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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Phase transitions and 2D spherical convection in a large icy satellite

Three ice phase transitions, based on experimental and theoretical results, were incorporated into a 2D spherical convection model. These phase transitions are the exothermic Ice 1-2, the endothermic Ice 2-6, and the exothermic Ice 6-8 phase transitions. The fluid is assumed isoviscous and the anelastic liquid formulation was used. The object is an icy satellite whose physical characteristics resemble those of Ganymede or Callisto. Structural models, similar to those of Mueller and McKinnon, with different core sizes, i.e. with different degree of differentiation were studied. The shells, i.e. the mantle of the satellite, is heated both internally and from below to account for the decaying radiogenic heating and the heat flow from the solid core. The lower boundary of the mantle is rigid and isothermal, the upper boundary is isothermal. Calculations with rigid and shear stress free upper boundary are carried out in order to assess the role of the different boundary conditions. Two different Rayleigh numbers, depending on the assumed value of the viscosity, were used in the calculations and the thermal evolution of the satellite was studied. The suit of calculations presented demonstrates that phase transition cannot be ignored when the thermal evolution of a large icy satellite has to be studied. The importance of the construction of the realistic phase diagram for ice was also documented. On the other hand the degree of differentiation, simulated with the structures with different core's radius does not seem to drastically influence the overall behavior of the convective activity. Within the limits of our simulations, the post-accretional evolution seems to be independent on the degree of primordial differentiation.

Forni, O.↗
NASA NTRS1999

Interaction Between Tropical Convection and its Embedding Environment: An Energetics Analysis of a 2-D Cloud Resolving Simulation

The phase relation between the perturbation kinetic energy (K') associated with the tropical convection and the horizontal-mean moist available potential energy (bar-P) associated with environmental conditions is investigated by an energetics analysis of a numerical experiment. This experiment is performed using a 2-D cloud resolving model forced by the TOGA-COARE derived vertical velocity. The imposed upward motion leads to a decrease of bar-P directly through the associated vertical advective cooling, and to an increase of K' directly through cloud related processes, feeding the convection. The maximum K' and its maximum growth rate lags and leads, respectively, the maximum imposed large-scale upward motion by about 1-2 hours, indicating that convection is phase locked with large-scale forcing. The dominant life cycle of the simulated convection is about 9 hours, whereas the time scales of the imposed large-scale forcing are longer than the diurnal cycle. In the convective events, maximum growth of K' leads maximum decay of the perturbation moist available potential energy (P') by about 3 hours through vertical heat transport by perturbation circulation, and perturbation cloud heating. Maximum decay of P' leads maximum decay of bar-P by about one hour through the perturbation radiative, processes, the horizontal-mean cloud heating, and the large-scale vertical advective cooling. Therefore, maximum gain of K' occurs about 4-5 hours before maximum decay of bar-P.

Li, Xiaofan↗
NASA NTRS1997

Environmental Impact Statement for the Cassini Mission

This Final Supplemental Environmental Impact Statement (FSEIS) to the 1995 Cassini mission Environmental Impact Statement (EIS) focuses on information recently made available from updated mission safety analyses. This information is pertinent to the consequence and risk analyses of potential accidents during the launch and cruise phases of the mission that were addressed in the EIS. The type of accidents evaluated are those which could potentially result in a release of plutonium dioxide from the three Radioisotope Thermoelectric Generators (RTGS) and the up to 129 Radioisotope Heater Units (RHUS) onboard the Cassini spacecraft. The RTGs use the heat of decay of plutonium dioxide to generate electric power for the spacecraft and instruments. The RHUs, each of which contains a small amount of plutonium dioxide, provide heat for controlling the thermal environment of the spacecraft and several of its instruments. The planned Cassini mission is an international cooperative effort of the National Aeronautics and Space Administration (NASA), the European Space Agency (ESA), and the Italian Space Agency (ASI) to conduct a 4-year scientific exploration of the planet Saturn, its atmosphere, moons, rings, and magnetosphere.

Source record↗
NASA NTRS2021

Astro-biological Exploration of Ocean Worlds, Enabled by an RPS Inside a Pressure Vessel

Exploring Ocean and Ice Worlds could help us to understand the origin and evolution of life in the universe. In our solar system we have identified six Ocean and Ice Worlds, namely Earth, Europa, Ganymede, Callisto, Enceladus, and Titan. Other potential targets include Dione, Triton, and Pluto. As documented in the Planetary Decadal Survey [1] and the NASA Roadmap to Ocean Worlds [2], these worlds are compelling science destinations, with oceans situated below their tens of kilometers thick ice shells. To reach them we need a new exploration paradigm with novel technological solutions. Key technological challenges revolve around the power for the probe and for melting, as well as protecting the payload against the extreme environments, including high pressure, low temperature, corrosion, and radiation. Far away from the Sun, and melted into the ice, we may only rely on long-lived internal power generation. Radioisotope Power Systems (RPS) with either static or dynamic conversion, utilizing the heat of decaying Plutonium-238, could be good candidates. We need suitable payloads that are protected and could survive the extreme environments, as well as enabling power and thermal systems for melting through the ice shield and to swim in the ocean below the ice. RPS could support the probe’s instruments and sub-systems, as well as provide a heat source for melting the ice while keeping the components at operating temperatures. Mitigating the external pressure while immersing inside the ice shell, and in the ocean, would require a new RPS design that operates inside a Pressure Vessel. In our paper, we will discuss general mission architecture trades and the sizing of a next generation RPS housed in a pressure vessel, broadly applicable to any of the Ocean Worlds satellites of interest. Through a technology focused approach, we address interconnected design and mission architecture aspects, including considerations for: the RPS and the Pressure Vessel; extreme environmental constraints; g-load tolerance; power and thermal systems sizing for science measurements; spacecraft operations through all mission phases; subsurface mobility; and planetary protection. The findings will inform the science community on instrument accommodation possibilities; the mission planning community on possible mission concepts; and the RPS development community on the science driven technology considerations.

Donitz, Benjamin P.↗
NASA NTRS1979

The magnetic field of Mercury

The paper examines the magnetic field observations and their analyses relating to the determination of the Mercury magnetic field. Methods of analyzing data included: (1) comparison of bow shock and magnetopause relative positions at Mercury to the earth, (2) direct spherical harmonic analysis, (3) magnetosphere modeling by an image dipole, and (4) scaling of a mathematical model for the terrestrial magnetosphere. Dipole moments were determined using partial quadrupole and octupole terms to improve the least-square fit of models to observations; analyses by method (2) yield a convergent series of dipole moments values considered to best represent the intrinsic planetary field. Finally, it is suggested that the origin of the magnetic field of Mercury cannot be uniquely determined, but the sources of convective energy may be radiogenic decay and heat release, gravitational settling, and differentiation of processional torques.

Ness, N. F.↗
NASA NTRS2005

Stirling Power Convertors Demonstrated in Extended Operation

A 110-W Stirling Radioisotope Generator (SRG110) is being developed by Lockheed Martin Astronautics of Valley Forge, Pennsylvania, under contract to the Department of Energy of Germantown, Maryland. The generator will be a high-efficiency electric power source for NASA space exploration missions that can operate in the vacuum of deep space or in a gaseous atmosphere, such as on the surface of Mars. The generator converts heat supplied by the decay of a plutonium heat source into electric power for the spacecraft. In support of the SRG110 project, the NASA Glenn Research Center has established a technology effort that will provide some of the key data to ensure a successful transition to flight for what will be the first dynamic power system to be used in space. High system efficiency is obtained through the use of free-piston Stirling power-conversion technology. Glenn tasks include in-house testing of Stirling convertors and controllers, materials evaluation and heater head life assessment, structural dynamics, evaluation of electromagnetic interference, assessment of organics, and reliability analysis. There is also an advanced technology effort that is complementary to the near-term technology effort, intended to reduce the mass of the Stirling convertor and increase efficiency.

Schreiber, Jeffrey G.↗
NASA NTRS2007

Processes in Early Planetesimals: Evidence from Ureilite Meteorites

Ureilites are primitive ultramafic achondrites composed largely of olivine and pigeonite, with minor augite, carbon, sulphide and metal. They represent very early material in the history of the Solar System and form a bridge between undifferentiated chondrites and fully differentiated asteroids. They show a mixture of chemical characteristics, some of which are considered to be nebula-derived (e.g. a negative correlation between Mg/Fe and Delta O-17 that resembles that of the ordinary chondrites but at lower Delta O-17 values) whereas others have been imposed by asteroidal differentiation. Carbon isotope data show a striking negative correlation of delta C-13 values with mg# in olivine. delta C-13 also correlates positively with Delta O-17, and therefore this isotopic variation was probably also nebula-derived. Thus, oxygen and carbon isotope compositions and Fe-Mg systematics of each monomict ureilite were established before differentiation processes began. Heated by decay of short-lived radioactive isotopes, the ureilite asteroid started to melt. Metal and sulphide would have melted first, forming a Fe-S eutectic liquid, which removed chalcophile elements and incompatible siderophile elements, and basaltic melts that removed Al, Ca and the LREE. Several elements show different abundances and/or correlations with Fo content in olivine, e.g. carbon shows a positive correlation in ferroan ureilites, and a weak or even negative correlation in more magnesian compositions. HSE such as Os and Ir also show different distributions, i.e. ureilites with Fo < 82 have very scattered Os and Ir concentrations, which reach high values, whereas ureilites with Fo > 82 tend to have much less scattered and overall lower Os and Ir abundances. A similar change in elemental behaviour is shown by the Fe-Mn relations in ureilitic olivines: those with Fo contents < 85 show a good negative correlation, whereas those with Fo > 85 show much greater scatter. This suggests that a major change affected the parent body at a time when melting had reached relatively magnesian bulk compositions. We consider that this event may have been a hit and run collision in which the ureilite parent body collided with a larger object. During the collision, the ureilite mantle broke up catastrophically but re-accreted in a jumbled state around the still-intact core. Mg-rich basaltic melts that were in the process of being formed at the time of break-up were retained in part as melt clasts that re-accreted to the regolith and are found in polymict ureilites.

Mittlefehldt, David W.↗
NASA NTRSDate not supplied

Multi-Anvil Experimentation Applied to Planetary Differentiation

Planets undergo differentiation that includes segregation of metal from silicate at high temperatures and pressures ranging from deep planetary core pressures (>300 GPa for Earth)to very shallow conditions of asteroids (<100 MPa).The multi-anvil solid media apparatus accesses the middle part of this range from 3 to 30 GPa –pressure relevant to the interior of Mercury, Venus, Earth, Earth’s Moon, and Mars. Early planets are thought to have experienced high temperatures from a combination of heat sources including radioactive decay, gravitational and accretional heating, and impact processes. These heating events led to melting of mantles and cores, thus requiring an understanding of solid-liquid equilibria in metal-silicate systems. In 2006 we established a multi-anvil facility at NASA-JSC combining an 880 ton press and a Kawai/Walker type module from Rockland Research. Our high PT work has been greatly facilitated by use of the COMPRES multi-anvil assemblies (1). Our recent work has included studies of element partitioning between liquid metal and liquid silicate(e.g., 2), as well as between minerals and melts(e.g., 3), both of which have led to better constraints on the timing and conditions of planetary differentiation(e.g. 4). Several examples involving sustained efforts will be summarized below and for the presentation. The distribution of siderophile (iron-loving) elements between core and mantle is controlled by metal-silicate equilibrium across a wide range of pressures. Therefore, experimentation across this pressure range helps to calibrate elemental partitioning models that can be applied to planets, and used to predict mantle chemistry and composition during planetary differentiation. Our studies have focused on a wide range of siderophile elements (refractory Ni, Co, W, Mo; volatile P, Ga, Cu, Sn, Sb; highly siderophile Au, Pd) that have constrained partitioning, valence, and isotopic fractionation, and applied to Earth, Moon, and Mars. When molten mantles (magma oceans) cool enough to initiate crystallization, the solids precipitate at depth and in large planets this involves high pressure phases like garnet, majorite, akimotoite, and ringwoodite. As these solids precipitate they can segregate from liquid by density contrasts, thus causing elemental fractionation which can be used to decipher timing of differentiation. Mineral/melt and metal/silicate equilibria in our lab have helped to better understand high pressure fractionation of isotopic parent/daughter pairs Hf/W, Mn/Cr, Pd/Ag, Pt/Os, Re/Os, and U/Pb, and their application to Earth, Moon and Mars. There remains great potential for multi-anvil experimentation to shed light on many pressure–dependent aspects of planetary evolution such as core formation, high pressure phase equilibria, redox equilibria, and volatile evolution and storage. References1. Leinenweber, K., et al.(2012) American Mineralogist,97, 353–368. 2.Righter, K., et al.(2020) Geochem. Persp. Lett.15, 1-6.3. Righter, K., et al.(2020) Met. Planet. Sci 55, 2741-2757.4. Righter, K., et al.(2020)Earth and Planetary Science Letters,552, 116590.

pressure↗
NASA NTRS1994

The heating of nova ejecta by radioactive decays of the beta-unstable nuclei

Recent nucleosynthesis and hydrodynamic calculations of the consequences of accretion onto massive ONeMg white dwarf stars show that under certain circumstances significant amounts of the beta-unstable nuclei can be produced and ejected by the resulting explosion. We use these calculations as a guide in order to obtain the conditions under which the heating of the ejected material by the nonthermal electrons and positrons produced by the decays of the beta-unstable nuclei is sufficient to overcome the cooling from adiabatic expansion and lead to the production of X-ray-emitting coronal gas. These conditions are as follows: (1) a mass fraction for Na-22 of the order of 10(exp -3) or greater, (2) an expansion velocity in the range approximately 10(exp 2) - 10(exp 3) km/s, (3) a photospheric radius of approximately 10(exp 14) cm, (4) if the density distribution in the atmosphere satisfies a power law, then the exponent must be less than 3 for heating to overcome adiabatic cooling. Both the simulations of the outburst and the model atmosphere fits to the observed energy distributions, however, imply that the exponent is greater than or = 3 during the early phases of the outburst. Nevertheless, for a value of the exponent of 2, we predict the time when hot coronal gas can form during the expansion phases of the envelope.

Pistinner, Shlomi↗
NASA NTRS2017

Hydrogen Balmer Line Broadening in Solar and Stellar Flares

The broadening of the hydrogen lines during flares is thought to result from increased charge (electron, proton) density in the flare chromosphere. However, disagreements between theory and modeling prescriptions have precluded an accurate diagnostic of the degree of ionization and compression resulting from flare heating in the chromosphere. To resolve this issue, we have incorporated the unified theory of electric pressure broadening of the hydrogen lines into the non-LTE radiative-transfer code RH. This broadening prescription produces a much more realistic spectrum of the quiescent, A0 star Vega compared to the analytic approximations used as a damping parameter in the Voigt profiles. We test recent radiative-hydrodynamic (RHD) simulations of the atmospheric response to high nonthermal electron beam fluxes with the new broadening prescription and find that the Balmer lines are overbroadened at the densest times in the simulations. Adding many simultaneously heated and cooling model loops as a 'multithread' model improves the agreement with the observations. We revisit the three component phenomenological flare model of the YZ CMi Megaflare using recent and new RHD models. The evolution of the broadening, line flux ratios, and continuum flux ratios are well-reproduced by a multithread model with high-flux nonthermal electron beam heating, an extended decay phase model, and a 'hot spot' atmosphere heated by an ultra relativistic electron beam with reasonable filling factors: approximately 0.1%, 1%, and 0.1% of the visible stellar hemisphere, respectively. The new modeling motivates future work to understand the origin of the extended gradual phase emission.

Kowalski, Adam F.↗
NASA NTRS1990

Heating and melting of small icy satellites by the decay of Al-26

The effect of radiogenic heating due to Al-26 on the thermal evolution of small icy satellites is studied. The object is to find the extent of internal melting as a function of the satellite radius and of the initial Al-26 abundance. The implicit assumption, based on observations of young stars, is that planet and satellite accretion occurred on a time scale of about 10 to the 6th yr (comparable with the lifetime of Al-26. The icy satellites are modeled as spheres of initially amorphous ice, with chondritic abundances of K-40, Th-232, U-235, and U-238, corresponding to an ice/dust mass ratio of 1. Evolutionary calculations are carried out, spanning 4.5 x 10 to the 9th yr, for different combinations of the two free parameters. Heat transfer by subsolidus convection is neglected for these small satellites. The main conclusion is that the initial Al-26 abundance capable of melting icy bodies of satellite size to a significant extent is more than 10 times lower than that prevailing in the interstellar medium (or that inferred from the Ca-Al rich inclusions of the Allende meteorite, about 7 x 10 to the -7th by mass).

Prialnik, Dina↗
NASA NTRS1990

Heating and melting of small icy satellites by the decay of 26Al

We study the effect of radiogenic heating due to 26Al on the thermal evolution of small icy satellites. Our object is to find the extent of internal melting as a function of the satellite radius and of the initial 26Al abundance. The implicit assumption, based on observations of young stars, is that planet and satellite accretion occurred on a time scale of approximately 10(6) yr (comparable with the lifetime of 26Al). The icy satellites are modeled as spheres of initially amorphous ice, with chondritic abundances of 40K, 232Th, 235U, 238U, corresponding to an ice/dust mass ratio of 1. Evolutionary calculations are carried out, spanning 4.5 x 10(9) yr, for different combinations of the two free parameters. Heat transfer by subsolidus convection is neglected for these small satellites. Our main conclusion is that the initial 26Al abundance capable of melting icy bodies of satellite size to a significant extent is more than 10 times lower than that prevailing in the interstellar medium (or that inferred from the Ca-Al rich inclusions of the Allende meteorite, approximately 7 x 10(-7) by mass). We find, for example, that an initial 26Al mass fraction of approximately 4 x 10(-8) is sufficient for melting almost completely icy spheres with radii of 800 km, typical of the larger icy planetary satellites. We also find that for any given 26Al abundance, there is a narrow range of radii below which only marginal melting occurs and above which most of the ice melts (and refreezes later). Since extensive melting may have important consequences, such as differentiation, gas release, and volcanic activity, the effect of 26Al should be included in future studies of satellite interiors.

Non-NASA Center↗
NASA NTRS1991

A technique to measure the thermal diffusivity of high Tc superconductors

High T(sub c) superconducting electrical current leads and ground straps will be used in cryogenic coolers in future NASA Goddard Space Flight Center missions. These superconducting samples are long, thin leads with a typical diameter of two millimeters. A longitudinal method is developed to measure the thermal diffusivity of candidate materials for this application. This technique uses a peltier junction to supply an oscillatory heat wave into one end of a sample and will use low mass thermocouples to follow the heat wave along the sample. The thermal diffusivity is calculated using both the exponential decay of the heat wave and the phase shift to the wave. Measurements are performed in a cryostat between 10 K and room temperature.

Powers, Charles E.↗
NASA NTRS1990

A technique to measure the thermal diffusivity of high T(sub c) superconductors

High T(sub c) superconducting electrical current leads and ground straps will be used in cryogenic coolers in future NASA Goddard Space Flight Center missions. These superconducting samples will be long, thin leads with a typical diameter of two millimeters. A longitudinal method is being developed to measure the thermal diffusivity of candidate materials for this application. This technique will use a peltier junction to supply an oscillatory heat wave into one end of a sample and will use low mass thermocouples to follow the heat wave along the sample. The thermal diffusivity will be calculated using both the exponential decay of the heat wave and the phase shift of the wave. Measurements will be done in a cryostat between 10 K and room temperature.

Powers, Charles E.↗
NASA NTRS2008

General Purpose Heat Source Simulator

The General Purpose Heat Source (GPHS) project seeks to combine the development of an electrically heated, single GPHS module simulator with the evaluation of potential nuclear surface power systems. The simulator is designed to match the form, fit, and function of actual GPHS modules which normally generate heat through the radioactive decay of Pu238. The use of electrically heated modules rather than modules containing Pu238 facilitates the testing of the subsystems and systems without sacrificing the quantity and quality of the test data gathered. Current GPHS activities are centered on developing robust heater designs with sizes and weights which closely match those of actual Pu238 fueled GPHS blocks. Designs are being pursued which will allow operation up to 1100 C.

Emrich, William J., Jr.↗
NASA NTRS2008

General Purpose Heat Source Simulator

The General Purpose Heat Source (GPHS) simulator project is designed to replicate through the use of electrical heaters, the form, fit, and function of actual GPHS modules which generate heat through the radioactive decay of Pu238. The use of electrically heated modules rather than modules containing Pu238 facilitates the testing of spacecraft subsystems and systems without sacrificing the quantity and quality of the test data gathered. Previous GPHS activities are centered around developing robust heater designs with sizes and weights that closely matched those of actual Pu238 fueled GPHS blocks. These efforts were successful, although their maximum temperature capabilities were limited to around 850 C. New designs are being pursued which also replicate the sizes and weights of actual Pu238 fueled GPHS blocks but will allow operation up to 1100 C.

Emrich, Bill↗
NASA NTRSDate not supplied

Radiation and Nuclear Technology in Planetary Cave Environments

Many technological and environmental challenges must be resolved to enable successful lunar habitation and exploration, and to maximize scientific return. This presentation is intended as a preliminary discussion on three such areas of interest with the intent to identify likely areas of mutual benefit for collaboration and data sharing between the space nuclear and radiological disciplines with the planetary cave community. First is the previously identified and studied possible application of lunar lava tubes or pits to reduce the solar and cosmic radiation environment burden on crew health and hardware reliability. This is an area of continued interest, and should be kept in the forefront of discussion during the selection of sites for potential exploration or long-term habitation. In theory, the prospect of using existing morphology presents an enticing opportunity to reduce the requirements on landed mass or construction while also reducing dose or fluence of harmful natural radiation. However, such discussions should also include the practical implications of relocating habitation hardware and personnel from a landing site to a subsurface location. Inherent risks associated with landing in proximity to the relevant terrain must also be considered and weighed against those imposed by the natural radiation environment. Second is a discussion on the means by which a long-term habitation module or base of operations may be powered throughout the lunar day-night cycle. Fission surface power presents an opportunity to establish round-the-clock power in any lunar surface environment, including permanently shadowed regions where solar panels cannot operate, or in any other non-polar region where solar radiation is available for no more than two weeks per four-week cycle. Among the drawbacks of fission surface power is the need to either land and co-locate a heavy shield to minimize radiological consequences to personnel or equipment, land and operate construction equipment capable of restructuring the in-situ regolith to provide appropriate shielding, or to make use of existing topology features (e.g. craters or pits) to serve as pre-formed radiation barriers. A realistic assessment of the practicality of this third option should involve the selection of candidate features from existing surveys, and assess the effectiveness of the approach using modern radiation transport methodologies. Consideration must be made for the needs to reject waste heat in the thermal power conversion process, which typically requires the use of large area radiators. Energy must be exchanged from the reactor and power conversion system to such radiators, and the impacts on thermal efficiency and secondary scatter of nuclear radiation must be considered. Further consideration should be made for the implications of placement of a power source such that it does not sacrifice valuable scientific opportunity. Placement of a reactor is likely to thereafter prevent personnel access within that feature. Third is a discussion on the use of portable radioisotope power systems (RPS) within confined spaces, both with respect to the dose effects of emitted nuclear radiation and also performance associated with emitted thermal radiation. Radioisotope power systems provide a unique capability to power objects with no reliance upon solar radiance. However, their useable power production relies upon the flow of heat from ‘hot side’ (decaying radioisotope) to ‘cold side’ (radiators emitting heat to space). In the case of a confined volume in vacuum such as a lunar lava tube, that radiated energy will absorb into the wall, which is already above the ‘cold background’ temperature of dark space, and then gradually rises in temperature. That temperature rise, and its implications on availability of useable electrical power, will depend upon factors such as enclosure volume, thermal emissivity/absorptivity, and thermal conductivity through the depth of absorbing media. The advantages of nuclear technology may prove to enable unique scientific exploration opportunities, both above the lunar surface and below. In turn, the unique advantages of lunar lava tubes or pits may present unique opportunities to enhance the application of these technologies and to mitigate the effects of radiation from both natural and technological sources. A discussion on these pairings may prove to be valuable to all, in our endeavor to explore our neighboring worlds.

Radiation↗
NASA NTRS1983

Mass and energy balance in the 1973 August 9 flare

The mass and energy balance of the thermal plasma during the decay phase of the solar flare of August 9, 1973, are studied. The analysis is based on observationally determined values for the differential emission measure, density, turbulent and bulk velocities, and physical dimensions. The total particle content and total thermal energy content of the flare plasmas with temperatures above 100,000 K and their variation with time are calculated. The particle loss and the energy losses through radiation, conduction, and convection are evaluated. The decrease in total particle content can be accounted for by the convective losses through the loop footprints at 100,000 K. Radiation is the dominant energy loss mechanism although convective losses at 100,000 K can be important. Conductive losses at 100,000 K into cooler chromospheric material appear to be negligible. The decrease in the total energy content during the decay phase is equal to the sum of the energy losses over the period of observation. No requirement is found for continued heating during the decay phase.

Dere, K. P.↗