Assessment of the solar-terrestrial data base management system

Members of the space science community used the present MSFC NEEDS network. The design and development of improvements and extension of the NEEDS network were designed and development of improvements and extension of the NEEDS network were discussed

Galilean Limit of Equilibrium Relativistic Mass Distribution

The low-temperature form of the equilibrium relativistic mass distribution is subject to the Galilean limit by taking $c\rightarrow \infty .$ In this limit the relativistic Maxwell-Boltzmann distribution passes to the usual nonrelativistic form and the Dulong-Petit law is recovered.Comment: TAUP-2081-9

Generalized Boltzmann Equation in a Manifestly Covariant Relativistic Statistical Mechanics

We consider the relativistic statistical mechanics of an ensemble of $N$ events with motion in space-time parametrized by an invariant ``historical time'' $\tau .$ We generalize the approach of Yang and Yao, based on the Wigner distribution functions and the Bogoliubov hypotheses, to find the approximate dynamical equation for the kinetic state of any nonequilibrium system to the relativistic case, and obtain a manifestly covariant Boltzmann-type equation which is a relativistic generalization of the Boltzmann-Uehling-Uhlenbeck (BUU) equation for indistinguishable particles. This equation is then used to prove the $H$-theorem for evolution in $\tau .$ In the equilibrium limit, the covariant forms of the standard statistical mechanical distributions are obtained. We introduce two-body interactions by means of the direct action potential $V(q),$ where $q$ is an invariant distance in the Minkowski space-time. The two-body correlations are taken to have the support in a relative $O( 2,1)$-invariant subregion of the full spacelike region. The expressions for the energy density and pressure are obtained and shown to have the same forms (in terms of an invariant distance parameter) as those of the nonrelativistic theory and to provide the correct nonrelativistic limit

Magnetospheric research

Research concerning the magnetosphere is discussed in terms of satellite data analysis, instrument studies and developments, solar terrestrial studies, meetings, and consultants

Plasma and magnetospheric research

Several programs and variations have been developed to determine statistical means of different plasma parameters when binned in different variables. These parameters include temperature, densities and spacecraft potentials for any of the ion species, as well as ratios of these variables for any other ion species to the corresponding variable for H(+). The variables for binning include L, radial distance, and geomagnetic latitude; and separate statistics are automatically run for local morning and local evening data. These programs all run from output files from the plasma parameter thin sheath analysis program. A variant program also bins for magnetic activity, using either Kp or Dst, which requires an additional magnetic activity input file. These programs can be run either interactively or in batch mode, using file listings generated by a DIRECTORY command. In addition to printed output, these programs generate output files which can be used to plot the results. Programs to plot these averaged data are under development

Investigation of low energy space plasma

A statistical study of 1982 data for occurrences of equatorially trapped plasma has been extended. The previous survey, which utilized only the MSFC summary fiche, has been supplemented with the GSFC summary fiche, which has had the effect of substantially improving the late 1982 coverage. It was found that in the post midnight region (1 - 3 LT), the trapped plasma is limited to + or - 5 degrees magnetic latitude, while in the early afternoon (13-15 LT), latitude ranges as high as + or 30 degrees are found. This survey has provided a link to earlier ATS-6 and ISEE studies of pancake distributions. Although the most energetic, and most anisotopic plasmas are trapped within a few degrees of the equator, the results of these equatorial interactions extend substantially along the magnetic field line in the afternoon and dusk region and these high latitude extensions were previously studied by the Huntsville group. Results of this study were incorporated into a revision of the equatorial ion paper, which has been resubmitted and accepted for publication

Space plasma research

Temperature and density analysis in the Automated Analysis Program (for the global empirical model) were modified to use flow velocities produced by the flow velocity analysis. Revisions were started to construct an interactive version of the technique for temperature and density analysis used in the automated analysis program. A sutdy of ion and electron heating at high altitudes in the outer plasmasphere was initiated. Also the analysis of the electron gun experiments on SCATHA were extended to include eclipse operations in order to test a hypothesis that there are interactions between the 50 to 100 eV beam and spacecraft generated photoelectrons. The MASSCOMP software to be used in taking and displaying data in the two-ion plasma experiment was tested and is now working satisfactorily. Papers published during the report period are listed

Plasma and magnetospheric research

Research developments in the following areas are discussed: (1) an ion trajectory computer code which plots the paths of ions ejected from the polar cusp ionosphere; (2) the response of plasmaspheric ion temperatures to geomagnetic activity; (3) spacecraft sheath effects; (4) plasma flow; (5) neutral gas temperatures; and (6) instrument fabrication, modification, and maintenance

Representation of Quantum Mechanical Resonances in the Lax-Phillips Hilbert Space

We discuss the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips $S$-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to these resonances (eigenfunctions of the generator of the semigroup) lie in the Lax-Phillips Hilbert space, and therefore all physical properties of the resonant states can be computed. We show that the Lax-Phillips $S$-matrix is unitarily related to the $S$-matrix of standard scattering theory by a unitary transformation parametrized by the spectral variable $\sigma$ of the Lax-Phillips theory. Analytic continuation in $\sigma$ has some of the properties of a method developed some time ago for application to dilation analytic potentials. We work out an illustrative example using a Lee-Friedrichs model for the underlying dynamical system.Comment: Plain TeX, 26 pages. Minor revision

Lyapunov vs. Geometrical Stability Analysis of the Kepler and the Restricted Three Body Problem

In this letter we show that although the application of standard Lyapunov analysis predicts that completely integrable Kepler motion is unstable, the geometrical analysis of Horwitz et al [1] predicts the observed stability. This seems to us to provide evidence for both the incompleteness of the standard Lyapunov analysis and the strength of the geometrical analysis. Moreover, we apply this approach to the three body problem in which the third body is restricted to move on a circle of large radius which induces an adiabatic time dependent potential on the second body. This causes the second body to move in a very interesting and intricate but periodic trajectory; however, the standard Lyapunov analysis, as well as methods based on the parametric variation of curvature associated with the Jacobi metric, incorrectly predict chaotic behavior. The geometric approach predicts the correct stable motion in this case as well.Comment: 9 pages, 14 figure