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Mathematical Optimization Techniques

The papers collected in this volume were presented at the Symposium on Mathematical Optimization Techniques held in the Santa Monica Civic Auditorium, Santa Monica, California, on October 18-20, 1960. The objective of the symposium was to bring together, for the purpose of mutual education, mathematicians, scientists, and engineers interested in modern optimization techniques. Some 250 persons attended. The techniques discussed included recent developments in linear, integer, convex, and dynamic programming as well as the variational processes surrounding optimal guidance, flight trajectories, statistical decisions, structural configurations, and adaptive control systems. The symposium was sponsored jointly by the University of California, with assistance from the National Science Foundation, the Office of Naval Research, the National Aeronautics and Space Administration, and The RAND Corporation, through Air Force Project RAND.

Bellman, R.↗

Electronographic cameras for space astronomy.

Magnetically-focused electronographic cameras have been under development at the Naval Research Laboratory for use in far-ultraviolet imagery and spectrography, primarily in astronomical and optical-geophysical observations from sounding rockets and space vehicles. Most of this work has been with cameras incorporating internal optics of the Schmidt or wide-field all-reflecting types. More recently, we have begun development of electronographic spectrographs incorporating an internal concave grating, operating at normal or grazing incidence. We also are developing electronographic image tubes of the conventional end-window-photo-cathode type, for far-ultraviolet imagery at the focus of a large space telescope, with image formats up to 120 mm in diameter.

Carruthers, G. R.↗

Optical grating evaluator - A device for detailed measurement of diffraction grating efficiencies in the vacuum ultraviolet

A device for detailed measurement of diffraction grating efficiencies and over-all performance in the VUV has been designed and constructed at the Naval Research Laboratory. The system employs semiautomated mechanisms to scan the face of the grating with a narrow monochromatic beam, and an efficiency map of the grating surface is produced on a strip chart recorder. Grating efficiency in the various diffracted orders and intensity of light scattered between orders may also be measured. A unique feature is the ability to determine the angle and effectiveness of grating blaze and variations in blaze under different conditions of illumination.

Michels, D. J.↗

Skylab Apollo Telescope Mount Calibration Rocket Project

The Calibration Rocket (CALROC) Project was established to provide calibration data for the Harvard College Observatory (S055) and the Naval Research Laboratory (S082) ultraviolet solar experiments on Skylab to provide compensation for any change in performance during the long mission in the space environment after the preflight calibration. The calibration instruments were smaller-scale, lighter-weight, but similar in performance to the S055 and S082 experiments. They were launched on Black Brant VC sounding rockets from White Sands Missile Range, New Mexico. The CALROC instruments were calibrated before launch and verified after flight. Each flight obtained approximately four minutes of data on an area of the sun which was then observed by the Skylab astronauts with the ATM experiments on three successive orbits.

Frank, M. W.↗

Instability of a gravity gradient satellite due to thermal distortion

A nonlinear analytical model and a corresponding computer program were developed to study the influence of solar heating on the anomalous low frequency, orbital instability of the Naval Research Laboratory's gravity gradient satellite 164. The model's formulation was based on a quasi-static approach in which deflections of the satellite's booms were determined in terms of thermally induced bending without consideration of boom vibration. Calculations, which were made for variations in absorptivity, sun angle, thermal lag, and hinge stiffness, demonstrated that, within the confines of a relatively narrow stability criteria, the quasi-static model of NRL 164 not only becomes unstable, but, in a number of cases, responses were computed that closely resembled flight data.

Goldman, R. L.↗

Results of the first 150 days of the NTS-1 solar cell experiments

Twelve solar cell experiments were on the Naval Research Laboratory NTS-1 satellite launched on 14 July 1974, into a 13,260 km circular orbit at an inclination of 125 deg. The experiment comprises: 2 ohm-cm n/p, lithium-diffused p/n, violet n/p, p(+) back surface field, and ultra-thin wrap around contact cells. The short-circuit current of the experiments ranged from 2 to 12 percent higher in space than under solar simulators. During the 5 year life of the satellite, the experiments will be exposed to radiation equivalent to 2 x 10 to the 15th power 1-MeV electron cm/2 and to nearly 5500 thermal cycles.

Statler, R. L.↗

XUV observations of coronal magnetic fields

Spectroheliograms obtained with the Naval Research Laboratory's Extreme Ultraviolet Spectrograph (S082A) on Skylab are compared with Kitt Peak National Observatory magnetograms. A principal result is the characteristic reconnection of flux from an emerging bipolar magnetic region to previously existing flux in its vicinity. Examples of the disappearance of magnetic flux from the solar atmosphere are also shown. The results of a particularly simple, potential field calculation are shown for comparison with the Skylab observations.

Sheeley, N. R., Jr.↗

Synoptic maps of solar coronal hole boundaries derived from He 2 304 A spectroheliograms from the manned skylab missions

The disk boundaries of coronal holes have been determined from He II 304 A spectroheliograms which were taken with the Naval Research Laboratory slitless XUV spectrograph during the manned Skylab missions. These boundaries are plotted by Carrington rotation as synoptic charts in both the standard rectangular as well as polar-view projections. The periods of time for which boundaries were determined are 24 May through 28 June 1973 (first manned Skylab mission), 2 August through 24 September 1973 (second manned mission), and 21 November 1973 through 2 February 1974 (third manned mission); the Carrington rotations covered (in part or totally) are 1601 and 02; 160r, 1604, 05 and 06; and 1608, 09 and 10, respectively.

Bohlin, J. D.↗

Ultraviolet emission line profiles of flares and active regions

A preliminary description of ultraviolet spectra of active regions and flares, photographed from Skylab by the Naval Research Laboratory's UV spectrograph, is given. The findings can be summarized as follows: (1) Line profiles of medium-ionized lines (transition-zone lines) show the most pronounced broadenings and shifts in flares and flare-like events; (2) typical full widths at half maximum of these lines correspond to Doppler velocities of 70 km/s; (3) shifts of the same magnitude can be observed; (4) intersystem lines are not broadened or shifted; (5) forbidden coronal lines and intersystem lines become enhanced in the flare spectrum at the moment when the turbulence seen in the allowed transitions disappears; and (6) a very broad line at 1354.2 A, which appears only in flare spectra, seems to be the forbidden transition 3P(1)-3P(0) of Fe XXI.

Brueckner, G. E.↗

An analysis of Skylab II S193 scatterometer data

Skylab II S193 scatterometer data for the passes of June 5, 1973, over the Gulf of Mexico and June 6, 1973, over Pacific Hurricane AVA were analyzed. These two passes were chosen since it was possible to correlate the scattering data with simultaneous measurements of the local ocean wind conditions. The S193 scatterometer measured the radar cross section of the ocean at 13.9 GHz (Ku-band) as a function of incidence angle. The S193 data of June 5, 1973, when a practically uniform wind field was present, show reasonable agreement with the Naval Research Laboratory (NRL) empirical and theoretical models. The data of June 6, 1973, are more complex, due to rapid variations in wind speeds and directions around Hurricane AVA. The NRL empirical model was interpolated to account for variation in wind heading relative to the S193 antenna pointing direction; a reasonable comparison could then be made with the corresponding S193 data of June 6, 1973.

Jordan, A. K.↗

Thin aluminum filters for use on the Apollo Telescope Mount XUV spectrographs

Thin, unbacked, aluminum film filters were used on two extreme ultraviolet (XUV) instruments flown on the Apollo Telescope Mount of Skylab by the Naval Research Laboratory to transmit the XUV radiation while blocking the longer wavelength radiation that would saturate the detector. The requirements placed on these filters - large size, resistance to degradation by high acoustic and vibration fields, and low pinhole transmittances - were far more severe than those placed on any filters previously flown. Special techniques were developed for vacuum evaporation of the aluminum, removal of the films from the substrates, supporting the films and mounting them to obtain finished filters, and storing them so that no degradation took place. A description of these techniques will be given.

Schumacher, R. J.↗

Measuring concave diffraction grating efficiencies at grazing incidence

The efficiency of a concave diffraction grating in a given order is obtained by measuring the intensities of the diffracted and incident beams and taking their ratio. A valid measurement requires that both the incident and diffracted beams be collected by the detector. At grazing incidence, however, the diffracted beam may spread beyond the detector due to aberrations. In addition, the diffracted beams of consecutive orders may overlap so that unambiguous efficiency measurements cannot be made. The effect of aberrations on efficiency measurements has been studied, using ray tracing, for the geometry of the measuring instrument in use at the Naval Research Laboratory. This instrument is attached to a VUV monochromator which furnishes a diverging beam. The main effect of aberrations for this instrument is a spread of the diffracted beam in the direction of dispersion. The width of the diffracted beam is wavelength dependent and is minimal at the horizontal focus, spreading to longer and shorter wavelengths. Reducing the divergence of the incident beam reduces the spread but, for small radius gratings, not always sufficiently so that the entire diffracted beam can be collected by the detector. The distance from the detector to the grating can also be adjusted to aid in collecting all the diffracted beam.

Hunter, W. R.↗

Spectral lines observed in solar flares between 171 and 630 angstroms

Several hundred spectral lines emitted in solar flares between 171 and 630 A have been recorded by the Naval Research Laboratory spectroheliograph aboard Skylab. The wavelengths, identifications, and intensity estimates of these lines are presented, based on measurements of all of the suitable flare plates. Nearly 100 new and unidentified lines have been observed. Identifications of three Fe XXI and two Fe XVII lines are suggested.

Dere, K. P.↗

Submicrosecond comparison of international clock synchronization by VLBI and the NTS satellite

The intercontinental clock synchronization capabilities of Very Long Baseline Interferometry (VLBI) and the Navigation Technology Satellite (NTS) were compared using both methods to synchronize the Cesium clocks at the NASA Deep Space Net complexes at Madrid, Spain and Goldstone, California. Verification of the accuracy of both systems was examined. The VLBI experiments used the Wideband VLBI Data Acquisition System developed at the NASA Jet Propulsion Laboratory. The NTS Satellites were designed and built by the Naval Research Laboratory used with NTS Timing Receivers developed by the Goddard Space Flight Center. The two methods agreed at about the one-half microsecond level.

Hurd, W. J.↗

Solar C III line intensity ratios observed from Skylab

Solar observations of C III line intensity ratios are analyzed which were obtained by the Naval Research Laboratory extreme-ultraviolet slit spectrograph on Skylab from quiet and active regions, coronal holes, prominences, and a flare. Electron densities are determined by comparing the observed intensity ratios to their theoretical variation as a function of electron density and temperature. Both isothermal line ratios that are evaluated at a characteristic emitting temperature and ratios that are integrated through the temperature and density structure of a model solar atmosphere are calculated. The density-sensitive ratios R(Si IV 1402/C III 1908) and R(Si III 1892/C III 1908) are also used to derive additional values of electron density. It is found that the ratios R(C III 1247/C III 1908), R(Si IV 1402/C III 1908), and R(Si III 1892/C III 1908) give consistent values of electron density for each feature. The C III 1908-A, Si III 1892-A, and Si IV 1402-A lines have recently been observed from the IUE satellite in spectra of late-type stars, and can serve as practical density diagnostics that are independent of assumptions about the stellar surface gravity.

Cook, J. W.↗

H2 emission in the solar atmosphere

New identifications of emission lines of molecular hydrogen in the EUV spectrum of sunspots are reported. The spectra were obtained during the first and second flights of the Naval Research Laboratory's High Resolution Telescope and Spectrograph (HRTS). While most of the lines originate in the Lyman bands, fluorescence from the Werner bands has been found for the first time in the solar atmosphere. H2 fluorescent emission has also been identified in the spectra of a solar flare observed with NRL's normal incidence spectrograph on Skylab. Column densities for H2 are derived from intensities of lines in the sunspot spectra.

Bartoe, J.-D. F.↗

EUV observations of quiescent prominences from Skylab

Measurements of line intensities and line widths for three quiescent prominences observed with Naval Research Laboratory slit spectrograph on ATM/Skylab are reported. The wavelengths of the observed lines cover the range 1175 A to 1960 A. The measured intensities have been calibrated to within approximately a factor 2 and are average intensities over a 2 arcsec by 60 arcsec slit. Nonthermal velocities from the measured line widths are derived. The nonthermal velocity is found to increase with temperature in the prominence transition zone. Electron densities and pressures are derived from density sensitive line ratios. Electron pressures for two of the prominences are found to lie in the range 0.04-0.08 dyn/sq cm, while values for the third and most intense and active of the three prominences are in the range 0.07-0.22 dyn/sq cm.

Moe, O. K.↗

Spectrum synthesis of EUV solar flare line profiles

A classic double ribbon flare of importance 1B occurred at approximately 1405 UT on June 15, 1973, reached an H alpha maximum at 1413 UT, and ended at 1455 UT. The flare occurred in an old and simplifying bipolar region at N18 W32. This flare was studied due to the extensive temporal data available. A total of 136 spectra of wavelength ranges from 1100 to 3000 A were taken during the flare's duration by the Naval Research Laboratory normal incidence slit spectrograph. Using this data the nature of the solar chromosphere of a flare event as a function of time was determined.

Tripp, D. A.↗