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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Assessing the impact of uniform rotation on the structure of neutron stars

Driven by recent laboratory experiments and astronomical observations, significant advances have deepened our understanding of neutron-star physics. NICER's Pulse Profile Modeling has refined our knowledge of neutron star masses and radii, while gravitational-wave detections have revealed key insights into the structure of neutron stars. Particularly relevant is the extraction of the tidal deformability by the LIGO-Virgo collaboration and the most recent determination of stellar radii by NICER, both suggesting a relatively soft equation of state (EOS) at intermediate densities. Additionally, measurements from the PREX collaboration and from pulsar timing suggest instead that the EOS is stiff in the vicinity of saturation density and at the highest densities accessible to date. But how stiff can the EOS be at these very high densities? Recent events featuring compact objects near the “lower mass gap” have raised questions about the existence of very massive neutron stars. Motivated by this finding and in light of new refinements to theoretical models, we explore the possibility that these massive objects may indeed be rapidly rotating neutron stars. Here, we explore how rotation affects both the maximum neutron star mass and their associated radii, and discuss the implications they may have on the equation of state.

Equations of state of nuclear matter↗
DOE OSTI2021

Ground-state properties of light 4 n self-conjugate nuclei in ab initio no-core Monte Carlo shell model calculations with nonlocal N N interactions

We report J π = 0 + ground-state energies and point-proton radii of 4 He, 8 Be, 12 C, 16 O, and 20 Ne nuclei calculated by the ab initio no-core Monte Carlo shell model with the JISP16 and Daejeon16 nonlocal NN interactions. Ground-state energies are obtained in the basis spaces up to seven oscillator shells (N shell =7) with several oscillator energies (ℏω) around the optimal oscillator energy for the convergence of ground-state energies. These energy eigenvalues are extrapolated to obtain estimates of converged ground-state energies in each basis space using energy variances of computed energy eigenvalues. We further extrapolate these energy-variance-extrapolated energies obtained in the finite basis spaces to infinite basis-space results with an empirical exponential form. This form features a dependence on the basis-space size but is independent of the value of ℏω used for the harmonic-oscillator basis functions. Point-proton radii for these states of atomic nuclei are also calculated following techniques employed for the energies. From these results, it is found that the Daejeon16 NN interaction provides good agreement with experimental data up to approximately 16 O, while the JISP16 NN interaction provides good agreement with experimental data up to approximately 12 C. Beyond these nuclei, the interactions produce overbinding accompanied by radii that are too small. These findings suggest and encourage further revisions of nonlocal NN interactions towards the investigation of nuclear structure in heavier-mass regions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Femtoscopic correlations of identical charged pions and kaons in $pp$ collisions at $\sqrt{s}$ = 13 TeV with event-shape selection

Collective behavior has been observed in high-energy heavy-ion collisions for several decades. Collectivity is driven by the high particle multiplicities that are produced in these collisions. At the CERN Large Hadron Collider (LHC), features of collectivity have also been seen in high-multiplicity proton-proton collisions that can attain particle multiplicities comparable to peripheral Pb-Pb collisions. One of the possible signatures of collective behavior is the decrease of femtoscopic radii extracted from pion and kaon pairs emitted from high-multiplicity collisions with increasing pair transverse momentum. This decrease can be described in terms of an approximate transverse mass scaling. In the present work, femtoscopic analyses are carried out by the ALICE Collaboration on charged pion and kaon pairs produced in pp collisions at $\sqrt{s}$=13TeV from the LHC to study possible collectivity in pp collisions. The event-shape analysis method based on transverse sphericity is used to select for spherical versus jetlike events, and the effects of this selection on the femtoscopic radii for both charged pion and kaon pairs are studied. This is the first time this selection method has been applied to charged kaon pairs. An approximate transverse-mass scaling of the radii is found in all multiplicity ranges studied when the difference in the Lorentz boost for pions and kaons is taken into account. This observation does not support the hypothesis of collective expansion of hot and dense matter that should only occur in high-multiplicity events. A possible alternate explanation of the present results is based on a scenario of common emission conditions for pions and kaons in pp collisions for the multiplicity ranges studied.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Atacama Cosmology Telescope: Modeling the gas thermodynamics in BOSS CMASS galaxies from kinematic and thermal Sunyaev-Zel’dovich measurements

The thermal and kinematic Sunyaev-Zel'dovich effects (tSZ, kSZ) probe the thermodynamic properties of the circumgalactic and intracluster medium (CGM and ICM) of galaxies, groups, and clusters, since they are proportional, respectively, to the integrated electron pressure and momentum along the line-of-sight. We present constraints on the gas thermodynamics of CMASS galaxies in the Baryon Oscillation Spectroscopic Survey (BOSS) using new measurements of the kSZ and tSZ signals obtained in a companion paper. Combining kSZ and tSZ measurements, we measure within our model the amplitude of energy injection $\epsilon M_\star c^2$, where $M_\star$ is the stellar mass, to be $\epsilon=(40\pm9)\times10^{-6}$, and the amplitude of the non-thermal pressure profile to be $\alpha_{\rm Nth}<0.2$ (2$\sigma$), indicating that less than 20% of the total pressure within the virial radius is due to a non-thermal component. We estimate the effects of including baryons in the modeling of weak-lensing galaxy cross-correlation measurements using the best fit density profile from the kSZ measurement. Our estimate reduces the difference between the original theoretical model and the weak-lensing galaxy cross-correlation measurements in arXiv:1611.08606 by half, but does not fully reconcile it. Comparing the kSZ and tSZ measurements to cosmological simulations, we find that they under predict the CGM pressure and to a lesser extent the CGM density at larger radii. This suggests that the energy injected via feedback models in the simulations that we compared against does not sufficiently heat the gas at these radii. We do not find significant disagreement at smaller radii. These measurements provide novel tests of current and future simulations. Here, this work demonstrates the power of joint, high signal-to-noise kSZ and tSZ observations, upon which future cross-correlation studies will improve.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Numerical relativity simulations of prompt collapse mergers: Threshold mass and phenomenological constraints on neutron star properties after GW170817

We determine the threshold mass for prompt (no bounce) black hole formation in equal-mass neutron star (NS) mergers using a new set of 227 numerical relativity simulations. We consider 23 phenomenological and microphysical finite-temperature equations of state (EOS), including models with hyperons and first-order phase transitions to deconfined quarks. We confirm the existence of EOS-insensitive relations between the threshold mass, binary tidal parameter at the threshold (Λth), maximum mass of nonrotating NSs, and radii of reference mass NSs. We combine the EOS-insensitive relations, phenomenological constraints on NS properties, and observational data from GW170817 to derive an improved lower limit on radii of maximum mass and a 1.6 M ⊙ NS of 9.81 and 10.90 km, respectively. We also constrain the radius and quadrupolar tidal deformability (Λ) of a 1.4 M ⊙ NS to be larger than 10.74 km and 172, respectively. We consider uncertainties in all independent parameters—fitting coefficients as well as GW170817 masses while reporting the range of radii constraints. We discuss an approach to constrain the upper as well as lower limit of NS maximum mass using future binary NS detections and their identification as prompt or delayed collapse. With future observations, it will be possible to derive even tighter constraints on the properties of matter at and above nuclear density using the method proposed in this work.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Ultracompact hybrid stars consistent with multimessenger astrophysics

In this work, we consider the consequences of phase transition in dense QCD on the properties of compact stars and implications for the observational program in gravitational wave and x-ray astrophysics. The key underlying assumption of our modeling is a strong first-order phase transition past the point where the hadronic branch of compact stars reaches the two-solar mass limit. Furthermore, our analysis predicts ultracompact stars with very small radii—in the range of 6–9 km—living on compact star sequences that are entirely consistent with the current multimessenger data. We show that sequences featuring two-solar mass hadronic stars consistent with radio-pulsar observations are also consistent with the inferences of large radii for massive neutron stars by NICER x-ray observations of neutron stars and the small radii predicted by gravitational waves analysis of the binary neutron star inspiral event GW170817 for our models that feature a strong first-order QCD phase transition.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Tomography of ultrarelativistic nuclei with polarized photon-gluon collisions

A linearly polarized photon can be quantized from the Lorentz-boosted electromagnetic field of a nucleus traveling at ultrarelativistic speed. When two relativistic heavy nuclei pass one another at a distance of a few nuclear radii, the photon from one nucleus may interact through a virtual quark-antiquark pair with gluons from the other nucleus, forming a short-lived vector meson (e.g., ρ 0 ). In this experiment, the polarization was used in diffractive photoproduction to observe a unique spin interference pattern in the angular distribution of ρ 0 → π + π – decays. The observed interference is a result of an overlap of two wave functions at a distance an order of magnitude larger than the ρ0 travel distance within its lifetime. The strong-interaction nuclear radii were extracted from these diffractive interactions and found to be 6.53 ± 0.06 fm ( 197 Au) and 7.29 ± 0.08 fm ( 238 U), larger than the nuclear charge radii. The observable is demonstrated to be sensitive to the nuclear geometry and quantum interference of nonidentical particles.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Project Title: Demonstration High Temperature Superconducting NonPlanar Stellarator Magnet with Advanced Manufactured Assemblies

This is the final report for the project “Demonstration High Temperature Superconducting Non- Planar Stellarator Magnet with Advanced Manufactured Assemblies”, funded by DOE, and performed by Type One Energy from September, 2020, to March 2024 involving the Fusion Technology Institute at the University of Wisconsin–Madison, the Plasma Science and Fusion Center (PSFC) at the Massachusetts Institute of Technology (MIT) and Commonwealth Fusion Systems (CFS) to design and fabricate the first non-planar HTS (REBCO) coil for a high-field stellarator based on the SPARC tokamak’s VIPER cable concept. Stellarators at high fields make high-temperature superconducting magnets necessary for a compact fusion device. But the asymmetric and non-planar nature of its components, especially the magnets make it difficult for scalable producibility. To address these challenges, two promising technologies have emerged: advanced manufacturing (AM) for the supporting plates for forming the magnets, and high-temperature superconducting (HTS) cables inside the plates. AM has advanced enough to produce stellarator components with the necessary geometric complexity, size, and the precision, leading to potentially significant reductions in production time, cost, and waste. The cost of HTS tape has decreased dramatically, and progress in HTS planar magnet development has reached a point where it can be proposed for application to complex 3D non-planar magnets. The main objective of this project is to develop, demonstrate and pre-commercialize a novel, non-planar HTS coil shape that remains superconducting to achieve production scalable reductions in time and cost and performance. The proposed technology is based on the novel concept of a precision sub-scale HTS nonplanar coil assembly. This project focuses on the design, fabrication, material optimization of cable design, and validation and demonstration of the high current carrying capability of superconducting magnets and their support in a complex 3D shape needed for application to stellarator magnetic plasma confinement. The specific objectives of this research program include: (1) The successful application of metal AM to build a precision sub-scale HTS nonplanar coil, (2) An HTS cable and cross-section design that can conform to the required nonplanar coil shape (bend radii as tight as 10-cm) and remains superconducting at an engineering current density of 1.35 kA/cm 2 at 77 K and 1 tesla at the conductor (5 kA in the cable). To achieve the above challenging goals, we have formed a multidisciplinary research team consisting of members from Type One Energy and UW-Madison, MIT PSFC and CFS with complementary skills and strong facilities. The team worked collaboratively on fundamental and applied research on the following three major technical areas: (1) Design, fabrication, and optimization of non-planar HTS Cable The ultimate goal of the project is to determine if commercial REBCO tapes and additive manufacturing can be used to fabricate high field (≥ 10T) non-planar coils with tight bending radii (≃ 100mm) and with a degradation of the critical current (Ic) smaller than 20% with respect to the expected performance. We started with shorter length cable to evaluate the scalability of the production process and eventually reached multiple turns for higher magnetic fields. Our findings suggest that a stellarator coil system of a relevant size, characterized by its asymmetric and non-planar components, can be fabricated using a formed cable in plate method. This system can be simulated using a large-scale modeling approach. The use of hybrid modeling 3 techniques will be pivotal in reducing the complexity of the model and in assessing expected performance in designs. (2) Modeling and simulation of the non-planar HTS Cable Multiphysics simulations are performed using the commercial software and are carried out in self-field conditions, involving 2D and 3D models and twisted around one slot of twist-pitched VIPER cable. Multiphysics simulations are mainly focused on the coil for the critical current evaluation, the magnetic field map, self-Lorentz forces and mechanical, and magnetothermal behavior and the quench dynamics. The detailed model and prediction of the superconducting performance of a stellarator-relevant demonstration cable from numerical simulations supports the results from the actual testing backing the results. A detailed description and results are provided in the later sections. (3) Design, fabrication, and optimization of support for the non-planar HTS Cable The team developed an additive manufactured (AM) coil positioning plate that formed into the required non-planar geometry (with bend radii as tight as 10-cm) and to acceptable tolerances required for a stellarator magnet: (+0.25-mm from ideal on dimensions of coil positioning plates and up to +1-mm from ideal for position of wound coil). The plate materials is also included in this selection process from fabrication and 3D printing perspective and commensurate with eventual application to a fusion reactor. From the cost effectiveness point of view, the HTS coil and plate has the potential to cost less than that made in conventional methods with less waste (<75% waste) reducing time (<50%) and cost (<50%), especially as the AM field matures. The application of advanced manufacturing in the construction of the support plates will also lead to cost reduction, as the cables can be easily replaced, thereby making the assembly modular. With such high primary cost and time savings, high current densities and magnetic field, the funded R&D work has validated the designs, proven the feasibility, and characterized the performance of the HTS coil and plate assembly, paving the way for a relevant-size stellarator coil system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Exploring Whether Super-puffs can be Explained as Ringed Exoplanets

An intriguing, growing class of planets are the “super-puffs,” objects with exceptionally large radii for their masses and thus correspondingly low densities (≲0.3 g cm{sup −3}). Here we consider whether they could have large inferred radii because they are in fact ringed. This would naturally explain why super-puffs have thus far only shown featureless transit spectra. We find that this hypothesis can work in some cases but not all. The close proximity of the super-puffs to their parent stars necessitates rings with a rocky rather than icy composition. This limits the radius of the rings, and makes it challenging to explain the large size of Kepler 51b, 51c, 51d, and 79d unless the rings are composed of porous material. Furthermore, the short tidal locking timescales for Kepler 18d, 223d, and 223e mean that these planets may be spinning too slowly, resulting in a small oblateness and rings that are warped by their parent star. Kepler 87c and 177c have the best chance of being explained by rings. Using transit simulations, we show that testing this hypothesis requires photometry with a precision of somewhere between ∼10 ppm and ∼50 ppm, which roughly scales with the ratio of the planet and star’s radii. We conclude with a note about the recently discovered super-puff HIP 41378f.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

On the Diversity of Asymmetries in Gapped Protoplanetary Disks

Protoplanetary disks with large inner dust cavities are thought to host massive planetary or substellar companions. These disks show asymmetries and rings in the millimeter continuum caused by dust trapping in pressure bumps and potentially vortices or horseshoes. The origin of the asymmetries and their diversity remains unclear. We present a comprehensive study of 16 disks for which the gas surface density profile has been constrained by CO isotopologue data. First, we compare the azimuthal extents of the dust continuum profiles with the local gas surface density in each disk and find that the asymmetries correspond to higher Stokes numbers or low gas surface density. We discuss which asymmetric structures can be explained by a horseshoe, a vortex, or spiral density waves. Second, we reassess the gas gap radii from the {sup 13}CO maps, which are about a factor of 2 smaller than the dust ring radii, suggesting that the companions in these disks are in the brown dwarf (∼15–50 M {sub Jup}) or super-Jovian (∼3–15 M {sub Jup}) mass regime on eccentric orbits. This is consistent with the estimates from contrast curves on companion mass limits. These curves rule out (sub)stellar companions (q > 0.05) for the majority of the sample at the gap location, but it remains possible at even smaller radii. Third, we find that spiral arms in scattered-light images are primarily detected around high-luminosity stars with disks with wide gaps, which can be understood by the dependence of the spiral arm pitch angle on disk temperature and companion mass.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

The SDSS-HET Survey of Kepler Eclipsing Binaries. A Sample of Four Benchmark Binaries

The purpose of this work is to extend a sample of accurately modeled, benchmark-grade eclipsing binaries (EBs) with accurately determined masses and radii. We select four "well-behaved" Kepler binaries, KIC 2306740, KIC 4076952, KIC 5193386 and KIC 5288543, each with at least eight double-lined spectra from the Apache Point Observatory Galactic Evolution Experiment instrument that is part of the Sloan Digital Sky Surveys III and IV, and from the Hobby–Eberly High Resolution Spectrograph. We obtain masses and radii with uncertainties of 2.5% or less for all four systems. Three of these systems have orbital periods longer than 9 days, and thus populate an undersampled region of the parameter space for extremely well-characterized detached EBs. We compare the derived masses and radii against MESA MIST isochrones to determine the ages of the systems. All systems were found to be coeval, showing that the results are consistent across MESA MIST and PHOEBE .

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Stellar Characterization and Radius Inflation of Hyades M-dwarf Stars from the APOGEE Survey

We present a spectroscopic analysis of a sample of 48 M-dwarf stars (0.2 M ⊙ < M < 0.6 M ⊙ ) from the Hyades open cluster using high-resolution H-band spectra from the Sloan Digital Sky Survey/Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey. Our methodology adopts spectrum synthesis with LTE MARCS model atmospheres, along with the APOGEE Data Release 17 line list, to determine effective temperatures, surface gravities, metallicities, and projected rotational velocities. The median metallicity obtained for the Hyades M dwarfs is [M/H] = 0.09 ± 0.03 dex, indicating a small internal uncertainty and good agreement with optical results for Hyades red giants. Overall, the median radii are larger than predicted by stellar models by 1.6% ± 2.3% and 2.4% ± 2.3%, relative to a MIST and DARTMOUTH isochrone, respectively. We emphasize, however, that these isochrones are different, and the fractional radius inflation for the fully and partially convective regimes have distinct behaviors depending on the isochrone. Using a MIST isochrone there is no evidence of radius inflation for the fully convective stars, while for the partially convective M dwarfs the radii are inflated by 2.7% ± 2.1%, which is in agreement with predictions from models that include magnetic fields. For the partially convective stars, rapid rotators present on average higher inflation levels than slow rotators. The comparison with SPOTS isochrone models indicates that the derived M-dwarf radii can be explained by accounting for stellar spots in the photosphere of the stars, with 76% of the studied M dwarfs having up to 20% spot coverage, and the most inflated stars with ~20%–40% spot coverage.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Can Neutron Star Tidal Effects Obscure Deviations from General Relativity?

Abstract One of the main goals of gravitational-wave astrophysics is to study gravity in the strong-field regime and constrain deviations from general relativity (GR). Any such deviation affects not only binary dynamics and gravitational-wave emission but also the structure and tidal properties of compact objects. In the case of neutron stars, masses, radii, and tidal deformabilities can all differ significantly between different theories of gravity. Currently, the measurement uncertainties in neutron star radii and tidal deformabilities are quite large. However, much less is known about how the large uncertainty in the nuclear equation of state (EOS) might affect tests of GR using binary neutron star mergers. Conversely, using the wrong theory of gravity might lead to incorrect constraints on the nuclear EOS. Here, we study this problem within scalar–tensor (ST) theory. We apply the recently derived ℓ = 2 tidal Love numbers in this theory to parameter estimation of GW170817. Correspondingly, we test if physics beyond GR could bias measurements of the nuclear EOS and neutron star radii. We find that parameter inference for both the GR and ST cases returns consistent component masses and tidal deformabilities. The radius and the EOS posteriors, however, differ between the two theories, but neither is excluded by current observational limits. This indicates that measurements of the nuclear EOS may be biased and that deviations from GR could go undetected when analyzing current binary neutron star mergers.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1971

The solar envelope

Processes which occur within the region between approximately 2 solar radii and 25 solar radii, which is called the solar envelope and the effect on the solar wind as seen at 1 AU are discussed. In the envelope the wind speed becomes supersonic and super-Alfvenic, the magnetic energy density is larger than the flow energy density, and the magnetic energy density is much larger than the thermal energy density. Large azimuthal gradients in the bulk speed are expected in the envelope, but the stream interactions near the outer edge of the envelope are probably relatively small. Cosmic ray observations suggest the presence of hydromagnetic waves in the envelope. The collisionless damping of such waves could heat protons out to approximately 25 solar radii and thereby cause an increase in V and T sub p consistent with the observed T sub p -V relation. A mechanism which couples protons and electrons would also heat and accelerate the wind. Alfven waves can accelerate the wind in the envelope without necessarily causing heating of protons; the Lorentz force might have a similar effect.

Burlaga, L. F.↗
NASA NTRS1972

The configuration of the geomagnetic field.

Spherical harmonic representations of the geomagnetic field based on ground-based and low-altitude spacecraft measurements adequately describe the field within several earth radii of the earth's surface. As the internal field decreases with increasing distance from the earth, external field sources become relatively more important. In the region of 3 to 6 earth radii, magnetospheric plasma inflates the field lines and decreases the field strength by an amount which is typically 10's of gammas and occasionally 100's of gammas. At greater distances on the day side of the earth, the solar wind compresses the field and produces equatorial field strengths of approximately 60 gammas at 10 earth radii. Field lines near the magnetopause intersect the earth at approximately 78 deg latitude in the sunward hemisphere. The solar wind drags high latitude field lines away from the earth in the night hemisphere forming the geomagnetic tail and neutral sheet. Asymmetric field inflation in the magnetosphere occurs during magnetic disturbances with the largest effects concentrated in the evening quadrant. The tail configuration can deviate substantially from the average configuration during magnetic disturbances.

Fairfield, D. H.↗
NASA NTRS1972

Large-scale coherence and high velocities of the earth's bow shock on February 12, 1969.

The earth's bow shock exhibited a clean laminar profile at low Mach number as it crossed and recrossed Ogo 5, Heos 1, and Explorer 33 on February 12, 1969. The approximate 120 earth radii distance between Heos and Explorer during one set of crossings indicated the abrupt character of the laminar shock 'front' and the absence of magnetosheath turbulence both in the dayside hemisphere above the ecliptic and in the flank of the shock 75 earth radii behind the earth and below the ecliptic. The abruptness of the shock and coplanarity of the loci of Ogo and Heos with the local shock normal permit the most reliable estimates yet obtained of shock velocities along the normal. These mean velocities ranged from 11 to at least 100 km/sec over distances of 2-7 earth radii.

Greenstadt, E. W.↗
NASA NTRS1973

Hydrogen and hydrocarbon diffusion flames in a weightless environment

An experimental investigation was performed on laminar hydrogen-, ethylene-, and propylene-air diffusion burning in a weightless environment. The flames burned on nozzles with radii ranging from 0.051 to 0.186 cm with fuel Reynolds numbers at the nozzle exit from 9 to 410. Steady-state diffusion flames existed in a weightless environment for all the fuels tested. A correlation was obtained for their axial length as a function of Schmidt number, Reynolds numbers, and stoichiometric mole fraction. The maximum flame radii were correlated with the ratio of nozzle radius to average fuel velocity. The flames of ethylene and propylene on nozzles with radii 0.113 or larger appeared to be constantly changing color and/or length throughout the test. No extinguishment was observed for any of the gases tested within the 2.2 seconds of weightlessness.

Haggard, J. B., Jr.↗
NASA NTRS1972

Plasma convection in the vicinity of the geosynchronous orbit.

An analytic function respresenting the quiet time magnetospheric electric field has been constructed with which it is possible to compute complete particle trajectories in a fraction of a second. The function was determined by a trial-and-error procedure such that it provides reasonable explanations for the characteristics of the plasma observed by the geosynchronous satellite ATS 5. It is believed that the model field is usefully accurate within the region of 5 to 7 earth radii on the dawn side of the magnetosphere and 5 to 10 earth radii on the dusk side. At a fixed distance of 6.7 earth radii the model field peaks at a value of 1.2 mV/m near local midnight and is at a minimum of 0.04 mV/m near 1900 LT.

Mcilwain, C. E.↗