The first order wave function in the 1/Z expansion
First order wave function in 1/Z expansion
Epstein, S. T.↗
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Electron-impact excitation of Li II in the distorted-wave approximation
The 1(1)S yields 2(3)P electron-impact-excitation cross section for Li II is calculated in the distorted-wave approximation. Two forms of the distorted-wave method are examined; in the first form both the initial and final wave functions are distorted, while in the second form only the initial wave function is distorted. In both forms a partial-wave expansion of the scattered amplitude is made, and exchange is incorporated in a consistent manner. The effects of including more than one configuration in the target-state wave function are also examined. For incident energies greater than 90 eV, distorted-wave calculations agree moderately well with recent experimental and theoretical results.
Pindzola, M. S.↗
Structure of the dayside reconnection layer in resistive MHD and hybrid models
Numerical simulations were performed to investigate the structure of the reconnection layer at the dayside magnetopause. Two typical cases are examined in detail; both are asymmetric in magnetic field and plasma density. In case 1, the guide fields in the magnetosheath and in the magnetosphere are set at zero and thus the tangential magnetic fields on the two sides of the initial current sheet are exactly antiparallel. In case 2, the angle between the tangential magnetic fields on the two sides of the initial current sheet is 145 deg. The results obtained from a resistive MHD model and from a hybrid model are found to be different. In the MHD simulation of case 1, a 2-4 intermediate shock is found to bound the reconnection layer on the magnetosheath side, while an Alfven wave pulse bounds the reconnection layer on the magnetospheric side. In case 2, it is found that a time-dependent intermediate shock (TDIS) bounds the reconnection layer on the magnetosheath side, with a slow expansion wave propagating behind. With the MHD simulations, in the general case in which the tangential magnetic fields on the two sides of the initial current sheet are not exactly antiparallel, a rotational discontinuity across which the tangential magnetic field rotates, a large angle is found to bound the reconnection layer on the magnetosheath side.
Lin, Y.↗
Investigation of the Attenuation of Plane Shock Waves Moving over very Rough Surfaces
Experimental measurements of the attenuation of plane shock waves moving over rough walls have been made in a shock tube. Measurements of the boundary-layer characteristics, including thickness and velocity distribution behind the shock, have also been made with the aid of new cal techniques which provide direct information on the local boundary-layer conditions at the rough walls. Measurements of shock speed and shock pressure ratio are presented for both smooth-wall and rough-wall flow over lengths of machined-smooth and rough strips which lined all four walls of the shock tube. A simplified theory based on Von Karman's expression for skin-friction coefficient for flow over rough walls, along with a wave-model concept and extensions to include time effects, is presented. In this theory, the shock-tube flow is assumed to be one-dimensional at all times and the wave-model concept is used to relate the local layer growth to decreases in shock strength. This concept assumes that local boundary-layer growths act as local mass-flow sinks, which give rise to expansion waves which, in turn, overtake the shock and lower its mass flow accordingly.
Huber, Paul W.↗
Hypersonic shock wave interaction and impingement
An experimental investigation was conducted on space shuttle type, body-wing configurations. The purpose of the investigation was to determine the effects of body and wing geometry on the hypersonic shock structure about these vehicles and on the resulting surface impingement of interior flow field shock and expansion waves. Schlieren photographs and thermographic phosphor paint data were obtained on three body cross sections with three wing planforms at 40, 50 and 60 degree angles of attack. Specific configuration data were obtained at 0 and 30 degree angles of attack to develop trends. These data were obtained at a nominal Mach number of 13.5 and a freestream unit Reynolds number of 0.7 million per foot. For comparison with these straight wing configurations, data were also obtained on a model of a point design, high cross-range, delta wing orbiter at 40, 50 and 60 degree angles of attack. As expected, the data on this delta wing orbiter indicated that the shock intersection/impingement phenomena associated with straight wing vehicles are considerably more complex than, and result in both windward and leeward surface heating regions not present on, the delta configuration.
Kessler, W. C.↗
A study on the spectral models for waves in finite water depth
From an extension of the Wallops Spectrum (Huang et al., 1981) for the deep water waves, spectral models for waves in finite water depths are developed. Stokes wave expansions are found to offer a good approximation for intermediate water depth. The spectral function in this case is controlled by three parameters: the significant slope, the nondimensional depth, and the peak frequency. It is pointed out that solitary and cnoidal wave models must be used for the shallow water waves. The controlling parameters now reduce to the Urell number and the peak frequency. Even though the resulting spectral models place special emphasis on the energy-containing range of the spectrum, they are not limited to this range and they are not limited to any particular sea state. They are seen as offering a possible explanation of the variations in the special slope observed by previous investigators.
Huang, N. E.↗
Slot Nozzle Effects for Reduced Sonic Boom on a Generic Supersonic Wing Section
NASA has conducted research programs to reduce or eliminate the operational restrictions of supersonic aircraft over populated areas. Restrictions are due to the disturbance from the sonic boom, caused by the coalescence of shock waves formed off the aircraft. Results from two-dimensional computational fluid dynamic (CFD) analyses (performed on a baseline Mach 2.0 nozzle in a simulated Mach 2.2 flow) indicate that over-expanded and under-expanded operation of the nozzle has an effect on the N-wave boom signature. Analyses demonstrate the feasibility of reducing the magnitude of the sonic boom N-wave by controlling the nozzle plume interaction with the nozzle boat tail shock structure. This work was extended to study the impact of integrating a high aspect ratio exhaust nozzle or long slot nozzle on the trailing edge of a supersonic wing. The nozzle is operated in a highly under-expanded condition, creating a large exhaust plume and a shock at the trailing edge of the wing. This shock interacts with and suppresses the expansion wave caused by the wing, a major contributor to the sonic boom signature. The goal was to reduce the near field pressures caused by the expansion using a slot nozzle located at the wing trailing edge. Results from CFD analysis on a simulated wing cross-section and a slot nozzle indicate potential reductions in sonic boom signature compared to a baseline wing with no propulsion or trailing edge exhaust. Future studies could investigate if this effect could be useful on a supersonic aircraft for main propulsion, auxiliary propulsion, or flow control.
Castner, Raymond S.↗
Slot Nozzle Effects for Reduced Sonic Boom on a Generic Supersonic Wing Section
NASA has conducted research programs to reduce or eliminate the operational restrictions of supersonic aircraft over populated areas. Restrictions are due to the disturbance from the sonic boom, caused by the coalescence of shock waves formed off the aircraft. Results from two-dimensional computational fluid dynamic (CFD) analyses (performed on a baseline Mach 2.0 nozzle in a simulated Mach 2.2 flow) indicate that over-expanded and under-expanded operation of the nozzle has an effect on the N-wave boom signature. Analyses demonstrate the feasibility of reducing the magnitude of the sonic boom N-wave by controlling the nozzle plume interaction with the nozzle boat tail shock structure. This work was extended to study the impact of integrating a high aspect ratio exhaust nozzle or long slot nozzle on the trailing edge of a supersonic wing. The nozzle is operated in a highly under-expanded condition, creating a large exhaust plume and a shock at the trailing edge of the wing. This shock interacts with and suppresses the expansion wave caused by the wing, a major contributor to the sonic boom signature. The goal was to reduce the near field pressures caused by the expansion using a slot nozzle located at the wing trailing edge. Results from CFD analysis on a simulated wing cross-section and a slot nozzle indicate potential reductions in sonic boom signature compared to a baseline wing with no propulsion or trailing edge exhaust. Future studies could investigate if this effect could be useful on a supersonic aircraft for main propulsion, auxiliary propulsion, or flow control.
Caster, Raymond S.↗
Direct Calculation of the Scattering Amplitude Without Partial Wave Decomposition: Inclusion of Correlation Effects - III
In the first two papers in this series, we developed a method for studying electron-hydrogen scattering that does not use partial wave analysis. We constructed an ansatz for the wave function in both the static and static exchange approximations and calculated the full scattering amplitude. Here we go beyond the static exchange approximation, and include correlation in the wave function via a modified polarized orbital. This correlation function provides a significant improvement over the static exchange approximation: the resultant elastic scattering amplitudes are in very good agreement with fully converged partial wave calculations for electron-hydrogen scattering. A fully variational modification of this approach is discussed in the conclusion of the article Popular summary of Direct calculation of the scattering amplitude without partial wave expansion. III ....." by J. Shertzer and A. Temkin. In this paper we continue the development of In this paper we continue the development of a new approach to the way in which researchers have traditionally used to calculate the scattering cross section of (low-energy) electrons from atoms. The basic mathematical problem is to solve the Schroedinger Equation (SE) corresponding the above physical process. Traditionally it was always the case that the SE was reduced to a sequence of one-dimensional (ordinary) differential equations - called partial waves which were solved and from the solutions "phase shifts" were extracted, from which the scattering cross section was calculated.
Shertzer, Janine↗
Application of spherical wave theory to Cassegrainianfed paraboloids.
Spherical wave expansion technique for analyzing Cassegrain paraboloidal antenna feed systems and synthesizing subreflector
Potter, P. D.↗
Potentials for three-body systems.
Coulomb, Gaussian and harmonic oscillator potentials for particle pairs in three body system, using S wave expansion
Whitten, R. C.↗
Evolution of a density discontinuity in a delta-function gas
Time and spatial evolution of shock and expansion wave evolution from density discontinuity for gas with repulsive delta function interaction between particles
Muriel, A.↗
A systematic development of the supersonic flow fields over and behind wings and wing-body configurations using a shock-capturing finite- difference approach
Three dimensional inviscid supersonic flow fields with primary and embedded shock and expansion waves determined over and behind wings and wing-body configurations
Kutler, P.↗
Boundary condition computational procedures for inviscid, supersonic steady flow field calculations
Results are given of a comparative study of numerical procedures for computing solid wall boundary points in supersonic inviscid flow calculatons. Twenty five different calculation procedures were tested on two sample problems: a simple expansion wave and a simple compression (two-dimensional steady flow). A simple calculation procedure was developed. The merits and shortcomings of the various procedures are discussed, along with complications for three-dimensional and time-dependent flows.
Abbett, M. J.↗
Non-partial wave treatment of reactive and non-reactive scattering Coupled integral equation formalism.
Coupled integral equations are derived for the full scattering amplitudes for both reactive and nonreactive channels. The equations do not involve any partial wave expansion and are obtained using channel operators for reactive and nonreactive collisions. These coupled integral equations are similar in nature to equations derived for purely nonreactive collisions of structureless particles. Using numerical quadrature techniques, these equations may be reduced to simultaneous algebraic equations which may then be solved.
Hayes, E. F.↗
Analysis of a dual-reflector antenna system using physical optics and digital computers
The application of physical-optics diffraction theory to a deployable dual-reflector geometry is discussed. The methods employed are not restricted to the Conical-Gregorian antenna, but apply in a general way to dual and even multiple reflector systems. Complex vector wave methods are used in the Fresnel and Fraunhofer regions of the reflectors. Field amplitude, phase, polarization data, and time average Poynting vectors are obtained via an IBM 360/91 digital computer. Focal region characteristics are plotted with the aid of a CalComp plotter. Comparison between the GSFC Huygens wavelet approach, JPL measurements, and JPL computer results based on the near field spherical wave expansion method are made wherever possible.
Schmidt, R. F.↗
A new method for calculating correction factors for near-field gain measurements.
A new method is demonstrated with which near-field antenna gain correction factors can be calculated directly from measured far-field pattern data by using a spherical wave expansion of the pattern. This eliminates the need for any assumptions regarding antenna aperture field distributions. For illustration, the method is applied to the case of a horn antenna. A comparison of the calculation results with direct measurement data shows an agreement within 0.03 dB. The method, when compared to the method used by Chu and Semplak (1965), is found to show similar agreement.
Ludwig, A. C.↗
Power conservation for reflector antennas with truncated feed patterns
Reflector-antenna calculations using idealised truncated feed patterns can lead to incorrect values of total secondary radiated power. It is demonstrated that this discrepancy is due to the presence of higher-order spherical modes incident on the reflector. When a proper spherical-wave expansion of the incident field is used, in conjunction with the physical-optics technique, to determine the scattered field, the total power of the scattered field will equal the power radiated by the feed.
Rush, W. V. T.↗