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NASA NTRS1982

Charge exchange in the Io torus and exosphere

Charge-exchange cross sections and their velocity dependence have been estimated for the most important reactions in the Io torus and exosphere. The methods used for calculating the cross sections are given and discussed in some detail. For symmetric-resonant single and double charge exchange, the cross sections are slowly varying functions of velocity. For inelastic charge-exchange collisions, the transition probabilities into a given final state can depend critically on velocity. Models are described which can be used to estimate both the most rapid charge-exchange processes and those states which play an important role. Calculated cross sections are used to obtain reaction rates as a function of radial position, demonstrating the importance of charge exchange in the inner torus. Charge-exchange reactions of torus ions with molecular species in Io's exosphere may yield a net supply of neutrals and plasma to the torus.

Johnson, R. E.↗

DOE OSTI2024

Semi-Lagrangian nodal discontinuous Galerkin method for the BGK model

In this work, we propose a semi-Lagrangian (SL) nodal discontinuous Galerkin (DG) solver for the BGK equation. The BGK model was introduced by Bhatnagar, Gross, and Krook [1] as a relaxation model for the fundamental Boltzmann equation [5], which describes the kinetic dynamic of rarefied gases with a probability distribution function. The challenges of designing efficient numerical schemes for the Boltzmann equation mainly come from its high dimensionality and complicated nonlinear collision operator. The BGK model gains interests since it has much lower computational cost, due to the relatively simple structure of the relaxation operator in replacement of the collision operator, while simultaneously preserving several important physical properties, such as macroscopic quantities and dissipation of entropy.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Pseudorapidity dependence of anisotropic flow and its decorrelations using long-range multiparticle correlations in Pb–Pb and Xe–Xe collisions

The pseudorapidity dependence of elliptic (v 2 ), triangular (v 3 ), and quadrangular (v 4 ) flow coefficients of charged particles measured in Pb–Pb collisions at a centre-of-mass energy per nucleon pair of $\sqrt{S_{NN}}$ = 5.02 TeV and in Xe–Xe collisions at $\sqrt{S_{NN}}$ = 5.44 TeV with ALICE at the LHC are presented. The measurements are performed in the pseudorapidity range − 3.5 < η < 5 for various centrality intervals using two- and multi-particle cumulants with the subevent method. The flow probability density function (p.d.f.) is studied with the ratio of flow coefficient v 2 calculated with four- and two-particle cumulant, and suggests that the variance of flow p.d.f. is independent of pseudorapidity. The decorrelation of the flow vector in the longitudinal direction is probed using two-particle correlations. The results measured with respect to different reference regions in pseudorapidity exhibit differences, argued to be a result of saturating decorrelation effect above a certain pseudorapidity separation, in contrast to previous publications which assign this observation to non-flow effects. The results are compared to 3 + 1 dimensional hydrodynamic and the AMPT transport model calculations. Neither of the models is able to simultaneously describe the pseudorapidity dependence of measurements of anisotropic flow and its fluctuations. The results presented in this work highlight shortcomings in our current understanding of initial conditions and subsequent system expansion in the longitudinal direction. Therefore, they provide input for its improvement.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1959

A Numerical Method for Obtaining Monoenergetic Neutron Flux Distributions and Transmissions in Multiple-Region Slabs

This method is investigated for semi-infinite multiple-slab configurations of arbitrary width, composition, and source distribution. Isotropic scattering in the laboratory system is assumed. Isotropic scattering implies that the fraction of neutrons scattered in the i(sup th) volume element or subregion that will make their next collision in the j(sup th) volume element or subregion is the same for all collisions. These so-called "transfer probabilities" between subregions are calculated and used to obtain successive-collision densities from which the flux and transmission probabilities directly follow. For a thick slab with little or no absorption, a successive-collisions technique proves impractical because an unreasonably large number of collisions must be followed in order to obtain the flux. Here the appropriate integral equation is converted into a set of linear simultaneous algebraic equations that are solved for the average total flux in each subregion. When ordinary diffusion theory applies with satisfactory precision in a portion of the multiple-slab configuration, the problem is solved by ordinary diffusion theory, but the flux is plotted only in the region of validity. The angular distribution of neutrons entering the remaining portion is determined from the known diffusion flux and the remaining region is solved by higher order theory. Several procedures for applying the numerical method are presented and discussed. To illustrate the calculational procedure, a symmetrical slab ia vacuum is worked by the numerical, Monte Carlo, and P(sub 3) spherical harmonics methods. In addition, an unsymmetrical double-slab problem is solved by the numerical and Monte Carlo methods. The numerical approach proved faster and more accurate in these examples. Adaptation of the method to anisotropic scattering in slabs is indicated, although no example is included in this paper.

Schneider, Harold↗

NASA NTRSDate not supplied

An Investigation Into Transecting Satellites in Future Space Traffic Management Scenarios

The number of satellites expected to populate the near-Earth space environment is set to dramatically increase in the coming decade as new large constellations are approved and deployed. Current strategies for placing new batches of these satellites on orbit often involve launching into an initial orbit, and then performing apogee raising maneuvers to reach a target altitude. Similarly, end-of-life planning for these constellation satellites can consist of de-orbit burns that lower perigee to permit disposal via re-entry. Both the raising and de-orbiting maneuvers can result in the individual satellites traveling in high-eccentricity orbits that have the potential to transect other spacecraft trajectories. While individual large constellations may be able to coexist in separate altitude and inclination bands, having thousands of satellites moving between these bands as new satellites are replaced and old ones are removed could pose additional collision risks. Similar concerns have been raised regarding the impact that large numbers of university-class CubeSats might have in terms of their overall collision risk, especially as these satellites typically do not have propulsion systems for active maneuvering. To assess the impact that transecting satellites might have to future space traffic management strategies, this study explored a variety of future realistic scenarios using a high-fidelity simulation tool. The model can simulate the orbit of tens of thousands of resident space objects (RSOs) simultaneously, to include active satellites, debris, rocket bodies, or even future hypothetical scenarios, using a realistic force model that incorporates non-spherical gravity, atmospheric drag, solar radiation pressure, and more. As the model is run forward in time, various statistics and meta-data are gathered on any predicted conjunction event, providing insight into the nature and frequency of potential collisions, e.g., what size are the two satellites, who operates the satellites, are they active or passive objects, etc. Additional customization is available in terms of how probability of collision is computed, and how the probability ellipsoids and screening volumes are determined. The simulation tool also allows for rule-based maneuvers for active satellites, e.g, given an advance conjunction “warning,” one or both of the satellites can maneuver to a safe distance. A wide range of maneuvers can be implemented using impulsive or low-thrust methods, and the latencies can also be varied, e.g., using maneuver lead times of 48 hours, 24 hours, or 12 hours. Validation of the simulation results is performed against current and historical datasets available, to include comparisons to prior conjunction data messages (CDMs), object properties (mass, volume, etc.), and two-line-element records from both public and internal sources. Using the simulation environment, an assessment on the general risks that transecting satellites might pose for hypothetical future space object environments will be presented. This will involve the simulation of approximately 50,000 new large constellation satellites, in addition to the existing catalog of approximately 20,000 known resident space objects (RSOs), over propagation periods of one month to one year. A description of the simulation methodologies, scenarios evaluated, and validation methods will also be presented, as well as a preliminary assessment of the effectiveness of several candidate maneuver strategies that have the potential to reduce collision risk between active satellites.

Brian Gunter↗

NASA NTRS2012

Impact of Non-Gaussian Error Volumes on Conjunction Assessment Risk Analysis

An understanding of how an initially Gaussian error volume becomes non-Gaussian over time is an important consideration for space-vehicle conjunction assessment. Traditional assumptions applied to the error volume artificially suppress the true non-Gaussian nature of the space-vehicle position uncertainties. For typical conjunction assessment objects, representation of the error volume by a state error covariance matrix in a Cartesian reference frame is a more significant limitation than is the assumption of linearized dynamics for propagating the error volume. In this study, the impact of each assumption is examined and isolated for each point in the volume. Limitations arising from representing the error volume in a Cartesian reference frame is corrected by employing a Monte Carlo approach to probability of collision (Pc), using equinoctial samples from the Cartesian position covariance at the time of closest approach (TCA) between the pair of space objects. A set of actual, higher risk (Pc >= 10 (exp -4)+) conjunction events in various low-Earth orbits using Monte Carlo methods are analyzed. The impact of non-Gaussian error volumes on Pc for these cases is minimal, even when the deviation from a Gaussian distribution is significant.

Ghrist, Richard W.↗

NASA NTRS1982

Orbital interactions - A new geometrical formalism

The geometry of encounters between two bodies on independent Keplerian orbits around a third body is considered by a novel analysis, which avoids approximations made in previous studies. For the case of most of the applications considered, the formulas for collision frequencies and orbital element rates of change due to close approaches which comprise the method agree with past results. It is shown that the method can be extended to such other applications as the consideration of oscillations in orbital elements due to secular perturbations, and the computation of probabilities of escape from the system.

Greenberg, R.↗

NASA NTRS2016

Covariance Manipulation for Conjunction Assessment

The manipulation of space object covariances to try to provide additional or improved information to conjunction risk assessment is not an uncommon practice. Types of manipulation include fabricating a covariance when it is missing or unreliable to force the probability of collision (Pc) to a maximum value ('PcMax'), scaling a covariance to try to improve its realism or see the effect of covariance volatility on the calculated Pc, and constructing the equivalent of an epoch covariance at a convenient future point in the event ('covariance forecasting'). In bringing these methods to bear for Conjunction Assessment (CA) operations, however, some do not remain fully consistent with best practices for conducting risk management, some seem to be of relatively low utility, and some require additional information before they can contribute fully to risk analysis. This study describes some basic principles of modern risk management (following the Kaplan construct) and then examines the PcMax and covariance forecasting paradigms for alignment with these principles; it then further examines the expected utility of these methods in the modern CA framework. Both paradigms are found to be not without utility, but only in situations that are somewhat carefully circumscribed.

Conjunction↗

NASA NTRS1990

Statistical mechanics models for motion and force planning

The models of statistical mechanics provide an alternative to the methods of classical mechanics more traditionally used in robotics. They have a potential to: improve analysis of object collisions; handle kinematic and dynamic contact interactions within the same frmework; and reduce the need for perfect deterministic world model information. The statistical mechanics models characterize the state of the system as a probability density function (p.d.f.) whose time evolution is governed by a partial differential equation subject to boundary and initial conditions. The boundary conditions when rigid objects collide reflect the conservation of momentum. The models are being developed to embedd in remote semi-autonomous systems with a need to reason and interact with a multiobject environment.

Rodriguez, G.↗

DOE OSTI2025

Assessing the Impact of Measurement Precision on Metabolite Identification Probability in Multidimensional Mass Spectrometry-Based, Reference-Free Metabolomics

Identification of compounds with minimal ambiguity remains a central challenge in mass spectrometry-based metabolomics. Conventional compound identification relies on comparing analytical signatures (e.g., mass-to-charge ratio, collision cross section, tandem mass spectra) against reference data obtained from measurements of authentic chemical standards. The breadth of annotatable compounds using this approach is necessarily limited by availability of authentic standards, analytical throughput, and resolving power of the separations that underly the measurements. The maturation of computational methods, both theory-driven and artificial intelligence/machine learning-based, for prediction of various molecular properties relevant to multidimensional mass spectrometry measurements has opened the door to a new “reference-free” paradigm of compound annotation. Through augmenting existing reference data for molecular properties with computational predictions, the universe of identifiable chemical species can be expanded significantly beyond its current limits. An unexplored aspect of this novel approach is understanding how to gauge confidence in resulting annotations, especially as the compound search space is expanded. Intuitively, the confidence of a compound annotation is related to the inherent discriminatory power of the molecular properties used for identification, as well as the precision with which the properties are measured or predicted. In this work, we characterize this relationship between measurement precision and identification probability in a systematic and quantitative fashion for a defined region of chemical space that includes organic small molecule metabolites. Importantly, this work establishes a framework for conducting metabolite identification probability analysis that enables others to quantify this relationship for their own compounds and properties of interest.

Metabolite Identification↗

NASA NTRS1978

Monte Carlo solution of Boltzmann equation for a simple model of highly nonequilibrium diatomic gases: Translational rotational energy relaxation

The semiclassical transition probability was incorporated in the simulation for energy exchange between rotational and translational energy. The results provide details on the fundamental mechanisms of gas kinetics where analytical methods were impractical. The validity of the local Maxwellian assumption and relaxation time, rotational-translational energy transition, and a velocity analysis of the inelastic collision were discussed in detail.

Yoshikawa, K. K.↗

DOE OSTI2025

Photonuclear tomography in ultraperipheral heavy-ion collisions

We present a theoretical investigation of photonuclear tomography as a novel technique for probing the internal structure of nuclei. In this approach, ultraperipheral heavy-ion collisions (UPCs) serve as a source of intense fluxes of virtual photons, which induce coherent production of vector mesons. By analyzing the probabilities and cross sections of these photon-induced processes, we propose a methodology for reconstructing the spatial distribution of nucleons within the nucleus. Our framework provides a systematic way to access information on the nuclear geometry probed in UPCs, offering new opportunities for studies of nuclear structure using particle production as a probe. Numerical calculations for selected examples illustrate the feasibility and potential of this method.

particle & resonance production↗

NASA NTRS1985

A model for the evolution of on-orbit manmade debris environment

Man-made debris in low-Earth orbit (LEO) and the conduct of operations/procedures which leave debris in orbit are discussed. With continued deposition and larger vehicles and longer times on orbit for LEO operations, the probability of collisions between such vehicles and some member of the debris population becomes large. Because the collisions will occur at very large relative speeds, a small object which would not normally be considered a hazard might pose a lethal threat to an operating spacecraft. Future debris states must be deduced from an evaluation of many models using a Monte Carlo method for future deposition events. A model for the population evolution is presented and results of model calculations are discussed. Contributions to the population which may be expected to arise from on-orbit collisions and explosions are examined. Results are presented as models for future space usage as an extrapolation of usage in the past, for an era of enhanced space usage, and for an era in which antisatellite tests provide a debris contribution.

Reynolds, R. C.↗

NASA NTRSDate not supplied

Setting the Bar for the Replacement of the Probability of Collision Metric

To date, satellite conjunction assessment (CA) risk analysis has largely embraced the probability of collision (Pc) as the omnibus metric to evaluate collision likelihood, and its use in such assessments has mostly been straightforward: at the point at which a conjunction mitigation decision is required, the calculated Pc is compared to a threshold; and if the calculated Pc exceeds that threshold, then a mitigation action is warranted. With only minor variation, this approach is employed by major CA risk assessment centers (e.g., NASA, EUSST, CNES, JAXA) and is advanced as the preferred method in the published CA best practices handbooks. Despite this near unanimity of operational practice, there is a major strain of secondary literature critical of the Pc and willing to propose alternatives. Alfano (2005) pointed out the ability of the Pc to underrepresent the risk in certain situations and counselled a maximum Pc construct. Carpenter (2017, 2019) reiterated this criticism and proposed using instead a confidence interval on the miss distance. Balch et al. (2019) identified what they argued was a defect in the entire Bayesian Pc construct and believed that the use of a more conservative methodology based on covariance ellipsoid overlap was necessary. Delande (2022) introduced the framework of collision “plausibility” to the risk assessment process and sketched out how this might be used operationally. Elkantassi (2022) published a full development of the miss distance confidence interval approach and applied it to several worked examples. While these different approaches to collision risk assessment do differ in their details, they all converge on two central points: first, the Pc’s failure to give an adequate expression of the risk in dilution region situations is a fatal flaw; and second, a conjunction should be presumed risky and in need of mitigation until the evidence of the situation can establish otherwise. These criticisms, if correct, would counsel a number of modifications to current CA operational practice; as such, they force a re-examination of fundamental aspects of the CA problem, including the following: 1. Is the CA risk assessment a probability problem, a statistics problem, or something else? 2. If it is a statistics problem, does it lend itself naturally to a hypothesis test construction? 3. If it can be construed as a hypothesis test, what form should the null hypothesis take, to wit: what constraints exist on the choice of the null hypothesis, what selections are in best alignment with all of the attendant parameters of the problem, and what is implied philosophically by different choices? 4. What are the implications of using the different proposed risk assessment parameters for CA? This question should be answered both in determining how frequently the dilution region situation cited by the critics of the Pc actually appears in an operationally significant manner and the missed detection and false alarm rates of all of the proposed risk assessment metrics, compared both to the Pc and to each other. This paper explores and offers preliminary answers to the above questions, presenting a researched treatment of the philosophical nature of the CA problem and the null hypothesis choice that achieves the greatest consistency with all of the different aspects of operational CA conduct. It then profiles all of the different proposed risk assessment metrics enumerated in the earlier paragraph against an extremely large database of conjunction events at both the 550km and 700km altitudes. The combination of the philosophical exploration of the CA problem and the results of the profiling activity articulates what a risk assessment metric will need to demonstrate, in terms of both innate construction and performance, in order to be a true competitor to the Pc.

conjunction assessment↗

NASA NTRS1972

Variance reduction in Monte Carlo analysis of rarefied gas diffusion.

The problem of rarefied diffusion between parallel walls is solved using the Monte Carlo method. The diffusing molecules are evaporated or emitted from one of the two parallel walls and diffuse through another molecular species. The Monte Carlo analysis treats the diffusing molecule as undergoing a Markov random walk, and the local macroscopic properties are found as the expected value of the random variable, the random walk payoff. By biasing the transition probabilities and changing the collision payoffs, the expected Markov walk payoff is retained but its variance is reduced so that the Monte Carlo result has a much smaller error.

Perlmutter, M.↗

DOE OSTI2021

A Feynman-Kac based numerical method for the exit time probability of a class of transport problems

The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport problems. In this work, we present an accurate and efficient numerical method for computing this probability for systems described by non-autonomous (time-dependent) stochastic differential equations (SDEs) or their equivalent Fokker-Planck partial differential equations. The method is based on the direct approximation of the Feynman-Kac formula that establishes a link between the adjoint Fokker-Planck equation and the forward SDE. The Feynman-Kac formula is approximated using the Gauss-Hermite quadrature rules and piecewise cubic Hermite interpolating polynomials, and a GPU accelerated matrix representation is used to compute the entire time evolution of the exit time probability using a single pass of the algorithm. The method is unconditionally stable, exhibits second order convergence in space, first order convergence in time, and it is straightforward to parallelize. Applications are presented to the advection diffusion of a passive tracer in a fluid flow exhibiting chaotic advection, and to the runaway acceleration of electrons in a plasma in the presence of an electric field, collisions, and radiation damping. Benchmarks against analytical solutions as well as comparisons with explicit and implicit finite difference standard methods for the adjoint Fokker-Planck equation are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2016

Architecture for Mitigating Short-Term Warning Cosmic Threats: READI Project

Earth is being constantly bombarded by a large variety of celestial bodies and has been since its formation 4.5 billion years ago. Among those bodies, mainly asteroids and comets, there are those that have the potential to create large scale destruction upon impact. The only extinction-level impact recorded to date was 65 million years ago, during the era of dinosaurs. The probability of another extinction-level, or even city-killer, impact may be negligible, but the consequences can be severe for the biosphere and for our species. Therefore it is highly imperative for us to be prepared for such a devastating impact in the near future, especially since humanity is at the threshold of wielding technologies that allow us to do so. Majority of scientists, engineers, and policymakers have focused on long-term strategies and warning periods for Earth orbit crossing Near-Earth Objects (NEOs), and have suggested methods and policies to tackle such problems. However, less attention has been paid to short warning period NEO threats. Such NEOs test current technological and international cooperation capabilities in protecting ourselves, and can create unpredictable devastation ranging from local to global scale. The most recent example is the Chelyabinsk incident in Russia. This event has provided a wakeup call for space agencies and governments around the world towards establishing a Planetary Defense Program. The Roadmap for EArth Defense Initiative (READI) is a project by a team of international, intercultural, and interdisciplinary participants of the International Space University's Space Studies Program 2015 hosted by Ohio University, Athens, OH proposing a roadmap for space agencies, governments, and the general public to tackle NEOs with a short warning before impact. Taking READI as a baseline, this paper presents a technical description of methodologies proposed for detection and impact mitigation of a medium-sized comet (up to 800m across) with a short-warning period of two years on a collision course with Earth. The hypothetical comet is on a highly-inclined orbit having a high probability for Earth impact after its perihelion. For detection, we propose a space-based infrared detection system consisting of two satellites located at the Earth-Moon Lagrange points L1 and L2 coupled with space observatories, like the James Webb telescope and the Centennial telescope. These telescopes are supported by ground-based telescopes, like the Arecibo and Green Bank telescope, in the search for NEOs. Upon detection, the comet is tracked constantly using space- and ground-based telescopes. The deflection system is two-pronged, firstly involving the use of a high energy Directed Energy Laser Terminals (DELT) placed at Sun-Earth Lagrange points L4 and L5 so as to initiate and increase the ablation rate of the comet and deviate it from its collision trajectory, and secondly by the Hypervelocity Comet Intercept Vehicle (HCIV), a space-borne system combining a kinetic impactor with a thermonuclear device. The policy and international collaboration aspects to implement these methods are also outlined in the paper. The techniques mentioned could also be applied to mitigate medium-to-large sized asteroids (up to 2km across).

Laser Applications↗

NASA NTRS2016

Planetary Defense Architecture for Mitigating Short-Term Warning Cosmic Threats: READI Project

Laser Applications↗