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Ablators - From Apollo to Future Missions to Moon, Mars and Beyond

Apollo was designed to carry astronauts safely back from the Moon at return speeds exceeding 11 km/s and requireddevelopment of a new ablative thermal protection system (TPS) to protect the capsule from entry heating. Mercuryand Gemini, that preceded Apollo, were focused on Earth orbiting system demonstration and lessons learned fromthem were used in Apollo. The ablative material and associated system development for Lunar return conditionsrequired considerable ground and flight testing. Mars Viking Lander missions required a new lighter weight ablatoras entry heating was benign compared to Apollo. Pioneer-Venus and Galileo Probe missions required a new and morecapable ablator than Apollo. After two decades, Mars Pathfinder followed by Mars Exploration Rover missions,smaller than Viking but more demanding, were able to use Viking ablative TPS. At the same time, advances in manufacturing and materials technology led to development of innovative lightweight ablators. These new ablators enabled Stardust and Genesis Sample Return Missions. Around the turn of this century, NASA decided on a scaled-upversion of the Apollo capsule for human exploration of Moon and Mars and the ablative heat shield to protect the CrewExploration Vehicle ended up being the Apollo ablative TPS. The Artemis 1 mission is currently fitted with tiledsystem, different than Orion EFT-1 but with the Apollo ablative material as a result of lessons learned. NASA iscurrently planning on sample return missions from Mars, and this will require robust ablative TPS that can providehigher reliability than any other past mission. There are still unexplored high scientific value destinations in the solarsystem. In situ exploration of Uranus, Neptune, Saturn and sample return missions with return speed much higher thanStardust will require ablators capable of withstanding extreme entry that are also efficient. New ablative TPS havebeen developed in anticipation of these future missions. This paper is intended to tell the story of these ablators,illustrated through examples. We see the use of flight proven ablators was sometimes a risky proposition and newablators perceived to be higher risk have proved otherwise. The history of ablators illustrates the challenges eachmission had to address, either through the use of flight proven or new ablative TPS, to be successful.

Venkatapathy, Ethiraj

Relationship between LIBS Ablation and Pit Volume for Geologic Samples: Applications for in situ Absolute Geochronology

In planetary sciences, in situ absolute geochronology is a scientific and engineering challenge. Currently, the age of the Martian surface can only be determined by crater density counting. However this method has significant uncertainties and needs to be calibrated with absolute ages. We are developing an instrument to acquire in situ absolute geochronology based on the K‐Ar method. The protocol is based on the laser ablation of a rock by hundreds of laser pulses. Laser Induced Breakdown Spectroscopy (LIBS) gives the potassium content of the ablated material and a mass spectrometer (quadrupole or ion trap) measures the quantity of 40Ar released. In order to accurately measure the quantity of released 40Ar in cases where Ar is an atmospheric constituent (e.g., Mars), the sample is first put into a chamber under high vacuum. The 40Arquantity, the concentration of K and the estimation of the ablated mass are the parameters needed to give the age of the rocks. The main uncertainties with this method are directly linked to the measures of the mass (typically some μg) and of the concentration of K by LIBS (up to 10%). Because the ablated mass is small compared to the mass of the sample, and because material is redeposited onto the sample after ablation, it is not possible to directly measure the ablated mass. Our current protocol measures the ablated volume and estimates the sample density to calculate ablated mass. The precision and accuracy of this method may be improved by using knowledge of the sample's geologic properties to predict its response to laser ablation, i.e., understanding whether natural samples have a predictable relationship between laser energy deposited and resultant ablation volume. In contrast to most previous studies of laser ablation, theoretical equations are not highly applicable. The reasons are numerous, but the most important are: a) geologic rocks are complex, polymineralic materials; b) the conditions of ablation are unusual (for example, variable vacuum pressure), and c) the ablation is made with hundreds of successive laser pulses. In this work, we aim to understand the effects that occur on LIBS spectra when a homogeneous rock or a mineral is ablated under high vacuum. Understanding these effects is important to define best practices for LIBS measurements and may lead to improved measurement (or possibly prediction) of the ablated volume. We will describe our laboratory approach and first results, and discuss its utility for situ absolute geochronology campaigns.

Devismes, D.

Ablation article and method

An ablation article, such as a conical heat shield, having an ablating surface is provided with at least one discrete area of at least one seed material, such as aluminum. When subjected to ablation conditions, the seed material is ablated. Radiation emanating from the ablated seed material is detected to analyze ablation effects without disturbing the ablation surface. By providing different seed materials having different radiation characteristics, the ablating effects on various areas of the ablating surface can be analyzed under any prevailing ablation conditions. The ablating article can be provided with means for detecting the radiation characteristics of the ablated seed material to provide a self-contained analysis unit.

Erickson, W. D.

Improving indirect-drive ablator performance through pulse shaping and material selection in double shell implosions

The double shell path to inertially confined volumetric thermonuclear burn relies on efficient kinetic energy transfer from an outer ablator shell to an inner shell containing DT fuel at implosion velocities near 250 km/s. In order to experimentally realize adequate compression, target imperfections and assembly features must be tightly controlled. Pulse shape and ablator material are critical design choices that impact all aspects of the implosion. In this article, we evaluate three designs: an Al ablator with single-shock radiation drive, a CH ablator with single-shock drive, and a CH ablator with reduced-adiabat 2-shock drive. All designs use the same W inner (pusher) shell overcoated with a glow discharge polymer tamper and filled with liquid-density DT. One-dimensional HYDRA simulations revealed that the plastic ablator design required the use of the 2-shock drive to match the performance of the Al design. Two-dimensional simulations resolving broadband surface roughness up to modes of several hundred placed only on the ablator showed plastic to greatly outperform Al. The plastic ablator designs did exhibit higher levels of inner shell instability growth when surface roughness was only placed at the pusher/tamper interface, which was mitigated with higher foam cushion densities. A unique and additional benefit of a plastic ablator is also discussed, where heating of the ablator by Au M-band radiation is predicted to rapidly expand the hemi-shell surfaces, closing the equatorial joint gap ahead of the first shock. Taken together, the properties of the plastic ablator for indirect-drive double shell implosions appear promising in removing several long-standing fabrication challenges.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Visualization of Capsule Reentry Vehicle Heat Shield Ablation Using Naphthalene PLIF

The Orion Multi-Purpose Crew Vehicle (MPCV) will use an ablative heat shield and improved understanding of the ablation process would be beneficial for design purposes. Given that ablation is a multi-physics process involving heat and mass transfer, codes aiming to predict heat shield ablation are in need of experimental data pertaining to the turbulent transport of ablation products for validation. At The University of Texas at Austin, a technique is being developed that uses planar laser-induced fluorescence (PLIF) of a low-temperature sublimating ablator (naphthalene) to visualize the transport of ablation products in a supersonic flow. Since ablation at reentry temperatures can be difficult to recreate in a laboratory setting it is desirable to create a limited physics problem and simulate the ablation process at relatively low temperature conditions using naphthalene. A scaled Orion MPCV model with a solid naphthalene heat shield has been tested in a Mach 5 wind tunnel at various angles of attack in the current work. PLIF imaging reveals the distribution of the ablation products as they are transported into the heat-shield boundary layer and over the capsule shoulders into the separated shear layer and backshell recirculation region. Visualizations of the capsule shear layer using both naphthalene PLIF and Schlieren imaging compared favorably. High concentrations of naphthalene in the capsule separated flow region, intermittent turbulent structures on the heat shield surface, and interesting details of the capsule shear layer structure were observed using the naphthalene PLIF technique. The capsule shear layer was also shown to generally appear to be more turbulent at lower angles of attack. Furthermore, the PLIF signal increased steadily over the course of a run indicating that during a wind tunnel run the model heated up and the rate of naphthalene ablation increased. The shear layer showed increasing signs of turbulence over the course of a wind tunnel run as well, likely because of the combination of increased surface roughness and surface blowing rate. PLIF imaging also detected regions with a relatively low concentration of naphthalene in the capsule backshell recirculation region that are most likely the result of cross-flow-induced vortices on the capsule afterbody.

Combs, Christopher S.

Depth-Resolved Lithiated Gradients in Pristine and Laser-Ablated Anodes During Fast Charging

Laser ablating 3D electrode microstructures is a technique to improve Li-ion battery fast-charge performance. This technique has been theoretically proposed and electrochemically validated previously in the literature. The fundamental principle underlying laser ablation is that the ablated features reduce Li-ion transport pathways, improving access to the electrode active material near the current collector. This, in turn, promotes more homogeneous electrode utilization. The present study seeks to directly affirm the physics attributed to laser ablation using operando high-speed synchrotron X-ray diffraction. In this study, depth-resolved graphite lithiation gradients are measured operando during high-rate (15 min) charging. The depth-resolved lithiation dynamics of both ablated and non-ablated anodes are compared. The results highlight that the laser-ablated graphite electrode has notably more homogeneous utilization as compared to the non-ablated electrode. Additionally, the ablated electrode has a significant delay in reaching the maximum graphite lithiation at the separator, indicating less propensity for lithium plating. During low rate delithiation/discharge (2 hr), the two cells' lithiation gradients converge. Notably, a calibrated physics-based electrochemical model accurately reflects experimental findings, suggesting the potential to use pseudo-4D models not only to optimize laser ablation parameters in fast-charge capable electrodes but also to guide fast charging protocols that avoid lithium plating.

25 ENERGY STORAGE

The Influence of Ablation on Radiative Heating for Earth Entry

Using the coupled ablation and radiation capability recently included in the LAURA flowfield solver, this paper investigates the influence of ablation on the shock-layer radiative heating for Earth entry. The extension of the HARA radiation model, which provides the radiation predictions in LAURA, to treat a gas consisting of the elements C, H, O, and N is discussed. It is shown that the absorption coefficient of air is increased with the introduction of the C and H elements. A simplified shock layer model is studied to show the impact of temperature, as well as the abundance of C and H, on the net absorption or emission from an ablation contaminated boundary layer. It is found that the ablation species reduce the radiative flux in the vacuum ultraviolet, through increased absorption, for all temperatures. However, in the infrared region of the spectrum, the ablation species increase the radiative flux, through strong emission, for temperatures above 3,000 K. Thus, depending on the temperature and abundance of ablation species, the contaminated boundary layer may either provide a net increase or decrease in the radiative flux reaching the wall. To assess the validity of the coupled ablation and radiation LAURA analysis, a previously analyzed Mars-return case (15.24 km/s), which contains significant ablation and radiation coupling, is studied. Exceptional agreement with previous viscous shock-layer results is obtained. A 40% decrease in the radiative flux is predicted for ablation rates equal to 20% of the free-stream mass flux. The Apollo 4 peak-heating case (10.24 km/s) is also studied. For ablation rates up to 3.4% of the free-stream mass flux, the radiative heating is reduced by up to 19%, while the convective heating is reduced by up to 87%. Good agreement with the Apollo 4 radiometer data is obtained by considering absorption in the radiometer cavity. For both the Mars return and the Apollo 4 cases, coupled radiation alone is found to reduce the radiative heating by 30 60% and the convective heating by less than 5%.

Johnston, Christopher O.

Assessment of tbe Performance of Ablative Insulators Under Realistic Solid Rocket Motor Operating Conditions (a Doctoral Dissertation)

Ablative insulators are used in the interior surfaces of solid rocket motors to prevent the mechanical structure of the rocket from failing due to intense heating by the high-temperature solid-propellant combustion products. The complexity of the ablation process underscores the need for ablative material response data procured from a realistic solid rocket motor environment, where all of the potential contributions to material degradation are present and in their appropriate proportions. For this purpose, the present study examines ablative material behavior in a laboratory-scale solid rocket motor. The test apparatus includes a planar, two-dimensional flow channel in which flat ablative material samples are installed downstream of an aluminized solid propellant grain and imaged via real-time X-ray radiography. In this way, the in-situ transient thermal response of an ablator to all of the thermal, chemical, and mechanical erosion mechanisms present in a solid rocket environment can be observed and recorded. The ablative material is instrumented with multiple micro-thermocouples, so that in-depth temperature histories are known. Both total heat flux and thermal radiation flux gauges have been designed, fabricated, and tested to characterize the thermal environment to which the ablative material samples are exposed. These tests not only allow different ablative materials to be compared in a realistic solid rocket motor environment but also improve the understanding of the mechanisms that influence the erosion behavior of a given ablative material.

Martin, Heath Thomas

Experimental Setup for the Laboratory Investigation of Micrometeoroid Ablation Using a Dust Accelerator

A facility has been developed to simulate the ablation of micrometeoroids in laboratory conditions. An electrostatic dust accelerator is used to generate iron particles with velocities of 10-70 kilometers. The particles are then introduced into a chamber pressurized with a target gas, where the pressure is adjustable between 0.01 and 0.5 Torr, and the particle partially or completely ablates over a short distance. An array of biased electrodes above and below the ablation path is used to collect the generated ions/electrons with a spatial resolution of 2.6 centimeters along the ablating particles path, thus allowing the study of the spatiotemporal evolution of the process. For completely ablated particles, the total collected charge directly yields the ionization coefficient of a given dust material-target gas combination. The first results of this facility measured the ionization coefficient of iron atoms with N2, air, CO2, and He target gases for impact velocities greater than 20 kilometers per second, and are reported by Thomas et al. The ablation chamber is also equipped with four optical ports that allow for the detection of the light emitted by the ablating particle. A multichannel photomultiplier tube system is used to observe the ablation process with a spatial and temporal resolution of 0.64 centimeters and 90 nanoseconds. The preliminary results indicate that it is possible to calculate the velocity of the ablating particle from the optical observations, and in conjunction with the spatially resolved charge measurements allow for experimental validation of ablation models in future studies.

Thomas, Evan

Demonstration of and future perspective on scaling ultrafast-laser-ablation microstructuring of Li-ion battery electrodes to roll-to-roll production and large-format cells

This work demonstrates integration of an ultrafast laser onto a roll-to-roll machine, the laser structuring of a double-sided, 700 m long roll of graphite battery anode and its subsequent manufacture into 27 Ah prismatic cells. The electrode was ablated with a novel hybrid-microstructure composed of both hexagonally arranged pores for enhanced rate performance and channels for fast electrolyte wetting. Subsequently, this anode and a non-ablated baseline anode are paired with an NMC111 cathode for cell building and electrochemical characterization. Compared to the baseline, laser ablated cells demonstrated a reduction in soaking time of at least 60%, an improvement in fast charge capability with >30% more capacity accepted during 6C charging, and an extension of cycle life of >40% during 0.5C cycling. Further, a perspective is provided on scaling ultrafast laser ablation of battery electrodes to industrial throughputs. Additionally, lessons learned from this pilot-scale demonstration are provided in regards to optical architecture, debris removal, and system control. A techno-economic analysis is used to demonstrate that laser ablation can be integrated into existing electrode manufacturing facilities with only ≈$\$$1.3 per kWh increase (≈2%) in manufacturing cost. Preemptive electrode design for laser ablation is discussed as a further method for enhancing performance. Finally, an analysis of available laser systems and beam-scanning architectures is used to determine design requirements to scale process throughput to a state-of-the-art speed of 50 m min −1 . This analysis demonstrates that laser ablating Li-ion battery electrodes has multiple benefits to manufacturing and battery performance, that the technology already exists to achieve high laser-ablation throughputs, and that integrating ultrafast laser ablation to electrode manufacturing will not create a cost or processing bottleneck.

25 ENERGY STORAGE

Criteria for identification of ablation debris from primitive meteoric bodies

Samples of ablated materials are analyzed to determine properties expected to be characteristic of particulates generated by the ablation of primitive meteoric bodies. Analyses of carbonaceous-chondrite fusion crusts and samples artificially ablated in the laboratory indicate that most meteor-ablation debris should consist of assemblages of silicate minerals, principally olivine, and micron-sized magnetic grains. It is expected that ablation debris of at least 10 microns should have abundances of Fe, Mg, Si, Ca, and Ni similar to those found in chondritic meteorites. Volatile species such as S, H2O, and Cl are lost during ablation and normally should not be found in ablated material. The major findings of this study are supported by analysis of spherules collected in the atmosphere which are thought, on separate grounds, to be genuine meteor-ablation products. The majority of meteoric bodies probably have cometary origins, and it is hoped that the ability to collect and identify meteor-ablation debris reliably will provide an opportunity to do laboratory analysis of cometary matter.-

Brownlee, D. E.

Higher Order Chemistry Models in the CFD Simulation of Laser-Ablated Carbon Plumes

Production of single-walled carbon nanotubes (SWNT) has taken place for a number of years and by a variety of methods such-as laser ablation, chemical vapor deposition, and arc-jet ablation. Yet, little is actually understood about the exact chemical kinetics and processes that occur in SWNT formation. In recent time, NASA Johnson Space Center has devoted a considerable effort to the experimental evaluation of the laser ablation production process for SWNT originally developed at Rice University. To fully understand the nature of the laser ablation process it is necessary to understand the development of the carbon plume dynamics within the laser ablation oven. The present work is a continuation of previous studies into the efforts to model plume dynamics using computational fluid dynamics (CFD). The ultimate goal of the work is to improve understanding of the laser ablation process, and through that improved understanding, refine the laser ablation production of SWNT. Fig. 1 shows a basic schematic of the laser-ablation oven at NASA-JSC. Construction of the facility is simple in concept. Two concentric quartz tubes of 1.5 mm thickness form the inner and outer tubes with inside diameters of 2.2 and 5.08 cm respectively. At one end of the inner tube are located two 60 Hz pulsed lasers operating at 1064 nm and 532 nm wavelength with beam diameters of 5 mm aligned coaxially with the longitudinal axis of the inner quartz tube. For standard nanotube production runs, a 10 ns 532 nm pulse is followed 50 ns later by a 10 ns 1064 nm pulse. Each pulse is of 300 mJ energy. A target of carbon graphite with approximately 1% nickel and cobalt catalysts is located at the other end of the inner quartz tube. In the ordinary processing of SWNT, a base flow of 100 sccm of argon is maintained from the laser location and exits past the carbon target at a pressure of 66.7 kPa. These conditions yield a baseline mass flow through the chamber of 2.723x10(exp -6)kg/s of argon. The whole oven facility is heated to a temperature of 1473 K prior to nanotube production runs. Upon laser irradiation, part of the carbon target ablates immediately and forms a carbon vapor plume that penetrates into the argon base flow towards the laser initially at supersonic velocities. In the previous studies either a single carbon species, C3, was used to model the plume development, or a simplified 11 species carbon model reduced down from the Krestinin and Moravsky model for full fullerene chemistry was used. While both of these options yielded significant results, it was felt that the actual chemistry occ&g in the carbon plume might have a greater affect on the plume than assumed. Indeed, in the earlier attempts at modeling the carbon plume, several thermophysical characteristics could never be matched to experimental observations of plume development - mainly the propagation distance of the plume itself. In the present study, two additional chemistry models will be used to duplicate the previous studies simulations of the carbon plume. The first chemistry model used in this study is again a reduced form of the Krestinin and Moravsky rates. However the highest order carbon species allowed has been increased from C6 to C30 - therefore allowing the simulation of up to a half of the standard C60 fullerene. The second chemistry model investigated is a reduced form of a full carbon nanotube model developed at NASA-JSC. The C30 studies have already been accomplished at the present time, and the reduced SWNT model studies are currently underway. To pursue the current study, one sacrifice had to be made in that the simulation grid spacing had to be increased from 0.5 mm spacing to 1 mm spacing for the sake of computational efficiency since computational effort is proportional to the square of the number of grid points multiplied by the number of species considered. propagation that is far more in line with the experimental results observed by Puretzky et al as shown in Fig. 2. e C6 studies had yielded a far greater propagation in previous studies. In addition, chemical species development with the C30 model indicates that many higher order carbon species are produced outside of the plume proper (indicated by plotting contours of the background argon concentrations in Fig. 3) - this result was not observed in previous studies. In fact, some species primarily occurred outside of the plume itself - as shown for C27 in Fig. 4 when it is compared to Fig. 3. It could be asserted that this has occurred because all of the C27 in the plume had already been consumed in the formation of C30, but this does not seem to be indicated over time. Several other factors that arose in the previous studies have also been made more clear by the use of the higher order chemical models - one being that the use of c6 as an indicator species was mistaken. C6 is the only carbon species in the previous studies that was not injected into the flowfield as a boundary condition; it was therefore hoped that this species would provide insight into the formation of higher order carbon species for comparison to full SWNT production. But, when the plot of total mass in the plume is examined on a species by species basis in Fig. 5, it is seen that Cg was a fairly insignificant contributor to the total carbon mass in the plume and would not provide information on higher order carbon formation. the thermophysical characteristics of the carbon plume as well as simulate the carbon plume using the reduced SWNT model to provide an even better simulation of full chemistry effects upon plume propagation.

Scott, C. D.

A Study of Ablation-Flowfield Coupling Relevant to the Orion Heatshield

The coupled interaction between an ablating surface and the surrounding aerothermal environment is studied. An equilibrium ablation model is coupled to the LAURA flowfield solver, which allows the char ablation rate (m-dot(sub c)) to be computed as part of the flowfield solution. The wall temperature (T(sub w)) and pyrolysis ablation rate (m-dot(sub g)) may be specified by the user, obtained from the steady-state ablation approximation, or computed from a a material response code. A 32 species thermochemical nonequilibrium flowfield model is applied, which permits the treatment of C, H, O, N, and Si containing species. Coupled ablation cases relevant to the Orion heatshield are studied. These consist of diffusion-limited oxidation cases with Avcoat as the ablation material. The m-dot(sub c) values predicted from the developed coupled ablation analysis were compared with those obtained from a typical uncoupled ablation analysis. The coupled results were found to be as much as 50% greater than the uncoupled values. This is shown to be a result of the cumulative effect of the two fundamental approximations inherent in the uncoupled analysis.

Johnston, Christopher O.

Ablators for Human and Robotic Exploration of the Moon, Mars and Beyond

When Apollo was designed to carry astronauts safely back from the Moon, at return speeds exceeding 11 km/s, it required development of a new lightweight ablative material to protect the capsule and crew from the intense heat of entry. Soon after the Apollo program, successful Mars Viking Lander missions employed a different and much lighter ablator in more benign entry conditions. On the other hand, the Pioneer-Venus and Galileo Probe missions that followed required yet another ablative system, to manage the extreme heating at those destinations, which was like flying a ballistic missile nose tip into a thermonuclear explosion. NASA had to invent a new heat-shield concept based on the rocket nozzle and ballistic missile ablative materials. In the mid 1990's, as the Science focus returned to Mars, advances in manufacturing, testing and materials technology led to innovative lightweight ablators that enabled comet and asteroid sample return missions and facilitated large lander missions such as MSL and Mars 2020. NASA's current plans for robotic and human exploration of the Moon, Mars and beyond introduce different constraints and new expectations for ablators. Human missions to Moon and Mars, sample return missions from Mars, and exploration of Uranus and Neptune, the two planets we are yet to explore, will require ablators that can withstand extreme environments, with verifiable robustness, and with raw materials and manufacturing approaches that are sustainable in the longer term. This talk will review the history of ablators as well as current ablative TPS development that addresses the requirements for future missions to Moon, Mars and beyond.

Mars and Beyond

Exploratory development of a flexible ablative covering for space shuttle application

An applied research program is considered for a preliminary design and development of a flexible ablative covering for the space shuttle vehicle that could be easily replaced and/or refurbished. The program was structured to concentrate resources on the major technical problem areas associated with the flexible ablator concept. These areas included: (1) fabrication of a suitable woven carpet reinforcement, (2) modification of a flexible ablator formulation for filling the woven carpet construction, and (3) testing of the flexible ablator concept. Several approaches were evaluated to obtain a flexible ablator. The final recommended solution was one in which the ablative filler was based on a low-density formulation of the elastomeric shield material series (ESM). The preferred approach is one in which a light-weight fabric backing is bonded to preformed and fully cured ESM, and the composite tufted with Astroquartz fiber to the desired tuft or pile density. Ablation tests performed in a hyperthermal arc facility demonstrated the ablation performance of the concept and overshoot capability of the system.

Hiltz, A. A.

On the origin of extraterrestrial stratospheric particles: Interplanetary dust or meteor ablation debris?

Meteor ablation debris was distinguished from unablated interplanetary dust in a collection of extraterrestrial particles collected in the stratosphere using NASA U-2 aircraft. A 62 g sample of the Murchison (C2) meteorite was artificially ablated to characterize ablation debris for comparison with the stratospheric particles. By using proper experimental conditions, artificial ablation debris can be produced that is similar to natural ablation debris. Analyses of natural fusion crusts, artificial fusion crust, and artificial ablation debris of the Murchison meteorite produced criteria for recognizing debris ablated by a primitive meteoroid. Ninety-five percent of the stratospheric particles can be described as either ablation debris from a primitive meteoroid, or as very primitive interplanetary dust.

Kyte, F. T.