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NASA NTRS1990

A time-dependent wave packet approach to atom-diatom reactive collision probabilities - Theory and application to the H + H2(J = 0) system

This paper describes a new approach to the study of atom-diatom reactive collisions in three dimensions employing wave packets and the time-dependent Schroedinger equation. The method uses a projection operator approach to couple the inelastic and reactive portions of the total wave function and optical potentials to circumvent the necessity of using product arrangement coordinates. Reactive transition probabilities are calculated from the state resolved flux of the wave packet as it leaves the interaction region in the direction of the reactive arrangement channel. The present approach is used to obtain such vibrationally resolved probabilities for the three-dimensional H + H2 (J = 0) hydrogen exchange reaction, using a body-fixed system of coordinates.

Neuhauser, Daniel↗
NASA NTRS2019

Computational Bayesian Methods Applied to Complex Problems in Bio and Astro Statistics

In this dissertation we apply computational Bayesian methods to three distinct problems. In the first chapter, we address the issue of unrealistic covariance matrices used to estimate collision probabilities. We model covariance matrices with a Bayesian Normal-Inverse-Wishart model, which we fit with Gibbs sampling. In the second chapter, we are interested in determining the sample sizes necessary to achieve a particular interval width and establish non-inferiority in the analysis of prevalences using two fallible tests. To this end, we use a third order asymptotic approximation. In the third chapter, we wish to synthesize evidence across multiple domains in measurements taken longitudinally across time, featuring a substantial amount of structurally missing data, and fit the model with Hamiltonian Monte Carlo in a simulation to analyze how estimates of a parameter of interest change across sample sizes.

Elrod, Chris↗
NASA NTRS2019

MultiLayer Clustered Sampling (MLCS) technique for near-earth asteroid impact hazard assessment

Because of planetary encounters, the motion of near-Earth asteroids is chaotic and small differences in the initial conditions tend to diverge exponentially. Linear approximations for propagating orbital uncertainties can lead to inaccurate estimates of the probability of an Earth collision. We present a novel fully nonlinear strategy for estimating the probability of an asteroid impact using sequential Monte Carlo layers. The method first explores a low-resolution layer to locate potentially relevant regions. Then, we conduct localized searches on deeper layers with higher resolution. The method retains the accuracy of brute-force Monte Carlo sampling while reducing the computational cost by only sampling relevant regions.

Farnocchia, Davide↗
NASA NTRS1975

Molecular spectroscopy and collisional excitation

The paper examines the basic principles underlying the molecular transitions responsible for interstellar molecular spectra. The energy levels of molecules are discussed in detail with special attention given to the Born-Oppenheimer approximation, the electronic Hamiltonian, and the parameters of vibrational and rotational energy. The probabilities for radiative and collisional transitions are calculated. A brief review of techniques for molecular spectroscopy is presented along with methods used to determine collision cross sections on both an experimental and a theoretical basis.

Green, S.↗
NASA NTRS1998

Cross Sections for Electron Impact Excitation of Ions Relevant to Planetary Atmospheres Observation

The goal of this research grant was to calculate accurate oscillator strengths and electron collisional excitation strengths for inelastic transitions in atomic species of relevance to Planetary Atmospheres. Large scale configuration-interaction atomic structure calculations have been performed to obtain oscillator strengths and transition probabilities for transitions among the fine-structure levels and R-matrix method has been used in the calculations of electron-ion collision cross sections of C II, S I, S II, S III, and Ar II. A number of strong features due to ions of sulfur have been detected in the spectra of Jupiter satellite Io. The electron excitation cross sections for the C II and S II transitions are studied in collaboration with the experimental atomic physics group at the Jet Propulsion Laboratory. There is excellent agreement between experiment and theory which provide an accurate and broad-base test of the ability of theoretical methods used in the calculation of atomic processes. Specifically, research problems have been investigated for: electron impact excitation cross sections of C II: electron impact excitation cross sections of S III; energy levels and oscillator strengths for transitions in S III; collision strengths for electron collisional excitation of S II; electron impact excitation of inelastic transitions in Ar II; oscillator strengths of fine-structure transitions in neutral sulfur; cross sections for inelastic scattering of electrons from atomic nitrogen; and excitation of atomic ions by electron impact.

Tayal, Swaraj S.↗
NASA NTRS2016

Covariance Manipulation for Conjunction Assessment

Use of probability of collision (Pc) has brought sophistication to CA. Made possible by JSpOC precision catalogue because provides covariance. Has essentially replaced miss distance as basic CA parameter. Embrace of Pc has elevated methods to 'manipulate' covariance to enable/improve CA calculations. Two such methods to be examined here; compensation for absent or unreliable covariances through 'Maximum Pc' calculation constructs, projection (not propagation) of epoch covariances forward in time to try to enable better risk assessments. Two questions to be answered about each; situations to which such approaches are properly applicable, amount of utility that such methods offer.

Probability↗
NASA NTRS2012

Statistical Orbit Determination using the Particle Filter for Incorporating Non-Gaussian Uncertainties

The tracking of space objects requires frequent and accurate monitoring for collision avoidance. As even collision events with very low probability are important, accurate prediction of collisions require the representation of the full probability density function (PDF) of the random orbit state. Through representing the full PDF of the orbit state for orbit maintenance and collision avoidance, we can take advantage of the statistical information present in the heavy tailed distributions, more accurately representing the orbit states with low probability. The classical methods of orbit determination (i.e. Kalman Filter and its derivatives) provide state estimates based on only the second moments of the state and measurement errors that are captured by assuming a Gaussian distribution. Although the measurement errors can be accurately assumed to have a Gaussian distribution, errors with a non-Gaussian distribution could arise during propagation between observations. Moreover, unmodeled dynamics in the orbit model could introduce non-Gaussian errors into the process noise. A Particle Filter (PF) is proposed as a nonlinear filtering technique that is capable of propagating and estimating a more complete representation of the state distribution as an accurate approximation of a full PDF. The PF uses Monte Carlo runs to generate particles that approximate the full PDF representation. The PF is applied in the estimation and propagation of a highly eccentric orbit and the results are compared to the Extended Kalman Filter and Splitting Gaussian Mixture algorithms to demonstrate its proficiency.

Mashiku, Alinda↗
NASA NTRS1993

Asteroidal collision probabilities

Several past calculations of collision probabilities between pairs of bodies on independent orbits have yielded inconsistent results. We review the methodologies and identify their various problems. Greenberg's (1982) collision probability formalism (now with a corrected symmetry assumption) is equivalent to Wetherill's (1967) approach, except that it includes a way to avoid singularities near apsides. That method shows that the procedure by Namiki and Binzel (1991) was accurate for those cases where singularities did not arise.

Bottke, William F., Jr.↗
NASA NTRS2015

Implementation of an Open-Scenario, Long-Term Space Debris Simulation Approach

This paper provides a status update on the implementation of a flexible, long-term space debris simulation approach. The motivation is to build a tool that can assess the long-term impact of various options for debris-remediation, including the LightForce space debris collision avoidance concept that diverts objects using photon pressure [9]. State-of-the-art simulation approaches that assess the long-term development of the debris environment use either completely statistical approaches, or they rely on large time steps on the order of several days if they simulate the positions of single objects over time. They cannot be easily adapted to investigate the impact of specific collision avoidance schemes or de-orbit schemes, because the efficiency of a collision avoidance maneuver can depend on various input parameters, including ground station positions and orbital and physical parameters of the objects involved in close encounters (conjunctions). Furthermore, maneuvers take place on timescales much smaller than days. For example, LightForce only changes the orbit of a certain object (aiming to reduce the probability of collision), but it does not remove entire objects or groups of objects. In the same sense, it is also not straightforward to compare specific de-orbit methods in regard to potential collision risks during a de-orbit maneuver. To gain flexibility in assessing interactions with objects, we implement a simulation that includes every tracked space object in Low Earth Orbit (LEO) and propagates all objects with high precision and variable time-steps as small as one second. It allows the assessment of the (potential) impact of physical or orbital changes to any object. The final goal is to employ a Monte Carlo approach to assess the debris evolution during the simulation time-frame of 100 years and to compare a baseline scenario to debris remediation scenarios or other scenarios of interest. To populate the initial simulation, we use the entire space-track object catalog in LEO. We then use a high precision propagator to propagate all objects over the entire simulation duration. If collisions are detected, the appropriate number of debris objects are created and inserted into the simulation framework. Depending on the scenario, further objects, e.g. due to new launches, can be added. At the end of the simulation, the total number of objects above a cut-off size and the number of detected collisions provide benchmark parameters for the comparison between scenarios. The simulation approach is computationally intensive as it involves tens of thousands of objects; hence we use a highly parallel approach employing up to a thousand cores on the NASA Pleiades supercomputer for a single run. This paper describes our simulation approach, the status of its implementation, the approach to developing scenarios and examples of first test runs.

laser↗
NASA NTRS1993

Excitation rate coefficients and line ratios for the optical and ultraviolet transitions in S II

New calculations are reported for electron excitation collision strengths, rate coefficients, transition probabilities, and line ratios for the astrophysically important optical and UV lines in S II. The collision strengths are calculated in the close coupling approximation using the R-matrix method. The present calculations are more extensive than previous ones, including all transitions among the 12 lowest LS terms and the corresponding 28 fine-structure levels in the collisional-radiative model for S II. While the present rate coefficients for electron impact excitation are within 10-30 percent of the previous values for the low-lying optical transitions employed as density diagnostics of H II regions and nebulae, the excitation rates for the UV transitions 4S super 0 sub 3/2 - 4Psub 1/2,3/2,5/2 differ significantly from earlier calculations, by up to factor of 2. We describe temperature and density sensitive flux ratios for a number of UV lines. The present UV results are likely to be of interest in a more accurate interpretation of S II emission from the Io plasma torus in the magnetosphere of Jupiter, as well as other UV sources observed from the IUE, ASTRO 1, and the HST.

Cai, Wei↗
NASA NTRS1991

Theoretical studies of molecular collisions

The following subject areas are covered: (1) total integral reactive cross sections and vibrationally resolved reaction probabilities for F + H2 = HF + H; (2) a theoretical study of inelastic O + N2 collisions; (3) body frame close coupling wave packet approach to gas phase atom-rigit rotor inelastic collisions; (4) wave packet study of gas phase atom-rigit motor scattering; (5) the application of optical potentials for reactive scattering; (6) time dependent, three dimensional body frame quantal wave packet treatment of the H + H2 exchange reaction; (7) a time dependent wave packet approach to atom-diatom reactive collision probabilities; (8) time dependent wave packet for the complete determination of s-matrix elements for reactive molecular collisions in three dimensions; (9) a comparison of three time dependent wave packet methods for calculating electron-atom elastic scattering cross sections; and (10) a numerically exact full wave packet approach to molecule-surface scattering.

Kouri, Donald J.↗
NASA NTRS1996

Self-Consistent Simulation of the Brownian Stage of Dust Growth

It is a widely accepted view that in proto-planetary accretion disks the collision and following sticking of dust particles embedded in the gas eventually leads to the formation of planetesimals (coagulation). For the smallest dust grains, Brownian motion is assumed to be the dominant source of their relative velocities leading to collisions between these dust grains. As the dust grains grow they eventually couple to the turbulent motion of the gas which then drives the coagulation much more efficiently. Many numerical coagulation simulations have been carried out to calculate the fractal dimension of the aggregates, which determines the duration of the ineffective Brownian stage of growth. Predominantly on-lattice and off-lattice methods were used. However, both methods require simplification of the astrophysical conditions. The aggregates found by those methods had a fractal dimension of approximately 2 which is equivalent to a constant, mass-independent friction time. If this value were valid for the conditions in an accretion disk, this would mean that the coagulation process would finally 'freeze out' and the growth of a planetesimal would be impossible within the lifetime of an accretion disk. In order to investigate whether this fractal dimension is model independent, we simulate self-consistently the Brownian stage of the coagulation by an N-particle code. This method has the advantage that no further assumptions about homogeneity of the dust have to be made. In our model, the dust grains are considered as aggregates built up of spheres. The equation of motion of the dust grains is based on the probability density for the diffusive transport within the gas atmosphere. Because of the very low number density of the dust grains, only 2-body-collisions have to be considered. As the Brownian stage of growth is very inefficient, the system is to be simulated over long periods of time. In order to find close particle pairs of the system which are most likely to undergo a collision, we use a particle-in-cell (PIC) method for the early stages of the simulation where the system is still very homogeneous and a tree method later when the particles are more clustered.

Kempf, S.↗
NASA NTRS2013

NASA Tech Briefs, May 2013

Topics include: Test Waveform Applications for JPL STRS Operating Environment; Pneumatic Proboscis Heat-Flow Probe; Method to Measure Total Noise Temperature of a Wireless Receiver During Operation; Cursor Control Device Test Battery; Functional Near-Infrared Spectroscopy Signals Measure Neuronal Activity in the Cortex; ESD Test Apparatus for Soldering Irons; FPGA-Based X-Ray Detection and Measurement for an X-Ray Polarimeter; Sequential Probability Ratio Test for Spacecraft Collision Avoidance Maneuver Decisions; Silicon/Carbon Nanotube Photocathode for Splitting Water; Advanced Materials and Fabrication Techniques for the Orion Attitude Control Motor; Flight Hardware Packaging Design for Stringent EMC Radiated Emission Requirements; RF Reference Switch for Spaceflight Radiometer Calibration; An Offload NIC for NASA, NLR, and Grid Computing; Multi-Scale CNT-Based Reinforcing Polymer Matrix Composites for Lightweight Structures; Ceramic Adhesive and Methods for On-Orbit Repair of Re-Entry Vehicles; Self-Healing Nanocomposites for Reusable Composite Cryotanks; Pt-Ni and Pt-Co Catalyst Synthesis Route for Fuel Cell Applications; Aerogel-Based Multilayer Insulation with Micrometeoroid Protection; Manufacturing of Nanocomposite Carbon Fibers and Composite Cylinders; Optimized Radiator Geometries for Hot Lunar Thermal Environments; A Mission Concept: Re-Entry Hopper-Aero-Space-Craft System on-Mars (REARM-Mars); New Class of Flow Batteries for Terrestrial and Aerospace Energy Storage Applications; Reliability of CCGA 1152 and CCGA 1272 Interconnect Packages for Extreme Thermal Environments; Using a Blender to Assess the Microbial Density of Encapsulated Organisms; Mixed Integer Programming and Heuristic Scheduling for Space Communication; Video Altimeter and Obstruction Detector for an Aircraft; Control Software for Piezo Stepping Actuators; Galactic Cosmic Ray Event-Based Risk Model (GERM) Code; Sasquatch Footprint Tool; and Multi-User Space Link Extension (SLE) System.

Source record↗
NASA NTRS1989

Charge exchange transition probability for collisions between unlike ions and atoms within the adiabatic approximation

A simple formula for the transition probability for electron exchange between unlike ions and atoms is established within the adiabatic approximation by employing the Linear Combination of Atomic Orbitals (LCAO) method. The formula also involves an adiabatic parameter, introduced by Massey, and thus the difficulties arising from the internal energy defect and the adiabatic approximation are avoided. Specific reactions Li(+++) + H to Li(++) + H(+) and Be(4+) + H to Be(3+) + H(+) are considered as examples. The calculated capture cross section results of the present work are compared with the experimental data and with the calculation of other authors over the velocity range of 10(7) cm/sec to 10(8) cm/sec.

Xu, Y. J.↗
NASA NTRS2010

Sequential Probability Ratio Test for Collision Avoidance Maneuver Decisions

When facing a conjunction between space objects, decision makers must chose whether to maneuver for collision avoidance or not. We apply a well-known decision procedure, the sequential probability ratio test, to this problem. We propose two approaches to the problem solution, one based on a frequentist method, and the other on a Bayesian method. The frequentist method does not require any prior knowledge concerning the conjunction, while the Bayesian method assumes knowledge of prior probability densities. Our results show that both methods achieve desired missed detection rates, but the frequentist method's false alarm performance is inferior to the Bayesian method's

Carpenter, J. Russell↗
NASA NTRS2016

A Numerical Approach to Estimate the Ballistic Coefficient of Space Debris from TLE Orbital Data

Low Earth Orbit (LEO) is full of space debris, which consist of spent rocket stages, old satellites and fragments from explosions and collisions. As of 2009, more than 21,000 orbital debris larger than 10 cm are known to exist], and while it is hard to track anything smaller than that, the estimated population of particles between 1 and 10 cm in diameter is approximately 500,000, whereas small as 1 cm exceeds 100 million. These objects orbit Earth with huge kinetic energies speeds usually exceed 7 kms. The shape of their orbit varies from almost circular to highly elliptical and covers all LEO, a region in space between 160 and 2,000 km above sea level. Unfortunately, LEO is also the place where most of our active satellites are situated, as well as, International Space Station (ISS) and Hubble Space Telescope, whose orbits are around 400 and 550 km above sea level, respectively.This poses a real threat as debris can collide with satellites and deal substantial damage or even destroy them.Collisions between two or more debris create clouds of smaller debris, which are harder to track and increase overall object density and collision probability. At some point, the debris density couldthen reach a critical value, which would start a chain reaction and the number of space debris would grow exponentially. This phenomenon was first described by Kessler in 1978 and he concluded that it would lead to creation of debris belt, which would vastly complicate satellite operations in LEO. The debris density is already relatively high, as seen from several necessary debris avoidance maneuvers done by Shuttle, before it was discontinued, and ISS. But not all satellites have a propulsion system to avoid collision, hence different methods need to be applied. One of the proposed collision avoidance concepts is called LightForce and it suggests using photon pressure to induce small orbital corrections to deflect debris from colliding. This method is very efficient as seen from theoretical simulations, even few continuous mode 10 kW ground-based lasers, focused by 1.5 m telescopes with adaptive optics, were enough to prevent significant amount of the debris collisions. Simulations were done by propagating all space objects in LEO by 1 year into the future and checking whether the probability of collision was high. For those space objects different ground-based lasers were used to divert them, afterwards collision probabilities were reevaluated. However, the actual accuracy of the LightForce software, which has been developed at NASA AmesResearch Center, depends on the veracity of the input parameters, one of which is the objects ballistic coefficient. It is a measure of bodys ability to overcome air resistance, which has a significant impact on the debris in LEO, and thus it is responsible for the shape of the trajectory of the debris. Having the exact values of the ballistic coefficient would make significantly better collision predictions, unfortunately, we do not know what are the values for most of the objects.In this research, we were working with part of LightForce code, which estimates the ballistic coefficient from ephemerides. Previously used method gave highly inaccurate values, when compared to known objects, and it needed to be changed. The goal of this work was to try out a different method of estimating the ballistic coefficient and to check whether or not it gives noticeable improvements.

Collisions↗
NASA NTRS1992

Damage areas due to impact craters on LDEF aluminum panels

Because of its exposure time and total exposed surface area, the LDEF provides a unique opportunity to analyze the effects of the natural and man-made particle populations in low earth orbit (LEO). This study concentrated on collecting and analyzing measurements of impact craters from seven painted aluminum surfaces at different locations on the satellite. These data are being used to: (1) update the current theoretical micrometeoroid and debris models for LEO; (2) characterize the effects of the LEO micrometeoroid and debris environment of satellite components and designs; (3) help assess the probability of collision between spacecraft in LEO and already resident debris and the survivability of those spacecraft that must travel through, or reside in, LEO; and (4) help define and evaluate future debris mitigation and disposal methods. Measurements were collected from one aluminum experiment tray cover (Bay C-12), two aluminum grapple plates (Bays C-01, C-10), and four aluminum experiment sun-shields (Bay E-09), all of which were coated with thermal paint. These measurements were taken at the Facility for Optical Interpretation of Large Surfaces (FOILS) Lab at JSC. Virtually all features greater than 0.2 mm in diameter possessed a spall zone in which all of the paint was removed from the aluminum surface, and which varied in size from 2-5 crater diameters. The actual craters vary from central pits without raised rims to morphologies more typical of craters formed in aluminum under hypervelocity impact conditions for larger features. Most craters exhibit a shock zone that varies in size from approximately 1-20 crater diameters. In general, only the outermost layer of paint was affected by this impact-related phenomenon, with several impacts possessing ridge-like structures encircling the area in which this outer-most paint layer was removed. Overall, there were no noticeable penetrations or bulges on the underside of the trays. One tray from the E-09 bay exhibited a spallation zone on the backside, approximately equal in size to that on the front side. Results from this study demonstrate that the impact damaged areas extend far beyond the actual craters in coated or painted surfaces. While the cratering damaged much greater than 1 percent of the total surface area, the total impact damage area exceeded 3 percent.

Coombs, Cassandra R.↗