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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Numerical convergence and validation of the DIMP inverse particle transport model

The data integration with modeled predictions (DIMP) model is a promising inverse radiation transport method for solving the special nuclear material (SNM) holdup problem. Unlike previous methods, DIMP is a completely passive nondestructive assay technique that requires no initial assumptions regarding the source distribution or active measurement time. DIMP predicts the most probable source location and distribution through Bayesian inference and quasi-Newtonian optimization of predicted detector re-sponses (using the adjoint transport solution) with measured responses. DIMP performs well with for-ward hemispherical collimation and unshielded measurements, but several considerations are required when using narrow-view collimated detectors. DIMP converged well to the correct source distribution as the number of synthetic responses increased. DIMP also performed well for the first experimental validation exercise after applying a collimation factor, and sufficiently reducing the source search vol-ume's extent to prevent the optimizer from getting stuck in local minima. DIMP's simple point detector response function (DRF) is being improved to address coplanar false positive/negative responses, and an angular DRF is being considered for integration with the next version of DIMP to account for highly collimated responses. Overall, DIMP shows promise for solving the SNM holdup inverse problem, especially once an improved optimization algorithm is implemented.

42 ENGINEERING↗
DOE OSTI2021

Laboratory disruption of scaled astrophysical outflows by a misaligned magnetic field

The shaping of astrophysical outflows into bright, dense, and collimated jets due to magnetic pressure is here investigated using laboratory experiments. Here we look at the impact on jet collimation of a misalignment between the outflow, as it stems from the source, and the magnetic field. For small misalignments, a magnetic nozzle forms and redirects the outflow in a collimated jet. For growing misalignments, this nozzle becomes increasingly asymmetric, disrupting jet formation. Our results thus suggest outflow/magnetic field misalignment to be a plausible key process regulating jet collimation in a variety of objects from our Sun’s outflows to extragalatic jets. Furthermore, they provide a possible interpretation for the observed structuring of astrophysical jets. Jet modulation could be interpreted as the signature of changes over time in the outflow/ambient field angle, and the change in the direction of the jet could be the signature of changes in the direction of the ambient field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

The evolution of gamma-ray burst jet opening angle through cosmic time

ABSTRACT Jet opening angles of long gamma-ray bursts (lGRBs) appear to evolve in cosmic time, with lGRBs at higher redshifts being on average more narrowly beamed than those at lower redshifts. We examine the nature of this anticorrelation in the context of collimation by the progenitor stellar envelope. First, we show that the data indicate a strong correlation between gamma-ray luminosity and jet opening angle, and suggest this is a natural selection effect – only the most luminous GRBs are able to successfully launch jets with large opening angles. Then, by considering progenitor properties expected to evolve through cosmic time, we show that denser stars lead to more collimated jets; we argue that the apparent anticorrelation between opening angle and redshift can be accounted for if lGRB massive star progenitors at high redshifts have higher average density compared to those at lower redshifts. This may be viable for an evolving initial mass function (IMF) – under the assumption that average density scales directly with mass, this relationship is consistent with the form of the IMF mass evolution suggested in the literature. The jet angle–redshift anticorrelation may also be explained if the lGRB progenitor population is dominated by massive stars at high redshift, while lower redshift lGRBs allow for a greater diversity of progenitor systems (that may fail to collimate the jet as acutely). Overall, however, we find both the jet angle–redshift anticorrelation and jet angle–luminosity correlation are consistent with the conditions of jet launch through, and collimation by, the envelope of a massive star progenitor.

Lloyd-Ronning, Nicole↗
DOE OSTI2017

An Algorithm of an X-ray Hit Allocation to a Single Pixel in a Cluster and Its Test-Circuit Implementation

An on-chip implementable algorithm for allocation of an X-ray photon imprint, called a hit, to a single pixel in the presence of charge sharing in a highly segmented pixel detector is described. Its proof-of-principle implementation is also given supported by the results of tests using a highly collimated X-ray photon beam from a synchrotron source. The algorithm handles asynchronous arrivals of X-ray photons. Activation of groups of pixels, comparisons of peak amplitudes of pulses within an active neighborhood and finally latching of the results of these comparisons constitute the three procedural steps of the algorithm. A grouping of pixels to one virtual pixel, that recovers composite signals and event driven strobes, to control comparisons of fractional signals between neighboring pixels are the actuators of the algorithm. The circuitry necessary to implement the algorithm requires an extensive inter-pixel connection grid of analog and digital signals, that are exchanged between pixels. A test-circuit implementation of the algorithm was achieved with a small array of 32 × 32 pixels and the device was exposed to an 8 keV highly collimated to a diameter of 3-μm X-ray beam. Furthermore, the results of these tests are given in this paper assessing physical implementation of the algorithm.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Dark Field Proton Radiography (Los Alamos LDRD Report)

Proton radiography at LANL (pRad) takes advantage of the high flux, high proton energy, and flexible timing structure of LANSCE's 800-MeV proton beam to visualize dense, dynamic systems under extreme strain. With recent needs identified for the development of the W93, the pRad team has been actively searching for ways to increase the facility's radiographic capabilities. Recently, we discovered that utilizing two magnetic lenses (one upstream and one downstream of the object), and specific combinations of collimator choices within the two lenses, that the signal-to-noise ratio was improved by more than a factor of two. However, we did not fully understand the mechanism, and found that results did not match forward modeling predictions. This work specifically sought to implement an engineering solution to solve this problem, through the development of an actuated collimator that reduced the time required to swap collimator settings from a typical 4-8 hours, to less than 30 seconds. This allowed, in combination with a unique multi-material, multi-resolution stepwedge, to acquire an unprecedently enormous dataset, with in total 24 collimation combinations, and multiple diffuser settings and pulse patterns, equivalent to almost a full run cycle's worth of data in a few days. This massive dataset is currently being harnessed to make a fully-predictive, ultra-fast Python-based model of the system, to dial in specific settings for any future experiments that fully optimize that radiographic sensitivity to the material of interest.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2017

THE TOPOLOGY OF CANONICAL FLUX TUBES IN FLARED JET GEOMETRY

Magnetized plasma jets are generally modeled as magnetic flux tubes filled with flowing plasma governed by magnetohydrodynamics (MHD). We outline here a more fundamental approach based on flux tubes of canonical vorticity, where canonical vorticity is defined as the circulation of the species’ canonical momentum. This approach extends the concept of magnetic flux tube evolution to include the effects of finite particle momentum and enables visualization of the topology of plasma jets in regimes beyond MHD. A flared, current-carrying magnetic flux tube in an ion-electron plasma with finite ion momentum is thus equivalent to either a pair of electron and ion flow flux tubes, a pair of electron and ion canonical momentum flux tubes, or a pair of electron and ion canonical vorticity flux tubes. We examine the morphology of all these flux tubes for increasing electrical currents, different radial current profiles, different electron Mach numbers, and a fixed, flared, axisymmetric magnetic geometry. Calculations of gauge-invariant relative canonical helicities track the evolution of magnetic, cross, and kinetic helicities in the system, and show that ion flow fields can unwind to compensate for an increasing magnetic twist. The results demonstrate that including a species’ finite momentum can result in a very long collimated canonical vorticity flux tube even if the magnetic flux tube is flared. With finite momentum, particle density gradients must be normal to canonical vorticities, not to magnetic fields, so observations of collimated astrophysical jets could be images of canonical vorticity flux tubes instead of magnetic flux tubes.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1973

Analysis and synthesis of coronal and interplanetary energetic particle, plasma, and magnetic field observations over three solar rotations.

In a previous paper (Krimigis et al., 1971), simultaneous observations in 1967 of solar particle events at low (less than 1 MeV) energies were presented. In the present paper, the full complement of simultaneous plasma, magnetic field, and energetic particle data is combined, and a complete analysis is made of all the events discussed in the original paper. The essential concept of 'collimated convection' is introduced, whereby the bulk velocity along the field lines of low-energy solar particles is independent of solar local plasma velocity, and the particles are strongly collimated along the field line with no transverse velocity component other than that of the field line itself. Collimated convection effects are shown to exist in small-scale convection and large-scale evolution of particle fluxes; the particle fluxes are, in turn, used to delineate the small-scale and large-scale evolution of the interplanetary magnetic field. Use of collimated convection is made in demonstrating a technique whereby energetic particle intensity profiles in the interplanetary medium can be related to equatorial high coronal magnetic field structures, by using the instantaneous solar wind velocity. This technique is applied in mapping particle intensities from Mariner 5 onto H alpha synoptic charts of chromospheric magnetic field structures for Carrington rotations 1523 to 1525.

Roelof, E. C.↗
NASA NTRS1980

improving maser frequency stability

Hydrogen maser frequency standard is more stable by addition of parallel pyrex capillary tube array collimator. With collimator, maser line width has been made as narrow as 0.24 hertz representing fivefold improvement over maser without collimator. Fluorocarbon coating in tubes virtually eliminates energy loss in collimator.

Crampton, S. B.↗
NASA NTRS1987

Laser schlieren crystal monitor

A system and method for monitoring the state of a crystal which is suspended in a solution is described which includes providing a light source for emitting a beam of light along an optical axis. A collimating lens is arranged along the optical axis for collimating the emitted beam to provide a first collimated light beam consisting of parallel light rays. By passing the first collimated light beam through a transparent container, a number of the parallel light rays are deflected off the surfaces of said crystal being monitored according to the refractive index gradient to provide a deflected beam of deflected light rays. A focusing lens is arranged along optical axis for focusing the deflected rays towards a desired focal point. A knife edge is arranged in a predetermined orientation at the focal point; and a screen is provided. A portion of the deflected beam is blocked with the knife edge to project only a portion of the deflected beam. A band is created at one edge of the image of the crystal which indicates the state of change of the surface of the crystal being monitored.

Owen, Robert B.↗
NASA NTRS1990

Images of shock-excited molecular hydrogen in young stellar outflows

High-angular resolution molecular hydrogen (H2) v = 1-0 S(1) line images of several well-known molecular outflow sources (DR 21, NGC 2071, HH 7-11, and HH 12) are presented. It is found that all of the outflow sources possess highly collimated jets of shock-excited gas that are extremely clumpy and often consist of bright knots that are placed periodically along the jet axis. The H2 emission-line jets are significantly more collimated than their corresponding CO outflows and remain collimated to large distances from their driving source. In DR 21 and NGC 2071, the H2 jets appear to become more collimated with increasing distance from the central source, suggesting that they are pressure-confined by the ambient cloud medium. In HH 7-11 and HH 12 the shock-excited ionized and molecular components are spatially coincident and appear to be of comparable shape and size; this suggests that the shocked gas is highly mixed on scales significantly smaller than the current spatial resolution.

Garden, Rognvald P.↗
NASA NTRS1997

Laboratory Plasma Source as an MHD Model for Astrophysical Jets

The significance of the work described herein lies in the demonstration of Magnetized Coaxial Plasma Gun (MCG) devices like CPS-1 to produce energetic laboratory magneto-flows with embedded magnetic fields that can be used as a simulation tool to study flow interaction dynamic of jet flows, to demonstrate the magnetic acceleration and collimation of flows with primarily toroidal fields, and study cross field transport in turbulent accreting flows. Since plasma produced in MCG devices have magnetic topology and MHD flow regime similarity to stellar and extragalactic jets, we expect that careful investigation of these flows in the laboratory will reveal fundamental physical mechanisms influencing astrophysical flows. Discussion in the next section (sec.2) focuses on recent results describing collimation, leading flow surface interaction layers, and turbulent accretion. The primary objectives for a new three year effort would involve the development and deployment of novel electrostatic, magnetic, and visible plasma diagnostic techniques to measure plasma and flow parameters of the CPS-1 device in the flow chamber downstream of the plasma source to study, (1) mass ejection, morphology, and collimation and stability of energetic outflows, (2) the effects of external magnetization on collimation and stability, (3) the interaction of such flows with background neutral gas, the generation of visible emission in such interaction, and effect of neutral clouds on jet flow dynamics, and (4) the cross magnetic field transport of turbulent accreting flows. The applicability of existing laboratory plasma facilities to the study of stellar and extragalactic plasma should be exploited to elucidate underlying physical mechanisms that cannot be ascertained though astrophysical observation, and provide baseline to a wide variety of proposed models, MHD and otherwise. The work proposed herin represents a continued effort on a novel approach in relating laboratory experiments to astrophysical jet observation. There exists overwhelming similarity among these flows that has already produced some fascinating results and is expected to continue a high pay off in future flow similarity studies.

Mayo, Robert M.↗
NASA NTRS1997

The Diagnostics of the External Plasma for the Plasma Rocket

Three regions of plasma temperature/energy are being investigated to understand fully the behavior of the plasma created by the propulsion device and the operation of the RPA. Each type of plasma has a RPA associated with it; i.e. a thermal RPA, a collimated RPA, and a high temperature RPA. Through the process of developing the thermal and collimated RPAs, the proper knowledge and experience has been gained to not only design a high temperature RPA for the plasma rocket, but to understand its operation, results, and uncertainty. After completing a literature search for, reading published papers on, and discussing the operation of the RPA with electric propulsion researchers, I applied the knowledge gained to the development of a RPA for thermal plasma. A design of a thermal RPA was made which compensates for a large Debye length and low ionized plasma. From this design a thermal RPA was constructed. It consists of an outer stainless steel casing, a phenolic insulator (outgases slightly), and stainless steel mesh for the voltage screens. From the experience and knowledge gained in the development of the thermal RPA, a RPA for collimated plasma was developed. A collimated RPA has been designed and constructed. It compensate for a smaller Debye length and much higher ionization than that existing in the thermal plasma. It is 17% of the size of the thermal RPA. A stainless steel casing shields the detector from impinging electrons and ions. An insulating material, epoxy resin, was utilized which has a negligible outgassing. This material can be molded in styrofoam and machined quite nicely. It is capable of withstanding moderately high temperatures. Attached to this resin insulator are inconel screens attached by silver plated copper wire to a voltage supply. All the work on the RPAs and thermal ion source, I performed in the University of Alabama in Huntsville's (UAH) engineering machine shop.

Karr, Gerald R.↗
NASA NTRS1998

Magnetohydrodynamic Origin of Jets from Accretion Disks

A review is made of magnetohydrodynamic (MHD) theory and simulation of outflows from disks for different distributions of magnetic field threading the disk. In one limit of a relatively weak, initially diverging magnetic field, both thermal and magnetic pressure gradients act to drive matter to an outflow, while a toroidal magnetic field develops which strongly collimates the outflow. The collimation greatly reduces the field divergence and the mass outflow rate decreases after an initial peak. In a second limit of a strong magnetic field, the initial field configuration was taken with the field strength on the disk decreasing outwards to small values so that collimation was reduced. As a result, a family of stationary solutions was discovered where matter is driven mainly by the strong magnetic pressure gradient force. The collimation in this case depends on the pressure of an external medium. These flows are qualitatively similar to the analytic solutions for magnetically driven outflows. The problem of the opening of a closed field line configuration linking a magnetized star and an accretion disk is also discussed.

Lovelace, R. V. E.↗
NASA NTRS2006

Nondestructive Evaluation of Foam Insulation on the Space Shuttle External Tank

Foam loss on the External Tank (ET) during launch can be caused by a number of factors. Voids are the best understood mechanism of foam loss, although it is known that delaminations, cracks and crushed foam can also lead to liberation of foam. Shortly after the Columbia accident, work began on non-destructive evaluation of foam targeted at finding voids and delaminations. After several months of searching for candidate methods capable of inspecting ET foam, the five most promising techniques were taken through a blind test and narrowed down to two methods to develop and use for inspection of the ET. These methods were backscatter radiography and terahertz imaging. The backscatter radiography system measures a test part by detecting Compton backscattered x-ray energy generated by a collimated beam of x-rays directed at the test subject. This collimated beam is scanned across the subject, recording scatter intensity data one pixel at a time until the area of interest is covered. The resulting data can be used to generate an image similar to a radiograph. Some depth information can be gathered utilizing apertures or collimation on the detectors. The detectors are located around the collimated source, making this a single sided inspection. The void detection limit with the currently utilized system is around 0.5 inches in diameter by 0.2 inches high. The terahertz imaging system inspects a test part by utilizing a transceiver to emit a pulse focused at the aluminum skin of the ET, which reflects it back to the transceiver where it is analyzed. The transceiver is scanned across the area of interest until a measurement has been taken at every location. Amplitude, time delay and frequency content are examined to note any discontinuities which may be the result of a void or other type of defect. The pulse currently utilized is in the millimeter wave regime. The void detection limit with this system is around 0.5 inches in diameter by 0.2 inches high. With increased interest in other causes of foam loss following the flight of Discovery in July 2005, laser shearography was added to the techniques used for inspecting ET foam. The shearography method records a sheared image of a laser speckle pattern projected on a test part before And after some sort of excitation. The resultant fringe pattern allows the slope of the out of plane displacement to be measured. For crushed and delaminated foam applications, a non-contact air coupled acoustic force is used to excite the surface of the foam. Regions without defects tend to respond differently to the sound energy than do regions with defects, generating a map of the foam integrity. Foam crushed to a depth of about 0.1 inches is detectable with shearography even after it has relaxed to its original shape.

Richter, Joel↗
NASA NTRS2011

Wide-Field Optic for Autonomous Acquisition of Laser Link

An innovation reported in Two-Camera Acquisition and Tracking of a Flying Target, NASA Tech Briefs, Vol. 32, No. 8 (August 2008), p. 20, used a commercial fish-eye lens and an electronic imaging camera for initially locating objects with subsequent handover to an actuated narrow-field camera. But this operated against a dark-sky background. An improved solution involves an optical design based on custom optical components for the wide-field optical system that directly addresses the key limitations in acquiring a laser signal from a moving source such as an aircraft or a spacecraft. The first challenge was to increase the light collection entrance aperture diameter, which was approximately 1 mm in the first prototype. The new design presented here increases this entrance aperture diameter to 4.2 mm, which is equivalent to a more than 16 times larger collection area. One of the trades made in realizing this improvement was to restrict the field-of-view to +80 deg. elevation and 360 azimuth. This trade stems from practical considerations where laser beam propagation over the excessively high air mass, which is in the line of sight (LOS) at low elevation angles, results in vulnerability to severe atmospheric turbulence and attenuation. An additional benefit of the new design is that the large entrance aperture is maintained even at large off-axis angles when the optic is pointed at zenith. The second critical limitation for implementing spectral filtering in the design was tackled by collimating the light prior to focusing it onto the focal plane. This allows the placement of the narrow spectral filter in the collimated portion of the beam. For the narrow band spectral filter to function properly, it is necessary to adequately control the range of incident angles at which received light intercepts the filter. When this angle is restricted via collimation, narrower spectral filtering can be implemented. The collimated beam (and the filter) must be relatively large to reduce the incident angle down to only a few degrees. In the presented embodiment, the filter diameter is more than ten times larger than the entrance aperture. Specifically, the filter has a clear aperture of about 51 mm. The optical design is refractive, and is comprised of nine custom refractive elements and an interference filter. The restricted maximum angle through the narrow-band filter ensures the efficient use of a 2-nm noise equivalent bandwidth spectral width optical filter at low elevation angles (where the range is longest), at the expense of less efficiency for high elevations, which can be tolerated because the range at high elevation angles is shorter. The image circle is 12 mm in diameter, mapped to 80 x 360 of sky, centered on the zenith.

Page, Norman A.↗
NASA NTRS2011

Results from Solar Reflective Band End-to-End Testing for VIIRS F1 Sensor Using T-SIRCUS

Verification of the Visible Infrared Imager Radiometer Suite (VIIRS) End-to-End (E2E) sensor calibration is highly recommended before launch, to identify any anomalies and to improve our understanding of the sensor on-orbit calibration performance. E2E testing of the Reflective Solar Bands (RSB) calibration cycle was performed pre-launch for the VIIRS Fight 1 (F1) sensor at the Ball Aerospace facility in Boulder CO in March 2010. VIIRS reflective band calibration cycle is very similar to heritage sensor MODIS in that solar illumination, via a diffuser, is used to correct for temporal variations in the instrument responsivity. Monochromatic light from the NIST T-SIRCUS was used to illuminate both the Earth View (EV), via an integrating sphere, and the Solar Diffuser (SD) view, through a collimator. The collimator illumination was cycled through a series of angles intended to simulate the range of possible angles for which solar radiation will be incident on the solar attenuation screen on-orbit. Ideally, the measured instrument responsivity (defined here as the ratio of the detector response to the at-sensor radiance) should be the same whether the EV or SD view is illuminated. The ratio of the measured responsivities was determined at each collimator angle and wavelength. In addition, the Solar Diffuser Stability Monitor (SDSM), a ratioing radiometer designed to track the temporal variation in the SD BRF by direct comparison to solar radiation, was illuminated by the collimator. The measured SDSM ratio was compared to the predicted ratio. An uncertainty analysis was also performed on both the SD and SDSM calibrations.

McIntire, Jeff↗
NASA NTRS2012

Wavefront Compensation Segmented Mirror Sensing and Control

The primary mirror of very large submillimeter-wave telescopes will necessarily be segmented into many separate mirror panels. These panels must be continuously co-phased to keep the telescope wavefront error less than a small fraction of a wavelength, to ten microns RMS (root mean square) or less. This performance must be maintained continuously across the full aperture of the telescope, in all pointing conditions, and in a variable thermal environment. A wavefront compensation segmented mirror sensing and control system, consisting of optical edge sensors, Wavefront Compensation Estimator/Controller Soft ware, and segment position actuators is proposed. Optical edge sensors are placed two per each segment-to-segment edge to continuously measure changes in segment state. Segment position actuators (three per segment) are used to move the panels. A computer control system uses the edge sensor measurements to estimate the state of all of the segments and to predict the wavefront error; segment actuator commands are computed that minimize the wavefront error. Translational or rotational motions of one segment relative to the other cause lateral displacement of the light beam, which is measured by the imaging sensor. For high accuracy, the collimator uses a shaped mask, such as one or more slits, so that the light beam forms a pattern on the sensor that permits sensing accuracy of better than 0.1 micron in two axes: in the z or local surface normal direction, and in the y direction parallel to the mirror surface and perpendicular to the beam direction. Using a co-aligned pair of sensors, with the location of the detector and collimated light source interchanged, four degrees of freedom can be sensed: transverse x and y displacements, as well as two bending angles (pitch and yaw). In this approach, each optical edge sensor head has a collimator and an imager, placing one sensor head on each side of a segment gap, with two parallel light beams crossing the gap. Two sets of optical edge sensors are used per segment-to-segment edge, separated by a finite distance along the segment edge, for four optical heads, each with an imager and a collimator. By orienting the beam direction of one edge sensor pair to be +45 away from the segment edge direction, and the other sensor pair to be oriented -45 away from the segment edge direction, all six degrees of freedom of relative motion between the segments can be measured with some redundancy. The software resides in a computer that receives each of the optical edge sensor signals, as well as telescope pointing commands. It feeds back the edge sensor signals to keep the primary mirror figure within specification. It uses a feed-forward control to compensate for global effects such as decollimation of the primary and secondary mirrors due to gravity sag as the telescope pointing changes to track science objects. Three segment position actuators will be provided per segment to enable controlled motions in the piston, tip, and tilt degrees of freedom. These actuators are driven by the software, providing the optical changes needed to keep the telescope phased.

Redding, David C.↗
NASA NTRS2012

Estimation of Orbital Neutron Detector Spatial Resolution by Systematic Shifting of Differential Topographic Masks

We present a method and preliminary results related to determining the spatial resolution of orbital neutron detectors using epithermal maps and differential topographic masks. Our technique is similar to coded aperture imaging methods for optimizing photonic signals in telescopes [I]. In that approach photon masks with known spatial patterns in a telescope aperature are used to systematically restrict incoming photons which minimizes interference and enhances photon signal to noise. Three orbital neutron detector systems with different stated spatial resolutions are evaluated. The differing spatial resolutions arise due different orbital altitudes and the use of neutron collimation techniques. 1) The uncollimated Lunar Prospector Neutron Spectrometer (LPNS) system has spatial resolution of 45km FWHM from approx. 30km altitude mission phase [2]. The Lunar Rennaissance Orbiter (LRO) Lunar Exploration Neutron Detector (LEND) with two detectors at 50km altitude evaluated here: 2) the collimated 10km FWHM spatial resolution detector CSETN and 3) LEND's collimated Sensor for Epithermal Neutrons (SETN). Thus providing two orbital altitudes to study factors of: uncollimated vs collimated and two average altitudes for their effect on fields-of-view.

McClanahan, T. P.↗