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At least 487 records · Page 27

Spacecraft radio scattering observations of the power spectrum of electron density fluctuations in the solar wind

Solar wind electron density power spectra in the solar equatorial region are inferred from observations of phase scintillations and spectral broadening made with the Viking, Helios, and Pioneer spacecraft. The heliocentric distance range covered is 2-215 solar radii and for some observations close to the sun the spectra extend to fluctuation frequencies as high as 100 Hz. For heliocentric distances of about 20 solar radii the equivalent spacecraft-measured one-dimensional density spectrum is well modeled by a single power law in the frequency range 0.0001-0.05 Hz. The flattening of the density spectrum within 20 solar radii is presumably associated with energy deposition in the near-sun region and acceleration of the solar wind.

Woo, R.↗

Current sheet Formation in a Conical Theta Pinch Faraday Accelerator with Radio-Frequency Assisted Discharge

The inductive formation of current sheets in a conical theta pinch FARAD (Faraday Accelerator with Radio-frequency Assisted Discharge) thruster is investigated experimentally with time-integrated photography. The goal is to help in understanding the mechanisms and conditions controlling the strength and extent of the current sheet, which are two indices important for FARAD as a propulsion concept. The profiles of these two indices along the inside walls of the conical acceleration coil are assumed to be related to the profiles of the strength and extent of the luminosity pattern derived from photographs of the discharge. The variations of these profiles as a function of uniform back-fill neutral pressure (with no background magnetic field and all parameters held constant) provided the first clues on the nature and qualitative dependencies of current sheet formation. It was found that there is an optimal pressure for which both indices reach a maximum and that the rate of change in these indices with pressure differs on either side of this optimal pressure. This allowed the inference that current sheet formation follows a Townsend-like breakdown mechanism modified by the existence of a finite pressure-dependent radio-frequency-generated electron density background. The observation that the effective location of the luminosity pattern favors the exit-half of the conical coil is explained as the result of the tendency of the inductive discharge circuit to operate near its minimal self-inductance. Movement of the peak in the luminosity pattern towards the upstream side of the cone with increasing pressure is believed to result from the need of the circuit to compensate for the increase in background plasma resistivity due to increasing pressure.

Hallock, Ashley K.↗

Semiannual Status Report

During the last six months, we have continued our study of the excitation of electromagnetic waves in the whistler frequency range and the role that these waves will play in the acceleration of electrons and ions in the auroral region. A paper entitled 'Electron Beam Excitation of Upstream Waves in the Whistler Mode Frequency Range' was listed in the Journal of Geophysical Research. In this paper, we have shown that an anisotropic electron beam (or gyrating electron beam) is capable of generating both left-hand and right-hand polarized electromagnetic waves in the whistler frequency range. Since right-hand polarized electromagnetic waves can interact with background electrons and left-hand polarized waves can interact with background ions through cyclotron resonance, it is possible that these beam generated left-hand and right-hand polarized electromagnetic waves can accelerate either ions or electrons (or both), depending on the physical parameters under consideration. We are currently carrying out a comprehensive study of the electromagnetic whistler and lower hybrid like waves observed in the auroral zone using both wave and particle data. Our first task is to identify these wave modes and compare it with particle observations. Using both the DE-1 particle and wave measurements, we can positively identify those electromagnetics lower hybrid like waves as fast magnetosonic waves and the upper cutoff of these waves is the local lower hybrid frequency. From the upper cutoff of the frequency spectrum, one can infer the particle density and the result is in very good agreement with the particle data. Since these electromagnetic lower hybrid like waves can have frequencies extended down to the local ion cyclotron frequency, it practically confirms that they are not whistler waves.

Source record↗

Accelerated Probabilistic Marching Cubes by Deep Learning for Time-Varying Scalar Ensembles

Visualizing the uncertainty of ensemble simulations is challenging due to the large size and multivariate and temporal features of en-semble data sets. One popular approach to studying the uncertainty of ensembles is analyzing the positional uncertainty of the level sets. Probabilistic marching cubes is a technique that performs Monte Carlo sampling of multivariate Gaussian noise distributions for positional uncertainty visualization of level sets. However, the technique suffers from high computational time, making interactive visualization and analysis impossible to achieve. This paper introduces a deep-learning-based approach to learning the level-set uncertainty for two-dimensional ensemble data with a multivariate Gaussian noise assumption. We train the model using the first few time steps from time-varying ensemble data in our workflow. We demonstrate that our trained model accurately infers uncertainty in level sets for new time steps and is up to 170X faster than that of the original probabilistic model with serial computation and 10X faster than that of the original parallel computation.

Han, Mengjiao↗

A general Bayesian algorithm for the autonomous alignment of beamlines

Autonomous methods to align beamlines can decrease the amount of time spent on diagnostics, and also uncover better global optima leading to better beam quality. The alignment of these beamlines is a high-dimensional expensive-to-sample optimization problem involving the simultaneous treatment of many optical elements with correlated and nonlinear dynamics. Bayesian optimization is a strategy of efficient global optimization that has proved successful in similar regimes in a wide variety of beamline alignment applications, though it has typically been implemented for particular beamlines and optimization tasks. In this paper, we present a basic formulation of Bayesian inference and Gaussian process models as they relate to multi-objective Bayesian optimization, as well as the practical challenges presented by beamline alignment. We show that the same general implementation of Bayesian optimization with special consideration for beamline alignment can quickly learn the dynamics of particular beamlines in an online fashion through hyperparameter fitting with no prior information. We present the implementation of a concise software framework for beamline alignment and test it on four different optimization problems for experiments on X-ray beamlines at the National Synchrotron Light Source II and the Advanced Light Source, and an electron beam at the Accelerator Test Facility, along with benchmarking on a simulated digital twin. We discuss new applications of the framework, and the potential for a unified approach to beamline alignment at synchrotron facilities.

47 OTHER INSTRUMENTATION↗

CyanoCyc cyanobacterial web portal

CyanoCyc is a web portal that integrates an exceptionally rich database collection of information about cyanobacterial genomes with an extensive suite of bioinformatics tools. It was developed to address the needs of the cyanobacterial research and biotechnology communities. The 277 annotated cyanobacterial genomes currently in CyanoCyc are supplemented with computational inferences including predicted metabolic pathways, operons, protein complexes, and orthologs; and with data imported from external databases, such as protein features and Gene Ontology (GO) terms imported from UniProt. Five of the genome databases have undergone manual curation with input from more than a dozen cyanobacteria experts to correct errors and integrate information from more than 1,765 published articles. CyanoCyc has bioinformatics tools that encompass genome, metabolic pathway and regulatory informatics; omics data analysis; and comparative analyses, including visualizations of multiple genomes aligned at orthologous genes, and comparisons of metabolic networks for multiple organisms. CyanoCyc is a high-quality, reliable knowledgebase that accelerates scientists’ work by enabling users to quickly find accurate information using its powerful set of search tools, to understand gene function through expert mini-reviews with citations, to acquire information quickly using its interactive visualization tools, and to inform better decision-making for fundamental and applied research.

59 BASIC BIOLOGICAL SCIENCES↗

The 3D Recognition, Generation, Fusion, Update and Refinement (RG4) Concept

This paper describes an active (real time) recognition strategy whereby information is inferred iteratively across several viewpoints in descent imagery. We will show how we use inverse theory within the context of parametric model generation, namely height and spectral reflection functions, to generate model assertions. Using this strategy in an active context implies that, from every viewpoint, the proposed system must refine its hypotheses taking into account the image and the effect of uncertainties as well. The proposed system employs probabilistic solutions to the problem of iteratively merging information (images) from several viewpoints. This involves feeding the posterior distribution from all previous images as a prior for the next view. Novel approaches will be developed to accelerate the inversion search using novel statistic implementations and reducing the model complexity using foveated vision. Foveated vision refers to imagery where the resolution varies across the image. In this paper, we allow the model to be foveated where the highest resolution region is called the foveation region. Typically, the images will have dynamic control of the location of the foveation region. For descent imagery in the Entry, Descent, and Landing (EDL) process, it is possible to have more than one foveation region. This research initiative is directed towards descent imagery in connection with NASA's EDL applications. Three-Dimensional Model Recognition, Generation, Fusion, Update, and Refinement (RGFUR or RG4) for height and the spectral reflection characteristics are in focus for various reasons, one of which is the prospect that their interpretation will provide for real time active vision for automated EDL.

Maluf, David A.↗

Uncertainty quantification for Multiphase-CFD simulations of bubbly flows: a machine learning-based Bayesian approach supported by high-resolution experiments

In this paper, we developed a machine learning-based Bayesian approach to inversely quantify and reduce the uncertainties of multiphase computational fluid dynamics (MCFD) simulations for bubbly flows. The proposed approach is supported by high-resolution two-phase flow measurements, including those by double-sensor conductivity probes, high-speed imaging, and particle image velocimetry. Local distributions of key physical quantities of interest (QoIs), including the void fraction and phasic velocities, are obtained to support the Bayesian inference. In the process, the epistemic uncertainties of the closure relations are inversely quantified while the aleatory uncertainties from stochastic fluctuations of the system are evaluated based on experimental uncertainty analysis. The combined uncertainties are then propagated through the MCFD solver to obtain uncertainties of the QoIs, based on which probability-boxes are constructed for validation. The proposed approach relies on three machine learning methods: feedforward neural networks and principal component analysis for surrogate modeling, and Gaussian processes for model form uncertainty modeling. The whole process is implemented within the framework of an open-source deep learning library PyTorch with graphics processing unit (GPU) acceleration, thus ensuring the efficiency of the computation. The results demonstrate that with the support of high-resolution data, the uncertainties of MCFD simulations can be significantly reduced. The proposed approach has the potential for other applications that involve numerical models with empirical parameters.

42 ENGINEERING↗

Feeling Gravity's Pull: Gravity Modeling. The Gravity Field of Mars

Most people take the constant presence of gravitys pull for granted. However, the Earth's gravitational strength actually varies from location to location. This variation occurs because mass, which influences an object's gravitational pull, is not evenly distributed within the planet. Changes in topography, such as glacial movement, an earthquake, or a rise in the ocean level, can subtly affect the gravity field. An accurate measurement of the Earth's gravity field helps us understand the distribution of mass beneath the surface. This insight can assist us in locating petroleum, mineral deposits, ground water, and other valuable substances. Gravity mapping can also help notice or verify changes in sea surface height and other ocean characteristics. Such changes may indicate climate change from polar ice melting and other phenomena. In addition, gravity mapping can indicate how land moves under the surface after earthquakes and other plate tectonic processes. Finally, changes in the Earth's gravity field might indicate a shift in water distribution that could affect agriculture, water supplies for population centers, and long-term weather prediction. Scientists can map out the Earth's gravity field by watching satellite orbits. When a satellite shifts in vertical position, it might be passing over an area where gravity changes in strength. Gravity is only one factor that may shape a satellite's orbital path. To derive a gravity measurement from satellite movement, scientists must remove other factors that might affect a satellite's position: 1. Drag from atmospheric friction. 2. Pressure from solar radiation as it heads toward Earth and. as it is reflected off the surface of the Earth 3. Gravitational pull from the Sun, the Moon, and other planets in the Solar System. 4. The effect of tides. 5. Relativistic effects. Scientists must also correct for the satellite tracking process. For example, the tracking signal must be corrected for refraction through the atmosphere of the Earth. Supercomputers can calculate the effect of gravity for specific locations in space following a mathematical process known as spherical harmonics, which quantifies the gravity field of a planetary body. The process is based on Laplace's fundamental differential equation of gravity. The accuracy of a spherical harmonic solution is rated by its degree and order. Minute variations in gravity are measured against the geoid, a surface of constant gravity acceleration at mean sea level. The geoid reference gravity model strength includes the central body gravitational attraction (9.8 m/sq s) and a geopotential variation in latitude partially caused by the rotation of the Earth. The rotational effect modifies the shape of the geoid to be more like an ellipsoid, rather than a perfect, circle. Variations of gravity strength from the ellipsoidal reference model are measured in units called milli-Galileos (mGals). One mGal equals 10(exp -5) m/sq s. Research projects have also measured the gravity fields of other planetary bodies, as noted in the user profile that follows. From this information, we may make inferences about our own planet's internal structure and evolution. Moreover, mapping the gravity fields of other planets can help scientists plot the most fuel-efficient course for spacecraft expeditions to those planets.

Lemoine, Frank↗

System Would Detect Foreign-Object Damage in Turbofan Engine

A proposed data-fusion system, to be implemented mostly in software, would further process the digitized and preprocessed outputs of sensors in a turbofan engine to detect foreign-object damage (FOD) [more precisely, damage caused by impingement of such foreign objects as birds, pieces of ice, and runway debris]. The proposed system could help a flight crew to decide what, if any, response is necessary to complete a flight safely, and could aid mechanics in deciding what post-flight maintenance action might be needed. The sensory information to be utilized by the proposed system would consist of (1) the output of an accelerometer in an engine-vibration-monitoring subsystem and (2) features extracted from a gas path analysis. ["Gas path analysis" (GPA) is a term of art that denotes comprehensive analysis of engine performance derived from readings of fuel-flow meters, shaft-speed sensors, temperature sensors, and the like.] The acceleration signal would first be processed by a wavelet-transform-based algorithm, using a wavelet created for the specific purpose of finding abrupt FOD-induced changes in noisy accelerometer signals. Two additional features extracted would be the amplitude of vibration (determined via a single- frequency Fourier transform calculated at the rotational speed of the engine), and the rate of change in amplitude due to an FOD-induced rotor imbalance. This system would utilize two GPA features: the fan efficiency and the rate of change of fan efficiency with time. The selected GPA and vibrational features would be assessed by two fuzzy-logic inference engines, denoted the "Gas Path Expert" and the "Vibration Expert," respectively (see Figure 1). Each of these inference engines would generate a "possibility" distribution for occurrence of an FOD event: Each inference engine would assign, to its input information, degrees of membership, which would subsequently be transformed into basic probability assignments for the gas path and vibration components. The outputs of the inference engines would be fused by use of Dempster s combination algorithm (more precisely, an algorithm, based on the Dempster-Shafer-Yager theory of evidence, for fusing uncertain or imprecise information) to provide a reduced body of information to a human or computer decision maker. Figure 2 depicts some outputs generated in response to simulated accelerometer and GPA signals

Torso, James A.↗

Determining the electrical conductivity of metals using the 2 MA Thor pulsed power driver

We present the development of a pulsed power experimental technique to infer the electrical conductivity of metals from ambient to high energy density conditions. The method is implemented on Thor, a moderate scale (1–2 MA) pulsed power driver. The electrical conductivity of copper at elevated temperature (>4000 K) and pressure (>10 GPa) is determined, and a new tabular material model is developed, guided by density functional theory, which preserves agreement with existing experimental data. Minor modifications (<10%) are found to be necessary to the previous Lee–More–Desjarlais model isotherms in the vicinity of the melt transition in order to account for observed discrepancies with the new experimental data. An analytical model for magnetic direct drive flyer acceleration and Joule heating induced vaporization based on the Tsiolkovsky “rocket equation” is presented to assess sensitivity of the method to minor changes in electrical conductivity.

47 OTHER INSTRUMENTATION↗

Improving the Quasi‐Biennial Oscillation via a Surrogate‐Accelerated Multi‐Objective Optimization

Accurate simulation of the quasi-biennial oscillation (QBO) is challenging due to uncertainties in representing convectively generated gravity waves. We develop an end-to-end uncertainty quantification workflow that calibrates these gravity wave processes in E3SM for a realistic QBO. Central to our approach is a domain knowledge-informed, compressed representation of high-dimensional spatio-temporal wind fields. By employing a parsimonious statistical model that learns the fundamental frequency from complex observations, we extract interpretable and physically meaningful quantities capturing key attributes. Building on this, we train a probabilistic surrogate model that approximates the fundamental characteristics of the QBO as functions of critical physics parameters governing gravity wave generation. Leveraging the Karhunen–Loève decomposition, our surrogate efficiently represents these characteristics as a set of orthogonal features, capturing cross-correlations among multiple physics quantities evaluated at different pressure levels and enabling rapid surrogate-based inference at a fraction of the computational cost of full-scale simulations. Finally, we analyze the inverse problem using a multi-objective approach. Our study reveals a tension between amplitude and period that constrains the QBO representation, precluding a single optimal solution. To navigate this, we quantify the bi-criteria trade-off and generate a set of Pareto optimal parameter values that balance the conflicting objectives. This integrated workflow improves the fidelity of QBO simulations and offers a versatile template for uncertainty quantification in complex geophysical models.

54 ENVIRONMENTAL SCIENCES↗

Detectors and beam monitors based on wide bandgap semiconductors at cryogenic temperatures

Wide-bandgap semiconductors, such as single-crystal diamond and sapphire, can be used to measure the flux of passing particles through a particle-induced conductivity effect. We recently demonstrated a diamond-based, electrodeless electron beam halo monitor. This monitor utilized a thin diamond blade placed within an open, high-quality microwave resonator. The blade partially intercepted the beam and changes in the RF properties of the resonator were used to infer beam parameters. To enhance the sensitivity of our semiconductor sensors, we propose two new techniques: (1) biasing the semiconductor sensor to support avalanche multiplication of free carriers, and (2) operating at cryogenic temperatures to reduce intrinsic semiconductor losses and increase the mobility of induced carriers. These techniques are applicable not only to particle beam diagnostics but also to the detection of various types of ionizing radiation.

Accelerator Physics↗

Plasma IMS Composition Measurements for Europa, Ganymede, and the Jovian System

NASA and ESA are now planning a reduced version of the joint Europa Jupiter System Mission (EJSM), potentially including a radically descoped Jupiter Europa Orbiter (JEO) but still with magnetometer and plasma instruments. Similar field and plasma instrumentation would also reside on ESA's Jupiter Ganymede Orbiter (JGO), which conceivably could carry out multiple flybys of Europa before entering orbit at Ganymede. We are developing the 3D Ion Mass Spectrometer (IMS) designed to measure both major and minor ion species within the high radiation environment of Jupiter's magnetosphere and the icy Galilean moons. The IMS covers the energy range from 10 eV to 30 keY, wide field-of-view (FOV) capability and 10-60 sec time resolution for major ions. This instrument has two main goals: 1) measure the plasma interaction between Europa and Jupiter's magnetosphere and 2) infer the global surface composition to trace elemental and significant isotopic levels; these goals are also applicable for in-situ measurements at Ganymede and Callisto, and remotely everywhere via the iogenic plasma for 10. The first goal supports the magnetometer (MAG) measurements, primarily directed at detection of Europa's sub-surface ocean, while the second goal gives information about transfer of material between the Galilean moons, e.g. mainly from 10 to the other moons, and further allows detection of oceanic materials emergent to the moon surfaces from subsurface layers putatively including salt water oceans. Outgassed exospheric materials are probed by the IMS by measuring pickup ions accelerated up to spacecraft altitudes of approximately 100-200 km in electric fields extending through the local magnetospheric environment and moon exosphere to the surface. Our 3D hybrid kinetic model of the moon-magnetosphere interaction is used to construct a global model of electric and magnetic fields for tracing of pickup ion trajectories back to the sources at approximate surface resolution of 100 km. We show that Europa's exospheric ionosphere is dominated by pickup ions with energies of 100-1000 eV. We also expect field aligned polar ion outflows driven by ionospheric electrons via the polarization electric field at Europa; the IMS will observe such outflows and thus sample the ionosphere below spacecraft orbit altitude approximately 100 km. Based on previous Ganymede studies, we also comment on IMS applications to a Ganymede orbiter. The IMS and the Europa interaction model are respectively being developed with support from NASA's Astrobiology Instrument Development (ASTID) and Outer Planets Research (OPR) programs.

Sittler, E. C., Jr.↗

Plasma IMS Composition Measurements for Europa, Ganymede, and the Jovian Systems

NASA and ESA are now planning a reduced version of the joint Europa Jupiter System Mission (EJSM), potentially including a radically descoped Jupiter Europa Orbiter (JEO) but still with magnetometer and plasma instruments. Similar field and plasma instrumentation would also reside on ESA's Jupiter Ganymede Orbiter (JGO), which conceivably could carry out multiple flybys of Europa before entering orbit at Ganymede. We are developing the 3D Ion Mass Spectrometer (IMS) designed to measure both major and minor ion species within the high radiation environment of Jupiter s magnetosphere and the icy Galilean moons. The IMS covers the energy range from 10 eV to 30 keV, wide field-ofview (FOV) capability and 10-60 sec time resolution for major ions. This instrument has two main goals: 1) measure the plasma interaction between Europa and Jupiter s magnetosphere and 2) infer the global surface composition to trace elemental and significant isotopic levels; these goals are also applicable for in-situ measurements at Ganymede and Callisto, and remotely everywhere via the iogenic plasma for Io. The first goal supports the magnetometer (MAG) measurements, primarily directed at detection of Europa's sub-surface ocean, while the second goal gives information about transfer of material between the Galilean moons, e.g. mainly from Io to the other moons, and further allows detection of oceanic materials emergent to the moon surfaces from subsurface layers putatively including salt water oceans. Outgassed exospheric materials are probed by the IMS by measuring pickup ions accelerated up to spacecraft altitudes of approximately 100-200 km in electric fields extending through the local magnetospheric environment and moon exosphere to the surface. Our 3D hybrid kinetic model of the moon-magnetosphere interaction is used to construct a global model of electric and magnetic fields for tracing of pickup ion trajectories back to the sources at approximate surface resolution of 100 km. We show that Europa's exospheric ionosphere is dominated by pickup ions with energies of 100-1000 eV. We also expect field aligned polar ion outflows driven by ionospheric electrons via the polarization electric field at Europa; the IMS will observe such outflows and thus sample the ionosphere below spacecraft orbit altitude approximately 100 km. Based on previous Ganymede studies, we also comment on IMS applications to a Ganymede orbiter. The IMS and the Europa interaction model are respectively being developed with support from NASA's Astrobiology Instrument Development (ASTID) and Outer Planets Research (OPR) programs.

Sittler, E.↗

Modeling Magnetospheric Sources

We have used global magnetohydrodynamic, simulations of the interaction between the solar wind and magnetosphere together with single particle trajectory calculations to investigate the sources of plasma entering the magnetosphere. In all of our calculations solar wind plasma primarily enters the magnetosphere when the field line on which it is convecting reconnects. When the interplanetary magnetic field has a northward component the reconnection is in the polar cusp region. In the simulations plasma in the low latitude boundary layer (LLBL) can be on either open or closed field lines. Open field lines occur when the high latitude reconnection occurs in only one cusp. In the MHD calculations the ionosphere does not contribute significantly to the LLBL for northward IMF. The particle trajectory calculations show that ions preferentially enter in the cusp region where they can be accelerated by non-adiabatic motion across the high latitude electric field. For southward IMF in the MHD simulations the plasma in the middle and inner magnetosphere comes from the inner (ionospheric) boundary of the simulation. Solar wind plasma on open field lines is confined to high latitudes and exits the tailward boundary of the simulation without reaching the plasma sheet. The LLBL is populated by both ionospheric and solar wind plasma. When the particle trajectories are included solar wind ions can enter the middle magnetosphere. We have used both the MHD simulations and the particle calculations to estimate source rates for the magnetosphere which are consistent with those inferred from observations.

Walker, Raymond J.↗

A Robust Response of the Hadley Circulation to Global Warming

Tropical rainfall is expected to increase in a warmer climate. Yet, recent studies have inferred that the Hadley Circulation (HC), which is primarily driven by latent heating from tropical rainfall, is weakened under global warming. Here, we show evidence of a robust intensification of the HC from analyses of 33 CMIP5 model projections under a scenario of 1 per year CO2 emission increase. The intensification is manifested in a deep-tropics squeeze, characterized by a pronounced increase in the zonal mean ascending motion in the mid and upper troposphere, a deepening and narrowing of the convective zone and enhanced rainfall in the deep tropics. These changes occur in conjunction with a rise in the region of maximum outflow of the HC, with accelerated meridional mass outflow in the uppermost branch of the HC away from the equator, coupled to a weakened inflow in the return branches of the HC in the lower troposphere.

Hadley Circulation↗

Rossi X-Ray Timing Explorer Guest Investigator Program

Rossi X-ray Timing Explorer (RXTE) observations of the bright supernova remnant Cas A have revealed a hard power law component above 10 keV in addition to two thermal components inferred from ASCA measurements of the many line centroids from low-Z elements. The power law can be shown to be consistent with synchrotron emission from radio to hard x-rays by electrons of up to 4 x 10(exp 13) eV. Measurement of the 1157 keV line by CGRO (Compton Gamma Ray Observatory) from SC-44 in the chain of decay of Ti-44 predicts that the two Ti-44 lines at 68 and 78 keV should appear at the CGRO intensity. RXTE has placed upper limits on such lines that are marginally consistent with the CGRO measurement. Implications of these results on sites for cosmic ray acceleration and nucleosynthesis are discussed.

Lingenfelter, Richard E.↗