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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS2013

Time-Dependent Photoionization of Gaseous Nebulae: The Pure Hydrogen Case

We study the problem of time-dependent photoionization of low density gaseous nebulae subjected to sudden changes in the intensity of ionizing radiation. To this end, we write a computer code that solves the full timedependent energy balance, ionization balance, and radiation transfer equations in a self-consistent fashion for a simplified pure hydrogen case. It is shown that changes in the ionizing radiation yield ionizationthermal fronts that propagate through the cloud, but the propagation times and response times to such fronts vary widely and nonlinearly from the illuminated face of the cloud to the ionization front (IF). IFthermal fronts are often supersonic, and in slabs initially in pressure equilibrium such fronts yield large pressure imbalances that are likely to produce important dynamical effects in the cloud. Further, we studied the case of periodic variations in the ionizing flux. It is found that the physical conditions of the plasma have complex behaviors that differ from any steady-state solution. Moreover, even the time average of ionization and temperature is different from any steady-state case. This time average is characterized by overionization and a broader IF with respect to the steady-state solution for a mean value of the radiation flux. Around the time average of physical conditions there is a large dispersion in instantaneous conditions, particularly across the IF, which increases with the period of radiation flux variations. Moreover, the variations in physical conditions are asynchronous along the slab due to the combination of nonlinear propagation times for thermal frontsIFs and equilibration times.

Seyfert↗
NASA NTRS2018

HZETRN Radiation Transport Validation Using Balloon-Based Experimental Data

The deterministic radiation transport code HZETRN (High charge (Z) and Energy TRaNsport) was developed by NASA to study the effects of cosmic radiation on astronauts and instrumentation shielded by various materials. This work presents an analysis of computed differential flux from HZETRN compared with measurement data from three balloon-based experiments over a range of atmospheric depths, particle types, and energies. Model uncertainties were quantified using an interval-based validation metric that takes into account measurement uncertainty both in the flux and the energy at which it was measured. Average uncertainty metrics were computed for the entire dataset as well as subsets of the measurements (by experiment, particle type, energy, etc.) to reveal any specific trends of systematic over- or under-prediction by HZETRN. The distribution of individual model uncertainties was also investigated to study the range and dispersion of errors beyond just single scalar and interval metrics. The differential fluxes from HZETRN were generally well-correlated with balloon-based measurements; the median relative model difference across the entire dataset was determined to be 30%. The distribution of model uncertainties, however, revealed that the range of errors was relatively broad, with approximately 30% of the uncertainties exceeding ± 40%. The distribution also indicated that HZETRN systematically under-predicts the measurement dataset as a whole, with approximately 80% of the relative uncertainties having negative values. Instances of systematic bias for subsets of the data were also observed, including a significant underestimation of alpha particles and protons for energies below 2.5 GeV/u. Muons were found to be systematically over-predicted at atmospheric depths deeper than 50 g/cm(sup 2) but under-predicted for shallower depths. Furthermore, a systematic under-prediction of alpha particles and protons was observed below the geomagnetic cutoff, suggesting that improvements to the light ion production cross sections in HZETRN should be investigated.

James E Warner↗
NASA NTRS2019

New Mission Concept: Investigation of the Galactic Center with the Galactic Center Explorer (GalCenEx)

The European Space Observatory INTEGRAL has been providing excellent results on X-ray and γ–ray astronomy since its launch in 2002. Among the most important results are the spectroscopy and imaging measurements of celestial γ-ray sources, including mapping the 511 keV radiation from the Galactic plane. However, the nature of the 511 keV positron annihilation line around the Galactic Center region is still a mystery. Similarly, the structure and nature of the Galactic Center supermassive black hole and its surroundings, as well as the structure of heavily populated sky regions such as Cygnus and Carina in γ-rays, remain unclear. We present a concept of a potential next-generation γ-ray telescope with the major science objectives: a) solve the mystery of the Galactic Center region 511 keV positron annihilation line by mapping the Galactic Center region with high energy (<1% FWHM) and angular (< 10 arcmin) resolution and with line sensitivity <10-5 ph cm-2 s-1; b) understand the nature of the Galactic Center supermassive black hole environment by creating a high-resolution spectral and intensity map of the surrounding region in 0.1 – 20 MeV γ rays; and c) explore Galactic chemical evolution and sites of explosive element synthesis by conducting high-sensitivity measurements of nuclear lines from Type 1a supernovae and other objects. The instrument is based on a novel high energy and position resolution CdZnTe Imager, coded aperture mask, and heavy-scintillator shield, and can be considered for a NASA Explorer mission.

Moiseev, Alexander↗
NASA NTRS2022

Resolving the fine structure in the energy landscapes of repeat proteins

Ankyrin (ANK) repeat proteins are coded by tandem occurrences of patterns with around 33 amino acids. They often mediate protein–protein interactions in a diversity of biological systems. These proteins have an elongated non-globular shape and often display complex folding mechanisms. This work investigates the energy landscape of representative proteins of this class made up of 3, 4 and 6 ANK repeats using the energy-landscape visualisation method (ELViM). By combining biased and unbiased coarse-grained molecular dynamics AWSEM simulations that sample conformations along the folding trajectories with the ELViM structure-based phase space, one finds a three-dimensional representation of the globally funnelled energy surface. In this representation, it is possible to delineate distinct folding pathways. We show that ELViMs can project, in a natural way, the intricacies of the highly dimensional energy landscapes encoded by the highly symmetric ankyrin repeat proteins into useful low-dimensional representations. These projections can discriminate between multiplicities of specific parallel folding mechanisms that otherwise can be hidden in oversimplified depictions.

Murilo N. Sanches↗
NASA NTRS2023

Thermal Electron Heat Fluxes Associated with Precipitated Auroral Electrons During the Saint Patrick's Days 2013 and 2015 Geomagnetic Storms

The Rice Convection Model-Equilibrium (RCM-E) and SuperThermal Electron Transport (STET) are combined to investigate electron heat flux formation in the region of the diffuse aurora for the geomagnetic storms of 17 March 2013 and 17 March 2015. The primary electron precipitation into the atmosphere resulting from wave particle scattering in the magnetosphere are simulated by the magnetically and electrically RCM-E during these two geomagnetic storms. The primary precipitating electron fluxes are modified by the STET model by taking into account atmospheric backscatter processes. The modified electron energy fluxes and their mean energies are coupled to the STET code to calculate electron thermal fluxes associated with diffuse aurora on a global scale. We use the simulated heat flux to estimate electron temperatures at the upper ionospheric altitudes and compare them with corresponding observations from the Defense Meteorological Satellite Program satellite.

George V. Khazanov↗
NASA NTRS1992

Solution of the Burnett equations for hypersonic flows near the continuum limit

The INCA code, a three-dimensional Navier-Stokes code for analysis of hypersonic flowfields, was modified to analyze the lower reaches of the continuum transition regime, where the Navier-Stokes equations become inaccurate and Monte Carlo methods become too computationally expensive. The two-dimensional Burnett equations and the three-dimensional rotational energy transport equation were added to the code and one- and two-dimensional calculations were performed. For the structure of normal shock waves, the Burnett equations give consistently better results than Navier-Stokes equations and compare reasonably well with Monte Carlo methods. For two-dimensional flow of Nitrogen past a circular cylinder the Burnett equations predict the total drag reasonably well. Care must be taken, however, not to exceed the range of validity of the Burnett equations.

Imlay, Scott T.↗
DOE OSTI2024

Nonlinear light-output calibration of the oxygenated xylene scintillators used in OMEGA neutron time-of-flight spectrometers

Neutron time-of-flight (nTOF) spectrometers are essential instruments for measuring and evaluating the performance of inertial confinement fusion implosions. The neutron spectrometers utilized for the OMEGA laser include two liquid-based scintillators, each consisting of a large volume filled with xylene that is coupled to four photomultiplier tubes. Analysis of the signal from these detectors requires detailed knowledge of the scintillator’s light output, which is needed to fit the nTOF spectrum, from which the neutron energy spectrum is informed. The light output is nonlinearly proportional to the neutron energy, which, in turn, affects the interpretation of the neutron energy spectrum from a TOF signal. A recent campaign on OMEGA was performed to calibrate the xylene detectors and infer the shape of the light-output curve. The campaign utilized materials with increasing Z placed in the OMEGA target chamber to initiate scattering events with the 14 MeV fusion neutrons. This process leads to the production of backscatter neutrons of varying energies that appear as peaks in the nTOF data. Simulations using a neutron transport code were combined with the measured deuterium–tritium neutron yields to calculate the expected backscattered neutron yields from the well-known scattering cross sections of each material. Furthermore, the neutron-energy dependent light output of the scintillator inferred from the experiment is compared to the light-output curve simulated with a neutron transport code for the following neutron energies: 1.5, 2.5, 6, and 14 MeV.

47 OTHER INSTRUMENTATION↗
NASA NTRS1991

Impact cratering calculations

In the course of carrying out finite difference calculations, it was discovered that for large craters, a previously unrecognized type of crater (diameter) growth occurred which was called lip wave propagation. This type of growth is illustrated for an impact of a 1000 km (2a) silicate bolide at 12 km/sec (U) onto a silicate half-space at earth gravity (1 g). The von Misses crustal strength is 2.4 kbar. The motion at the crater lip associated with this wave type phenomena is up, outward, and then down, similar to the particle motion of a surface wave. It is shown that the crater diameter has grown d/a of approximately 25 to d/a of approximately 4 via lip propagation from Ut/a = 5.56 to 17.0 during the time when rebound occurs. A new code is being used to study partitioning of energy and momentum and cratering efficiency with self gravity for finite-sized objects rather than the previously discussed planetary half-space problems. These are important and fundamental subjects which can be addressed with smoothed particle hydrodynamic (SPH) codes. The SPH method was used to model various problems in astrophysics and planetary physics. The initial work demonstrates that the energy budget for normal and oblique impacts are distinctly different than earlier calculations for silicate projectile impact on a silicate half space. Motivated by the first striking radar images of Venus obtained by Magellan, the effect of the atmosphere on impact cratering was studied. In order the further quantify the processes of meteor break-up and trajectory scattering upon break-up, the reentry physics of meteors striking Venus' atmosphere versus that of the Earth were studied.

Ahrens, Thomas J.↗
NASA NTRS2000

Modeling Natural Space Ionizing Radiation Effects on External Materials

Predicting the effective life of materials for space applications has become increasingly critical with the drive to reduce mission cost. Programs have considered many solutions to reduce launch costs including novel, low mass materials and thin thermal blankets to reduce spacecraft mass. Determining the long-term survivability of these materials before launch is critical for mission success. This presentation will describe an analysis performed on the outer layer of the passive thermal control blanket of the Hubble Space Telescope. This layer had degraded for unknown reasons during the mission, however ionizing radiation (IR) induced embrittlement was suspected. A methodology was developed which allowed direct comparison between the energy deposition of the natural environment and that of the laboratory generated environment. Commercial codes were used to predict the natural space IR environment model energy deposition in the material from both natural and laboratory IR sources, and design the most efficient test. Results were optimized for total and local energy deposition with an iterative spreadsheet. This method has been used successfully for several laboratory tests at the Marshall Space Flight Center. The study showed that the natural space IR environment, by itself, did not cause the premature degradation observed in the thermal blanket.

Alstatt, Richard L.↗
NASA NTRS2016

Systematic Comparison of Photoionized Plasma Codes with Application to Spectroscopic Studies of AGN in X-Rays

Atomic data and plasma models play a crucial role in the diagnosis and interpretation of astrophysical spectra, thus influencing our understanding of the Universe. In this investigation we present a systematic comparison of the leading photoionization codes to determine how much their intrinsic differences impact X-ray spectroscopic studies of hot plasmas in photoionization equilibrium. We carry out our computations using the Cloudy, SPEX, and XSTAR photoionization codes, and compare their derived thermal and ionization states for various ionizing spectral energy distributions. We examine the resulting absorption-line spectra from these codes for the case of ionized outflows in active galactic nuclei. By comparing the ionic abundances as a function of ionization parameter, we find that on average there is about 30 deviation between the codes in where ionic abundances peak. For H-like to B-like sequence ions alone, this deviation in is smaller at about 10 on average. The comparison of the absorption-line spectra in the X-ray band shows that there is on average about 30 deviation between the codes in the optical depth of the lines produced at log 1 to 2, reducing to about 20 deviation at log 3. We also simulate spectra of the ionized outflows with the current and upcoming high-resolution X-ray spectrometers, on board XMM-Newton, Chandra, Hitomi, and Athena. From these simulations we obtain the deviation on the best-fit model parameters, arising from the use of different photoionization codes, which is about 10 to40. We compare the modeling uncertainties with the observational uncertainties from the simulations. The results highlight the importance of continuous development and enhancement of photoionization codes for the upcoming era of X-ray astronomy with Athena.

plasmas – atomic processes – atomic data – t↗
NASA NTRS1987

Navier-Stokes and viscous shock-layer solutions for radiating hypersonic flows

Results are presented from the Navier-Stokes and viscous shock-layer (VSL) calculations with nonequilibrium and equilibrium chemistry, respectively. These calculations contain coupling to the Aerotherm radiation code RAD. A simplified form of the electron energy equation is used to obtain an electron temperature in the Navier-Stokes calculations. The radiation in the flowfield is calculated using this temperature. The Navier-Stokes code is used at high altitude only, whereas the VSL code is employed for the entire entry period to make estimates of the radiative and convective heating to the Fire II vehicle. Results from the Navier-Stokes code have also been compared with the predictions of Lee and Kawamura, who used gray-gas radiation model and thin-layer Navier-Stokes equations. Quite good agreement is obtained between the measured and computed values of radiative and convective heating from the VSL code in th medium-to-low altitude flight regime of the Fire II vehicle. At high altitudes, the Navier-Stokes calculations considerably overpredict the Fire II flight data for radiative intensity. This is attributed to the deficiencies in the Aerotherm radiation model when used for low-density flight conditions. This model contains the thermal equilibrium assumption and precludes accounting for the collision-limiting phenomenon at high altitudes. Present Navier-Stokes calculations highlight the effect of these assumptions on radiative heating calculations for such conditions.

Gupta, Roop N.↗
NASA NTRS1995

Shielding materials for highly penetrating space radiations

Interplanetary travel involves the transfer from an Earth orbit to a solar orbit. Once outside the Earth's magnetosphere, the major sources of particulate radiation are solar cosmic rays (SCR's) and galactic cosmic rays (GCR's). Intense fluxes of SCR's come from solar flares and consist primarily of protons with energies up to 1 GeV. The GCR consists of a low flux of nuclei with energies up to 10(exp 10) GeV. About 70 percent of the GCR are protons, but a small amount (0.6 percent) are nuclei with atomic numbers greater than 10. High energy charged particles (HZE) interact with matter by transferring energy to atomic electrons in a Coulomb process and by reacting with an atomic nucleus. Energy transferred in the first process increases with the square of the atomic number, so particles with high atomic numbers would be expected to lose large amounts of energy by this process. Nuclear reactions produced by (HZE) particles produce high-energy secondary particles which in turn lose energy to the material. The HZE nuclei are a major concern for radiation protection of humans during interplanetary missions because of the very high specific ionization of both primary and secondary particles. Computer codes have been developed to calculate the deposition of energy by very energetic charged particles in various materials. Calculations show that there is a significant buildup of secondary particles from nuclear fragmentation and Coulomb dissociation processes. A large portion of these particles are neutrons. Since neutrons carry no charge, they only lose energy by collision or reaction with a nucleus. Neutrons with high energies transfer large amounts of energy by inelastic collisions with nuclei. However, as the neutron energy decreases, elastic collisions become much more effective for energy loss. The lighter the nucleus, the greater the fraction of the neutron's kinetic energy that can be lost in an elastic collision. Thus, hydrogen-containing materials such as polymers are most effective in reducing the energy of neutrons. Once neutrons are reduced to very low energies, the probability for undergoing a reaction with a nucleus (the cross section) becomes very high. The product of such a reaction is often radioactive and can involve the release of a significant amount of energy. Thus, it is important to provide protection from low energy neutrons during a long duration space flight. Among the light elements, lithium and boron each have an isotope with a large thermal neutron capture cross section, Li-6 and B-10. However, B-10 is more abundant in the naturally-occurring element than Li-6, has a thermal neutron capture cross section four times that of Li-6, and produces the stable products, He-4 and Li-7 in the interaction while Li-6 produces radioactive tritium (H-3). Thus, boron is the best light-weight material for thermal neutron absorption in spacecraft. The work on this project was focused in two areas: computer design where existing computer codes were used, and in some cases modified, to calculate the propagation and interactions of high energy charged particles through various media, and materials development where boron was incorporated into high performance materials.

Kiefer, Richard L.↗
DOE OSTI2025

Gas-Cooled High-Temperature Pebble-Bed Reactor Reference Plant Model Updates

This work presents the latest improvements to, and investigations performed with, the pebble-bed high-temperature gas-cooled reactor (PB-HTGR) reference plant models for the United States Nuclear Regulatory Commission. These models serve as the foundation for the future development of detailed design evaluation models based on license applications. The reference plant models have been developed with the Comprehensive Reactor Analysis Bundle, or BlueCRAB, which is the code suite proposed for non-light-water reactor systems safety analysis. It incorporates various simulation tools developed by the Nuclear Energy Advanced Modeling and Simulation program, including the Griffin code for reactor physics, the Pronghorn and SAM codes for core thermal fluids, the BISON code for solid conduction and fuel performance, and the SAM code for system analysis. The primary objective of the work that was performed was to assess BlueCRAB’s level of readiness for modeling a PB-HTGR. To do so, we first developed numerical models in BlueCRAB that include the key physics for this technology to ensure an adequate level of fidelity for modeling PB-HTGR core performance and for performing multiphysics simulations for equilibrium core conditions and different accident scenarios. Then we simulated transient scenarios, including depressurized and pressurized loss of forced cooling accidents, over-cooling, and control rod withdrawal events with delayed and prompt supercritical reactivity insertions. The analysis in this report includes comparisons of the 2D thermal fluid porous media models in Pronghorn and SAM, and comparisons of coupled SAM/Griffin/SAM and coupled Pronghorn/Griffin for depressurized and pressurized loss of forced cooling, over-cooling, and control rod withdrawal events. In addition, we compare 3D, 2D, and 0D/PKE neutronic models for the two control rod withdrawal scenarios with coupled Pronghorn/Griffin. The comparisons show that the BlueCRAB models lead to physically intuitive solutions for the scenarios examined. The changes in the various scalar and vector fields, such as neutron flux, power, temperature, density, pressure, and velocity, are within the expected ranges, and their distributions can be explained by the system response of the transients and the geometric and material variations. Several comparisons suggest that the porous media models in Pronghorn and SAM can lead to similar solutions, even though they are based on different methodologies. This work further highlights the need for flexible tools with various levels of fidelity to cover the breadth and depth of needs that may arise in future technical evaluations of the PB-HTGR. We believe that the BlueCRAB capabilities will be a significant asset for confirmatory analyses in order to resolve important safety questions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRSDate not supplied

Monte Carlo simulations of neutrino and charged lepton propagation in the Earth with nuPyProp

An accurate modeling of neutrino flux attenuation and the distribution of leptons they produce in transit through the Earth is an essential component to determine neutrino flux sensitivities of underground, sub-orbital and space-based detectors. Through neutrino oscillations over cosmic distances, astrophysical neutrino sources are expected to produce nearly equal fluxes of electron, muon and tau neutrinos. Of particular interest are tau neutrinos that interact in the Earth at modest slant depths to produce leptons. Some leptons emerge from the Earth and decay in the atmosphere to produce extensive air showers. Future balloon-borne and satellite-based opticalCherenkov neutrino telescopes will be sensitive to upward air showers from tau neutrino induced lepton decays. We present nuPyProp, a python code that is part of the nuSpaceSim package. nuPyProp generates look-up tables for exit probabilities and energy distributions for (see paper for proper equation) propagation in the Earth. This flexible code runs with either stochastic or continuous electromagnetic energy losses for the lepton transit through the Earth. Current neutrino cross section models and energy loss models are included along with templates for user input of other models. Results from nuPyProp are compared with other recent simulation packages for neutrino and charged lepton propagation. Sources of modeling uncertainties are described and quantified.

Yosui Akaike↗
NASA NTRS1994

LSENS: A General Chemical Kinetics and Sensitivity Analysis Code for homogeneous gas-phase reactions. Part 1: Theory and numerical solution procedures

LSENS, the Lewis General Chemical Kinetics and Sensitivity Analysis Code, has been developed for solving complex, homogeneous, gas-phase chemical kinetics problems and contains sensitivity analysis for a variety of problems, including nonisothermal situations. This report is part 1 of a series of three reference publications that describe LENS, provide a detailed guide to its usage, and present many example problems. Part 1 derives the governing equations and describes the numerical solution procedures for the types of problems that can be solved. The accuracy and efficiency of LSENS are examined by means of various test problems, and comparisons with other methods and codes are presented. LSENS is a flexible, convenient, accurate, and efficient solver for chemical reaction problems such as static system; steady, one-dimensional, inviscid flow; reaction behind incident shock wave, including boundary layer correction; and perfectly stirred (highly backmixed) reactor. In addition, the chemical equilibrium state can be computed for the following assigned states: temperature and pressure, enthalpy and pressure, temperature and volume, and internal energy and volume. For static problems the code computes the sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of the dependent variables and/or the three rate coefficient parameters of the chemical reactions.

Radhakrishnan, Krishnan↗
DOE OSTI2025

Fluoride-Cooled High-Temperature Pebble-Bed Reactor Reference Plant Model Updates

This work presents the latest improvements to, and investigations performed with, the Fluoride-Cooled High-Temperature Pebble-Bed Reactor reference plant models for the United States Nuclear Regulatory Commission. These models, developed with the Comprehensive Reactor Analysis Bundle, or BlueCRAB, serve as the foundation for the future development of detailed design evaluation models based on license applications. BlueCRAB is the code suite proposed for non-light-water reactor systems safety analyses, and it incorporates various simulation tools developed by the Nuclear Energy Advance Modeling and Simulation program, including the Griffin code for reactor physics, the Pronghorn and SAM codes for core thermal fluids, the BISON code for solid conduction and fuel performance, and the SAM code for system analysis. The primary objective of this work is to assess the level of readiness of BlueCRAB for modeling fluoride-cooled high-temperature pebble-bed reactors. We first developed numerical models in BlueCRAB that include the key physics for this technology, ensuring an adequate level of fidelity for modeling the core performance during accident scenarios. This was followed by simulation of transient scenarios, two loss-of-forced-cooling events (one protected and one unprotected), and two control rod withdrawal events (one delayed and one prompt supercritical reactivity insertion). The analysis includes comparisons between the 2-D thermal fluid porous media models in Pronghorn and SAM, comparisons between coupled Pronghorn-Griffin and coupled SAM-Griffin models for two loss-of-forced cooling events and one control rod withdrawal event, and comparisons between SAM single-solve and domain-overlapping approaches for multi-scale thermal fluid coupling. In addition, we performed comparisons between 3-D, 2-D, and 0-D neutronic models for the two control rod withdrawal scenarios with Pronghorn-Griffin. The results show that the BlueCRAB models led to physically intuitive solutions for the scenarios examined. The changes in the various scalar and vector fields such as the neutron flux, power, temperatures, densities, pressures, and velocities are all within the expected ranges, and their distributions can be explained from the system response of the transients and the geometric and material variations. Several comparisons suggest that the porous media models in Pronghorn and SAM can lead to similar solutions, even though they are based on different methodologies. The simulations demonstrate that there are differences between the various levels of fidelity, and it is advisable to have flexible tools that can cover the breadth and depth of needs that may arise in future technical evaluations. We believe that BlueCRAB’s capabilities represent a significant asset for confirmatory analyses aimed at resolving important safety questions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1994

Measurements of trapped protons and cosmic rays from recent shuttle flights

We have flown two new charged particle detectors in five recent Shuttle flights. In this paper we report on the dose rate, equivalent dose rate, and radiation quality factor for trapped protons and cosmic radiation separately. A comparison of the integral Linear Energy Transfer (LET) spectra with recent transport code calculations show significant disagreement. Using the calculated dose rate from the omni-directional AP8MAX model with IGRF reference magnetic field epoch 1970, and observed dose rate as a function of (averaged over all geographic latitude) and longitude, we have determined the westward drift of the South Atlantic anomaly. We have also studied the east-west effect, and observed a 'second' radiation belt. A comparison of the galactic cosmic radiation lineal energy transfer spectra with model calculations shows disagreement comparable to those of the trapped protons.

Badhwar, G. D.↗