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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 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

The Asteroid Rotation Period Survey Using the China Near-Earth Object Survey Telescope (CNEOST)

We initiated the bilateral collaboration between the Lulin Observatory and the Purple Mountain Observatory to collect asteroid lightcurves using the Chinese Near-Earth Object Survey Telescope at the Xuyi Observation Station. The primary goal of this collaboration was to discover super-fast rotators (SFRs) and study their physical properties. Two campaigns have been conducted: (a) a survey of ∼45 deg{sup 2} using 8 minute cadence during 2017 February 26–March 2, and (b) a survey of ∼60 deg{sup 2} using 10 minute cadence during 2018 March 9–12. Our samples are mainly main-belt asteroids and some Hildas and Jupiter Trojans. Out of 4522 collected lightcurves, 506 reliable rotation periods were obtained. Among the reliable rotation periods, we found 16 candidates with a possible rotation period of <2.2 hr, in which (134291) 2006 DZ6 shows a very convincing folded lightcurve and the other 15 candidates only have a likely trend. Further confirmation is needed for the rotation periods of these SFR candidates. In addition, (2280) Kunikov seems to have an eclipsing feature on its lightcurve with a relatively long rotation period suggesting that it is likely a fully synchronized binary asteroid. When the preliminary spin-rate distributions were carried out for asteroids using different sizes, no obvious difference was found.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

A Search for L4 Earth Trojan Asteroids Using a Novel Track-before-detect Multiepoch Pipeline

We report Earth Trojan asteroids are an important but elusive population that co-orbit with Earth at the L4 and L5 Lagrange points. There is only one known, but a large population is theoretically stable and could provide insight into our solar system’s past and present, as well as planetary defense. In this paper, we present the results of an Earth Trojan survey that uses a novel shift-and-stack detection method on 2 nights of data from the Dark Energy Camera. We find no new Earth Trojan asteroids. We calculate an upper limit on the population that is consistent with previous searches despite much less sky coverage. Additionally, we elaborate on previous upper-limit calculations using current asteroid population statistics and an extensive asteroid simulation to provide the most up-to-date population constraints. We find an L4 Earth Trojan population of N ET < 1 for H = 13.93, N ET < 10 for H = 16, and N ET < 938 for H = 22.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Evaluating Short-warning Mitigation via Intentional Robust Disruption of a Hypothetical Impact of Asteroid 2023 NT1

We investigate various short-warning mitigation scenarios via fragmentation for a hypothetical impact of asteroid 2023 NT1, a near-Earth object (NEO) that was discovered on 2023 July 15, two days after its closest approach to Earth on July 13. The asteroid passed by Earth within ∼0.25 lunar distances, with a closest approach of ∼1 × 10 5 km and a velocity of 11.27 km s −1 . Its size remains largely uncertain, with an estimated diameter range of 26–58 m and a most probable estimate of 34 m (JPL Sentry, 2023 September 15; weighted by the NEO size frequency distribution). If 2023 NT1 had collided with Earth, it could have caused significant local damage. Assuming a spherical asteroid with a diameter of 34 m, uniform density of 2.6 g cm −3 , and impact velocity of 15.59 km s −1 , a collision would have yielded an estimated impact energy of ∼1.5 Mt, approximately 3 times the energy of the Chelyabinsk airburst in 2013. We analyze the effectiveness of mitigation via intentional robust disruption for objects similar to 2023 NT1. We utilize Pulverize It (PI), a NASA Innovative Advanced Concepts study of planetary defense via fragmentation, to model potential mitigation scenarios through simulations of hypervelocity asteroid disruption and atmospheric ground effects in the case of a terminal defense mode. Simulations suggest that PI is an effective multimodal approach for planetary defense that can operate in extremely short interdiction modes, in addition to long interdiction timescales with extended warning. Our simulations support the proposition that threats like 2023 NT1 can be effectively mitigated with intercepts of 1 day (or less) prior to impact, yielding minimal to no ground damage.

Asteroids↗
DOE OSTI2023

X-Ray Energy Deposition Model for Simulating Asteroid Response to a Nuclear Planetary Defense Mitigation Mission

Abstract In the event of a potentially catastrophic asteroid impact, with sufficient warning time, deploying a nuclear device remains a powerful option for planetary defense if a kinetic impactor or other means of deflection proves insufficient. Predicting the effectiveness of a potential nuclear deflection or disruption mission depends on accurate multiphysics simulations of the device's X-ray energy deposition into the asteroid and the resulting material ablation. The relevant physics in these simulations span many orders of magnitude, require a variety of different complex physics packages, and are computationally expensive. Having an efficient and accurate way of modeling this system is necessary for exploring a mission's sensitivity to the asteroid's range of physical properties. To expedite future simulations, we present a completed X-ray energy deposition model developed using the radiation-hydrodynamics code Kull that can be used to initiate a nuclear mitigation mission calculation. The model spans a wide variety of possible mission initial conditions: four different asteroid-like materials at a range of porosities, two different source spectra, and a broad range of radiation fluences, source durations, and angles of incidence. Using blowoff momentum as the primary metric, the model-initiated simulation results match the full radiation-hydrodynamics results to within 10%.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2013

OSIRIS-REx Will Return a Sample of Asteroid 1999 RQ36 for Astrochemistry

Origins, Spectral Interpretation, Resource Identification, Security, Regolith Explorer (OSIRIS-REx) is the third mission in NASA's New Frontiers program. OSIRIS-REx launches in 2016 and will return the first pristine samples of carbonaceous material from the surface of a primitive asteroid in 2023. The target, (101955) 1999 RQ36, is 1/2 km diameter roughly spherical Apollo near-Earth asteroid. It is expected to be carbonaceous, similar to CI or CM carbonaceous chondrites. This organic-rich remnant from the early Solar System is also among the most potentially hazardous asteroids known with a 1 in 2500 chance of impacting the Earth in the late 22nd century. OSIRIS-REx will measure the Yarkovsky effect to better constrain future orbit and impact potential of this and other asteroids. OSIRIS-REx will image, map, and spectrally characterize RQ36 from 0.4-50 icron. The returned sample of regolith will be >60g (and up to 2kg) and thus the largest extraterrestrial sample returned from space since Apollo 17. Unlike meteorites, the sample will come from a known, well-characterized source and will be collected and transported to Earth pristine from terrestrial contamination. It will be available for study by the global astrochemistry community to address fundamental questions about the origin and evolution of the solar system and the life it harbors.

organic-rich↗
NASA NTRS2014

Concepts of Operations for Asteroid Rendezvous Missions Focused on Resources Utilization

Several asteroids are the targets of international robotic space missions currently manifested or in the planning stage. This global interest reflects a need to study these celestial bodies for the scientific information they provide about our solar system, and to better understand how to mitigate the collision threats some of them pose to Earth. Another important objective of these missions is providing assessments of the potential resources that asteroids could provide to future space architectures. In this paper, we examine a series of possible mission operations focused on advancing both our knowledge of the types of asteroids suited for different forms of resource extraction, and the capabilities required to extract those resources for mission enhancing and enabling uses such as radiation protection, propulsion, life support, shelter and manufacturing. An evolutionary development and demonstration approach is recommended within the framework of a larger campaign that prepares for the first landings of humans on Mars. As is the case for terrestrial mining, the development and demonstration approach progresses from resource prospecting (understanding the resource, and mapping the 'ore body'), mining/extraction feasibility and product assessment, pilot operations, to full in-situ resource utilization (ISRU). Opportunities to gather specific knowledge for ISRU via resource prospecting during science missions to asteroids are also examined to maximize the pace of development of needed ISRU capabilities and technologies for deep space missions.

radiation protection↗
NASA NTRS2015

The OSIRIS-REx Asteroid Sample Return Mission Operations Design

OSIRIS-REx is an acronym that captures the scientific objectives: Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer. OSIRIS-REx will thoroughly characterize near-Earth asteroid Bennu (Previously known as 1019551999 RQ36). The OSIRIS-REx Asteroid Sample Return Mission delivers its science using five instruments and radio science along with the Touch-And-Go Sample Acquisition Mechanism (TAGSAM). All of the instruments and data analysis techniques have direct heritage from flown planetary missions. The OSIRIS-REx mission employs a methodical, phased approach to ensure success in meeting the mission's science requirements. OSIRIS-REx launches in September 2016, with a backup launch period occurring one year later. Sampling occurs in 2019. The departure burn from Bennu occurs in March 2021. On September 24, 2023, the Sample Return Capsule (SRC) lands at the Utah Test and Training Range (UTTR). Stardust heritage procedures are followed to transport the SRC to Johnson Space Center, where the samples are removed and delivered to the OSIRIS-REx curation facility. After a six-month preliminary examination period the mission will produce a catalog of the returned sample, allowing the worldwide community to request samples for detailed analysis. Traveling and returning a sample from an Asteroid that has not been explored before requires unique operations consideration. The Design Reference Mission (DRM) ties together spacecraft, instrument and operations scenarios. Asteroid Touch and Go (TAG) has various options varying from ground only to fully automated (natural feature tracking). Spacecraft constraints such as thermo and high gain antenna pointing impact the timeline. The mission is sensitive to navigation errors, so a late command update has been implemented. The project implemented lessons learned from other "small body" missions. The key lesson learned was 'expect the unexpected' and implement planning tools early in the lifecycle. This paper summarizes the ground and spacecraft design as presented at OSIRIS-REx Critical Design Review(CDR) held April 2014.

mission operations↗
NASA NTRS2013

Terminal Guidance Navigation for an Asteroid Impactor Spacecraft

Near Earth Asteroids could potentially cause a great deal of devastation if one were to impact the Earth. If such an asteroid were found, the next step would be to mitigate the threat by one of several options, the most viable of which is to deflect the asteroids trajectory such that it misses the Earth by hitting it at a very high velocity with a spacecraft. The technology to perform such a deflection has been demonstrated by the Deep Impact (DI) mission, which successfully collided with comet Tempel 1 in July 2005 using an onboard autonomous navigation system, called AutoNav, for the terminal phase of the mission. In this paper, we evaluate the ability of AutoNav to impact a wide range of scenarios that an deflection mission could encounter, varying parameters such as the approach velocity, phase angle, size of the asteroid, and the determination of spacecraft attitude. Using realistic Monte Carlo simulations, we tabulated the probability of success of the deflection as a function of these parameters, and find the highest sensitivity to be due the spacecraft attitude determination mode. We conclude with some recommendations for future work.

autonomous navigation↗
NASA NTRS2014

Concerning the Charging of an Exploration Craft on and near a Small Asteroid

Introduction: An object immersed in an airless plasma environment will experience a natural process of surface charging in order to acheieve current balance, or zero net electric current to the object. It has been shown in recent computer simulations that the small-body plasma environment is very complex [1], considering effects of photoemission, topography, and formation of a plasma wake. For this work we consider an exploration craft (or astronaut) immersed within a plasma environment near an asteroid, which exhibits widely varying solar wind and photoelectric particle fluxes and continuously evolving illumination conditions. Objective: We aim to determine how an explo-ration craft or astronaut suit accumulates charge while located in the "nightside" asteroid wake where the particle fluxes are reduced, and in the dayside near-surface photoelectron sheath, by combining an object charging model [2] with kinetic simulations of a near-asteroid plasma environment [1]. We consider an astronaut floating near the asteroid while not in contact with the surface, as well as an astronaut moving along the surface using their hands/gloves to crawl along. Results: The modeling results suggest that remediation of triboelectric charge via accumulation of plasma currents is an important factor to consider when designing future NEA mission infrastructure, especially if repeated and frequent contact with the surface is planned. In shadowed regions such as the location shown in Fig. 1a, the plasma currents are so low (and the effective charge-remediation timescale so long, e.g. minutes to hours) that repeated contact with the surface tribocharges the glove in an uncontrollable fashion, as shown for two representative electron temperatures in Fig. 2a. The resulting buildup of significant negative charge would eventually initiate some other "current of last resort" [4] such as transport of positively-charged dust, field-emission from the glove, or significant alteration of environmental ion currents within the wake. In contrast, the few-meters-thick dayside photoelectron sheath in which the astronaut of Fig. 1b is immersed in is so rich in electrons (and hence so electrically conductive) that accumulated tribocharge dissipates almost instantaneously (e.g. in less than a ms) as shown in Fig. 2b. As our model astronaut orbits the NEA they would experience plasma currents and associated charge re-mediation times spanning many orders of magnitude, and the fusion between our numerical models provides a detailed understanding of the charging hazards possibly associated with contact-based NEA exploration.

Asteroid↗
NASA NTRS2015

Investigating the Efficacy of CubeSats for Asteroid Detection

A simulation to examine the potential of a network of CubeSats for detecting Near Earth Objects is discussed, in terms of goals, methods used and initial results obtained. By designing a basic optical system and the orbital parameters of the satellites in this network, their effectiveness for detecting asteroids is examined, with a small sample of cataloged asteroids considered.The conditions to be satisfied for detection cover both the geometrical aspects of astronomy such as field of view and line of sight, along with more technical optics-based conditions such as resolution and sensitivity of our telescopes. Of special interest to us in this work is the region of the sky between 45 deg. and 90 deg. from the Sun, as seen from the Earth. This part of the sky is currently unobservable by ground-based surveys and so provides the primary reason to consider a space-based one. There exist a number of issues with the simulation which call these results into question, but an eort has been made to remove those results which exceed the possible capabilities of the satellite network, and identify those aspects of the mission which should be examined in order to provide an in-depth assessment of it's performance. With these filters applied to the overall data, a tentative result of 1458 total detections over an 85 year period has been obtained, with 14 of the 22 asteroids in the sample being detected at least once. A number of ways in which the simulation could be improved are also proposed, both in-terms of addressing the aforementioned issues, as well as how to improve on the accuracy of the simulation and capture as many aspects of a space-based optical astronomy mission as possible,with the possible nal form of the simulation being a tool for assessing the performance of any space-based optical mission to detect asteroids.

Near Earth Objects↗
NASA NTRS2016

Tsunami Generation from Asteroid Airburst and Ocean Impact and Van Dorn Effect

Airburst - In the simulations explored energy from the airburst couples very weakly with the water making tsunami dangerous over a shorter distance than the blast for asteroid sizes up to the maximum expected size that will still airburst (approx.250MT). Future areas of investigation: - Low entry angle airbursts create more cylindrical blasts and might couple more efficiently - Bursts very close to the ground will increase coupling - Inclusion of thermosphere (>80km altitude) may show some plume collapse effects over a large area although with much less pressure center dot Ocean Impact - Asteroid creates large cavity in ocean. Cavity backfills creating central jet. Oscillation between the cavity and jet sends out tsunami wave packet. - For deep ocean impact waves are deep water waves (Phase speed = 2x Group speed) - If the tsunami propagation and inundation calculations are correct for the small (<250MT) asteroids in these simulations where they impact deep ocean basins, the resulting tsunami is not a significant hazard unless particularly close to vulnerable communities. Future work: - Shallow ocean impact. - Effect of continental shelf and beach profiles - Tsunami vs. blast damage radii for impacts close to populated areas - Larger asteroids below presumed threshold of global effects (Ø200 - 800m).

Tsunami↗
NASA NTRS2017

Hybrid Guidance Control for a Hypervelocity Small Size Asteroid Interceptor Vehicle

Near-Earth Objects (NEOs) are comets and/or asteroids that have orbits in proximity with Earth's own orbit. NEOs have collided with the Earth in the past, which can be seen at such places as Chicxulub crater, Barringer crater, and Manson crater, and will continue in the future with potentially significant and devastating results. Fortunately such NEO collisions with Earth are infrequent, but can happen at any time. Therefore it is necessary to develop and validate techniques as well as technologies necessary to prevent them. One approach to mitigate future NEO impacts is the concept of high-speed interceptor. This concept is to alter the NEO's trajectory via momentum exchange by using kinetic impactors as well as nuclear penetration devices. The interceptor has to hit a target NEO at relative velocity which imparts a sufficient change in NEO velocity. NASA's Deep Impact mission has demonstrated this scenario by intercepting Comet Temple 1, 5 km in diameter, with an impact relative speed of approximately 10 km/s. This paper focuses on the development of hybrid guidance navigation and control (GNC) algorithms for precision hypervelocity intercept of small sized NEOs. The spacecraft's hypervelocity and the NEO's small size are critical challenges for a successful mission as the NEO will not fill the field of view until a few seconds before intercept. The investigation needs to consider the error sources modeled in the navigation simulation such as spacecraft initial state uncertainties in position and velocity. Furthermore, the paper presents three selected spacecraft guidance algorithms for asteroid intercept and rendezvous missions. The selected algorithms are classical Proportional Navigation (PN) based guidance that use a first order difference to compute the derivatives, Three Plane Proportional Navigation (TPPN), and the Kinematic Impulse (KI). A manipulated Bennu orbit that has been changed to impact Earth will be used as a demonstrative example to compare the three methods. In addition, a hybrid approach that is a combination between proportional navigation and kinematic impulse will be investigated to find an effective, error tolerant, and power saving approach. A 3-dimension mission scenario for both the asteroid and the interceptor spacecraft software simulator is developed for testing of the controllers. The current result demonstrates that a miss distance magnitude of less than 10m is found using the PN and TPPN guidance laws for small asteroid in the presence of error in the spacecraft states. Moreover, the paper presents these results and also the hybrid control approach simulation results.

asteroid↗
NASA NTRS2017

Asteroid Generated Tsunami Workshop: Summary of NASA/NOAA Workshop

A two-day workshop on tsunami generated by asteroid impacts in the ocean resulted in a broad consensus that the asteroid impact tsunami threat is not as great as previously thought, that airburst events in particular are unlikely to produce significant damage by tsunami, and that the tsunami contribution to the global ensemble impact hazard is substantially less than the contribution from land impacts. The workshop, led by Ethiraj Venkatapathy and David Morrison of NASA Ames, was organized into three sessions: 1) Near-field wave generation by the impact; 2) Long distance wave propagation; 3) Damage from coastal run-up and inundation, and associated hazard. Workshop approaches were to compare simulations to understand differences in the results and gain confidence in the modeling for both formation and propagation of tsunami from asteroid impacts, and to use this information for preliminary global risk assessment. The workshop focus was on smaller asteroids (diameter less than 250m), which represent the most frequent impacts.

Asteroid↗
NASA NTRS2018

Genetic Algorithm-Based Optimization to Match Asteroid Energy Deposition Curves

An asteroid entering Earth's atmosphere deposits energy along its path due to thermal ablation and dissipative forces that can be measured by ground-based and spaceborne instruments. Inference of pre-entry asteroid properties and characterization of the atmospheric breakup is facilitated by using an analytic fragment-cloud model (FCM) in conjunction with a Genetic Algorithm (GA). This optimization technique is used to inversely solve for the asteroid's entry properties, such as diameter, density, strength, velocity, entry angle, and strength scaling, from simulations using FCM. The previous parameters' fitness evaluation involves minimizing error to ascertain the best match between the physics-based calculated energy deposition and the observed meteors. This steady-state GA provided sets of solutions agreeing with literature, such as the meteor from Chelyabinsk, Russia in 2013 and Tagish Lake, Canada in 2000, which were used as case studies in order to validate the optimization routine. The assisted exploration and exploitation of this multi-dimensional search space enables inference and uncertainty analysis that can inform studies of near-Earth asteroids and consequently improve risk assessment.

Depositio↗
NASA NTRSDate not supplied

Investigating Space Weathering Effects on Carbonaceous Asteroids Using High-flux and Low-flux Ion Irradiation of the Murchison Meteorite

Airless planetary bodies are continuously altered by space weathering processes such as solar wind irradiation and micrometeoroid bombardment. These processes change the microstructural, chemical, and optical properties of planetary regoliths and, in turn, complicate interpretations of surface composition from remote sensing data. Previous space weathering investigations have focused primarily on lunar and ordinary chondrite materials, the latter of which have been directly linked to S-type asteroids [1]. However, relatively little is known about space weathering of primitive carbonaceous chondrites, which contain a combination of hydrous silicate and organic phases and are hypothesized to be fragments of C-complex asteroids [2]. To address this knowledge gap and maximize the science return of missions targeting C-complex asteroids (e.g., NASA OSIRIS-REx targeting Bennu and JAXA Hayabusa2 targeting Ryugu)[3-4], we examine the spectral, microstructural, and chemical effects of simulated solar wind weathering on a carbonaceous asteroid analog material. Here, we present the results from coordinated analyses of Murchison (CM2) meteorite slabs irradiated with 1 keV/amu H+ and He+ ions.

space weathering↗
NASA NTRS2015

Asteroid (90) Antiope: Another Icy Member of the Themis Family?

Many members of the Themis family show evidence of hydration in the form of oxidized iron in phyllosilicates (Florczak, M. et al. [1999]. Astron. Astrophys. Suppl. Ser. 134, 463–471), and OH-bearing minerals (Takir, D., Emery, J.P. [2012]. Icarus 219, 641–654). The largest member, (24) Themis, has H2O ice covering its surface (Campins, H. et al. [2010]. Nature 464, 1320–1321; Rivkin, A.S., Emery, J.P. [2010]. Nature 464, 1322–1323). We have investigated the second largest Themis-family asteroid, (90) Antiope, which Castillo-Rogez and Schmidt (Castillo-Rogez, J.C., Schmidt, B.E. [2010]. Geophys. Res. Lett. 37, L10202) predict to have a composition that includes water ice and organics. We obtained 2–4-lm spectroscopy of (90) Antiope in 2006 and 2008, and we find an absorption in the 3-lm region clearly present in our 2008 spectrum and likely in our 2006 spectrum. Both spectra have rounded, bowl-shaped absorptions consistent with those ascribed to water ice as in the spectrum of Asteroid (24) Themis. We also present and compare Spitzer 8–12-lm mid-infrared spectra of (24) Themis and (90) Antiope. We find that (90) Antiope is lacking a ‘‘fairy castle’’ dusty surface, which is in contrast to (24) Themis, other Themis family members (Licandro, J. et al. [2012]. Astron. Astrophys. 537, A73), and Jupiter Trojans (e.g. Emery, J.P., Cruikshank, D.P., Van Cleve, J. [2006]. Icarus 182, 496–512). We conclude that the surface structure of (90) Antiope is most similar to Cybele Asteroid (121) Hermione (Hargrove, K.D. et al. [2012]. Icarus 221, 453–455).

Asteroids↗
DOE OSTI2015

Modeling Momentum Transfer from Kinetic Impacts: Implications for Redirecting Asteroids

Kinetic impactors are one way to deflect a potentially hazardous object headed for Earth. The Asteroid Impact and Deflection Assessment (AIDA) mission is designed to test the effectiveness of this approach and is a joint effort between NASA and ESA. The NASA-led portion is the Double Asteroid Redirect Test (DART) and is composed of a ~300-kg spacecraft designed to impact the moon of the binary system 65803 Didymos. The deflection of the moon will be measured by the ESA-led Asteroid Impact Mission (AIM) (which will characterize the moon) and from ground-based observations. Because the material properties and internal structure of the target are poorly constrained, however, analytical models and numerical simulations must be used to understand the range of potential outcomes. Here, we describe a modeling effort combining analytical models and CTH simulations to determine possible outcomes of the DART impact. We examine a wide parameter space and provide predictions for crater size, ejecta mass, and momentum transfer following the impact into the moon of the Didymos system. For impacts into “realistic” asteroid types, these models produce craters with diameters on the order of 10 m, an imparted Δv of 0.5–2 mm/s and a momentum enhancement of 1.07 to 5 for a highly porous aggregate to a fully dense rock.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Calculating the momentum enhancement factor for asteroid deflection studies

The possibility of kinetic-impact deflection of threatening near-Earth asteroids will be tested for the first time in the proposed AIDA (Asteroid Impact Deflection Assessment) mission, involving NASAs DART (Double Asteroid Redirection Test). The impact of the DART spacecraft onto the secondary of the binary asteroid 65803 Didymos at a speed of 5 to 7 km/s is expected to alter the mutual orbit by an observable amount. Furthermore, the velocity transferred to the secondary depends largely on the momentum enhancement factor, typically referred to as beta. Here, we use two hydrocodes developed at Los Alamos, RAGE and PAGOSA, to calculate an approximate value for beta in laboratory-scale benchmark experiments. Convergence studies comparing the two codes show the importance of mesh size in estimating this crucial parameter.

79 ASTRONOMY AND ASTROPHYSICS↗