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Modifications of impulse approximation allowing for motion of bound electrons, providing simple analytic expressions for atomic ionization and detachment cross sections
The impulse approximation and full N-body experiments are used to investigate the changes in mass and binding energy which result from gravitational encounters between spherical galaxies. Models with King (1966) and de Vaucouleurs (1948) surface density profiles, and radial, tangential, and isotropic velocity distributions. Results based on the impulse approximation depend on two collision parameters (the impact parameter and the ratio of the perturbing mass to the relative velocity at infinity); they agree well with N-body results. The asymptotic limit, valid for distant encounters, is found to approximate the correct results only for impact parameters larger than 10 effective radii. It is therefore of little use in most situations of interest. No simple 'linear' or 'quadratic' dependence of energy and mass loss on collision strength is found, but rather, a smooth intermediate behavior. Cross sections depend very little on the internal velocity structure of the galaxy, but quite strongly on the surface density profile in its outer parts. The reasons why these results disagree with the conclusions of previous workers are discussed.
A high-energy (28 kJ per pulse) two-stage pulsed plasma thruster (MSFC PPT-1) has been constructed and tested. The motivation of this project is to develop a high power (approximately 500 kW), high specific impulse (approximately 10000 s), highly efficient (greater than 50%) thruster for use as primary propulsion in a high power nuclear electric propulsion system. PPT-1 was designed to overcome four negative characteristics which have detracted from the utility of pulsed plasma thrusters: poor electrical efficiency, poor propellant utilization efficiency, electrode erosion, and reliability issues associated with the use of high speed gas valves and high current switches. Traditional PPTs have been plagued with poor efficiency because they have not been operated in a plasma regime that fully exploits the potential benefits of pulsed plasma acceleration by electromagnetic forces. PPTs have generally been used to accelerate low-density plasmas with long current pulses. Operation of thrusters in this plasma regime allows for the development of certain undesirable particle-kinetic effects, such as Hall effect-induced current sheet canting. PPT-1 was designed to propel a highly collisional, dense plasma that has more fluid-like properties and, hence, is more effectively pushed by a magnetic field. The high-density plasma loading into the second stage of the accelerator is achieved through the use of a dense plasma injector (first stage). The injector produces a thermal plasma, derived from a molten lithium propellant feed system, which is subsequently accelerated by the second stage using mega-amp level currents, which eject the plasma at a speed on the order of 100 kilometers per second. Traditional PPTs also suffer from dynamic efficiency losses associated with snowplow loading of distributed neutral propellant. The twostage scheme used in PPT-I allows the propellant to be loaded in a manner which more closely approximates the optimal slug loading. Lithium propellant was chosen to test whether or not the reduced electrode erosion found in the Lithium Lorentz Force Accelerator (LiLFA) could also be realized in a pulsed plasma thruster. The use of the molten lithium dense plasma injector also eliminates the need for a gas valve and electrical switch; the injector design fulfills both roles, and uses no moving parts to provide, in principle, a highly reliable propellant feed and electrical switching system. Experimental results reported in this paper include: second-stage current traces, high-speed photographic and holographic imaging of the thruster exit plume, and internal mapping of the discharge chamber magnetic field from B-dot probe data. The magnetic field data is used to create a two-dimensional description of the evolution of the current sheet inside the thruster.
Impulsive emission of approximately 40-kev electrons from Sun observed from Mariner IV
Impulsive emission of high energy electrons from sun and diffusive propagation through interplanetary medium observed by Mariner IV PARTICLE detectors
A mathematically rigorous derivation is given of first order corrections to multi-impulse approximations to the solutions to space flight optimization problems with bang-bang control. The rocket was subjected to an inverse square gravitational force and to a thrust force with constant magnitude. The mass decreased linearly with time. An optimal impulsive solution was obtained for a problem with given initial and final conditions. The method was then used to obtain first-order corrections to the initial values of the costate variables. Indications are given on how the theory may be extended to higher order corrections. The theory was applied to intercept and rendezvous problems.
The feasibility of conducting human missions to the Moon is examined assuming the use of three 'high leverage' technologies: (1) a single-stage-to-orbit (SSTO) launch vehicle, (2) 'in-situ' resource utilization (ISRU)--specifically 'lunar-derived' liquid oxygen (LUNOX), and (3) LOX-augmented nuclear thermal rocket (LANTR) propulsion. Lunar transportation system elements consisting of a LANTR-powered lunar transfer vehicle (LTV) and a chemical propulsion lunar landing/Earth return vehicle (LERV) are configured to fit within the 'compact' dimensions of the SSTO cargo bay (diameter: 4.6 m/length: 9.0 m) while satisfying an initial mass in low Earth orbit (IMLEO) limit of approximately 60 t (3 SSTO launches). Using approximately 8 t of LUNOX to 'reoxidize' the LERV for a 'direct return' flight to Earth reduces its size and mass allowing delivery to LEO on a single 20 t SSTO launch. Similarly, the LANTR engine's ability to operate at any oxygen/ hydrogen mixture ratio from 0 to 7 with high specific impulse (approximately 940 to 515 s) is exploited to reduce hydrogen tank volume, thereby improving packaging of the LANTR LTV's 'propulsion' and 'propellant modules'. Expendable and reusable, piloted and cargo missions and vehicle designs are presented along with estimates of LUNOX production required to support the different mission modes. Concluding remarks address the issue of lunar transportation system costs from the launch vehicle perspective.
Impulse approximation for pion absorption on light nuclei with emission of fast nucleons
Plane wave impulse approximation for deriving momentum distribution for nucleon in atomic nucleus
Spectra of outgoing protons for various targets using scintillation counter, interpreting data by means of impulse-approximation calculation
Inner-shell ionizations by proton impact calculated for cross section using impulse approximation model, comparing results with Born approximations
K shell X ray production by proton impact compared with binary encounter impulse approximation
The survey of negative pion absorption reactions on light and medium nuclei was continued. Muon spin precession was studied using an iron target. An impulse approximation model of the pion absorption process implied that the ion will absorb almost exclusively on nucleon pairs, single nucleon absorption being suppressed by energy and momentum conservation requirements. For measurements on both paramagnetic and ferromagnetic iron, the external magnetic field was supplied by a large C-type electromagnet carrying a current of about 100 amperes.
A set of missions was postulated that was considered to be representative of those likely to be desirable/feasible over the next three decades. The characteristics of these missions, and their payloads, that most impact the choice/design of the requisite propulsion system were determined. A system-level model of the near-Earth transportation process was constructed, which incorporated these mission/system characteristics, as well as the fundamental parameters describing the technology/performance of an ion bombardment based electric propulsion system. The model was used for sensitivity studies to determine the interactions between the technology descriptors and program costs, and to establish the most cost-effective directions for technology advancement. The most important factor was seen to be the costs associated with the duration of the mission, and this in turn makes the development of advanced electric propulsion systems having moderate to high efficiencies ( 50 percent) at intermediate ranges of specific impulse (approximately 1000 seconds) very desirable.
Nuclear gamma-rays in coincidence with outgoing pions or protons following single nucleon removal from Mg-24 by 200 MeV pions (+) were detected with Ge(Li) detectors. Differential cross sections are reported for gamma-rays from the first excited mirror states of Na-23 and Mg-23 in coincidence with positive pions or protons detected in particle telescopes at 30, 60, 90, 120, and 150 deg; angle-integrated absolute cross sections and cross section ratios are calculated. These results are compared with the predictions of a Pauli-blocked plane-wave impulse approximation (PWIA) and the intranuclear cascade (INC) and nucleon charge exchange (NCX) reaction models. The PWIA and the INC calculations generally agree with the angular dependence of the experimental results but not the absolute magnitude. The NCX calculation does not reproduce the observed cross section charge ratios.
Neutron total cross sections are represented for Li to Pu targets at energies above 0.1 MeV and less than 100 MeV using a modified nuclear Ramsauer formalism. The formalism is derived for energies above 100 MeV by fitting theoretical cross sections. Neutron absorption cross sections are represented by analytic expressions of similar form, but shape resonance phenomena of the Ramsauer effect is not present. Elastic differential cross sections are given as a renormalized impulse approximation. These cross section data bases are useful for nucleon transport applications.
A covariant formulation of the multiple scattering series for the optical potential is presented. The case of a scalar nucleon interacting with a spin zero isospin zero A-body target through meson exchange, is considered. It is shown that a covariant equation for the projectile-target t-matrix can be obtained which sums the ladder and crossed ladder diagrams efficiently. From this equation, a multiple scattering series for the optical potential is derived, and it is shown that in the impulse approximation, the two-body t-matrix associated with the first order optical potential is the one in which one particle is kept on mass-shell. The meaning of various terms in the multiple scattering series is given. The construction of the first-order optical potential for elastic scattering calculations is described.
A study of the expected frequency of merging galaxies is conducted, using the impulsive approximation. Results indicate that if we consider mergers involving galaxy pairs without halos in a single crossing time or orbital period, the expected frequency of mergers is two orders of magnitude below the observed value for the present epoch. If we consider mergers involving several orbital periods or crossing times, the expected frequency goes up by an order of magnitude. Preliminary calculation indicate that if we consider galaxy mergers between pairs with massive halos, the merger is very much hastened.