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At least 1,531 records · Page 85
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NASA NTRS1999

Energetic Neutral Atom Imaging at Low Altitudes from the Swedish Microsatellite Astrid: Extraction of the Equatorial Ion Distribution

Energetic neutral atom (ENA) images obtained by the ENA imager on- board the Astrid satellite in the polar cap at 1000 km during a moderate magnetic storm (Dst greater than or equal to 80 nT) on 8 February 1995 are simulated using a parameterized model of the equatorial ion distribution and a six-component Chamberlain exo-sphere with parameters from the MSISE-90 model. By changing the ion parameters until a matching ENA image is obtained one can extract the equatorial ion distribution. Four consecutive images from different view points several of minutes apart are simulated assuming H(+) and O(+), respectively, as parent ions. The optimal set of parameters is extracted by minimizing the chi(exp 2) difference between simulated and observed ENA image using Powell's minimization algorithm. The optimal equatorial model ion distribution consists of O(+) peaked in around dusk. The lower intensity of fluxes obtained from vantage points closer to the pole is an effect of the loss cone of the parent ion distribution being empty.

Brandt, Pontus C:son↗
NASA NTRS1999

A Simulation to Study Speed Distributions in a Solar Plasma

We (Peter Cheeseman of NASA Ames/Caelum Research) & Jose Luis Alvarellos of the SJSU Physics Department/SJSU Foundation.) have carried out a numerical simulation of a plasma with characteristics similar to those found in the core of the Sun. Particular emphasis is placed on the Coulomb interaction between the ions and electrons, which could result in a relative velocity distribution different from the Maxwell-Boltzmann (MB) distribution generally assumed for a plasma. The fact that the distribution may not exactly follow the MB distribution could have very important consequences for a variety of problems in solar physics, especially the neutrino problem. Very briefly. the neutrino problem is that the observed neutrino detections from the Sun are smaller than what the standard solar theory predicts. In Section 1 we introduce the problem and in section 2 we discuss the approach to try to solve the problem: i.e., a molecular dynamics approach. In section 3 we provide details about the integration method, and any simplifications that can be applied to the problem. In section 4 (the core of this report) we state our results, first for the specific case of 1000 particles and then for other cases with different number of particles. In section 5 we summarize our findings and state our conclusions. Sections 6 and 7 provide the list of figures, reference material and acknowledgments respectively.

Cheeseman, Peter↗
NASA NTRS1999

Principal Investigator Microgravity Services Role in ISS Acceleration Data Distribution

Measurement of the microgravity acceleration environment on the International Space Station will be accomplished by two accelerometer systems. The Microgravity Acceleration Measurement System will record the quasi-steady microgravity environment, including the influences of aerodynamic drag, vehicle rotation, and venting effects. Measurement of the vibratory/transient regime comprised of vehicle, crew, and equipment disturbances will be accomplished by the Space Acceleration Measurement System-II. Due to the dynamic nature of the microgravity environment and its potential to influence sensitive experiments, Principal Investigators require distribution of microgravity acceleration in a timely and straightforward fashion. In addition to this timely distribution of the data, long term access to International Space Station microgravity environment acceleration data is required. The NASA Glenn Research Center's Principal Investigator Microgravity Services project will provide the means for real-time and post experiment distribution of microgravity acceleration data to microgravity science Principal Investigators. Real-time distribution of microgravity environment acceleration data will be accomplished via the World Wide Web. Data packets from the Microgravity Acceleration Measurement System and the Space Acceleration Measurement System-II will be routed from onboard the International Space Station to the NASA Glenn Research Center's Telescience Support Center. Principal Investigator Microgravity Services' ground support equipment located at the Telescience Support Center will be capable of generating a standard suite of acceleration data displays, including various time domain and frequency domain options. These data displays will be updated in real-time and will periodically update images available via the Principal Investigator Microgravity Services web page.

McPherson, Kevin↗
NASA NTRS1997

Areal Distribution of the Oxygen-Isotope Ratio in Greenland

Mean values of the oxygen-isotope ratio relative to standard mean ocean water reported for 46 sites on the Greenland ice sheet are compiled together with data on mean annual surface temperature, latitude, 6180 elevation, and mean annual shortest distance to the open ocean denoted by the 10% sea-ice concentration boundary. Stepwise regression analyses, with 6180 as the dependent variable, define two robust models. In the forward mode at the 99.9% confidence level, only temperature enters the model. In the backward mode at the 95% confidence level, only temperature, latitude, and distance to the open ocean remain in the model. Inversions of the models on the basis of 160 gridpoint locations 100 km apart in the area delimited by the surface equilibrium line produce four contoured distributions of 6"0. Two distributions are based on the bivariate model and two on the multivariate model. The second distribution for each model is obtained substituting mean annual surface-temperature values obtained from the Nimbus-7 Temperature Humidity Infrared Radiometer (THIR) database. All four distributions are considered valid, and differences between them are evaluated using contoured anomaly maps. It is suggested that the inversion of the multivariate model using THIR data provides the more reliable pattern for studies of atmospheric advection or for the derivation of ice-flow adjustments for 6180 series obtained from deep-core or ablation-zone sites.

Zwally, H. Jay↗
NASA NTRS1999

The Distribution of Titanium in Lunar Soils on the Basis of Sensor and In Situ Data Fusion

A variety of remote-sensing measurements have been used to map the distribution of elements on the Moon as a means of providing constraints on the processes from which its crust and major terranes originated. Discussed here is Ti, which is incorporated into refractory minerals such as ilmenite during the latter stages of differentiation, and is thus a most useful element for understanding mare basalt petrogenesis. One of the earliest Ti maps showed Ti variations in nearside maria on the basis of groundbased spectral reflectance measurements. A map of Ti derived from gamma-ray measurements on Apollo 15 and 16 was produced at about the same time, and was improved upon considerably by Davis and coworkers, who effectively removed sources of spurious variation from Fe and Al or REE (e.g., Th) interference, and calibrated Ti on the bases of landing-site soil averages. In recent years, spectral reflectance measurements from Clementine have been used by Lucey and coworkers to produce global Ti distribution maps as well. As we indicated previously, the Lucey and Davis maps agree to first order. Meanwhile, we are using the concept of sensor data fusion to combine measurements from the AGR (Apollo gamma-ray) and CSR (Clementine Spectral Reflectance) techniques with ground truth from lunar soils to utilize the differences between the two maps to understand the distribution of Ti within lunar soil components, as we have done with Fe. This technique should be verified and applied on Lunar Prospector gamma-ray measurements of Ti, as the calibrated data become available within the next couple of years. Lunar Ti is found principally in the mineral ilmenite, and is associated with certain components of lunar soil: crystalline Ilmenite mineral fragments and high Ti-bearing glass. All data indicate that Ti is associated with maria and mafic minerals. In AGR and CSR datasets, Ti is highest on the nearside and in the maria, particularly in southern Serenitatis/northern Tranquillitatis and northwestern Procellarum. Unlike CSR-derived values, AGR Ti values show modest increase (up to 0.7%) on the northern farside. Both techniques show a primarily unimodal distribution with a shoulder in the high Ti direction and a primary mode at approximately 0.2% (0.15% for CSR and 0.25% for AGR data), but the AGR Ti data have more structure in the shoulder, including an apparent minor mode at 1.2% Ti, representing non-highland areas. Recalibrating the two datasets on the basis of matching the peaks and range on the histograms would not account for this additional structure in the AGR data. Low Ti areas, which occur predominantly on the farside, are not represented well in the lunar sample collection, although several meteorites thought to be of lunar highland origin show Ti abundances averaging about 0.2%. (Error bars on AGR Ti values are about 0.5%.) Gamma-ray measurements reflect intrinsic Ti surface composition, regardless of the physical or chemical state of Ti. Lucey and coworkers have attempted to produce an equivalent bulk Ti map by normalizing the spectral feature at 415 nm to remove the effects of physical variations from soil to soil. The normalization is based on laboratory measurements of available samples, primarily nearside maria, and is undoubtedly optimized for the proportions in which Ti- components are found in these soils. In particular, mare soils tend to have a much higher proportion of opaque mineral grains, which appears to be well correlated with Ti abundance. The relationship between Ti abundance and proportion of Ti-bearing glass (weighted for Ti abundance) is not as direct. Also shows the relationship between landing site soil average, AGR, and CSR Ti abundances (with CSR filtered to match resolution and field of view of AGR data). AGR Ti values show the best agreement with Ti soil averages, CSR Ti values being somewhat higher in high-Ti soils, and lower in low-Ti soils. These results would tend to support the argument that the technique for deriving Ti from the CSR measurements is optimized for one of the primary Ti-bearing components, most likely opaque mineral grains, and is thus over-compensating and reporting higher Ti values in mare areas, and underreporting Ti in highland areas with much lower proportions of opaque mineral grains. More information is contained in original.

Clark, P. E.↗
NASA NTRS2000

Developing CORBA-Based Distributed Scientific Applications from Legacy Fortran Programs

Recent progress in distributed object technology has enabled software applications to be developed and deployed easily such that objects or components can work together across the boundaries of the network, different operating systems, and different languages. A distributed object is not necessarily a complete application but rather a reusable, self-contained piece of software that co-operates with other objects in a plug-and-play fashion via a well-defined interface. The Common Object Request Broker Architecture (CORBA), a middleware standard defined by the Object Management Group (OMG), uses the Interface Definition Language (IDL) to specify such an interface for transparent communication between distributed objects. Since IDL can be mapped to any programming language, such as C++, Java, Smalltalk, etc., existing applications can be integrated into a new application and hence the tasks of code re-writing and software maintenance can be reduced. Many scientific applications in aerodynamics and solid mechanics are written in Fortran. Refitting these legacy Fortran codes with CORBA objects can increase the codes reusability. For example, scientists could link their scientific applications to vintage Fortran programs such as Partial Differential Equation(PDE) solvers in a plug-and-play fashion. Unfortunately, CORBA IDL to Fortran mapping has not been proposed and there seems to be no direct method of generating CORBA objects from Fortran without having to resort to manually writing C/C++ wrappers. In this paper, we present an efficient methodology to integrate Fortran legacy programs into a distributed object framework. Issues and strategies regarding the conversion and decomposition of Fortran codes into CORBA objects are discussed. The following diagram shows the conversion and decomposition mechanism we proposed. Our goal is to keep the Fortran codes unmodified. The conversion- aided tool takes the Fortran application program as input and helps programmers generate C/C++ header file and IDL file for wrapping the Fortran code. Programmers need to determine by themselves how to decompose the legacy application into several reusable components based on the cohesion and coupling factors among the functions and subroutines. However, programming effort still can be greatly reduced because function headings and types have been converted to C++ and IDL styles. Most Fortran applications use the COMMON block to facilitate the transfer of large amount of variables among several functions. The COMMON block plays the similar role of global variables used in C. In the CORBA-compliant programming environment, global variables can not be used to pass values between objects. One approach to dealing with this problem is to put the COMMON variables into the parameter list. We do not adopt this approach because it requires modification of the Fortran source code which violates our design consideration. Our approach is to extract the COMMON blocks and convert them into a structure-typed attribute in C++. Through attributes, each component can initialize the variables and return the computation result back to the client. We have tested successfully the proposed conversion methodology based on the f2c converter. Since f2c only translates Fortran to C, we still needed to edit the converted code to meet the C++ and IDL syntax. For example, C++/IDL requires a tag in the structure type, while C does not. In this paper, we identify the necessary changes to the f2c converter in order to directly generate the C++ header and the IDL file. Our future work is to add GUI interface to ease the decomposition task by simply dragging and dropping icons.

Sang, Janche↗
NASA NTRS2000

Efficient Use of Distributed Systems for Scientific Applications

Distributed computing has been regarded as the future of high performance computing. Nationwide high speed networks such as vBNS are becoming widely available to interconnect high-speed computers, virtual environments, scientific instruments and large data sets. One of the major issues to be addressed with distributed systems is the development of computational tools that facilitate the efficient execution of parallel applications on such systems. These tools must exploit the heterogeneous resources (networks and compute nodes) in distributed systems. This paper presents a tool, called PART, which addresses this issue for mesh partitioning. PART takes advantage of the following heterogeneous system features: (1) processor speed; (2) number of processors; (3) local network performance; and (4) wide area network performance. Further, different finite element applications under consideration may have different computational complexities, different communication patterns, and different element types, which also must be taken into consideration when partitioning. PART uses parallel simulated annealing to partition the domain, taking into consideration network and processor heterogeneity. The results of using PART for an explicit finite element application executing on two IBM SPs (located at Argonne National Laboratory and the San Diego Supercomputer Center) indicate an increase in efficiency by up to 36% as compared to METIS, a widely used mesh partitioning tool. The input to METIS was modified to take into consideration heterogeneous processor performance; METIS does not take into consideration heterogeneous networks. The execution times for these applications were reduced by up to 30% as compared to METIS. These results are given in Figure 1 for four irregular meshes with number of elements ranging from 30,269 elements for the Barth5 mesh to 11,451 elements for the Barth4 mesh. Future work with PART entails using the tool with an integrated application requiring distributed systems. In particular this application, illustrated in the document entails an integration of finite element and fluid dynamic simulations to address the cooling of turbine blades of a gas turbine engine design. It is not uncommon to encounter high-temperature, film-cooled turbine airfoils with 1,000,000s of degrees of freedom. This results because of the complexity of the various components of the airfoils, requiring fine-grain meshing for accuracy. Additional information is contained in the original.

Taylor, Valerie↗
NASA NTRS2001

Estimating Bias Error Distributions

This paper formulates the general methodology for estimating the bias error distribution of a device in a measuring domain from less accurate measurements when a minimal number of standard values (typically two values) are available. A new perspective is that the bias error distribution can be found as a solution of an intrinsic functional equation in a domain. Based on this theory, the scaling- and translation-based methods for determining the bias error distribution arc developed. These methods are virtually applicable to any device as long as the bias error distribution of the device can be sufficiently described by a power series (a polynomial) or a Fourier series in a domain. These methods have been validated through computational simulations and laboratory calibration experiments for a number of different devices.

Liu, Tian-Shu↗
NASA NTRS2001

Characterizing the Spatial and Temporal Distribution of Aerosol Optical Thickness Over the Atlantic Basin Utilizing GOES-8 Multispectral Data

In recent years, modeling and analysis efforts have suggested that the direct and indirect radiative effects of both anthropogenic and natural aerosols play a major role in the radiative balance of the earth and are an important factor in climate change calculations. The direct effects of aerosols on radiation and indirect effects on cloud properties are not well understood at this time. In order to improve the characterization of aerosols within climate models it is important to accurately parameterize aerosol forcing mechanisms at the local, regional, and global scales. This includes gaining information on the spatial and temporal distribution of aerosols, transport regimes and mechanisms, aerosol optical thickness, and size distributions. Although there is an expanding global network of ground measurements of aerosol optical thickness and size distribution at specific locations, satellite data must be utilized to characterize the spatial and temporal extent of aerosols and transport regimes on regional and global scales. This study was part of a collaborative effort to characterize aerosol radiative forcing over the Atlantic basin associated with the following three major aerosol components in this region: urban/sulfate, Saharan dust, and biomass burning. In-situ ground measurements obtained by a network of sun photometers during the Smoke Clouds and Radiation Experiment in Brazil (SCAR-B) and the Tropospheric Aerosol Radiative Forcing Observational Experiment (TARFOX) were utilized to develop, calibrate, and validate a Geostationary Operational Environmental Satellite (GOES)-8 aerosol optical thickness (AOT) product. Regional implementation of the GOES-8 AOT product was used to augment point source measurements to gain a better understanding of the spatial and temporal distributions of Atlantic basin aerosols during SCAR-B and TARFOX.

Fox, Robert↗
NASA NTRS2000

Expected Utility Distributions for Flexible, Contingent Execution

This paper presents a method for using expected utility distributions in the execution of flexible, contingent plans. A utility distribution maps the possible start times of an action to the expected utility of the plan suffix starting with that action. The contingent plan encodes a tree of possible courses of action and includes flexible temporal constraints and resource constraints. When execution reaches a branch point, the eligible option with the highest expected utility at that point in time is selected. The utility distributions make this selection sensitive to the runtime context, yet still efficient. Our approach uses predictions of action duration uncertainty as well as expectations of resource usage and availability to determine when an action can execute and with what probability. Execution windows and probabilities inevitably change as execution proceeds, but such changes do not invalidate the cached utility distributions, thus, dynamic updating of utility information is minimized.

Bresina, John L.↗
NASA NTRS2001

Spatial Distribution of Cyanobacteria in Modern Stromatolites

Living stromatolites consist of complex microbial communities with distinct distribution patterns for different microbial groups. The cyanobacterial populations of Highborne Cay Bahamas exemplify this phenomenon. Field observations reveal distinct distribution patterns for several of these cyanobacterial species. To date 10 different cyanobacterial cultures, including both filamentous and endolithic species, have been isolated from these stromatolites. We will present data on the growth and motility characteristics as well as on the nutritional requirements of these isolates. These data will then be correlated with the field observed distributions for these species. Lastly laboratory simulations of stromatolites grown under various conditions of irradiance, flow and cyanobacterial community composition will be presented. These experiments allow us to evaluate our predictions regarding controls on cyanobacterial distribution.

Prufert-Bebout, Lee↗
NASA NTRS2001

An XML-Based Protocol for Distributed Event Services

A recent trend in distributed computing is the construction of high-performance distributed systems called computational grids. One difficulty we have encountered is that there is no standard format for the representation of performance information and no standard protocol for transmitting this information. This limits the types of performance analysis that can be undertaken in complex distributed systems. To address this problem, we present an XML-based protocol for transmitting performance events in distributed systems and evaluate the performance of this protocol.

Smith, Warren↗
NASA NTRS2001

Global Lidar Observations of Aerosol Distribution and Radiative Influence

A very visible impact of human activities is the brownish aerosol haze that pervades many industrialized regions as well as areas in the subtropics and tropics where biomass burning occurs. Well known examples are the Asian Brown Cloud, Arctic Haze and East Coast Haze. Atmospheric transport transforms this haze into regional and hemispheric aerosol layers of significant concentrations. The overall impact on the radiation balance of the atmosphere, surface solar irradiance and other meteorology factors is recognized as a major uncertainty for climate change. In order to understand the impact, the global distribution of aerosol and their properties must be known. . A missing element of observations, but critical for understanding transport has been the height distribution of aerosol. Lidar measurements of aerosol height distribution have been important in GLOBE, ACE, INDOEX and other field studies A network of continuously operating eye safe lidar ground sites has now been established for baseline aerosol profiling. In 2002 NASA will launch the Geoscience Laser Altimeter System (GLAS) mission which will provide for the first time global observations of the height distribution of aerosol. The combination of these and other modem satellite observations, field experiments and models of global aerosol composition and transport should begin to unravel the impacts of particles in the atmosphere.

Spinhirne, James↗
NASA NTRS1998

A Distributed Simulation Facility to Support Human Factors Research in Advanced Air Transportation Technology

A distributed real-time simulation of the civil air traffic environment developed to support human factors research in advanced air transportation technology is presented. The distributed environment is based on a custom simulation architecture designed for simplicity and flexibility in human experiments. Standard Internet protocols are used to create the distributed environment, linking all advanced cockpit simulator, all Air Traffic Control simulator, and a pseudo-aircraft control and simulation management station. The pseudo-aircraft control station also functions as a scenario design tool for coordinating human factors experiments. This station incorporates a pseudo-pilot interface designed to reduce workload for human operators piloting multiple aircraft simultaneously in real time. The application of this distributed simulation facility to support a study of the effect of shared information (via air-ground datalink) on pilot/controller shared situation awareness and re-route negotiation is also presented.

Amonlirdviman, Keith↗
NASA NTRS2002

Visualizing Spatially Varying Distribution Data

Box plot is a compact representation that encodes the minimum, maximum, mean, median, and quarters information of a distribution. In practice, a single box plot is drawn for each variable of interest. With the advent of more accessible computing power, we are now facing the problem of visual icing data where there is a distribution at each 2D spatial location. Simply extending the box plot technique to distributions over 2D domain is not straightforward. One challenge is reducing the visual clutter if a box plot is drawn over each grid location in the 2D domain. This paper presents and discusses two general approaches, using parametric statistics and shape descriptors, to present 2D distribution data sets. Both approaches provide additional insights compared to the traditional box plot technique

Kao, David↗
NASA NTRS2002

Lessons Learned In Developing Multiple Distributed Planning Systems for the International Space Station

The planning processes for the International Space Station (ISS) Program are quite complex. Detailed mission planning for ISS on-orbit operations is a distributed function. Pieces of the on-orbit plan are developed by multiple planning organizations, located around the world, based on their respective expertise and responsibilities. The "pieces" are then integrated to yield the final detailed plan that will be executed onboard the ISS. Previous space programs have not distributed the planning and scheduling functions to this extent. Major ISS planning organizations are currently located in the United States (at both the NASA Johnson Space Center (JSC) and NASA Marshall Space Flight Center (MSFC)), in Russia, in Europe, and in Japan. Software systems have been developed by each of these planning organizations to support their assigned planning and scheduling functions. Although there is some cooperative development and sharing of key software components, each planning system has been tailored to meet the unique requirements and operational environment of the facility in which it operates. However, all the systems must operate in a coordinated fashion in order to effectively and efficiently produce a single integrated plan of ISS operations, in accordance with the established planning processes. This paper addresses lessons learned during the development of these multiple distributed planning systems, from the perspective of the developer of one of the software systems. The lessons focus on the coordination required to allow the multiple systems to operate together, rather than on the problems associated with the development of any particular system. Included in the paper is a discussion of typical problems faced during the development and coordination process, such as incompatible development schedules, difficulties in defining system interfaces, technical coordination and funding for shared tools, continually evolving planning concepts/requirements, programmatic and budget issues, and external influences. Techniques that mitigated some of these problems will also be addressed, along with recommendations for any future programs involving the development of multiple planning and scheduling systems. Many of these lessons learned are not unique to the area of planning and scheduling systems, so may be applied to other distributed ground systems that must operate in concert to successfully support space mission operations.

Maxwell, Theresa G.↗
NASA NTRS2003

Electron Bremsstrahlung Hard X-Ray Spectra, Electron Distributions and Energetics in the 2002 July 23 Solar Flare

We present and analyze the first high-resolution hard X-ray spectra from a solar flare observed in both X-ray/gamma-ray continuum and gamma-ray lines. The 2002 July 23 flare was observed by the Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The spatially integrated photon flux spectra are well fitted between 10 and 300 keV by the combination of an isothermal component and a double power law. The flare plasma temperature peaks at 40 MK around the time of peak hard X-ray emission and remains above 20 MK 37 min later. We derive the evolution of the nonthermal mean electron flux distribution by directly fitting the RHESSI X-ray spectra with the thin-target bremsstrahlung from a double power-law electron distribution with a low-energy cutoff. We also derive the evolution of the electron flux distribution on the assumption that the emission is thick-target bremsstrahlung. We find that the injected nonthermal electrons are well described throughout the flare by this double power-law distribution with a low-energy cutoff that is typically between 20 - 40 keV. Using our thick-target results, we compare the energy contained in the nonthermal electrons with the energy content of the thermal flare plasma observed by RHESSI and GOES. We find that the minimum total energy deposited into the flare plasma by nonthermal electrons, 2.6 x 10(exp 31) erg, is on the order of and possibly less than the energy in the thermal plasma. However, these fits do not rule out the possibility that the energy in nonthermal electrons exceeds the energy in the thermal plasma. This work was supported in part by the RHESSI Project and the NASA Sun-Earth Connection program.

Holman, G. D.↗
NASA NTRS2003

Electron Bremsstrahlung Hard X-Ray Spectra, Electron Distributions and Energetics in the 2002 July 23 Solar Flare

We present and analyze the first high-resolution hard X-ray spectra from a solar flare observed in both X-ray/gamma-ray continuum and gamma-ray lines. The 2002 July 23 flare was observed by the Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The spatially integrated photon flux spectra are well fitted between 10 and 300 keV by the combination of an isothermal component and a double power law. The flare plasma temperature peaks at 40 MK around the time of peak hard X-ray emission and remains above 20 MK 37 min later. We derive the evolution of the nonthermal mean electron flux distribution by directly fitting the RHESSI X-ray spectra with the thin-target bremsstrahlung from a double power-law electron distribution with a low-energy cutoff. We also derive the evolution of the electron flux distribution on the assumption that the emission is thick-target bremsstrahlung. We find that the injected nonthermal electrons are well described throughout the flare by this double power-law distribution with a low-energy cutoff that is typically between 20-40 keV. Using our thick-target results, we compare the energy contained in the nonthermal electrons with the energy content of the thermal flare plasma observed by RHESSI and GOES. We find that the minimum total energy deposited into the flare plasma by nonthermal electrons, 2.6 x 10(exp 31)erg, is on the order of and possibly less than the energy in the thermal plasma. However, these fits do not rule out the possibility that the energy in nonthermal electrons exceeds the energy in the thermal plasma.

Holman, Gordon D.↗