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At least 667 records · Page 37

Solid Lubricants and Coatings for Extreme Environments: State-of-the-Art Survey

An investigation was conducted to survey anticipated requirements for solid lubricants in lunar and Martian environments, as well as the effects of these environments on lubricants and their performance and durability. The success of habitats and vehicles on the Moon and Mars, and ultimately, of the human exploration of and permanent human presence on the Moon and Mars, are critically dependent on the correct and reliable operation of many moving mechanical assemblies and tribological components. The coefficient of friction and lifetime of any lubricant generally vary with the environment, and lubricants have very different characteristics under different conditions. It is essential, therefore, to select the right lubrication technique and lubricant for each mechanical and tribological application. Several environmental factors are hazardous to performance integrity on the Moon and Mars. Potential threats common to both the Moon and Mars are low ambient temperatures, wide daily temperature swings (thermal cycling), solar flux, cosmic radiation, and large quantities of dust. The surface of Mars has the additional challenges of dust storms, winds, and a carbon dioxide atmosphere. Solid lubricants and coatings are needed for lunar and Martian applications, where liquid lubricants are ineffective and undesirable, and these lubricants must perform well in the extreme environments of the Moon, Mars, and space, as well as on Earth, where they will be assembled and tested. No solid lubricants and coatings and their systems currently exist or have been validated that meet these requirements, so new solid lubricants must be designed and validated for these applications.

Miyoshi, Kazuhisa↗

Aerosol Physics for the Lunar Environment: Equations for Lunar Dust Control and Mitigation Technologies

Sticky and jagged dust was ubiquitous during the Apollo missions, causing soiling and abrasion problems with seals, coatings and equipment, in addition to eye irritation and breathing discomfort in the cabin. The Artemis Program of NASA aims to place astronauts on the lunar surface by 2024 and establish a sustainable presence in the following decade. Returning to the Moon requires controlling and mitigating the dust which will be inevitably brought inside the cabins. The state-of-the-science for effective collection of aerosols is based on dynamics of airborne particulate matter under terrestrial conditions. However, the governing physics does not apply to extra-vehicular activity in the hard-vacuum lunar condition. For example, the substantial difference in gravity will dictate particle transport both outside and inside the cabin. In this study, we revisited the aerosol physical phenomena that are assumed in the design of Earth-based aerosol instruments and extend the applicability to different scenarios in lunar missions. As shown, long-term lunar habitats, transfer vehicles to lunar orbital platforms, and low pressure cabin atmospheres have different aerosol dynamics. In all cases, the impact of dust control strategies using gravitational, electrical, and thermal techniques for various mitigation and monitoring hardware is explored. The guidelines provided through this study will show how terrestrial aerosol equipment can translate to lunar dust applications.

Nima Afshar-Mohajer↗

G-189A analytical simulation of the integrated waste management-water system using radioisotopes for thermal energy

An analytical simulation of the RITE-Integrated Waste Management and Water Recovery System using radioisotopes for thermal energy was prepared for the NASA-Manned Space Flight Center (MSFC). The RITE system is the most advanced concept water-waste management system currently under development and has undergone extended duration testing. It has the capability of disposing of nearly all spacecraft wastes including feces and trash and of recovering water from usual waste water sources: urine, condensate, wash water, etc. All of the process heat normally used in the system is produced from low penalty radioisotope heat sources. The analytical simulation was developed with the G189A computer program. The objective of the simulation was to obtain an analytical simulation which can be used to (1) evaluate the current RITE system steady state and transient performance during normal operating conditions, and also during off normal operating conditions including failure modes; and (2) evaluate the effects of variations in component design parameters and vehicle interface parameters on system performance.

Coggi, J. V.↗

Thermal analysis of conceptual designs for GPHS/FPSE power systems of 250 We and 500 We

Thermal analyses were performed for two distinct configurations of a proposed space nuclear power system which combines General Purpose Heat Source (GPHS) modules with the state of the art Free-Piston Stirling Engines (FPSEs). The two configurations correspond to systems with power levels of 250 and 500 W(sub e). The 250 W(sub e) GPHS/FPSE power system utilizes four GPHS modules and one FPSE, and the 500 W(sub e) contains eight GPHS modules and two FPSEs. The configurations of the systems and the bases for selecting the configurations are described. Brief introductory sections are included to describe the GPHS modules and free piston Stirling engines. The primary focus of the thermal analyses is on the temperature of the iridium fuel clad within the GPHS modules. A design goal temperature of 1573 K was selected as the upper limit for the fuel clad during normal operating conditions. The basis for selecting this temperature limit is discussed in detail. Results obtained from thermal analysis of the 250 W(sub e) GPHS/FPSE power system indicate fuel clad temperatures which slightly exceed the design goal temperature of 1573 K. The results are considered favorable due to the numerous conservative assumptions used in developing the thermal model and performing the thermal analysis. To demonstrate the effects of the conservatism, a brief sensitivity analysis is performed in which a few of the key system parameters are varied to determine their effect on the fuel clad temperatures. It is concluded that thermal analysis of a more detailed thermal model would be expected to yield fuel clad temperatures below the design foal temperature limiy 1573 K.

Mccomas, Thomas J.↗

Characterization Testing of Lockheed Martin Micro1-2 Cryocoolers Optimized for 220 K Environment

The Mapping Imaging Spectrometer for Europa (MISE) Instrument on the Europa Clipper mission has baselined a Lockheed Martin high-power Micro1-2 pulse tube cryocooler operating at 135 Hz with a 220 K heat rejection temperature. This paper describes the testing and results of two Lockheed Martin Micro1-2 coolers optimized for these conditions. The thermal performance of the microcoolers was measured in vacuum for heat reject temperatures between 220 and 230 K. The coolers were operated with input powers ranging from 5 W to 40 W and drive frequency between 125 Hz and 145 Hz. The optimal drive frequency was strongly dependent on heat reject temperature. In addition, the exported forces and torques of the coolers were measured at 300 K heat rejection for input powers ranging from 5 W to 60 W and drive frequency between 120 Hz and 160 Hz. The exported forces were dependent on both piston amplitude and drive frequency. Moreover, the following were measured on one of the coolers: DC and AC magnetic fields at various locations, the off-state conductance of the pulse tube, and the effect of inclination angle of the pulse tube relative to gravity on the performance of the cooler. Finally, one of the coolers was subjected to random vibration testing.

Rodriguez, J.I.↗

Nonequilibrium radiation and chemistry models for aerocapture vehicle flowfields

The primary accomplishments of the project were as follows: (1) From an overall standpoint, the primary accomplishment of this research was the development of a complete gasdynamic-radiatively coupled nonequilibrium viscous shock layer solution method for axisymmetric blunt bodies. This method can be used for rapid engineering modeling of nonequilibrium re-entry flowfields over a wide range of conditions. (2) Another significant accomplishment was the development of an air radiation model that included local thermodynamic nonequilibrium (LTNE) phenomena. (3) As part of this research, three electron-electronic energy models were developed. The first was a quasi-equilibrium electron (QEE) model which determined an effective free electron temperature and assumed that the electronic states were in equilibrium with the free electrons. The second was a quasi-equilibrium electron-electronic (QEEE) model which computed an effective electron-electronic temperature. The third model was a full electron-electronic (FEE) differential equation model which included convective, collisional, viscous, conductive, vibrational coupling, and chemical effects on electron-electronic energy. (4) Since vibration-dissociation coupling phenomena as well as vibrational thermal nonequilibrium phenomena are important in the nonequilibrium zone behind a shock front, a vibrational energy and vibration-dissociation coupling model was developed and included in the flowfield model. This model was a modified coupled vibrational dissociation vibrational (MCVDV) model and also included electron-vibrational coupling. (5) Another accomplishment of the project was the usage of the developed models to investigate radiative heating. (6) A multi-component diffusion model which properly models the multi-component nature of diffusion in complex gas mixtures such as air, was developed and incorporated into the blunt body model. (7) A model was developed to predict the magnitude and characteristics of the shock wave precursor ahead of vehicles entering the Earth's atmosphere. (8) Since considerable data exists for radiating nonequilibrium flow behind normal shock waves, a normal shock wave version of the blunt body code was developed. (9) By comparing predictions from the models and codes with available normal shock data and the flight data of Fire II, it is believed that the developed flowfield and nonequilibrium radiation models have been essentially validated for engineering applications.

Carlson, Leland A.↗

Application of a Near Infrared Imaging System for Thermographic Imaging of the Space Shuttle during Hypersonic Re-Entry

High resolution calibrated near infrared (NIR) imagery was obtained of the Space Shuttle s reentry during STS-119, STS-125, and STS-128 missions. The infrared imagery was collected using a US Navy NP-3D Orion aircraft using a long-range infrared optical package referred to as Cast Glance. The slant ranges between the Space Shuttle and Cast Glance were approximately 26-41 nautical miles at point of closest approach. The Hypersonic Thermodynamic Infrared Measurements (HYTHIRM) project was a NASA Langley led endeavor sponsored by the NASA Engineering Safety Center, the Space Shuttle Program Office and the NASA Aeronautics Research Mission Directorate to demonstrate a quantitative thermal imaging capability. HYTHIRM required several mission tools to acquire the imagery. These tools include pre-mission acquisition simulations of the Shuttle trajectory in relationship to the Cast Glance aircraft flight path, radiance modeling to predict the infrared response of the Shuttle, and post mission analysis tools to process the infrared imagery to quantitative temperature maps. The spatially resolved global thermal measurements made during the Shuttle s hypersonic reentry provides valuable flight data for reducing the uncertainty associated with present day ground-to-flight extrapolation techniques and current state-of-the-art empirical boundary-layer transition or turbulent heating prediction methods. Laminar and turbulent flight data is considered critical for the development of turbulence models supporting NASA s next-generation spacecraft. This paper will provide the motivation and details behind the use of an upgraded NIR imaging system used onboard a Navy Cast Glance aircraft and describe the characterizations and procedures performed to obtain quantitative temperature maps. A brief description and assessment will be provided of the previously used analog NIR camera along with image examples from Shuttle missions STS-121, STS-115, and solar tower test. These thermal observations confirmed the challenge of a long-range acquisition during re-entry. These challenges are due to unknown atmospheric conditions, image saturation, vibration etc. This provides the motivation for the use of a digital NIR sensor. The characterizations performed on the digital NIR sensor included radiometric, spatial, and spectral measurements using blackbody radiation sources and known targets. An assessment of the collected data for three Space Shuttle atmospheric re-entries, STS-119, STS-125, and STS-128, are provided along with a description of various events of interest captured using the digital NIR imaging system such as RCS firings and boundary layer transitions. Lastly the process used to convert the raw image counts to quantitative temperatures is presented along with comparisons to the Space Shuttle's onboard thermocouples.

Zalameda, Joseph N.↗

Thermal Insulation Test Apparatuses

The National Aeronautics and Space Administration (NASA) seeks to license its Thermal Insulation Test Apparatuses. Designed by the Cryogenics Test Laboratory at the John F. Kennedy Space Center (KSC) in Florida, these patented technologies (U.S. Patent Numbers: Cryostat 1 - 6,742,926, Cryostat 2 - 6,487,866, and Cryostat 4 - 6,824,306) allow manufacturers to fabricate and test cryogenic insulation at their production and/or laboratory facilities. These new inventions allow for the thermal performance characterization of cylindrical and flat specimens (e.g., bulk-fill, flat-panel, multilayer, or continuously rolled) over the full range of pressures, from high vacuum to no vacuum, and over the full range of temperatures from 77K to 300K. In today's world, efficient, low-maintenance, low-temperature refrigeration is taking a more significant role, from the food industry, transportation, energy, and medical applications to the Space Shuttle. Most countries (including the United States) have laws requiring commercially available insulation materials to be tested and rated by an accepted methodology. The new Cryostat methods go beyond the formal capabilities of the ASTM methods to provide testing for real systems, including full-temperature differences plus full-range vacuum conditions.

Berman, Brion↗

Testing of an Ammonia EVA Vent Tool for the International Space Station

When components of the International Space Station ammonia External Active Thermal Control System are replaced on-orbit, they must be vented immediately after removal from the system. Venting ensures that the component is not hard packed with liquid and thus does not pose a hazard. An extravehicular activity (EVA) vent tool has been developed to perform this function. However, there were concerns that the tool could whip, posing a hazard to the EVA astronaut, or would freeze. The ammonia vent tool was recently tested in a thermal/vacuum chamber to demonstrate that it would operate safely and would not freeze during venting. During the test, ammonia mimicking the venting conditions for six different heat exchanger initial conditions was passed through representative test articles. In the present work, the model that was used to develop the ammonia state and flow for the test points is discussed and the test setup and operation is described. The qualitative whipping and freezing results of the test are discussed and vent plume pressure measurements are described and interpreted.

Ungar, Eugene K.↗

Evaluating the Adsorptive Capabilites of Chemsorb 1000 and Chemsorb 1425

The removal of trace contaminants from spacecraft cabin air is necessary for crew health and comfort during long duration space exploration missions. The air revitalization technologies used in these future exploration missions will evolve from current ISS ISS State-of-Art (SOA) and is being designed and tested by the Advanced Exploration Systems (AES) Program's Atmosphere Resource Recovery and Environmental Monitoring (ARREM) project. The ARREM project is working to mature optimum atmosphere revitalization and environmental monitoring system architectures to enable exploration beyond Lower Earth Orbit (LEO). The Air Revitalization Lab at KSC is one of six NASA field centers participating in the ARREM that specializes in adsorbent and catalyst characterization with simulated spacecraft gas streams using combinations of pressure, O2 partial pressure, CO2 partial pressure, and humidity that are representative of a range of anticipated cabin atmospheric conditions and loads. On board ISS, the Trace Contaminant Control Subassembly (TCCS) provides active control of trace contaminants from the cabin atmosphere utilizing physical adsorption, thermal catalytic oxidation, and chemical adsorption processes. High molecular weight contaminants and ammonia (NH3) are removed a granular activated carbon treated with approx. 10% by weight phosphoric acid (H3PO4) (B-S Type 3032 4×6 mesh), which is expendable and is periodically refurbished. The Type 3032 granular activated carbon bed is no longer commercially available and therefore it is important to characterize the efficiency and capacity of commercially available NH3 sorbents. This paper describes the characterization of two Molecular Products LTD activated carbons: Chemsorb 1000 and Chemsorb 1425. Untreated activated carbons (e.g. Chemsorb 1000) remove contaminants by physisorption, which concentrates the contaminant within the pores of the carbon while letting air to pass through the sorbent4. Low molecular weight or polar gases (e.g. HCl, SO2, formaldehyde, and NH3) are not removed by physisorption and typically require chemisorption for removal. Treated activated carbons (e.g. Chemsorb 1425) are impregnated with a a chemical agent (e.g. phosphoric acid) that reacts with those gases, converting them to solids or salts within the carbon and removes them from the air stream. This process occurs via neutralization or catalysis reactions and adsorption capacity is exhaustedwhen the available impregnated chemicals are consumed. Moisture affects removal performance since adsorption sites within the pores are filled with water. The performance of impregnated carbons may be enhanced by moisture content because the mechanisms of contaminant removal are chemical reactions that occur in reagents contained within the pores. The adsorptive capacity data (mol/kg) of Chemsorb 1000 and 1425 for gas mixtures (ethanol, acetone, toluene, acetaldehyde, dichloromethane, and xylene) was measured with 40% relative humidity at 23 deg C air temperature. The adsorptive capacity data (mol/kg) of Chemsorb 1425 was measured using NH3 gas streams.

adsorptive capacities↗

Molecular Tagging Velocimetry Development for In-situ Measurement in High-Temperature Test Facility

The High Temperature Test Facility, HTTF, at Oregon State University (OSU) is an integral-effect test facility designed to model the behavior of a Very High Temperature Gas Reactor (VHTR) during a Depressurized Conduction Cooldown (DCC) event. It also has the ability to conduct limited investigations into the progression of a Pressurized Conduction Cooldown (PCC) event in addition to phenomena occurring during normal operations. Both of these phenomena will be studied with in-situ velocity field measurements. Experimental measurements of velocity are critical to provide proper boundary conditions to validate CFD codes, as well as developing correlations for system level codes, such as RELAP5 (http://www4vip.inl.gov/relap5/). Such data will be the first acquired in the HTTF and will introduce a diagnostic with numerous other applications to the field of nuclear thermal hydraulics. A laser-based optical diagnostic under development at The George Washington University (GWU) is presented; the technique is demonstrated with velocity data obtained in ambient temperature air, and adaptation to high-pressure, high-temperature flow is discussed.

Andre, Matthieu A.↗

Evaluation of the heat transfer module (FAHT) of Failure Analysis Nonlinear Thermal And Structural Integrated Code (FANTASTIC)

The heat transfer module of FANTASTIC Code (FAHT) is studied and evaluated to the extend possible during the ten weeks duration of this project. A brief background of the previous studies is given and the governing equations as modeled in FAHT are discussed. FAHT's capabilities and limitations based on these equations and its coding methodology are explained in detail. It is established that with improper choice of element size and time step FAHT's temperature field prediction at some nodes will be below the initial condition. The source of this unrealistic temperature prediction is identified and a procedure is proposed for avoiding this phenomenon. It is further shown that the proposed procedure will converge to an accurate prediction upon mesh refinement. Unfortunately due to lack of time FAHT's ability to accurately account for pyrolysis and surface ablation has not been verified. Therefore, at the present time it can be stated with confidence that FAHT can accurately predict the temperature field for a transient multi-dimensional, orthotropic material with directional dependence, variable property, with nonlinear boundary condition. Such a prediction will provide an upper limit for the temperature field in an ablating decomposing nozzle liner. The pore pressure field, however, will not be known.

Keyhani, Majid↗

Numerical Study of Flow Augmented Thermal Management for Entry and Re-Entry Environments

The use of a flow augmented thermal management system for entry and re-entr environments is one method for reducing heat and drag loads. This concept relies on jet penetration from supersonic and hypersonic counterflowing jets that could significantly weaken and disperse the shock-wave system of the spacecraft flow field. The objective of this research effort is to conduct parametric studies of the supersonic flow over a 2.6% scale model of the Apollo capsule, with and without the counterflowing jet, using time-accurate and steady-state computational fluid dynamics simulations. The numerical studies, including different freestream Mach number angle of attack counterflowing jet mass flow rate, and nozzle configurations, were performed to examine their effect on the drag and beat loads and to explore the counternowing jet condition. The numerical results were compared with the test data obtained from transonic blow-down wind-tunnel experiments conducted independently at NASA MSFC.

Cheng, Gary C.↗

Improvements to Thermal Protection System Design of Aerocapture Systems for Uranus Orbiters

The National Academies Planetary Science and Astrobiology Decadal Survey identified Uranus and Neptune - called Ice Giants - as the priority destinations for science. The survey assessed both a mission to Uranus through the Uranus Orbiter and Probe (UOP) concept, and Neptune through the Neptune-Triton Odyssey concept and determined that Uranus is the highest priority for a Flagship class mission. The UOP mission concept planned to deliver an in situ probe and conduct a multi-year orbital tour of the system to meet the science objectives. While the Uranus mission is currently viable with launch windows starting in 2031 using existing launch vehicles, the mission has a cruise phase of at least 12 years and would require more than half of its weight in fuel propellant to achieve the change in velocity necessary for orbital insertion. Aerocapture uses aerodynamic forces generated on a vehicle by the planet's atmosphere to modulate a spacecraft's trajectory, decreasing spacecraft velocity, and allowing mission designers to target the final orbital state. Aerocapture reduces the time-of-flight from Earth to Uranus over a fully propulsive solution, opening up more launch opportunities to arrive in the 2040's to the mission's science objectives. Aerocapture also allows a payload mass increase by mitigating the need for fuel to retropropulsively insert the payload into orbit, thereby increase the science that can be performed. For an aerocapture mission structure using a traditional aeroshell to deliver the UOP scientific payload to Uranus, Conformal Phenolic Impregnated Carbon Ablator (C-PICA) was determined to be the best-performing forebody thermal protection system (TPS) and other candidate aftbody TPS options were presented as feasible. This paper focuses on A) evaluating C-PICA as a forebody TPS using stressing entry conditions associated with a large range of potential Uranus flagship launch vehicles and interplanetary trajectories, B) widening the aftbody TPS candidates for new mass-efficient and cost-efficient solutions, and C) a summary list of actions remaining to provide a technically feasible and supply-robust set of TPS for an aerocapture vehicle to the Ice Giants is presented.

C-PICA↗

Improvements to Thermal Protection System Design of Aerocapture Systems for Uranus Orbiters

The National Academies Planetary Science and Astrobiology Decadal Survey identified Uranus and Neptune - called Ice Giants - as the priority destinations for science. The survey assessed both a mission to Uranus through the Uranus Orbiter and Probe (UOP) concept, and Neptune through the Neptune-Triton Odyssey concept and determined that Uranus is the highest priority for a Flagship class mission. The UOP mission concept planned to deliver an in situ probe and conduct a multi-year orbital tour of the system to meet the science objectives. While the Uranus mission is currently viable with launch windows starting in 2031 using existing launch vehicles, the mission has a cruise phase of at least 12 years and would require more than half of its weight in fuel propellant to achieve the change in velocity necessary for orbital insertion. Aerocapture uses aerodynamic forces generated on a vehicle by the planet's atmosphere to modulate a spacecraft's trajectory, decreasing spacecraft velocity, and allowing mission designers to target the final orbital state. Aerocapture reduces the time-of-flight from Earth to Uranus over a fully propulsive solution, opening up more launch opportunities to arrive in the 2040's to the mission's science objectives. Aerocapture also allows a payload mass increase by mitigating the need for fuel to retropropulsively insert the payload into orbit, thereby increase the science that can be performed. For an aerocapture mission structure using a traditional aeroshell to deliver the UOP scientific payload to Uranus, Conformal Phenolic Impregnated Carbon Ablator (C-PICA) was determined to be the best-performing forebody thermal protection system (TPS) and other candidate aftbody TPS options were presented as feasible. This paper focuses on A) evaluating C-PICA as a forebody TPS using stressing entry conditions associated with a large range of potential Uranus flagship launch vehicles and interplanetary trajectories, B) widening the aftbody TPS candidates for new mass-efficient and cost-efficient solutions, and C) a summary list of actions remaining to provide a technically feasible and supply-robust set of TPS for an aerocapture vehicle to the Ice Giants is presented.

C-PICA↗

The Role of Asymmetries in Thermal Nonequilibrium

Thermal nonequilibrium (TNE) is a fascinating situation that occurs in coronal magnetic flux tubes (loops) for which no solution to the steady-state fluid equations exists. The plasma is constantly evolving even though the heating that produces the hot temperatures does not. This is a promising explanation for isolated phenomena such as prominences, coronal rain, and long-period pulsating loops, but it may also have much broader relevance. As known for some time, TNE requires that the heating be both (quasi-)steady and concentrated at low coronal altitudes. Recent studies indicate that asymmetries are also important, with large enough asymmetries in the heating and/or cross-sectional area resulting in steady flow rather than TNE. Using reasonable approximations, we have derived two formulae for quantifying the conditions necessary for TNE. As a rough rule of thumb, the ratio of apex to footpoint heating rates must be less than about 0.1, and asymmetries must be less than about a factor of 3. The precise values are case-dependent. We have tested our formulae with 1D hydrodynamic loop simulations and find a very acceptable agreement. These results are important for developing physical insight about TNE and assessing how widespread it may be on the Sun.

Klimchuk, James A.↗

Controlled Parametric Forcing During Directional Solidification of a Bulk Organic Alloy Under Microgravity

The response of dendritic microstructures to step-like pulling velocity conditions is investigated using microgravity directional solidification experiments conducted on DECLIC-DSI combined with phase-field simulations. Under a constant pulling velocity of 1.5 µm/s, the evolution toward steady-state growth is characterized in terms of primary spacing, dendrite drift, and tip dynamics. For the first time, side-view observations enabled direct measurement of tip radius and sidebranching frequency. When step-like oscillations of the pulling velocity are imposed, the dendritic array exhibits a strongly period-dependent response: short periods lead to rapid tip adaptation, whereas longer periods induce a phase lag between tip position and morphology, resulting in progressive tip flattening and, above a critical period, interface destabilization and dendrite splitting. Quantitative phase-field simulations, including a realistic thermal field and stochastic noise, reproduce the experimental observations and provide insight into the governing mechanisms, highlighting the role of characteristic relaxation times, sequence-dependent effects, and the irreversible reorganization of the microstructure following splitting.

Microgravity↗

Electron Flow to a Satellite at High Positive Potential

The Tethered Satellite System (TSS) is designed to deploy a 1.6 m diameter spherical satellite a distance of 20 km above the space shuttle orbiter on an insulated conducting tether. Because of the passage of the conducting tether through the earth's magnetic field, an emf is generated producing a positive satellite potential of about 5000 V. Electron flow under the influence of this high positive potential is the focus of the present analysis. The ionospheric parameters at TSS orbit altitude are; thermal velocity of electrons, 1.9 x 10(exp 5) M/S, thermal velocity of the ions, 1.1 x 10(exp 3) m/s, velocity of the satellite 8 x 10(exp 3) m/s. The electrons, with a Debye length, lambda(D) = 0.49 cm, spiral about the earth's magnetic field lines (0.4 Gauss) with a radius of about 3 cm and the ions spiral with a radius of 5 m. Under these conditions, the electron thermal energy, kT is 0.17 eV. The TSS satellite radius, r(p) is 163 Debye lengths. There is an extensive literature on the interaction of satellites with the near-earth ionospheric plasma. The space charge limitation to the electron current collected by a sphere at positive electrical potential was calculated by Langmuir and Blodgett (1924). Parker and Murphy (1967) recognized the importance of the influence of the earth's magnetic field and used the guiding center approximation to calculate the electron current collected by a positive charged satellite. More recently Ma and Schunk (1989) have calculated the time dependent flow of electrons to a spherical satellite at positive potential utilizing numerical methods and Sheldon (1994) used similar methods to solve this problem for the steady state. In order to analyze some of the phenomena that occurred in the ionosphere during the TSS flights, it would be useful to have analytic expressions for these electron flows. The governing equations are very complex and an exact analytical solution is not likely. An approximate analytical solution is feasible however, and the results of one attempt are presented herein.

Sheldon, John W.↗