Experimental research studies on tools for extravehicular maintenance in space, phase 2 Final report
Space tool configurations for extravehicular maintenance
Havener, P. W.↗
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Linear canonical transformations of coherent and squeezed states in the Wigner phase space
It is shown that classical linear canonical transformations are possible in the Wigner phase space. Coherent and squeezed states are shown to be linear canonical transforms of the ground-state harmonic oscillator. It is therefore possible to evaluate the Wigner functions for coherent and squeezed states from that for the harmonic oscillator. Since the group of linear canonical transformations has a subgroup whose algebraic property is the same as that of the (2+1)-dimensional Lorentz group, it may be possible to test certain properties of the Lorentz group using optical devices. A possible experiment to measure the Wigner rotation angle is discussed.
Han, D.↗
Phase space model for He/plus/ plus N2 reactions - Consideration of dispersion and short range forces
Statistical phase space cross sections for helium ion-nitrogen molecule reactions, including dispersion and short range forces in intramolecular potential energy function
Fullerton, D. C.↗
Phase-space analysis of charged and optical beam transport: Wigner rotation angle
The possibility of using the phase space formalism to establish a correspondence between the dynamical behavior of squeezed states and optical or charged beams, propagating through linear systems, has received a great deal of attention during the last years. In this connection, it has been indicated how optical experiments may be conceived to measure the Wigner rotation angle. In this paper we address the topic within the context of the paraxial propagation of optical or charged beams and suggest a possible experiment for measuring the Wigner angle using an electron beam passing through quadrupoles and drift sections. The analogous optical system is also discussed.
Dattoli, G.↗
Linear canonical transformations of coherent and squeezed states in the Wigner phase space. II - Quantitative analysis
It is possible to calculate expectation values and transition probabilities from the Wigner phase-space distribution function. Based on the canonical transformation properties of the Wigner function, an algorithm is developed for calculating these quantities in quantum optics for coherent and squeezed states. It is shown that the expectation value of a dynamical variable can be written in terms of its vacuum expectation value of the canonically transformed variable. Parallel-axis theorems are established for the photon number and its variant. It is also shown that the transition probability between two squeezed states can be reduced to that of the transition from one squeezed state to vacuum.
Han, D.↗
Concatenated shift registers generating maximally spaced phase shifts of PN-sequences
A large class of linearly concatenated shift registers is shown to generate approximately maximally spaced phase shifts of pn-sequences, for use in pseudorandom number generation. A constructive method is presented for finding members of this class, for almost all degrees for which primitive trinomials exist. The sequences which result are not normally characterized by trinomial recursions, which is desirable since trinomial sequences can have some undesirable randomness properties.
Hurd, W. J.↗
Voyager observations of ion phase space densities in the Jovian magnetosphere
Data from the Voyager low-energy charged particle experiment (LECP) were used to calculate ion phase space densities in Jupiter's magnetosphere. The calculation of F at constant mu and J(2) requires the determination of particle fluxes at specific pitch angles and energies. It is shown that the greatest uncertainties in the determination of F from LECP data arise from the fits to the measured pitch angle distributions and differential energy spectra. An estimate is provided of this uncertainty and of others arising from model radial diffusion coefficients and magnetic fields. The general nature of the curves is consistent with inward diffusion of these energetic ions from the outer magnetosphere combined with losses near but starting beyond the orbit of Io. These losses are not consistent with simple satellite sweeping by Io alone and are probably due to an Io-torus wave-particle interaction. The lifetime against loss deduced from the data is approximately 20,000 s near Io and is a value consistent with strong diffusion losses. The measured ion loss rate declines much more rapidly than the strong diffusion loss rate as L increases from 7 to 9, suggesting that the loss rate is well below the strong-diffusion rate beyond 7 Jupiter radii for ions observed by the LECP.
Paonessa, M.↗
Application of the statistical phase-space theory to the reactions of rare-gas ions with nitrogen molecules
Rare gas ions molecular and dissociative charge transfer reactions with nitrogen, using statistical phase-space theory of chemical reactions
Fullerton, D. C.↗
Phase-space-Lagrangian action principle and the generalized K-X theorem
The covariant coupled equations for plasma dynamics and the Maxwell field are expressed as a phase-space-Lagrangian action principle. The linear interaction is transformed to the bilinear beat Hamiltonian by a gauge-invariant Lagrangian Lie transform. The result yields the generalized linear susceptibility directly.
Kaufman, Allan N.↗
Linear canonical transformations of coherent and squeezed states in the Wigner phase space. III - Two-mode states
It is shown that the basic symmetry of two-mode squeezed states is governed by the group SP(4) in the Wigner phase space which is locally isomorphic to the (3 + 2)-dimensional Lorentz group. This symmetry, in the Schroedinger picture, appears as Dirac's two-oscillator representation of O(3,2). It is shown that the SU(2) and SU(1,1) interferometers exhibit the symmetry of this higher-dimensional Lorentz group. The mathematics of two-mode squeezed states is shown to be applicable to other branches of physics including thermally excited states in statistical mechanics and relativistic extended hadrons in the quark model.
Han, D.↗
The classical solution of a definite integral occurring in the satellite theory in the extended phase space
A method of integrating the functions defined by Scheifele and Graf (1974), arising in the elimination of time from the arguments of satellite theory using Delaunay elements in the extended phase space, is proposed. By repeated applications of an identity of Stiefel and Scheifele (1971), neglecting certain terms, and assuming a solution in the form of a product of Bessel functions, a solution expanded in the eccentricity is obtained.
Bond, V. R.↗
Phase space localization for anti-de Sitter quantum mechanics and its zero curvature limit
Using techniques of geometric quantization and SO(sub 0)(3,2)-coherent states, a notion of optimal localization on phase space is defined for the quantum theory of a massive and spinning particle in anti-de Sitter space time. It is shown that this notion disappears in the zero curvature limit, providing one with a concrete example of the regularizing character of the constant (nonzero) curvature of the anti-de Sitter space time. As a byproduct a geometric characterization of masslessness is obtained.
Elgradechi, Amine M.↗
Spacecraft flight control with the new phase space control law and optimal linear jet select
An autopilot designed for rotation and translation control of a rigid spacecraft is described. The autopilot uses reaction control jets as control effectors and incorporates a six-dimensional phase space control law as well as a linear programming algorithm for jet selection. The interaction of the control law and jet selection was investigated and a recommended configuration proposed. By means of a simulation procedure the new autopilot was compared with an existing system and was found to be superior in terms of core memory, central processing unit time, firings, and propellant consumption. But it is thought that the cycle time required to perform the jet selection computations might render the new autopilot unsuitable for existing flight computer applications, without modifications. The new autopilot is capable of maintaining attitude control in the presence of a large number of jet failures.
Bergmann, E. V.↗
A Global Climatology of Extratropical Transition Part II: Statistical Performance of the Cyclone Phase Space
This study analyzes the differences between an objective, automated identification of tropical cyclones (TCs) that undergo extratropical transition (ET), and the designation of ET determined subjectively by human forecasters in best-track data in all basins globally. The objective identification of ET is based on the cyclone phase space (CPS), calculated from the Japanese 55-year Reanalysis (JRA-55) or the ECMWF Interim Reanalysis (ERA-Interim). The resulting classification into “ET storms” and “non-ET storms” underlies the global climatology of ET presented in Part I of this study. Here, the authors investigate how well the CPS classifications agree with those in the best-track records calculated from JRA-55 or from ERA-Interim data. According to F1 scores and Matthews correlation coefficients (MCCs), the classification of ET storms in the CPS agrees best with the best-track classification in the Western North Pacific (MCC > 0.7) and the North Atlantic (MCC > 0.5). In other basins, the correlation between the CPS classification and the best-track classification is only slightly higher than that of a random classification. The JRA-55 classification achieves higher performance scores than does the ERA-Interim classification, and the differences are statistically significant in all basins. The lower performance of ERA-Interim is mainly due to a higher false alarm rate, particularly in the Eastern North Pacific. Overall, the results show that while the CPS-based classifications are good enough to be useful for many purposes, there is almost certainly room for improvement – in the representation of the storms in reanalyses, in our objective metrics of ET, and in our scientific understanding of the ET process.
Melanie Bieli↗
A phase-space fluid simulation of a two-component narrow planetary ring - Particle size segregation, edge formation, and spreading rates
The Krook kinetic equation for identical planetary ring particles is presently generalized for the case of two-component systems, and the equations are numerically solved on the basis of Brophy and Esposito's (1989) phase-space CFD method. Attention is given to the simulation results obtained for a two-component narrow ring, in which the large particles are eight times as massive as the small particles. This ring's unconstrained edge dynamics are resolved by the simulation, and are found to exhibit a sharpening that would not have been expected in single-component rings.
Brophy, Thomas G.↗
Phase space flow of particles in squeezed states
The manipulation of noise and uncertainty in squeezed states is governed by the wave nature of the quantum mechanical particles in these states. This paper uses a deterministic model of quantum mechanics in which real guiding waves control the flow of localized particles. This model will be used to examine the phase space flow of particles in typical squeezed states.
Ceperley, Peter H.↗
The Dependence of Cirrus Gamma Size Distributions Expressed as Volumes in N(sub 0)-Lambda-Mu Phase Space and Bulk Cloud Properties on Environmental Conditions: Results from the Small Ice Particles in Cirrus Experiment (SPARTICUS)
The variability of cirrus ice microphysical properties is investigated using observations obtained during the Small Particles in Cirrus (SPARTICUS) campaign. An existing approach that represents a size distribution (SD) as a single gamma function using an ellipsoid of equally realizable solutions in (N(sub 0), lambda, mu) phase space is modified to automatically identify multiple modes in SDs and characterize each mode by such an ellipsoid. The modified approach is applied to ice crystals with maximum dimension D greater than15 micrometers collected by the 2-D stereo and 2-D precipitation probes on the Stratton Park Engineering Company Learjet. The dependencies of N(sub 0), mu, and lambda from each mode, total number concentration, bulk extinction, ice water content (IWC), and mass median maximum dimension D(sub mm) as a function of temperature T and cirrus type are then analyzed. The changes in the observed codependencies between N(sub 0), mu, and lambda, bulk extinction, IWC, and D(sub mm) with environmental conditions indicate that particles were larger at higher T during SPARTICUS. At most two modes were observed in any SD during SPARTICUS, with the average boundary between them at 115 micrometers, similar to past studies not using probes with shatter mitigating tips and artifact removal algorithms. The bimodality of the SDs increased with T. This and the differences in N(sub 0), mu, and lambda between the modes suggest that particles with smaller D nucleated more recently than particles with larger D, which grew via vapor deposition and aggregation. Because smaller crystals, whose concentrations are uncertain, make marginal contributions to higher order moments, the use of higher moments for evaluating model fields is suggested.
Ellipsoids↗
Gradual Diffusion and Punctuated Phase Space Density Enhancements of Highly Relativistic Electrons: Van Allen Probes Observations
The dual-spacecraft Van Allen Probes mission has provided a new window into mega electron volt (MeV) particle dynamics in the Earth's radiation belts. Observations (up to E (is) approximately 10MeV) show clearly the behavior of the outer electron radiation belt at different timescales: months-long periods of gradual inward radial diffusive transport and weak loss being punctuated by dramatic flux changes driven by strong solar wind transient events. We present analysis of multi-MeV electron flux and phase space density (PSD) changes during March 2013 in the context of the first year of Van Allen Probes operation. This March period demonstrates the classic signatures both of inward radial diffusive energization and abrupt localized acceleration deep within the outer Van Allen zone (L (is) approximately 4.0 +/- 0.5). This reveals graphically that both 'competing' mechanisms of multi-MeV electron energization are at play in the radiation belts, often acting almost concurrently or at least in rapid succession.
Van Allen Probes↗