Collisional transfer contributions in the quantum theory of transport coefficients.
Transport coefficients for gases investigated for addition of collision transfer contributions to phase-space transformation functions
Curtiss, C. F.↗
SEARCH · Search NASA
Results for “PHASE SPACE”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Momentum operators in quantum mechanics.
Representation for real functions of quantum mechanical momentum operator obtained by functional integration in phase space
Arthurs, A. M.↗
Particle motions in a magnetic field
Particle motions in magnetic field, demonstrating existence of adiabatic region in particle phase space for Van Allen belt region
Braun, M.↗
The topology of the regularized integral surfaces of the 3-body problem
Momentum, angular momentum, and energy of integral surfaces in the planar three-body problem are considered. The end points of orbits which cross an isolating block are identified. It is shown that this identification has a unique extension to an identification which pairs the end points of orbits entering the block and which end in a binary collision with the end points of orbits leaving the block and which come from a binary collision. The problem of regularization is that of showing that the identification of the end points of crossing orbits has a continuous, unique extension. The regularized phase space for the three-body problem was obtained, as were regularized integral surfaces for the problem on which the three-body equations of motion induce flows. Finally the topology of these surfaces is described.
Easton, R.↗
Spectroscopy of dimers.
The method of Stogryn and Hirschfelder, which divides two-particle phase space into bound, metastable, and free particle parts, is applied to the statistical averages which determine the first three spectroscopic moments of 'collision-induced' far-infrared and Raman spectra. Numerical results are presented for a number of models of noble gas systems. It is shown that for some systems, but not all, dimers make important, although not necessarily well-separated, contributions to the spectrum.
Levine, H. B.↗
Random gravitational encounters and the evolution of spherical systems. III - Halo.
The accumulation of stars in the halo of a spherical stellar system, together with the escape of stars from the system, result from stellar encounters within a dense central core. The resultant halo structure is studied both analytically and numerically for an isolated system. On the assumption that conditions in the central core remain constant with time, a simple steady-state solution is obtained for the outermost halo, or 'fringe', defined as the region from which stars may escape after a few additional orbits through the central core of the system. In this steady-state solution the density in phase space, obtained from a simple integral equation for the fringe region, is found to vary nearly linearly with the total energy of a star per unit mass for energies which are less than the energy of escape.
Spitzer, L., Jr.↗
Tracking and data system support for the Pioneer project. Volume 1: Pioneer 10-prelaunch planning through second trajectory correction, 4 December 1969 - 1 April 1972
The tracking and data system support of the launch, near-earth, and deep space phases of the Pioneer 10 mission, which sent a Pioneer spacecraft into a flyby of Jupiter that would eventually allow the spacecraft to escape the solar system is discussed. The support through the spacecraft's second trajectory correction is reported. During this period, scientific instruments aboard the spacecraft registered information relative to interplanetary particles and fields, and radiometric data generated by the network continued to improve knowledge of the celestial mechanics of the solar system. In addition to network support activity detail, network performance and special support activities are covered.
Siegmeth, A. J.↗
Tracking and data system support for the pioneer project. Volume 11 Pioneers 6-9. Extended missions: 1 July 1971 - 1 July 1973
The Tracking and Data System supported the deep space phases of the Pioneer 6, 7, 8, and 9 missions, with two spacecraft in an inward trajectory and two spacecraft in an outward trajectory from the earth in heliocentric orbits. Scientific instruments aboard each of the spacecraft continued to register information relative to interplanetary particles and fields, and radio metric data generated by the network continued to improve our knowledge of the celestial mechanics of the solar system. In addition to network support activity detail, network performance and special support activities are covered.
Renzetti, N. A.↗
Ion optical design with applications to a solar wind mass spectrometer
The design of charged particle beam transport systems at lower energies is discussed. Topics discussed include: index of refraction, photometry, phase space, matrices, lenses and imaging, charged particle trajectories in crossed electric and magnetic fields, design parameters for the Wien filter, and electrostatic energy analyzer design, an annotated bibliography is presented.
Coplan, M.↗
Absorption of trapped particles by Jupiter's moons
Absorption effects of the four innermost moons in the radial transport equations for electrons and protons in Jupiter's magnetosphere are presented. The phase space density n at 2 R sub J for electrons with equatorial pitch angles less than 69 deg is reduced by a factor of 4.2 x 1000 when lunar absorption is included in the calculation. For protons with equatorial pitch angles less than 69 deg, the corresponding reduction factor is 3.2 x 100000. The effect of the satellites becomes progressively weaker for both electrons and protons as equatorial pitch angles of pi/2 are approached, because the likelihood of impacting a satellite becomes progressively smaller. The large density decreases which we find at the orbits of Io, Europa, and Ganymede result in corresponding particle flux decreases that should be observed by spacecraft making particle measurements in Jupiter's magnetosphere. The characteristic signature of satellite absorption should be a downward pointing cusp in the flux versus radius curve at the L-value corresponding to each satellite.
Hess, W. N.↗
Tracking and data system support for the Pioneer project. Pioneers 6-9, extended missions: 1 July 1972 - 1 July 1973, volume 12
The Tracking and Data System supported the deep space phases of the Pioneer 6, 7, 8, and 9 missions, with two spacecraft in an inward trajectory and two spacecraft in an outward trajectory from the earth in heliocentric orbits. During the period of this report, scientific instruments aboard each of the spacecraft continued to register information relative to interplanetary particles and fields, and radiometric data generated by the network continued to contribute to knowledge of the celestial mechanics of the solar system. In addition, to network support activity detail, network performance and special support activities are covered.
Miller, R. B.↗
Guiding center model to interpret neutral particle analyzer results
The theoretical model is discussed, which accounts for drift and cyclotron components of ion motion in a partially ionized plasma. Density and velocity distributions are systematically precribed. The flux into the neutral particle analyzer (NPA) from this plasma is determined by summing over all charge exchange neutrals in phase space which are directed into apertures. Especially detailed data, obtained by sweeping the line of sight of the apertures across the plasma of the NASA Lewis HIP-1 burnout device, are presented. Selection of randomized cyclotron velocity distributions about mean azimuthal drift yield energy distributions which compared well with experiment. Use of data obtained with a bending magnet on the NPA showed that separation between energy distribution curves of various mass species correlate well with a drift divided by mean cyclotron energy parameter of the theory. Use of the guiding center model in conjunction with NPA scans across the plasma aid in estimates of ion density and E field variation with plasma radius.
Englert, G. W.↗
Particle distribution functions in modulation theory
Development of a simple formulation of the cosmic ray modulation problem which involves the use of the omnidirectional part of the distribution function in phase space, and the magnitude of the momentum or the rigidity. It is shown that, by employing the proposed formulation, the Compton-Getting factor is greatly simplified, and the well-known force-field equation is reduced to a one-dimensional Vlasov equation. In addition, another Vlasov equation can be written for the very low energy galactic particles which are convected by the solar wind.
Forman, M. A.↗
Absorption of trapped particles by Jupiter's moons
Inclusion of absorption effects of the four innermost moons in the radial transport equations for electrons and protons in Jupiter's magnetosphere. It is found that the phase space density n at 2 Jupiter radii for electrons with equatorial pitch angles less than 69 deg is reduced by a factor of 42,000 when lunar absorption is included in the calculation. For protons with equatorial pitch angles less than 69 deg the corresponding reduction factor is 2,300,000. The effect of the satellites becomes progressively weaker for both electrons and protons as equatorial pitch angles of 90 deg are approached, because the likelihood of impacting a satellite becomes progressively smaller. The large density decreases found at the orbits of Io, Europa, and Ganymede result in corresponding particle flux decreases that should be observed by spacecraft making particle measurements in Jupiter's magnetosphere. The characteristic signature of satellite absorption should be a downward-pointing vertex in the flux versus radius curve at the L value corresponding to each satellite.
Hess, W. N.↗
Tracking and data system support for the Pioneer project. Volume 2: Pioneer 11 prelaunch planning through second trajectory correction, to 1 May 1973
The tracking and data system support of the planning, testing, launch, near-earth, and deep space phases of the Pioneer 11 Jupiter Mission are described, including critical phases of spacecraft flight and guidance. Scientific instruments aboard the spacecraft registered information relative to interplanetary particles and fields. Knowledge of the celestial mechanics of the solar system was improved through radiometric data gathering. Network performance, details of network support activity, and special support activities are discussed.
Barton, W. R.↗
Spectral line profiles for a planetary corona
The Lyman and Balmer emission of a planetary corona depend on the exospheric temperature, the integrated column density of solar-illuminated hydrogen, and the region of phase space occupied by particles. Measurements of the intensity alone are incapable of defining the exosphere unambiguously. Line profiles, with high spectral resolution, can show whether a nonthermal component of the escaping hydrogen is present, and can indicate at what altitude satellite orbits of hydrogen atoms are depleted.
Chamberlain, J. W.↗
Use of the Wigner representation in scattering problems
The basic equations of quantum scattering were translated into the Wigner representation, putting quantum mechanics in the form of a stochastic process in phase space, with real valued probability distributions and source functions. The interpretative picture associated with this representation is developed and stressed and results used in applications published elsewhere are derived. The form of the integral equation for scattering as well as its multiple scattering expansion in this representation are derived. Quantum corrections to classical propagators are briefly discussed. The basic approximation used in the Monte-Carlo method is derived in a fashion which allows for future refinement and which includes bound state production. Finally, as a simple illustration of some of the formalism, scattering is treated by a bound two body problem. Simple expressions for single and double scattering contributions to total and differential cross-sections as well as for all necessary shadow corrections are obtained.
Bemler, E. A.↗
Interpretation of neutral particle analyzer measurements on plasmas having azimuthal drift
The theoretical model accounts for drift and cyclotron components of ion motion in a partially ionized plasma. Density and velocity distributions are systematically prescribed. The flux into the neutral particle analyzer (NPA) from this plasma is determined by summing over all charge exchange neutrals in phase space which are directed into apertures. Calculation of the process is continued through the NPA using appropriate cross section data to obtain analyzer output distributions. Theoretical results were compared with NPA measurements on four plasma heating devices having radial electric, E, and axial magnetic, B, fields. Drift velocity, in the azimuthal direction is identified with E/B. Selection of randomized cyclotron velocity distributions about mean azimuthal drift yield energy distributions which compare well with experiment.
Englert, G. W.↗