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At least 163 records · Page 9

Progress of the LASSO experiment

The LASSO (Later Synchronisation from Stationary Orbit) experiment, designed to demonstrate the feasibility of achieving time synchronization between remote atomic clocks with an accuracy of one nanosecond or better by using laser techniques for the first time is described. The experiment uses groundbased laser stations and the SIRIO-2 geostationary satellite to be launched towards the end of 1981. The qualification of the LASSO on-board equipment is discussed with a brief description of the electrical and optical test equipment used. The progress of the operational organization is included.

Serene, B. E. H.↗

An Updated Model for the Effect of Atmospheric Absorption on Sounding Rockets

A very high-resolution R > 20,000 Far Ultraviolet full-disk, solar spectrograph will be launched in the Spring of 2023. This paper describes the in-flight wavelength calibration techniques and the fortuitous retrieval of Earth’s thermospheric information during the flight. Building and calibration of the Full-sun Ultraviolet Rocket Spectrograph (FURST) is currently underway. The purpose of this instrument is to obtain the highest resolution and most complete Far Ultra-Violet (FUV) spectra of the full disk Sun. This so-called "Sun-as-a-star" spectra will allow direct comparisons between our Sun and other stars measured by the Hubble Space Telescope(HST) and the upcoming James Webb Space Telescope (JWST). The Solar Physics groups at NASA Marshall Space Flight Center (MSFC) and Montana State University (MSU) have been developing the tools and procedures necessary to achieve the high spectral resolution goal. These include, among other things, improved tracking of error propagation, in-situ monitoring of the camera gain with a radioactive Fe-55 source, and the development of a simulated spectral calibration map under a noisy diagnostic-lamp signal. This mapping introduces a clocked CCD in order to obtain sub-pixel spectral resolution and overcome the Nyquist limit by about a factor of 2. Aside from the main purpose of FURST, we have been investigating the effect of absorption in the upper atmosphere at sounding-rocket altitudes (about 100-300 km). We present here an improved model of the optical depth caused by the thermospheric Oxygen cross-section and H and O self-absorption. This data-based model uses concentric spherical shells to account for the curvature of the Earth’s atmosphere and refraction. Using these calculations, we present the anticipated effect on the signal received by FURST, how that signal changes over the course of the flight-path These absorption peaks would provide wavelength fiducials at line-center that might add to in-flight calibration of the instrument. Many studies have found ways to correct for these so-called "Telluric" lines. However, it may be that these lines can in fact be a useful tool to further improve our calibration, rather than simply a nuisance to be corrected for! Finally, we discuss the inversion problem: how we could take actual flight data and back-out the atmospheric data (such as density and temperature) from any such sounding rocket flight that shows evidence of atmospheric absorption.

Nicolas Donders↗

Jitter model and signal processing techniques for pulse width modulation optical recording

A jitter model and signal processing techniques are discussed for data recovery in Pulse Width Modulation (PWM) optical recording. In PWM, information is stored through modulating sizes of sequential marks alternating in magnetic polarization or in material structure. Jitter, defined as the deviation from the original mark size in the time domain, will result in error detection if it is excessively large. A new approach is taken in data recovery by first using a high speed counter clock to convert time marks to amplitude marks, and signal processing techniques are used to minimize jitter according to the jitter model. The signal processing techniques include motor speed and intersymbol interference equalization, differential and additive detection, and differential and additive modulation.

Liu, Max M.-K.↗

Stabilizing an optoelectronic microwave oscillator with photonic filters

This paper compares methods of active stabilization of an optoelectronic microwave oscillator (OEO) based on insertion of a source of optical group delay into an OEO loop. The performance of an OEO stabilized with either a high- optical cavity or an atomic cell is analyzed. We show that the elements play a role of narrow-band microwave filters improving an OEO stability.

Atomic clocks electromagnetically induced transpar↗

WFIRST/AFTA coronograph contrast performance sensitivity studies: simulation versus experiment

The WFIRST/AFTA 2.4 m space telescope currently under study includes a stellar coronagraph for the imaging and the spectral characterization of extrasolar planets. The coronagraph employs sequential deformable mirrors to compensate for phase and amplitude errors. Using the optical model of an Occulting Mask Coronagraph (OMC) testbed at the Jet Propulsion Laboratory, we have investigated through modeling and simulations the sensitivity of dark hole contrast in a Hybrid Lyot Coronagraph (HLC) for several error cases, including lateral and longitudinal translation errors of two deformable mirrors, DM1 and DM2, lateral and/or longitudinal translation errors of an occulting mask and a Lyot-Stop, clocking errors of DM1 and DM2, and the mismatch errors between the testbed and the model sensitivity matrices. We also investigated the effects of a control parameter, namely the actuator regularization factor, on the control efficiency and on the final contrast floor. We found several error cases which yield contrast results comparable to that observed on the HLC testbed. We present our findings in this paper.

Nemati, Bijan↗

NASA Tech Briefs, May 2007

Topics include: Noise-Canceling Helmet Audio System; Program Analyzes Spacecraft/Ground Radio Links; Two-Way Communication Using RFID Equipment and Techniques; Six-Message Electromechanical Display System; Scanning Terahertz Heterodyne Imaging Systems; Master Clock and Time-Signal-Distribution System; Synchronous Phase-Resolving Flash Range Imaging; Integrated Radial Probe Transition From MMIC to Waveguide; Bar-Code System for a Microbiological Laboratory; MMIC Amplifier Produces Gain of 10 dB at 235 GHz; Mapping Nearby Terrain in 3D by Use of a Grid of Laser Spots; Digital Beam Deflectors Based Partly on Liquid Crystals; Narrow-Band WGM Optical Filters With Tunable FSRs; Better Finite-Element Analysis of Composite Shell Structures; Computing Spacecraft-Pointing Vectors for Limb Tracking; Enhanced Master Controller Unit Tester; Rover Graphical Simulator; Increasing Durability of Flame-Sprayed Strain Gauges; Multifunctional, High-Temperature Nanocomposites; Multilayer Impregnated Fibrous Thermal Insulation Tiles; Radiation-Shielding Polymer/Soil Composites; Film/Adhesive Processing Module for Fiber-Placement Processing of Composites; Fabrication of Submillimeter Axisymmetric Optical Components; Electrochemical Disposal of Hydrazines in Water; Statistical Model of Evaporating Multicomponent Fuel Drops; Resistively Heated SiC Nozzle for Generating Molecular Beams; Compact Packaging of Photonic Millimeter-Wave Receiver; Diffractive Combiner of Single-Mode Pump Laser-Diode Beams; Wide-Band, High-Quantum-Efficiency Photodetector; A Robustly Stabilizing Model Predictive Control Algorithm; Modeling Evaporation of Drops of Different Kerosenes; Development of Vapor-Phase Catalytic Ammonia Removal System; Several Developments in Space Tethers; Design Concept for a Nuclear Reactor-Powered Mars Rover; Formation-Initialization Algorithm for N Spacecraft; and DNSs of Multicomponent Gaseous and Drop-Laden Mixing Layers Achieving Transition to Turbulence.

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Optical timing receiver for the NASA laser ranging system. Part 2: High precision time interval digitizer

The development of a high precision time interval digitizer is described. The time digitizer is a 10 psec resolution stop watch covering a range of up to 340 msec. The measured time interval is determined as a separation between leading edges of a pair of pulses applied externally to the start input and the stop input of the digitizer. Employing an interpolation techniques and a 50 MHz high precision master oscillator, the equivalent of a 100 GHz clock frequency standard is achieved. Absolute accuracy and stability of the digitizer are determined by the external 50 MHz master oscillator, which serves as a standard time marker. The start and stop pulses are fast 1 nsec rise time signals, according to the Nuclear Instrument means of tunnel diode discriminators. Firing level of the discriminator define start and stop points between which the time interval is digitized.

Leskovar, B.↗

A synchronous fiber optic ring local area network for multigigabit/s mixed-traffic communication

A synchronous-ring fiber optic local area network is reported that facilitates the simultaneous transmission of packet and real-time traffic at gigabit/s rates, minimizes the amount of high-speed logic, and simplifies the user interface to the network. The novelty of the technique is based on (1) suspending in transit around the ring's circumference an integral number of data frames and (2) achieving this condition by skewing the frame clock rate a small amount. Rather than use the whole data frame as one packet destined to a specific user, many individual channels are instead time-multiplexed into the data frame. This technique only becomes feasible for local networks as data rates approach the Gbit/s range. This departure from other synchronous rings results in several advantages both in terms of system performance and hardware simplicity.

Bergman, L. A.↗

GaAs VLSI for aerospace electronics

Advanced aerospace electronics systems require high-speed, low-power, radiation-hard, digital components for signal processing, control, and communication applications. GaAs VLSI devices provide a number of advantages over silicon devices including higher carrier velocities, ability to integrate with high performance optical devices, and high-resistivity substrates that provide very short gate delays, good isolation, and tolerance to many forms of radiation. However, III-V technologies also have disadvantages, such as lower yield compared to silicon MOS technology. Achieving very large scale integration (VLSI) is particularly important for fast complex systems. At very short gate delays (less than 100 ps), chip-to-chip interconnects severely degrade circuit clock rates. Complex systems, therefore, benefit greatly when as many gates as possible are placed on a single chip. To fully exploit the advantages of GaAs circuits, attention must be focused on achieving high integration levels by reducing power dissipation, reducing the number of devices per logic function, and providing circuit designs that are more tolerant to process and environmental variations. In addition, adequate noise margin must be maintained to ensure a practical yield.

Larue, G.↗

Time transfer between the Goddard Optical Research Facility and the U.S. Naval Observatory using 100 picosecond laser pulses

A horizontal two-way time comparison link in air between the University of Maryland laser ranging and time transfer equipment at the Goddard Optical Research Facility (GORF) 1.2 m telescope and the Time Services Division of the U.S. Naval Observatory (USNO) was established. Flat mirrors of 25 cm and 30 cm diameter respectively were placed on top of the Washington Cathedral and on a water tower at the Beltsville Agricultural Research Center. Two optical corner reflectors at the USNO reflect the laser pulses back to the GORF. Light pulses of 100 ps duration and an energy of several hundred microjoules are sent at the rate of 10 pulses per second. The detection at the USNO is by means of an RCA C30902E avalanche photodiode and the timing is accomplished by an HP 5370A computing counter and an HP 1000 computer with respect to a 10 pps pulse train from the Master Clock.

Alley, C. O.↗

Technology Demonstration Missions

Technology Demonstration Missions (TDM) is in its third year of execution, being initiated in 2010 and baselined in January of 2012. There are 11 projects that NASA Marshall Space Flight Center (MSFC) has contributed to or led: (1) Evolvable Cryogenics (eCryo): Cyrogenic Propellant Storage and Transfer Engineering Development Unit (EDU), a proof of manufacturability effort, used to enhance knowledge and technology related to handling cryogenic propellants, specifically liquid hydrogen. (2) Composites for Exploration Upper Stage (CEUS): Design, build, test, and address flight certification of a large composite shell suitable for the second stage of the Space Launch System (SLS). (3) Deep Space Atomic Clock (DSAC): Spaceflight to demo small, low-mass atomic clock that can provide unprecedented stability for deep space navigation. (4) Green Propellant Infusion Mission (GPIM): Demo of high-performance, green propellant propulsion system suitable for Evolved Expendable Launch Vehicle (EELV) Secondary Payload Adapter (ESPA)-class spacecraft. (5) Human Exploration Telerobotics (HET): Demonstrating how telerobotics, remote control of a variety of robotic systems, can take routine, highly repetitive, dangerous or long-duration tasks out of human hands. (6) Laser Communication Relay Demo (LCRD): Demo to advance optical communications technology toward infusion into deep space and near Earth operational systems, while growing the capabilities of industry sources. (7) Low Density Supersonic Decelerator (LDSD): Demo new supersonic inflatable decelerator and parachute technologies to enable Mars landings of larger payloads with greater precision at a wider range of altitudes. (8) Mars Science Laboratory (MSL) Entry Descent & Landing Instrumentation (MEDLI): Demo of embedded sensors embedded in the MSL heat shield, designed to record the heat and atmospheric pressure experienced during the spacecraft's high-speed, hot entry in the Martian atmosphere. (9) Solar Electric Propulsion (SEP): 50-kW class spacecraft that uses flexible blanket solar arrays for power generation and an electric propulsion system that delivers payload from low-Earth orbit to higher orbits. (10) Solar Sail Demonstration (SSD): Demo to validate sail deployment techniques for solar sails that are propelled by the pressure of sunlight. (11) Terrestrial HIAD Orbit Reentry (THOR): Demo of a 3.7-m Hypersonic Inflatable Aerodynamic Decelerator (HIAD) entry vehicle to test second generation aerothermal performance and modeling.

McDougal, John↗

Progress Toward a Compact, Highly Stable Ion Clock

There was an update on the subject of two previous NASA Tech Briefs articles: Compact, Highly Stable Ion Clock (NPO-43075), Vol. 32, No. 5 (May 2008), page 63; and Neon as a Buffer Gas for a Mercury-Ion Clock (NPO-42919), Vol. 32, No. 7 (July 2008), page 62. To recapitulate: A developmental miniature mercury-ion clock has stability comparable to that of a hydrogen-maser clock. The ion-handling components are housed in a sealed vacuum tube, wherein a getter pump maintains the partial vacuum, and the evacuated tube is backfilled with mercury vapor in a neon buffer gas. There was progress in the development of the clock, with emphasis on the design, fabrication, pump-down, and bake-out of the vacuum tube (based on established practice in the travelingwave- tube-amplifier industry) and the ability of the tube to retain a vacuum after a year of operation. Other developments include some aspects of the operation of mercury-vapor source (a small appendage oven containing HgO) so as to maintain the optimum low concentration of mercury vapor, and further efforts to miniaturize the vacuum and optical subsystems to fit within a volume of 2 L.

Prestage, John↗

Optical Time Transfer for Bistatic SAR Spacecraft

A spacecraft-to-spacecraft optical time-transfer simulation has been developed as a tool for informing NASA’s Surface Deformation and Change (SDC) mission architecture. The SDC mission will combine radar images from multiple spacecraft to improve understanding of the Earth’s sea-level and landscape changes. Spacecraft must be precisely synchronized in order to create sharp radar images. Simulation of multiple spacecraft time-synchronizing via laser communication can inform technology choices of a mission by providing a picosecond-precision level estimate of clock error. This timing and ranging simulation has been combined with a radar system performance analysis pipeline. The simulated timing errors are used to predict performance of bistatic SAR systems in the presence of oscillator noise and time synchronization in accuracy. This analysis includes both analytic approximation equations from existing literature, and a numerical radar simulation to extract key system performance parameters like phase error and signal-to-noise ratio (SNR)degradation. Precision time-transfer techniques facilitate the accurate synchronization of clocks between any combination of terminals. Most time-transfer technology for comparing two clocks at different terminals use radio frequencies (RF) to measure the time delay between the sending and receiving of signals. Laser technology offers the capability to transmit high data rates with systems that are of smaller size and lower power than comparable RF systems. The clocks on independent spacecraft will have some phase and frequency errors between them that result in clock drift. The two clock models that are included in this bi-directional MATLAB simulation are a cesium-based Chip-Scale Atomic Clock (CSAC) and a rubidium-based Miniature Atomic Clock (MAC). The CSAC has flown as hardware for small satellite missions such as the University of Florida’s CHOMPTT mission. A study of example orbits, including that of NASA NASA-ISRO Synthetic Aperture Radar Mission (NISAR) mission, and lasing rates demonstrate the impact of flight configuration parameters on the synchronization error between two spacecraft. The MATLAB timing simulation uses a Runge-Kutta 4th-order method to propagate spacecraft orbits and computes the light-travel time estimate between them. The simulation outputs the estimated range and estimated clock error based on a user-defined spacecraft cluster configuration. The radar simulation and analytic approximations are applied to evaluate a potential future NASA bistatic SAR constellation architecture. In the proposed architecture, satellites follow each other in the same orbit at 800 km altitude, with a 210 km baseline. We also baseline the CSAC as an ultra stable oscillator, and use NASA’s NISAR for baseline radar system parameters to compute a clock-system introduced phase error of 5.6 degrees without synchronization by frequent time transfer. We build on this base case with a sensitivity analysis of radar performance over a proposed range of constellation and radar system parameters. With this analysis pipeline, we comment on which radar parameters should or should not be changed to minimize synchronization requirements. This analysis technique could be extended or modified to evaluate the timing requirements of other geometries for other future multistatic SAR missions, or other interferometric satellite missions.

Surface Deformation and Change↗

Hydrogen maser clocks in space for solid-Earth research and time-transfer applications: Experiment overview and evaluation of Russian miniature sapphire loaded cavity

The Observatoire Cantonal de Neuchatel (ON) is developing for ESTEC a compact H-maser for space use based upon a miniature sapphire loaded microwave cavity, a technique pioneered at VNIIFTRI. Various contacts between West-European parties, headed by ESA, and the Russian parties, headed by ESA, led to the proposal for flying two H-masers on Meteor 3M, a Russian meteorology satellite in low polar orbit. The experiment will include two masers, one provided by ON and the other by VNIIFTRI. T/F transfer and precise positioning will be performed by both a microwave link, using PRARE equipment, and an optical link, using LASSO-like equipment. The main objectives of the experiment are precise orbit determination and point positioning for geodetic/geophysical research, ultra-accurate time comparison and dissemination as well as in-orbit demonstration of operation and performance of H-masers. Within the scope of a preliminary space H-maser development phase performed for ESTEC at ON in preparation to the joint experiment, a Russian miniature sapphire loaded microwave cavity, on loan from VNIIFTRI, was evaluated in a full-size EFOS hydrogen maser built by ON. The experimental evaluation confirmed the theoretical expectation that with a hydrogen storage volume of only 0.65 liter an atomic quality factor of 1.5 x 10(exp 9) can be obtained for a -105 dBm output power. This represents a theoretical Allan deviation of 1.7 x 10(exp -15) averaged on a 1000 s time interval. From a full-size design to a compact one, therefore, the sacrifice in performance due to the reduction of the storage volume is very small.

Busca, G.↗

A Technology Demonstration Experiment for Laser Cooled Atomic Clocks in Space

We have been developing a laser-cooling apparatus for flight on the International Space Station (ISS), with the intention of demonstrating linewidths on the cesium clock transition narrower than can be realized on the ground. GLACE (the Glovebox Laser- cooled Atomic Clock Experiment) is scheduled for launch on Utilization Flight 3 (UF3) in 2002, and will be mounted in one of the ISS Glovebox platforms for an anticipated 2-3 week run. Separate flight definition projects funded at NIST and Yale by the Micro- gravity Research Division of NASA as a part of its Laser Cooling and Atomic Physics (LCAP) program will follow GLACE. Core technologies for these and other LCAP missions are being developed at JPL, with the current emphasis on developing components such as the laser and optics subsystem, and non-magnetic vacuum-compatible mechanical shutters. Significant technical challenges in developing a space qualifiable laser cooling apparatus include reducing the volume, mass, and power requirements, while increasing the ruggedness and reliability in order to both withstand typical launch conditions and achieve several months of unattended operation. This work was performed at the Jet Propulsion Laboratory under a contract with the National Aeronautics and Space Administration.

Klipstein, W. M.↗

Magnetic Compensation for Second-Order Doppler Shift in LITS

The uncertainty in the frequency of a linear-ion-trap frequency standard (LITS) can be reduced substantially by use of a very small magnetic inhomogeneity tailored to compensate for the residual second-order Doppler shift. An effect associated with the relativistic time dilatation, one cause of the second-order Doppler shift, is ion motion that is attributable to the trapping radio-frequency (RF)electromagnetic field used to trap ions. The second-order Doppler shift is reduced by using a multi-pole trap; however it is still the largest source of systematic frequency shift in the latest generation of LITSs, which are among the most stable clocks in the world. The present compensation scheme reduces the frequency instability of the affected LITS to about a tenth of its previous value. The basic principles of prior generation LITSs were discussed in several prior NASA Tech Briefs articles. Below are recapitulated only those items of basic information necessary to place the present development in context. A LITS includes a microwave local oscillator, the frequency of which is stabilized by comparison with the frequency of the ground state hyperfine transition of 199Hg+ ions. The comparison involves a combination of optical and microwave excitation and interrogation of the ions in a linear ion trap in the presence of a nominally uniform magnetic field. In the current version of the LITS, there are two connected traps (see figure): (1) a quadrupole trap wherein the optical excitation and measurement take place and (2) a 12-pole trap (denoted the resonance trap), wherein the microwave interrogation takes place. The ions are initially loaded into the quadrupole trap and are thereafter shuttled between the two traps. Shuttling ions into the resonance trap allows sensitive microwave interrogation to take place well away from loading interference. The axial magnetic field for the resonance trap is generated by an electric current in a finely wound wire coil surrounded by magnetic shields. In the quadrupole and 12-pole traps, the potentials are produced by RF voltages applied to even numbers (4 and 12, respectively) of parallel rods equally spaced around a circle. The polarity of the voltage on each rod is opposite that of the voltage on the adjacent rod. As a result, the amplitude of the RF trapping field is zero along the centerline and increases, with radius, to a maximum value near the rods.

Burt, Eric↗

Orion Absolute Navigation System Progress and Challenges

The Orion spacecraft is being designed as NASA's next-generation exploration vehicle for crewed missions beyond Low-Earth Orbit. The navigation system for the Orion spacecraft is being designed in a Multi-Organizational Design Environment (MODE) team including contractor and NASA personnel. The system uses an Extended Kalman Filter to process measurements and determine the state. The design of the navigation system has undergone several iterations and modifications since its inception, and continues as a work-in-progress. This paper seeks to benchmark the current state of the design and some of the rationale and analysis behind it. There are specific challenges to address when preparing a timely and effective design for the Exploration Flight Test (EFT-1), while still looking ahead and providing software extensibility for future exploration missions. The primary measurements in a Near-Earth or Mid-Earth environment consist of GPS pseudorange and deltarange, but for future explorations missions the use of star-tracker and optical navigation sources need to be considered. Discussions are presented for state size and composition, processing techniques, and consider states. A presentation is given for the processing technique using the computationally stable and robust UDU formulation with an Agee-Turner Rank-One update. This allows for computational savings when dealing with many parameters which are modeled as slowly varying Gauss-Markov processes. Preliminary analysis shows up to a 50% reduction in computation versus a more traditional formulation. Several state elements are discussed and evaluated, including position, velocity, attitude, clock bias/drift, and GPS measurement biases in addition to bias, scale factor, misalignment, and non-orthogonalities of the accelerometers and gyroscopes. Another consideration is the initialization of the EKF in various scenarios. Scenarios such as single-event upset, ground command, pad alignment, cold start are discussed as are strategies for whole and partial state updates as well as covariance considerations. Strategies are given for dealing with latent measurements and high-rate propagation using multi-rate architecture. The details of the rate groups and the data ow between the elements is discussed and evaluated.

Holt, Greg N.↗

NASA Tech Briefs, February 2012

This issue contains the following briefs: (1) Optical Comb from a Whispering Gallery Mode Resonator for Spectroscopy and Astronomy Instruments Calibration (2) Real-Time Flight Envelope Monitoring System (3) Nemesis Autonomous Test System (4) Mirror Metrology Using Nano-Probe Supports (5) Automated Lab-on-a-Chip Electrophoresis System (6) Techniques for Down-Sampling a Measured Surface Height Map for Model Validation (7) Multi-Component, Multi-Point Interferometric Rayleigh/Mie Doppler Velocimeter (8) Frequency to Voltage Converter Analog Front-End Prototype (9) Dust-Tolerant Intelligent Electrical Connection System (10) Gigabit Ethernet Asynchronous Clock Compensation FIFO (11) High-Speed, Multi-Channel Serial ADC LVDS Interface for Xilinx Virtex-5 FPGA (12) Glovebox for GeoLab Subsystem in HDU1-PEM (13) Modified Process Reduces Porosity when Soldering in Reduced Gravity Environments (14) Use of Functionalized Carbon Nanotubes for Covalent Attachment of Nanotubes to Silicon (15) Flexible Plug Repair for Shuttle Wing Leading Edge (16) Three Dimensionally Interlinked, Dense, Solid Form of Single-Walled CNT Ropes (17) Axel Robotic Platform for Crater and Extreme Terrain Exploration (18) Site Tamper and Material Plow Tool - STAMP (19) Magnetic Interface for Segmented Mirror Assembly (20) Transpiration-Cooled Spacecraft-Insulation-Repair Fasteners (21) Fluorescence-Based Sensor for Monitoring Activation of Lunar Dust (22) Aperture Ion Source (23) Virtual Ultrasound Guidance for Inexperienced Operators (24) Model-Based Fault Diagnosis: Performing Root Cause and Impact Analyses in Real Time (25) Interactive Schematic Integration Within the Propellant System Modeling Environment (26) Magnetic and Electric Field Polarizations of Oblique Magnetospheric Chorus Waves (27) Variable Sampling Mapping.

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