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NASA NTRS1972

Approximation method for the kinetic Boltzmann equation

The further development of a method for approximating the Boltzmann equation is considered and a case of pseudo-Maxwellian molecules is treated in detail. A method of approximating the collision frequency is discussed along with a method for approximating the moments of the Boltzmann collision integral. Since the return collisions integral and the collision frequency are expressed through the distribution function moments, use of the proposed methods make it possible to reduce the Boltzmann equation to a series of approximating equations.

Shakhov, Y. M.↗

NASA NTRS2017

The Effect of the Spin-Forbidden Co((sup 1) Sigma plus) plus O((sup 3) P) Yields CO2 (1 Sigma (sub G) plus) Recombination Reaction on Afterbody Heating of Mars Entry Vehicles

Vibrationally excited CO2, formed by two-body recombination from CO((sup 1) sigma plus) and O((sup 3) P) in the wake behind spacecraft entering the Martian atmosphere reaction, is potentially responsible for the higher than anticipated radiative heating of the backshell, compared to pre-flight predictions. This process involves a spin-forbidden transition of the transient triplet CO2 molecule to the longer-lived singlet. To accurately predict the singlet-triplet transition probability and estimate the thermal rate coefficient of the recombination reaction, ab initio methods were used to compute the first singlet and three lowest triplet CO2 potential energy surfaces and the spin-orbit coupling matrix elements between these states. Analytical fits to these four potential energy surfaces were generated for surface hopping trajectory calculations, using Tully's fewest switches surface hopping algorithm. Preliminary results for the trajectory calculations are presented. The calculated probability of a CO((sup 1) sigma plus) and O((sup 3) P) collision leading to singlet CO2 formation is on the order of 10 (sup -4). The predicted flowfield conditions for various Mars entry scenarios predict temperatures in the range of 1000 degrees Kelvin - 4000 degrees Kelvin and pressures in the range of 300-2500 pascals at the shoulder and in the wake, which is consistent with a heavy-particle collision frequency of 10 (sup 6) to 10 (sup 7) per second. Owing to this low collision frequency, it is likely that CO((sup 1) sigma plus) molecules formed by this mechanism will mostly be frozen in a highly nonequilibrium rovibrational energy state until they relax by photoemission.

CO2 recombination↗

NASA NTRS1994

Thermodynamic effect of the ion sound instability in the ionosphere

During geomagnetic disturbances when the ring current interacts intensely with the plasmasphere, the plasma of this region undergoes a strong heating due to an ion cyclotron instability. This is followed by the transfer of heat along geomagnetic field lines from the heating region to the ionosphere. One of the results of this process is the formation of non-isothermal region (in which T(sub e) greater than 3.4 T(sub i) at ionospheric heights) caused by a rapid cooling the H(+) ions due to their resonant charge exchange with neutral hydrogen. Heat transfer from the top of the flux tube to the ionosphere is investigated using a hydrodynamic model for the ionosphere-plasmasphere coupling. Field-aligned currents, present in the topside ionosphere, are often accompanied by ion sound turbulence. The turbulence scatters electrons, increasing the total electron collision frequency through wave-particle effects. The influence of wave-particle interactions introduces an anomalous component to the total collision frequency, which modifies substantially the heat conduction coefficient of the plasma. As a result, the plasma is heated more intensely above than below this region of ion sound turbulence.

Khazanov, G. V.↗

NASA NTRS1982

Speed-dependent collision effects on radar back-scattering from the ionosphere

The question whether the differences between fluctuation spectra for linearly speed-dependent and speed-independent collision frequencies could account for disagreements between rocket and incoherent scatter estimate was addressed. The basic theory used for computing the fluctuation spectrum is outlined. The speed-dependence of the charge-neutral collision frequency is discussed, with special emphasis on its derivation from the mobility measurements. Various developments of the computer code used for the computation of the fluctuation spectrum are described. The range of values of input parameters typical to the collision-dominated ionosphere are briefly described. The computational results are presented, and the significance and limitation of these results and the future scope of the research are discussed.

Behl, Y. K.↗

NASA NTRS1974

Accuracy of rocket measurements of lower ionosphere electron concentrations

Measurements of electron concentration taken at the same time and at the same place in the lower ionosphere by independent instrumentation mounted on the same rocket are described. The technique utilizes Faraday rotation and differential absorption of radio waves propagating from the ground to the rocket at two different frequencies. Agreement near 90 km within 7%, 6%, 8%, and 3% is demonstrated by the four available cases of coincidence in time and altitude. Maximum dispersion at other altitudes is calculated from known random errors. Stronger variation of electron collision frequency with altitude than with season is indicated by 34 measurements between 75 and 100 km. Insensitivity of electron concentration determinations at 72 km to errors in extrapolated collision frequency models is demonstrated.

Mechtly, E. A.↗

NASA NTRS1981

Speed-dependent collision effects on radar back-scattering from the ionosphere

A computer code to accurately compute the fluctuation spectrum for linearly speed dependent collision frequencies was developed. The effect of ignoring the speed dependence on the estimates of ionospheric parameters was determined. It is shown that disagreements between the rocket and the incoherent scatter estimates could be partially resolved if the correct speed dependence of the i-n collision frequency is not ignored. This problem is also relevant to the study of ionospheric irregularities in the auroral E-region and their effects on the radio communication with satellites.

Theimer, O.↗

NASA NTRS1954

Determination of Flame Temperatures from 2000 to 3000 K by Microwave Absorption

Equations are derived for the measurement of flame temperatures from the attenuation of a microwave beam by temperature-induced free electrons from chemical elements introduced in the flame. Corrections are developed to account for the electron distribution in the flame. Procedure for obtaining the temperature from absorption is outlined. The free electron collision frequency and an effective ionization potential for four alkali elements were determined experimentally. The data were taken on a gas burner with a temperature range from 1900deg to 2400deg K. The effective ionization potential of sodium agrees with the spectral-line limit value. From these experimental ionization potentials and the experimental collision frequency, an accuracy of +/-600 K in the temperature was obtained. Fluctuating and average temperature data of a liquid propellant burner are presented primarily from 1.25-centimeter-wavelength microwave measurements in comparison with simultaneous two-color pyrometer and sound intensity measurements in the region from 2200deg to 2900deg K.

Kuhns, Perry W↗

NASA NTRS2015

Numerical Simulations of the XR-5 Hall Thruster for Life Assessment at Different Operating Conditions

NASA's Jet Propulsion Laboratory has been investigating the applicability of Aerojet Rocketdyne's XR-5 thruster, a 4.5 kW class Hall thruster, for deep-space missions. Major considerations for qualifying the XR-5 for deep-space missions are demonstration of a wide throttling envelope and a usable life capability in excess of 10,000 h. Numerical simulations with the 2-D axisymmetric code Hall2De are employed to inform the qualification process by assessing erosion rates at the thruster surfaces in a wide range of throttling conditions without the need for conducting costly endurance testing. In previous work at JPL by Jorns et al., the anomalous collision frequency distribution for 11 different throttling conditions of the XR-5 spanning 0.3-4.5 kW were identified based on probe measurements of the electron temperature in the near plume region. In this paper, we provide estimates for the erosion rates at the channel walls and pole covers for the same 11 conditions. Uncertainties in the plasma measurements and in the anomalous collision frequency distribution are addressed by determining upper and lower bounds of the erosion rates. Results suggest that erosion of the walls only occurs in the last 5% of the acceleration channel and the rate of such erosion decreases as the geometry of the thruster changes in time due to magnetic shielding. A quasi-zero-erosion state is eventually achieved in all the examined throttling conditions. Examination of the results for pole surface erosion and estimated cathode life indicates that the XR-5 propellant throughput capability will exceed 700 kg, which provides 50% margin over the usable throughput capability of 466 kg as already demonstrated in wear testing.

Lopez Ortega, Alejandro↗

NASA NTRS1989

Comments on comet shapes and aggregation processes

An important question for a comet mission is whether comet nuclei preserve information clarifying aggregation processes of planetary matter. New observational evidence shows that Trojan asteroids, as a group, display a higher fraction of highly-elongated objects than the belt. More recently evidence has accumulated that comet nuclei, as a group, also display highly-elongated shapes at macro-scale. This evidence comes from the several comets whose nuclear lightcurves or shapes have been well studied. Trojans and comet nuclei share other properties. Both groups have extremely low albedos and reddish-to neutral-black colors typical of asteroids of spectral class D, P, and C. Both groups may have had relatively low collision frequencies. An important problem to resolve with spacecraft imaging is whether these elongated shapes are primordial, or due to evolution of the objects. Two hypotheses that might be tested by a combination of global-scale and close-up imaging from various directions are: (1) The irregular shapes are primordial and related to the fact that these bodies have had lower collision frequencies than belt asteroids; or (2) The irregular shapes may be due to volatile loss.

Hartmann, William K.↗

NASA NTRS1994

Heating of the nighttime D region by very low frequency transmitters

VLF signals propagating in the Earth-ionosphere waveguide are used to probe the heated nighttime D region over three U.S. Navy very low frequency (VLF,3-30 kHz) transmitters. Ionospheric cooling and heating are observed when a transmitter turns off and on in the course of normal operations. Heating by the 24.0-kHz NAA transmitter in Cutler, Maine, (1000 kW radiated power) was observed by this method in 41 of 52 off/on episodes during December 1992, increasing the amplitude and retarding the phase of the 21.4-kHz NSS probe wave propagating from Annapolis, Maryland, to Gander, Newfoundland, by as much as 0.84 dB and 5.3 deg, respectively. In 6 of these 41 episodes, the amplitude of the 28.5-kHz NAU probe wave propagating from Puerto Rico to Gander was also perturbed by as much as 0.29 dB. The latter observations were unexpected due to the greater than 770 km distance between NAA and the NAU-Gander great circle path. Heating by the NSS (21.4 kHz, 265 kW) and NLK (24.8 kHz, 850 kW) transmitters was observed serendipitously in data from earlier measurements of the amplitudes of VLF signals propagating in the Earth-ionosphere waveguide. A three-dimensional model of wave absorption and electron heating in a magnetized, weakly ionized plasma is used to calculate the extent nad shape of the collision frequency (i.e., electron temperature) enhancement above a VLF transmitter. The enhancements are annular, with a geomagnetic north-south asymmetry and a radius at the outer half-maximum of the collision frequency enhancement of about 150 km. Heating by the NAA transmitter is predicted to increase the nighttime D region electron temperature by as much as a factor of 3. The calculated changes in the D region conductivity are used in a three-dimensional model of propagation in the Earth-ionosphere wavelength to predict the effect of the heated patch on a subionospheric VLF probe wave. The range of predicted scattered field amplitudes is in general consistent with the observed signal perturbations. Discrepanices in the predictions are attributed to lack of knowledge of the D region electron density profile along the probe wave great circle paths.

Rodriguez, Juan V.↗

NASA NTRS1997

Future Laser-Cooled Microwave Clock Performance

Limitations to the performance of laser-cooled earth and space-based Cs clocks will be critically discussed. The most significant limitation to the stability and accuracy of laser-cooled atomic clocks is the frequency shift due to cold collisions. Because of it, laser-cooled Cs clocks must be operated at low density and this implies that space based Cs clock performance will not be significantly better than earth based. To regain some of the high accuracy and stability lost to the low density, clocks can be designed to multiply launch (or juggle) atoms. Clocks based on other atoms, in particular Rb-87 or possibly Rb-85, may have much smaller cold collision frequency shifts and therefore be capable of higher stability and accuracy, especially in a space environment.

Gibble, Kurt↗

NASA NTRS1995

Vibrational and Electronic Energy Transfer and Dissociation of Diatomic Molecules by Electron Collisions

At high altitudes and velocities equal to or greater than the geosynchronous return velocity (10 kilometers per second), the shock layer of a hypersonic flight will be in thermochemical nonequilibrium and partially ionized. The amount of ionization is determined by the velocity. For a trans atmospheric flight of 10 kilometers per second and at an altitude of 80 kilometers, a maximum of 1% ionization is expected. At a velocity of 12 - 17 kilometer per second, such as a Mars return mission, up to 30% of the atoms and molecules in the flow field will be ionized. Under those circumstances, electrons play an important role in determining the internal states of atoms and molecules in the flow field and hence the amount of radiative heat load and the distance it takes for the flow field to re-establish equilibrium. Electron collisions provide an effective means of transferring energy even when the electron number density is as low as 1%. Because the mass of an electron is 12,760 times smaller than the reduced mass of N2, its average speed, and hence its average collision frequency, is more than 100 times larger. Even in the slightly ionized regime with only 1% electrons, the frequency of electron-molecule collisions is equal to or larger than that of molecule-molecule collisions, an important consideration in the low density part of the atmosphere. Three electron-molecule collision processes relevant to hypersonic flows will be considered: (1) vibrational excitation/de-excitation of a diatomic molecule by electron impact, (2) electronic excitation/de-excitation, and (3) dissociative recombination in electron-diatomic ion collisions. A review of available data, both theory and experiment, will be given. Particular attention will be paid to tailoring the molecular physics to the condition of hypersonic flows. For example, the high rotational temperatures in a hypersonic flow field means that most experimental data carried out under room temperatures are not applicable. Also, the average electron temperature is expected to be between 10,000 and 20,000 K. Thus only data for low energy electrons are relevant to the model.

Huo, Winifred M.↗

NASA NTRS1997

A model for the kinetics of homotypic cellular aggregation under static conditions

We present the formulation and testing of a mathematical model for the kinetics of homotypic cellular aggregation. The model considers cellular aggregation under no-flow conditions as a two-step process. Individual cells and cell aggregates 1) move on the tissue culture surface and 2) collide with other cells (or aggregates). These collisions lead to the formation of intercellular bonds. The aggregation kinetics are described by a system of coupled, nonlinear ordinary differential equations, and the collision frequency kernel is derived by extending Smoluchowski's colloidal flocculation theory to cell migration and aggregation on a two-dimensional surface. Our results indicate that aggregation rates strongly depend upon the motility of cells and cell aggregates, the frequency of cell-cell collisions, and the strength of intercellular bonds. Model predictions agree well with data from homotypic lymphocyte aggregation experiments using Jurkat cells activated by 33B6, an antibody to the beta 1 integrin. Since cell migration speeds and all the other model parameters can be independently measured, the aggregation model provides a quantitative methodology by which we can accurately evaluate the adhesivity and aggregation behavior of cells.

Non-NASA Center↗

NASA NTRS1974

Sweet's mechanism in the solar wind

Sweet's mechanism occurs in the solar wind, at D-sheets near 1 AU. Conductivities on the order of 10,000 esu are obtained, which is on the order of the local plasma frequency. This implies that the effective collision frequency is on the order of the plasma frequency. The lateral extent of D-sheets is approximately 0.01 AU to 0.001 AU. Hundreds of such D-sheets are probably present between the orbits of Venus and Earth at any instant.

Burlaga, L. F.↗

NASA NTRS1993

A laser-cooled cesium fountain frequency standard and a measurement of the frequency shift due to ultra-cold collisions

A frequency standard based on an atomic fountain of cesium atoms may have an accuracy of 10(exp -16) due to longer interaction times and smaller anticipated systematic errors. All of the known systematic effects that now limit the accuracy of the Cs frequency standard increase either linearly or as some higher power of the atom's velocity. The one systematic frequency shift which is dramatically different is the frequency shift due to the collisions between the laser cooled atoms. At a temperature of a few micro-K, the de Broglie wavelength (lambda(sub deB) = h/p, where h is Planck's constant and p is the momentum of the atom) is much larger than the scale of the interatomic potential. Under these conditions the collision cross sections can be as large as (lambda(sub deB)(sup 2))/Pi and the frequency shift due to these collisions was recently calculated. In our Cs atomic fountain, we laser cooled and trapped 10(exp 10) Cs atoms in 0.4 s. By shifting the frequencies of the laser beams, the atoms were launched upwards at 2.5 m/s and a fraction of the atoms were optically pumped into the F=3 ground state. The unwanted atoms in the F=4 ground state were removed from the fountain with radiation pressure from a laser beam tuned to excite only those atoms. The Cs atoms in the F=3 state traveled ballistically upwards, were excited by the microwave cavity, and then returned back through the same cavity in the atomic fountain configuration. By varying the cold atom density, a density dependent shift of -12.9 +/- 0.7 mHz or -1.4 x 10-12 for an average fountain density of (2.7 +/- 1.5) 10(exp 9) atoms/cm(sup 3) was measured.

Gibble, Kurt↗

NASA NTRS1972

Shock-wave structure using nonlinear model Boltzmann equations.

The structure of strong plane shock waves in a perfect monatomic gas was studied using four nonlinear models of the Boltzmann equation. The models involved the use of a simplified collision operator with velocity-independent collision frequency, in place of the complicated Boltzmann collision operator. The models employed were the BGK and ellipsoidal models developed by earlier authors, and the polynomial and trimodal gain function models developed during the work. An exact set of moment equations was derived for the density, velocity, temperature, viscous stress, and heat flux within the shock. This set was reduced to a pair of coupled nonlinear integral equations and solved using specially adapted numerical techniques. A new and simple Gauss-Seidel iteration was developed during the work and found to be as efficient as the best earlier iteration methods.

Segal, B. M.↗

NASA NTRS2012

High-latitude E Region Ionosphere-thermosphere Coupling: A Comparative Study Using in Situ and Incoherent Scatter Radar Observations

We present in situ and ground-based measurements of the ratio k of ion cyclotronangular frequency to ion-neutral momentum transfer collision frequency to investigateionosphere-thermosphere (IT) coupling in the auroral E region. In situ observations were obtained by NASA sounding rocket 36.234, which was launched into the nightsideE region ionosphere at 1229 UT on 19 January 2007 from Poker Flat, AK. The payload carried instrumentation to determine ion drift angle and electric field vectors. Neutral winds were measured by triangulating a chemical tracer released from rocket 41.064 launched two minutes later. k is calculated from the rotation of the ion drift angle relative to the E-cross-B drift direction in a frame co-rotating with the payload. Between the altitudes of 118 km and 130 km k increases exponentially with a scale height of 9.3 +/- 0.7 km, deviating from an exponential above 130 km. k = 1 at an altitude z(sub0) of 119.9 +/- 0.5 km. The ratio was also estimated from Poker Flat Incoherent Scatter Radar (PFISR) measurements using the rotation of ion velocity with altitude. Exponential fits to the PFISR measurements made during the flight of 41.064 yield z(sub0) 115.9 +/- 1.2 km and a scale height of 9.1 +/- 1.0 km. Differences between in situ and ground-based measurements show that the E region atmospheric densities were structured vertically and/or horizontally on scales of 1 km to 10 km. There were no signs of ionospheric structure in ion density or ion temperature below scales of 1 km. The observations demonstrate the accuracy with which the in situ and PFISR data may be used as probes of IT coupling.

Burchill, J. K.↗

NASA NTRS1972

Effect of velocity-changing collisions on the output of a gas laser.

A theoretical model for the pressure dependence of the intensity of a gas laser is presented in which only velocity-changing collisions with foreign-gas atoms are included. This is a special case where the phase shifts are the same for the two atomic-laser levels or are so small that deflections are the dominant effect of collisions. A collision model for hard-sphere repulsive interactions is derived and the collision parameters, persistence of velocity and collision frequency, are assumed to be independent of velocity. The collision theory is applied to a third-order expansion of the polarization in powers of the cavity electric field (weak-signal theory). The resulting expression for the intensity shows strong pressure dependence. The collisions reduce the amount of saturation and the laser intensity increases with pressure in a characteristic fashion.

Borenstein, M.↗