415 nm, a(415), and back-scattering coefficients at 671 nm, b sub b (671) for Tampa Bay waters were used to create images from AVIRIS data of the dissolved component of a(415) due to gelbstoff, a sub g (415), and salinity. Images of a sub g (415), salinity, and b sub b (671) were used to depict the distribution of dissolved and particulate constituents, respectively, for Tampa Bay plume during late, ebb-tidal conditions. Salinity covaried with a sub g (415), which provided a means of mapping salinity from the a sub g (415) imagery. The concentration of suspended particles, as inferred from b sub g (671), was extremely variable in the shallow regions where waves and currents interacted. Pollutants covarying with fresh water or suspended sediments can be mapped from a sub g (415) and b sub b (671) images, respectively.

Carder, K. L.↗

NASA NTRS1995

Mars Global Surveyor Mission: Environmental Assessment

This environmental assessment addresses the proposed action to complete the integration and launch the Mars Global Surveyor (MGS) spacecraft from Cape Canaveral Air Station (CCAS), Florida, during the launch window in November 1996. Mars Global Surveyor is part of the Solar System Exploration Program to the inner planets designed to maintain a sufficient level of scientific investigation and accomplishment so that the United States retains a leading position in solar system exploration through the end of the century. The Program consists of a specific sequence of missions, based on technological readiness, launch opportunities, rapidity of data return, and a balance of scientific disciplines. The purpose of the MGS mission would be to deliver a spacecraft platform to a low-altitude polar orbit around Mars where it would collect global observations of basic geological, geophysical, and climatological processes of the planet. To satisfy this purpose, the MGS mission would support a scientific set of objectives. Detailed global maps of surface topography, the distribution of minerals, the planet's mass, size, and shape, the characterization of Mars gravitational and magnetic fields, and the monitoring of global weather, collected over the period of one Martian year (about two Earth years), would help answer some of the questions about the evolution of Mars. Such an investigation would help scientists better understand the current state of water on Mars, the evolution of the planet's atmosphere, and the factors that led to major changes in the Martian climate. It would also provide much needed information on the magnetic field of Mars. Data collected from this mission would provide insight into the evolution of both Earth and the solar system, as well as demonstrate technological approaches that could be applicable to future Mars missions.

Source record↗

NASA NTRS1999

Water Ice Cloud Opacities and Temperatures Derived from the Viking IRTM Data Set

The degree to which water ice clouds play a role in the Mars climate is unknown. Latent heating of water ice clouds is small and since most hazes appeared to be thin (tau less than or = 1) their radiative effects have been neglected. Condensation likely limits the vertical extent of water vapor in the water column and a lowering of the condensation altitude, as seen in the northern spring and summer, could increase the seasonal exchange of water between the atmosphere and the surface. It has been suggested that water ice cloud formation is more frequent and widespread in the aphelic hemisphere (currently the northern). This may limit water to the northern hemisphere through greater exchange with the regolith and through restricted southward transport of water vapor by the Mars Hadley circulation. In addition, it has been suggested that water ice cloud formation also controls the vertical distribution of atmospheric dust in some seasons. This scavenging of dust may Continuing from the IRTM cloud maps, derived cloud opacities and cloud temperatures for several locations and seasons will be presented. Sensitivities to cloud particle sizes, surface temperature, and dust opacity will be discussed.

TamppariL. K.↗

NASA NTRS2019

CMB-HD: An Ultra-Deep, High-Resolution Millimeter-Wave Survey Over Half the Sky

A millimeter-wave survey over half the sky, that spans frequencies in the range of 30 to 350 GHz, and that is both an order of magnitude deeper and of higher-resolution than currently funded surveys would yield an enormous gain in understanding of both fundamental physics and astrophysics. By providing such a deep, high-resolution millimeter-wave survey (about 0.5 Karcmin noise and 15 arcsecond resolution at 150 GHz), CMB-HD will enable major advances.It will allow 1.) the use of gravitational lensing of the primordial microwave background to map the distribution of matter on small scales (k 10 hMpc1), which probes dark matter particle properties. It will also allow 2.) measurements of the thermal and kinetic Sunyaev-Zel'dovich effects on small scales to map the gas density and gas pressure profiles of halos over a wide field,which probes galaxy evolution and cluster astrophysics. In addition, CMB-HD would allow us to cross critical thresholds in fundamental physics: 3.) ruling out or detecting any new, light (< 0:1 eV), thermal particles, which could potentially be the dark matter, and 4.) testing a wide class of multi-field models that could explain an epoch of inflation in the early Universe. Such a survey would also 5.) monitor the transient sky by mapping the full observing region every few days,which opens a new window on gamma-ray bursts, novae, fast radio bursts, and variable active galactic nuclei. Moreover, CMB-HD would 6.) provide a census of planets, dwarf planets, andasteroids in the outer Solar System, and 7.) enable the detection of exo-Oort clouds around othersolar systems, shedding light on planet formation. The combination of CMB-HD with contemporaryground and space-based experiments will also provide powerful synergies. CMB-HD willdeliver this survey in 5 years of observing 20,000 square degrees, using two new 30-meter-classoff-axis cross-Dragone telescopes to be located at Cerro Toco in the Atacama Desert. The telescopeswill field about 2.4 million detectors (600,000 pixels) in total. The CMB-HD survey willbe made publicly available, with usability and accessibility a priority.

Sehgal, Neelima↗

NASA NTRS2017

Vascular Patterning Analysis by VESGEN 2D/3D with Bioinformatics: Updates for Rodent Tissues

Fractally branching vascular systems are a complex physiological requirement shared by humans with all higher terrestrial life forms, including other vertebrates, insects, and higher land plants. Vascular trees, networks, and tree-network composites are therefore mapped and quantified by the VESsel GENeration Analysis (VESGEN) software according to weighted physiological vascular rules that include vessel connectivity, tapering and bifurcational branching. According to fluid dynamics, successful vascular transport depends upon a complex distributed system of highly regulated laminar flow. VESGEN has elucidated changes in vascular patterning resulting from inflammatory, developmental and other signaling pathways within numerous tissues of major model organisms important for Space Biology, especially for rodents. Important early stage regenerative opportunities have been identified by VESGEN vascular analysis for visual impairments in the human retina, and is currently being used for research into astronaut visual and ocular disorders associated with long duration missions. The VESGEN 2D software is a mature, automated, widely published capability for which beta testing and public release by NASA is planned for the upcoming year. Early-stage capabilities for VESGEN 3D analysis are under development for the rodent retina and intestine as prototype tissues. A prototype VESGEN 2D Bioinformatics software capability has also been developed to associate phenotypic changes in molecular expression with vascular structure and function. By new VESGEN bioinformatic innovations, expression patterns of the genetic, transcriptional, protein and other markers for regulatory molecules such as vascular endothelial growth factor (VEGF) and their receptors, often indicators of tissue oxygenation status, are co-localized with alterations in vascular pattern. Biomarkers are therefore mapped and quantified as information dimensions directly correlated with the spatial dimensions of a vascular pattern. Further important technology innovations by NASA include substantial image segmentation advances for more automated binary extraction of the grayscale vascular patterns, together with informative associated image quality assessments. Vascular mapping and quantification capabilities for the rodent retina and intestine are illustrated for VESGEN 2D, along with technology status reports on VESGEN 3D and Bioinformatic capabilities. Research partially supported by Ames Center Innovation Awards.

Parsons-Wingerter, P.↗

NASA NTRS2016

Erasing the Milky Way: New Cleaning Technique Applied to GBT Intensity Mapping Data

We present the first application of a new foreground removal pipeline to the current leading HI intensity mapping dataset, obtained by the Green Bank Telescope (GBT). We study the 15- and 1-h field data of the GBT observations previously presented in Masui et al. (2013) and Switzer et al. (2013), covering about 41 square degrees at 0.6 less than z is less than 1.0, for which cross-correlations may be measured with the galaxy distribution of the WiggleZ Dark Energy Survey. In the presented pipeline, we subtract the Galactic foreground continuum and the point source contamination using an independent component analysis technique (fastica), and develop a Fourier-based optimal estimator to compute the temperature power spectrum of the intensity maps and cross-correlation with the galaxy survey data. We show that fastica is a reliable tool to subtract diffuse and point-source emission through the non-Gaussian nature of their probability distributions. The temperature power spectra of the intensity maps is dominated by instrumental noise on small scales which fastica, as a conservative sub-traction technique of non-Gaussian signals, can not mitigate. However, we determine similar GBT-WiggleZ cross-correlation measurements to those obtained by the Singular Value Decomposition (SVD) method, and confirm that foreground subtraction with fastica is robust against 21cm signal loss, as seen by the converged amplitude of these cross-correlation measurements. We conclude that SVD and fastica are complementary methods to investigate the foregrounds and noise systematics present in intensity mapping datasets.

Wolz, L.↗

DOE OSTI2026

Modeling of injected current stream-induced 3D perturbations in local helicity injection plasmas

Solenoid-free tokamak startup techniques are essential for spherical tokamaks and offer a pathway to cost reduction and design simplification in fusion energy systems. Local helicity injection (LHI) is one such approach, employing compact edge current sources to drive open field line current that initiates and sustains tokamak plasmas. The recently commissioned Pegasus-III Experiment provides a platform for advancing this and other solenoid-free startup methods. This study investigates the effect of LHI on magnetic topology in Pegasus-III plasmas. A helical filament model represents the injected current, and the linear plasma response to its three-dimensional field is calculated with M3D-C1. Poincaré mapping reveals substantial flux surface degradation in all modeled cases. The onset of overlapping magnetic structures and large-scale surface deformation begins near Ψ N ≈ 0.37, indicating a broad region of perturbed topology extending toward the edge. In rotating plasmas, both single-fluid and two-fluid models exhibit partial screening of the n = 1 perturbation, with two-fluid calculations showing stronger suppression near the edge. In contrast, the absence of rotation leads to strong resonant field amplification in the single-fluid case, while the two-fluid case with zero electron rotation mitigates this amplification and preserves edge screening. Magnetic probe measurements indicate that modeling the stream with spatial spreading—representing distributed current and/or oscillatory motion—better reproduces measured magnetic power profiles than a rigid filament model. The results underscore the role of rotation and two-fluid physics in screening stream perturbations and point to plasma flow measurements and refined stream models as key steps toward improving predictive fidelity.

Schaefer, Carolyn E. [Univ. of Wisconsin, Madison,↗

DOE OSTI2020

Physical, numerical, and computational challenges of modeling neutrino transport in core-collapse supernovae

The proposal that core collapse supernovae are neutrino driven is still the subject of active investigation more than 50 years after the seminal paper by Colgate and White. The modern version of this paradigm, which we owe to Wilson, proposes that the supernova shock wave is powered by neutrino heating, mediated by the absorption of electron-flavor neutrinos and antineutrinos emanating from the proto-neutron star surface, or neutrinosphere. Neutrino weak interactions with the stellar core fluid, the theory of which is still evolving, are flavor and energy dependent. The associated neutrino mean free paths extend over many orders of magnitude and are never always small relative to the stellar core radius. Thus, neutrinos are never always fluid like. Instead, a kinetic description of them in terms of distribution functions that determine the number density of neutrinos in the six-dimensional phase space of position, direction, and energy, for both neutrinos and antineutrinos of each flavor, or in terms of angular moments of these neutrino distributions that instead provide neutrino number densities in the four-dimensional phase-space subspace of position and energy, is needed. In turn, the computational challenge is twofold: (i) to map the kinetic equations governing the evolution of these distributions or moments onto discrete representations that are stable, accurate, and, perhaps most important, respect physical laws such as conservation of lepton number and energy and the Fermi–Dirac nature of neutrinos and (ii) to develop efficient, supercomputer-architecture-aware solution methods for the resultant nonlinear algebraic equations. In this review, we present the current state of the art in attempts to meet this challenge.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Detecting deviations from Gaussianity in high-redshift CMB lensing maps

ABSTRACT While the probability density function of the cosmic microwave background (CMB) convergence field approximately follows a Gaussian distribution, primordial non-Gaussianities, and small contributions from structures at low redshifts make the overall distribution slightly non-Gaussian. Some of the late-time component can be modelled using the distribution of galaxies and subtracted off from the original CMB lensing map to produce a map of matter distribution at high redshifts. Using this high-redshift mass map, we are able to directly study the early phases of structure formation. In this work, we forecast the detectability of signatures of non-Gaussianity due to non-linear structure formation at z > 1.2. Assuming the optimal case of no systematics, we find that it is challenging to detect such signatures in current surveys, but future experiments such as the deep field of CMB-S4 will be able to make detections of ∼7σ.

Astronomy & Astrophysics↗

DOE OSTI2024

Enhanced Bottom Anode Monitoring in DC Electric Arc Furnaces Using Fiber-Optic Sensors

A pin style bottom anode employs conductive steel rods that serve as the pathway for the high electrical power through rammed refractory at the bottom of a DC Electric Arc Furnace (EAF). Anode wear during operation is important to monitor, as anode replacement is expensive and impacts EAF productivity. Liquid steel penetration into the un-sintered refractory layer can result from rapid electrical power ramp-up, dips in furnace temperature, or operating the anode for too long between EAF campaigns. In extreme cases, the liquid steel may penetrate the bottom of the furnace when anode wear progresses too close to the bottom shell, which is extremely dangerous and must be avoided. The current state of the art for monitoring bottom anode wear employs thermocouples imbedded in the anode pins at points in the anode. However, this approach is not sensitive enough to detect localized damage to the anode, especially when cracking occurs. Here, the present work utilizes fiber optic sensors to monitor the health of the anode, by creating a real-time spatially distributed temperature map of the anode. Unlike the traditional thermocouples, these sensors can be mounted at significantly greater depths, provide distributed temperature measurements, and can withstand temperatures of up to 900°C. Additionally, they are able to perform temperature measurements with a spatial resolution of 1.3 mm at a 5 Hz acquisition rate, providing unprecedented high-density real time monitoring of anode health and increasing the efficiency, and safety of EAF operation.

Bottom Anode↗

NASA NTRS1997

MODIS Snow and Ice Products from the NSIDC DAAC

The National Snow and Ice Data Center (NSIDC) Distributed Active Archive Center (DAAC) provides data and information on snow and ice processes, especially pertaining to interactions among snow, ice, atmosphere and ocean, in support of research on global change detection and model validation, and provides general data and information services to cryospheric and polar processes research community. The NSIDC DAAC is an integral part of the multi-agency-funded support for snow and ice data management services at NSIDC. The Moderate Resolution Imaging Spectroradiometer (MODIS) will be flown on the first Earth Observation System (EOS) platform (AM-1) in 1998. The MODIS Instrument Science Team is developing geophysical products from data collected by the MODIS instrument, including snow and ice products which will be archived and distributed by NSIDC DAAC. The MODIS snow and ice mapping algorithms will generate global snow, lake ice, and sea ice cover products on a daily basis. These products will augment the existing record of satellite-derived snow cover and sea ice products that began about 30 years ago. The characteristics of these products, their utility, and comparisons to other data set are discussed. Current developments and issues are summarized.

Scharfen, Greg R.↗

NASA NTRS1991

Mesoscale and large-scale variability of the Antarctic circumpolar current

This investigation of the physical oceanography of the Southern Ocean will carry out two parallel efforts during the years preceding the launch of TOPEX/POSEIDON. First, the Geosat data will be used to develop a preliminary descriptive picture of the mesoscale and large-scale, low-frequency surface circulation of the Southern Ocean. Some of this analysis of Geosat data has already begun. For example, as a measure of the geographical distribution of mesoscale variability, a color-coded map of the standard deviation of sea level from two years of Geosat data is shown. Efforts are presently under way to investigate the seasonal and year-to-year variability of this mesoscale energy. The data are also being used to generate low-pass filtered fields of sea level from which the temporal evolution of large-scale variability in the Southern Ocean may be investigated. The second parallel effort is the development and test of modeling and data assimilation techniques that will later be applied to TOPEX/POSEIDON data during the postlaunch phase. One objective of the modeling and data assimilation is to investigate the relation between mesoscale sea level variations and eddy flux in the Southern Ocean. Uncertainties in present estimates of the various components of meridional oceanic heat transport are large. The evidence presented indicates that the very energetic mesoscale variability in the ACC apparently accounts for much of the estimated 0.45x10(exp 15) watts of poleward heat transport across the ACC required to balance the heat budget. Eddy variability is strongly coherent vertically in the ACC, at least in the vicinity of Drake Passage where nearly all of the historical in situ data have been collected.

Chelton, Dudley B.↗

NASA NTRS1974

Energy and pitch angle distributions for auroral ions using the current sheet acceleration model

Using a dipole-plus-tail magnetic field model, H(+), He(+2), and O(+6) ions are followed numerically, backward in time, from an output plane perpendicular to the axis of the geomagnetic tail, to their point of entrance to the magnetosphere as solar wind particles in the magnetosheath. An adiabatic or guiding center approximation is used in regions where the particles do not interact directly with the current sheet. A Maxwellian distribution with bulk flow is assumed for solar wind particles in the magnetosheath. Bulk velocity, density, and temperature along the magnetopause are taken from the fluid calculations of Spreiter. Using Liouville's theorem, and varying initial conditions at the output plane, the distribution function is found as a function of energy and pitch angle at the output plane. These results are then mapped to the auroral ionosphere using guiding center theory.

Jaeger, E. F.↗