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NASA NTRS2011

Experimental Determination of the Dynamic Hydraulic Transfer Function for the J-2X Oxidizer Turbopump: Methodology - Part One

An advanced methodology for extracting the hydraulic dynamic pump transfer matrix (Yp) for a cavitating liquid rocket engine turbopump inducer+impeller has been developed. The transfer function is required for integrated vehicle pogo stability analysis as well as optimization of local inducer pumping stability. Laboratory pulsed subscale waterflow test of the J-2X oxygen turbo pump is introduced and our new extraction method applied to the data collected. From accurate measures of pump inlet and discharge perturbational mass flows and pressures, and one-dimensional flow models that represents complete waterflow loop physics, we are able to derive Yp and hence extract the characteristic pump parameters: compliance, pump gain, impedance, mass flow gain. Detailed modeling is necessary to accurately translate instrument plane measurements to the pump inlet and discharge and extract Yp. We present the MSFC Dynamic Lump Parameter Fluid Model Framework and describe critical dynamic component details. We report on fit minimization techniques, cost (fitness) function derivation, and resulting model fits to our experimental data are presented. Comparisons are made to alternate techniques for spatially translating measurement stations to actual pump inlet and discharge.

Zoladz, Tom↗

NASA NTRS2012

A Statistics-Based Material Property Analysis to Support TPS Characterization

Accurate characterization of entry capsule heat shield material properties is a critical component in modeling and simulating Thermal Protection System (TPS) response in a prescribed aerothermal environment. The thermal decomposition of the TPS material during the pyrolysis and charring processes is poorly characterized and typically results in large uncertainties in material properties as inputs for ablation models. These material property uncertainties contribute to large design margins on flight systems and cloud re- construction efforts for data collected during flight and ground testing, making revision to existing models for entry systems more challenging. The analysis presented in this work quantifies how material property uncertainties propagate through an ablation model and guides an experimental test regimen aimed at reducing these uncertainties and characterizing the dependencies between properties in the virgin and charred states for a Phenolic Impregnated Carbon Ablator (PICA) based TPS. A sensitivity analysis identifies how the high-fidelity model behaves in the expected flight environment, while a Monte Carlo based uncertainty propagation strategy is used to quantify the expected spread in the in-depth temperature response of the TPS. An examination of how perturbations to the input probability density functions affect output temperature statistics is accomplished using a Kriging response surface of the high-fidelity model. Simulations are based on capsule configuration and aerothermal environments expected during the Mars Science Laboratory (MSL) entry sequence. We identify and rank primary sources of uncertainty from material properties in a flight-relevant environment, show the dependence on spatial orientation and in-depth location on those uncertainty contributors, and quantify how sensitive the expected results are.

Copeland, Sean R.↗

DOE OSTI2024

Shock wave formation in radiative plasmas

The temporal evolution of weak shocks in radiative media is theoretically investigated in this work. The structure of radiative shocks has traditionally been studied in a stationary framework. Their systematic classification is complex because layers of optically thick and thin regions alternate to form a radiatively-driven precursor and a temperature-relaxation layer, between which the hydrodynamic shock is embedded. In this work, we analyze the formation of weak shocks when two radiative plasmas with different pressures are put in contact. Applying a reductive perturbative method yields a Burgers-type equation that governs the temporal evolution of the perturbed variables including the radiation field. The conditions upon which optically thick and thin solutions exist have been derived and expressed as a function of the shock strength and Boltzmann number. Below a certain Boltzmann number threshold, weak shocks always become optically thick asymptotically in time, while thin solutions appear as transitory structures. The existence of an optically thin regime is related to the presence of an overdense layer in the compressed material. Scaling laws for the characteristic formation time and shock width are provided for each regime. The theoretical analysis is supported by FLASH simulations, and a comprehensive testcase has been designed to benchmark radiative hydrodynamic codes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

A Multiyear Gridded Data Ensemble of Surface Biogenic Carbon Fluxes for North America: Evaluation and Analysis of Results

Accurate and fine-scale estimates of biogenic carbon fluxes are critical for measuring and monitoring the biosphere's responses and feedback to the climate system. Currently available data products from flux towers and model-intercomparison projects struggle to adequately represent spatiotemporal dynamics of surface biogenic carbon fluxes, and to quantify their uncertainties, which also are crucial to atmospheric inversion systems. To address these gaps, we introduce a new perturbed-parameter model ensemble with the CASA model to estimate surface biogenic carbon fluxes at monthly and 3-hourly scales for North America at ~500-m and 5-km resolutions. We first use the Extended Fourier Amplitude Sensitivity Testing to choose the three most sensitive parameters to be perturbed, maximum light use efficiency (E max ), optimal temperature of photosynthesis (T opt ), and temperature response of respiration (Q 10 ). The initial range for each parameter is broadly sampled for the L1 ensemble, but then we pruned E max with site-level primary productivity to derive an L2 ensemble with narrower uncertainty ranges. Ensembles are strongly correlated with site-level results at both monthly and 3-hourly scales, and the spread across L1/L2 ensemble members encompasses the range of AmeriFlux observations. Monthly variability in the L2 ensemble mean is 85% of the observed variability. The L2 ensemble outperforms diverse data products with the highest Taylor skill scores at diurnal to annual scales. Finally, the ensemble's seasonality agrees well with other models for most biome types and in high and middle latitudes, but inconsistencies are found in subtropical and tropical ecoregions and for annual totals over North America.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Coupled neutronic-thermal-hydraulic simulations of the European SFR core

Within the European SFR (Sodium-cooled Fast Reactor) - Safety Measures Assessment and Research Tools (ESFR-SMART) project, steady-state coupled simulation of the ESFR core has been performed using several core analysis packages, with the objective of quantifying the coupling effect. Focus is on the fuel Doppler effect and coolant expansion effect. Standalone neutronics calculations in TRACE/PARCS (PSI), DYN3D (HZDR) and WIMS (Jacobs) showed superb agreement with the reference Serpent power distribution (root mean square - rms discrepancies of 1.3%, 1.5% and 0.7% respectively). Results for COUNTHER (CIEMAT) were also in reasonable agreement, but with a somewhat higher discrepancy of 3.7%. Temperature distributions from thermal-hydraulic calculations were also compared and are found to be in good agreement. The effect of Doppler and coolant density feedback on core power distribution was predicted by TRACE/PARCS, DYN3D and WIMS to be between 0.4% and 0.8% rms difference in assembly powers. Reactivity coefficients for perturbations in the inlet temperature, flow rate and core power were shown to be negative for these three codes, with values of roughly -0.5 pcm/C. degree, -0.3 pcm/C. degree and -3.5 pcm/C. degree respectively. A preliminary investigation of differential thermal expansion effects indicates that this may have a significant effect on core power distribution of a few %, greater than anticipated a priori and may warrant inclusion in coupled core analysis to ensure the accurate calculation of power distributions. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

NASA NTRS1986

Observed perturbations of the Earth's Radiation Budget - A response to the El Chichon stratospheric aerosol layer?

The Earth Radiation Budget experiment, launched aboard the Nimbus-7 polar-orbiting spacecraft in late 1978, has now taken over seven years of measurements. The dataset, which is global in coverage, consists of the individual components of the earth's radiation budget, including longwave emission, net radiation, and both total and near-infrared albedos. Starting some six months after the 1982 eruption of the El Chichon volcano, substantial long-lived positive shortwave irradiance anomalies were observed by the experiment in both the northern and southern polar regions. Analysis of the morphology of this phenomena indicates that the cause is the global stratospheric aerosol layer which formed from the cloud of volcanic effluents. There was little change in the emitted longwave in the polar regions. At the north pole the largest anomaly was in the near-infrared, but at the south pole the near UV-visible anomaly was larger. Assuming an exponential decay, the time constant for the north polar, near-infrared anomaly was 1.2 years. At mid- and low latitudes the effect of the El Chichon aerosol layer could not be separated from the strong reflected-shortwave and emitted-longwave perturbations issuing from the El Nino/Southern Oscillation event of 1982-83.

Ardanuy, P. E.↗

DOE OSTI2026

Identifying Differential Equations in Fourier Domain (FourierIdent)

We investigate identifying differential equations in the frequency domain. Fourier analysis is an important tool in theoretical analysis and numerical solvers of differential equations, yet there is limited work in exploring this connection in the identification of differential equations. This paper aims to identify the underlying differential equation in the frequency domain, from a given single realization of the differential equation perturbed by noise. Such setting imposes difficulties which are different from other identification methods where computation is carried out in the physical domain. We propose several ways to mitigate the challenges arising from noise in data and large differences in the magnitudes of frequency responses. The main takeaways are that identifying differential equations solely in the frequency domain is challenging, the method we propose is based on a form of domain partitions in the frequency domain, and this method shows benefits for complex data even with high level of noise. We introduce a Fourier feature denoising, and define the meaningful data region and the core regions of features to reduce the effect of noise in the frequency domain and to enhance the accuracy in coefficient identification. The proposed method is tested on various differential equations with linear, nonlinear, and high-order derivative feature terms, and shows advantages on complex data with many frequency modes, even under high level of noise.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Energy-Storing Cryogenic Carbon Capture™ for Utility and Industrial-scale Processes (Final Report)

This project leverages work completed under funding from previous U.S. Department of Energy (DOE) projects and other sources of funding around the Cryogenic Carbon Capture Process™ (CCC). The purpose of this project is to further develop a perturbation of the CCC process that stores energy called the Cryogenic Carbon Capture™ Energy Storing (CCC-ES) process. The successful completion of the tasks in this project has prepared the CCC-ES process for scaling and developed initial plans and a feasibility analysis for an engineering-scale or small-commercial scale system that can store at least 10 MWh of energy. The specific areas of work in this project are: (1) Develop a conceptual, site-specific integrated process flow diagram: Sustainable Energy Solutions (SES) developed a conceptual, site-specific plan including a process flow diagram for integrating CCC-ES at a specific location. The proposed system was based on a typical engineering-scale CCC system designed to capture 30-50 metric tonnes of CO 2 per day (TPD), with modifications and additional changes and equipment put in place to add the energy storage element to the system. The 30-50 TPD scale corresponds to the required 10 MWh of stored energy. This task includes updating simulation software for transient analysis. SES also coordinated with the Jim Bridger Power Plant in Point of Rocks, Wyoming to get site-specific data. Using these data, SES completed site-specific preliminary process flow diagrams, estimated capital and operating costs for the CCC-ES system, and used the upgraded software package to estimate the primary figures of merit. (2) Complete a technoeconomic analysis (TEA): SES completed a full-scale TEA of the CCC-ES system to meet specific success criteria. This TEA used process information from the host site selected above. (3) Technology and data gap assessment for the CCC-ES process: As part of the technology gap assessment, SES performed an assessment of the best alternative energy storage solutions including figures of merit and operational strengths and weaknesses. SES then compared the proposed system with a discussion of how it addresses the weaknesses of alternative systems, showing for example a cost of stored energy at less than $50/MWh and with a roundtrip efficiency of greater than 95%. This assessment includes technical and other risk analyses and technology gaps with research and development needs to commercialize the process by 2030. Finally, work includes a commercialization roadmap/development pathway outlining the major milestones to move to a commercially operating CCC-ES system. (4) Phase II pre-FEED project plan: SES completed a project plan for the Phase II pre-FEED analysis using the same host site as in the Phase I conceptual study.

03 NATURAL GAS↗

NASA NTRS1990

On the instabilities of supersonic mixing layers - A high-Mach-number asymptotic theory

The stability of a family of tanh mixing layers is studied at large Mach numbers using perturbation methods. It is found that the eigenfunction develops a multilayered structure, and the eigenvalue is obtained by solving a simplified version of the Rayleigh equation (with homogeneous boundary conditions) in one of these layers which lies in either of the external streams. This analysis leads to a simple hypersonic similarity law which explains how spatial and temporal phase speeds and growth rates scale with Mach number and temperature ratio. Comparisons are made with numerical results, and it is found that this similarity law provides a good qualitative guide for the behavior of the instability at high Mach numbers. In addition to this asymptotic theory, some fully numerical results are also presented (with no limitation on the Mach number) in order to explain the origin of the hypersonic modes (through mode splitting) and to discuss the role of oblique modes over a very wide range of Mach number and temperature ratio.

Balsa, Thomas F.↗

NASA NTRS1992

Detection of land degradation with polarimetric SAR

Multispectral radar polarimeter data were collected over the Manix Basin Area of the Mojave desert using an airborne SAR. An analysis of the data reveals unusual polarization responses which are attributed to the formation of wind ripples on the surfaces of fields that have been abandoned for more than 5 years. This hypothesis has been confirmed through field observations, and a second-order perturbation model is shown to effectively model the polarization responses. The results demonstrate the usefulness of remote sensing techniques for the study of land degradation at synoptic scales.

Ray, Terrill W.↗

NASA NTRS2006

Strict Constraint Feasibility in Analysis and Design of Uncertain Systems

This paper proposes a methodology for the analysis and design optimization of models subject to parametric uncertainty, where hard inequality constraints are present. Hard constraints are those that must be satisfied for all parameter realizations prescribed by the uncertainty model. Emphasis is given to uncertainty models prescribed by norm-bounded perturbations from a nominal parameter value, i.e., hyper-spheres, and by sets of independently bounded uncertain variables, i.e., hyper-rectangles. These models make it possible to consider sets of parameters having comparable as well as dissimilar levels of uncertainty. Two alternative formulations for hyper-rectangular sets are proposed, one based on a transformation of variables and another based on an infinity norm approach. The suite of tools developed enable us to determine if the satisfaction of hard constraints is feasible by identifying critical combinations of uncertain parameters. Since this practice is performed without sampling or partitioning the parameter space, the resulting assessments of robustness are analytically verifiable. Strategies that enable the comparison of the robustness of competing design alternatives, the approximation of the robust design space, and the systematic search for designs with improved robustness characteristics are also proposed. Since the problem formulation is generic and the solution methods only require standard optimization algorithms for their implementation, the tools developed are applicable to a broad range of problems in several disciplines.

Crespo, Luis G.↗

NASA NTRS2014

Using Tests Designed to Measure Individual Sensorimotor Subsystem Perfomance to Predict Locomotor Adaptability

Astronauts experience sensorimotor disturbances during the initial exposure to microgravity and during the readapation phase following a return to a gravitational environment. These alterations may lead to disruption in the ability to perform mission critical functions during and after these gravitational transitions. Astronauts show significant inter-subject variation in adaptive capability following gravitational transitions. The way each individual's brain synthesizes the available visual, vestibular and somatosensory information is likely the basis for much of the variation. Identifying the presence of biases in each person's use of information available from these sensorimotor subsystems and relating it to their ability to adapt to a novel locomotor task will allow us to customize a training program designed to enhance sensorimotor adaptability. Eight tests are being used to measure sensorimotor subsystem performance. Three of these use measures of body sway to characterize balance during varying sensorimotor challenges. The effect of vision is assessed by repeating conditions with eyes open and eyes closed. Standing on foam, or on a support surface that pitches to maintain a constant ankle angle provide somatosensory challenges. Information from the vestibular system is isolated when vision is removed and the support surface is compromised, and it is challenged when the tasks are done while the head is in motion. The integration and dominance of visual information is assessed in three additional tests. The Rod & Frame Test measures the degree to which a subject's perception of the visual vertical is affected by the orientation of a tilted frame in the periphery. Locomotor visual dependence is determined by assessing how much an oscillating virtual visual world affects a treadmill-walking subject. In the third of the visual manipulation tests, subjects walk an obstacle course while wearing up-down reversing prisms. The two remaining tests include direct measures of knee and ankle proprioception and a functional movement assessment that screens for movement restrictions and asymmetries. To assess each subject's locomotor adaptability subjects walk for twenty minutes on a treadmill that oscillates laterally at 0.3 Hz. Throughout the test metabolic cost provides a measure of exertion and step frequency provides a measure of stability. Additionally, at four points during the perturbation period, reaction time tests are used to probe changes in the amount of mental effort being used to perform the task. As with the adaptive capability observed in astronauts during gravitational transitions, our data shows significant variability between subjects. To aid in the analysis of the results, custom software tools have been developed to enhance in the visualization of the large number of output variables. Preliminary analyses of the data collected to date do not show a strong relationship between adaptability and any single predictor variable. Analysis continues to identify a multifactorial predictor outcome "signature" that do inform us of locomotor adaptability.

Peters, B. T.↗

NASA NTRS2021

The Dynamics of a High Mach Number Quasi-Perpendicular Shock: MMS Observations

Shock parameters at Earth’s bow shock, in rare instances, can approach the Mach numbers predicted at astrophysical shocks and supernova remnants. We present our analysis of a high Alfv ́en Mach number (MA= 27) shock, by utilizing multipoint measurements from the Magnetospheric Multiscale (MMS) spacecraft during a crossing of Earth’s quasi-perpendicular bow shock. We find that the shock dynamics are mostly driven by reflected ions, perturbations that they generate, and nonlinear amplification of the perturbations. Our analyses indicate that reflected ions create modest magnetic enhancements upstream of the shock front which evolve in a nonlinear manner as they traverse the shock foot. They can transform into proto-shocks that propagate at small angles to the magnetic field and towards the bow shock. The nonstationary bow shock shows signatures of both reformation and surface ripples. Our observations indicate that although shock reformation occurs, the main shock layer never disappears. These observations are at high plasmaβ, a parameter regime which has not been well explored by numerical models.

H Madanian↗

NASA NTRS1992

Analysis of TIMS performance subjected to simulated wind blast

The results of the performance of the Thermal Infrared Multispectral Scanner (TIMS) when it is subjected to various wind conditions in the laboratory are described. Various wind conditions were simulated using a 24 inch fan or combinations of air jet streams blowing toward either or both of the blackbody surfaces. The fan was used to simulate a large volume of air flow at moderate speeds (up to 30 mph). The small diameter air jets were used to probe TIMS system response in reaction to localized wind perturbations. The maximum nozzle speed of the air jet was 60 mph. A range of wind directions and speeds were set up in the laboratory during the test. The majority of the wind tests were conducted under ambient conditions with the room temperature fluctuating no more than 2 C. The temperature of the high speed air jet was determined to be within 1 C of the room temperature. TIMS response was recorded on analog tape. Additional thermistor readouts of the blackbody temperatures and thermocouple readout of the ambient temperature were recorded manually to be compared with the housekeeping data recorded on the tape. Additional tests were conducted under conditions of elevated and cooled room temperatures. The room temperature was varied between 19.5 to 25.5 C in these tests. The calibration parameters needed for quantitative analysis of TIMS data were first plotted on a scanline-by-scanline basis. These parameters are the low and high blackbody temperature readings as recorded by the TIMS and their corresponding digitized count values. Using these values, the system transfer equations were calculated. This equation allows us to compute the flux for any video count by computing the slope and intercept of the straight line that relates the flux to the digital count. The actual video of the target (the lab floor in this case) was then compared with a simulated target. This simulated target was assumed to be a blackbody at emissivity of .95 degrees and the temperature was assumed to be at ambient temperature as recorded by the TIMS for each scanline. Using the slope and the intercept the flux corresponding to this target was converted into digital counts. The counts were observed to have a strong correlation with the actual video as recorded by the TIMS. The attached graphs describe the performance of the TIMS when compressed air is blown at each one of the blackbodies at different speeds. The effect of blowing a fan and changing the room temperature is also being analyzed. Results indicate that the TIMS system responds to variation in wind speed in real time and maintains the capability to produce accurate temperatures on a scan line basis.

Jaggi, S.↗

DOE OSTI2019

Interactive Effects of Microbes and Nitrogen on Panicum virgatum Root Functional Traits and Patterns of Phenotypic Selection

Premise of research. Plants in natural and agricultural systems are influenced in myriad ways by their microbial communities, particularly by providing goods and services that change plant functional traits. Microbes are considered an influential part of the environmental context that change plant trait expression, but often, microbe-mediated effects are contingent on local resources, such as nitrogen. Here, we ask how microbes and nitrogen affect belowground functional traits and patterns of phenotypic selection. Methodology. We performed a fully factorial greenhouse experiment with switchgrass (Panicum virgatum), manipulating microbial community composition and nitrogen availability. We measured plant performance and belowground functional traits and performed 16S amplicon sequencing of the root-associated microbial communities. We looked for correlations between microbial taxa and root functional traits, and we performed phenotypic selection analysis on five belowground functional traits to determine how traits affect plant relative performance across biotic and abiotic contexts. Pivotal results. All belowground plant functional traits except root tissue density were affected by adding nitrogen. We found that a microbial taxon (amplicon sequence variant [ASV]) in the genus Micromonospora correlated with shorter root lengths. We also found strong positive selection for longer roots regardless of the abiotic or biotic environment. In contrast, selection favored lower root-to-shoot ratios in high-nitrogen conditions, and selection on root tissue density was highest in treatments that had high nitrogen levels and perturbed microbial communities. Conclusions. We did not detect microbial effects on the expression of plant traits (ecological effects); however, patterns of phenotypic selection (evolutionary effects) on root tissue density differed depending on the biotic and abiotic environment. Additionally, we detected strong selection for increased root length across treatments; we also found that one ASV correlated with decreased root length, indicating potential conflict between root microbiome components and plant fitness. Future work would be to include microbial taxa in phenotypic selection analysis and to conduct manipulations of the microbes correlated with functional traits to determine causality.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS2016

A51F-0123: Model Analysis of Tropospheric Aerosol Variability and Sources over the North Atlantic During NAAMES 2015-2016

The North Atlantic Aerosols and Marine Ecosystems Study (NAAMES) is a five-year Earth-Venture Suborbital-2 Mission to characterize the plankton ecosystems and their influences on remote marine aerosols, boundary layer clouds, and their implications for climate in the North Atlantic. While marine-sourced aerosols have been shown to make important contributions to surface aerosol loading, cloud condensation nuclei and ice nuclei concentrations over remote marine and coastal regions, it is still a challenge to differentiate the marine biogenic aerosol signal from the strong influence of continental pollution outflow. We examine here the spatiotemporal variability and quantify the sources of tropospheric aerosols over the North Atlantic during the first two phases (November 2015 and May-June 2016) of NAAMES using a state-of-the-art chemical transport model (GEOS-Chem). The model is driven by the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) from the NASA Global Modeling and Assimilation Office (GMAO). It includes sulfate-nitrate-ammonium aerosol thermodynamics coupled to ozone-NOx-hydrocarbon-aerosol chemistry, mineral dust, sea salt, elemental and organic carbon aerosols, and especially a recently implemented parameterization for the marine primary organic aerosol emission. The simulated aerosols over the North Atlantic are evaluated with available satellite (e.g., MODIS) observations of aerosol optical depths (AOD), and aircraft and ship aerosol measurements. We diagnose transport pathways for continental pollution outflow over the North Atlantic using carbon monoxide, an excellent tracer for anthropogenic pollution transport. We also conduct model perturbation experiments to quantify the relative contributions of terrestrial and oceanic sources to the aerosol loading, AOD, and their variability over the North Atlantic.

aerosols↗

NASA NTRS2005

Bayesian Analysis of the Power Spectrum of the Cosmic Microwave Background

There is a wealth of cosmological information encoded in the spatial power spectrum of temperature anisotropies of the cosmic microwave background. The sky, when viewed in the microwave, is very uniform, with a nearly perfect blackbody spectrum at 2.7 degrees. Very small amplitude brightness fluctuations (to one part in a million!!) trace small density perturbations in the early universe (roughly 300,000 years after the Big Bang), which later grow through gravitational instability to the large-scale structure seen in redshift surveys... In this talk, I will discuss a Bayesian formulation of this problem; discuss a Gibbs sampling approach to numerically sampling from the Bayesian posterior, and the application of this approach to the first-year data from the Wilkinson Microwave Anisotropy Probe. I will also comment on recent algorithmic developments for this approach to be tractable for the even more massive data set to be returned from the Planck satellite.

Bayesian inference↗

NASA NTRS2012

Launch Window Analysis for the Magnetospheric Multiscale Mission

The NASA Magnetospheric Multiscale (MMS) mission will fly four spinning spacecraft in formation in highly elliptical orbits to study the magnetosphere of the Earth. This paper describes the development of an MMS launch window tool that uses the orbitaveraged Variation of Parameter equations as the basis for a semi-analytic quantification of the dominant oblateness and lunisolar perturbation effects on the MMS orbit. This approach, coupled with a geometric interpretation of all of the MMS science and engineering constraints, allows a scan of 180(sup 2) = 32,400 different (RAAN, AOP) pairs to be carried out for a specified launch day in less than 10 s on a typical modern laptop. The resulting plot indicates the regions in (RAAN, AOP) space where each constraint is satisfied or violated: their intersection gives, in an easily interpreted graphical manner, the final solution space for the day considered. This tool, SWM76, is now used to provide launch conditions to the full fidelity (but far slower) MMS simulation code: very good agreement has been observed between the two methods.

MAGNETOSPHERIC↗