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NASA NTRS1994

Electron time dispersion

Observations of electrons during a sounding rocket flight from Sondrestromfjord, Greenland, in 1985 showed numerous instances of electron time-of-flight dispersion, that is, a coherent structure in which fast electrons arrived before slow electrons. The instrumentation measured many pitch angles simultaneously with high time resolution, providing a detailed view of the temporal evolution of the electron signature at rocket altitudes which was indicative of an impulsive injection of electrons over a range of energies. A model utilizing an extended, quasi-static (static on a timescale of 1 s), parallel electric field was developed to investigate a possible mechanism for the injection of these electrons. The model is found to fit the data well only when a background is added which cannot be self-consistently generated by the model, although other parameters used in the model are in general agreement with previous reports. This leads to the conclusion that electron dispersion is more probably generated by a wave acceleration mechanism.

Kletzing, C. A.↗

NASA NTRS1999

Mars Global Surveyor Thermal Emission Spectrometer (TES) Observations: Atmospheric Temperatures During Aerobraking and Science Phasing

Between September 1997, when the Mars Global Surveyor spacecraft arrived at Mars, and September 1998 when the final aerobraking phase of the mission began, the Thermal Emission Spectrometer (TES) has acquired an extensive data set spanning approximately half of a Martian year. Nadir-viewing spectral measurements from this data set within the 15-micrometers CO2 absorption band are inverted to obtain atmospheric temperature profiles from the surface up to about the 0.1 mbar level. The computational procedure used to retrieve the temperatures is presented. Mean meridional cross sections of thermal structure are calculated for periods of time near northern hemisphere fall equinox, winter solstice, and spring equinox, as well as for a time interval immediately following the onset of the Noachis Terra dust storm. Gradient thermal wind cross sections are calculated from the thermal structure. Regions of possible wave activity are identified using cross sections of rms temperature deviations from the mean. Results from both near-equinox periods show some hemispheric asymmetry with peak eastward thermal winds in the north about twice the magnitude of those in the south. The results near solstice show an intense circumpolar vortex at high northern latitudes and waves associated with the vortex jet core. Warming of the atmosphere aloft at mid-northern latitudes suggests the presence of a strong cross-equatorial Hadley circulation. Although the Noachis dust storm did not become global in scale, strong perturbations to the atmospheric structure are found, including an enhanced temperature maximum aloft at high northern latitudes resulting from intensification of the Hadley circulation. TES results for the various seasonal conditions are compared with published results from Mars general circulation models, and generally good qualitative agreement is found.

Conrath, Barney J.↗

NASA NTRS2002

On the Exit Boundary Condition for One-Dimensional Calculations of Pulsed Detonation Engine Performance

In one-dimensional calculations of pulsed detonation engine (PDE) performance, the exit boundary condition is frequently taken to be a constant static pressure. In reality, for an isolated detonation tube, after the detonation wave arrives at the exit plane, there will be a region of high pressure, which will gradually return to ambient pressure as an almost spherical shock wave expands away from the exit, and weakens. Initially, the flow is supersonic, unaffected by external pressure, but later becomes subsonic. Previous authors have accounted for this situation either by assuming the subsonic pressure decay to be a relaxation phenomenon, or by running a two-dimensional calculation first, including a domain external to the detonation tube, and using the resulting exit pressure temporal distribution as the boundary condition for one-dimensional calculations. These calculations show that the increased pressure does affect the PDE performance. In the present work, a simple model of the exit process is used to estimate the pressure decay time. The planar shock wave emerging from the tube is assumed to transform into a spherical shock wave. The initial strength of the spherical shock wave is determined from comparison with experimental results. Its subsequent propagation, and resulting pressure at the tube exit, is given by a numerical blast wave calculation. The model agrees reasonably well with other, limited, results. Finally, the model was used as the exit boundary condition for a one-dimensional calculation of PDE performance to obtain the thrust wall pressure for a hydrogen-air detonation in tubes of length to diameter ratio (L/D) of 4, and 10, as well as for the original, constant pressure boundary condition. The modified boundary condition had no performance impact for values of L/D > 10, and moderate impact for L/D = 4.

Wilson, Jack↗

NASA NTRSDate not supplied

Inner Magnetospheric Physics

The inner magnetosphere extends from just above the topside ionosphere to approximately 8 RE geocentric distance. Magnetospheric physics is a young science that only started to be recognized as a region with the space observations by Explorer 1 in 1958. The region is mostly populated by ionized gas or plasma from Earth’s ionosphere. Plasma populations are differentiated by their energies primarily. From the least energetic to most are the plasmasphere, ring current, and radiation belts, extending from about 1 eV to 10 MeV in energy and from 1,000s cm-3 down to a few particles per cubic centimeter and less, respectively. The solar wind and solar erupted coronal mass ejections (CMEs) arriving and interacting with Earth’s magnetic field creates a dynamo effect that drives million ampere currents along magnetic field lines that close through the ionosphere. The solar wind dynamo also creates a 100s kV electric field across the magnetosphere that drives convective motion of the plasma within it. The solar wind driven currents compress Earth’s magnetic field on the sunward side and greatly extents the field on the nightside to form the magnetotail. The energy stored in the magnetotail is impulsively released when magnetic field lines there merge, releasing energy into the plasma trapped by the magnetic field. Those plasma become the ring current that loses plasma into the atmosphere to produce the aurora and at the same time ring current plasma can be further energized by wave-particle interactions to become the radiation belts. The presentation will review these topics and a few of the underlying physical processes that are involved in this highly coupled planetary system.

inner magnetosphere↗

NASA NTRS1984

Structure of the magnetotail at 220 earth radii and its response to geomagnetic activity

Using plasma electron and magnetic field measurements from ISEE 3, 220 earth radii from earth, it is found that the magnetotail at that distance is a coherent structure that evidently waves about through distances comparable to its own lateral scale size. For about one-third of the time it was inside the magnetotail, ISEE 3 was in the plasma sheet. During quiet times the plasma sheet is apparently quite thin, but in response to geomagnetic activity it expands, becoming filled with hot plasma flowing tailward at speeds sometimes exceeding 1000 km/sec, and forces the magnetotail cross-section itself to expand. The plasma sheet's expansion is delayed typically by about 30 minutes from the onset of the associated geomagnetic activity (often a clearly identified isolated substorm). The magnetic field in the newly-expanded plasma sheet usually exhibits a few-minute steep northward excursion followed by a more prolonged (and often steep) southward excursion. These are believed to be the signatures of arrival of a plasmoid formed and released near the earth at the onset of the corresponding geomagnetic activity. The discreteness of these plasma releases through the magnetotail and their close association with onsets of geomagnetic activity at earth suggest that they are consequences of spontaneous release, probably by magnetic reconnection, of energy and plasma earlier stored in the magnetotail.

Hones, E. W., Jr.↗

NASA NTRS2010

NASA Tech Briefs, December 2010

Topics include: Coherent Frequency Reference System for the NASA Deep Space Network; Diamond Heat-Spreader for Submillimeter-Wave Frequency Multipliers; 180-GHz I-Q Second Harmonic Resistive Mixer MMIC; Ultra-Low-Noise W-Band MMIC Detector Modules; 338-GHz Semiconductor Amplifier Module; Power Amplifier Module with 734-mW Continuous Wave Output Power; Multiple Differential-Amplifier MMICs Embedded in Waveguides; Rapid Corner Detection Using FPGAs; Special Component Designs for Differential-Amplifier MMICs; Multi-Stage System for Automatic Target Recognition; Single-Receiver GPS Phase Bias Resolution; Ultra-Wideband Angle-of-Arrival Tracking Systems; Update on Waveguide-Embedded Differential MMIC Amplifiers; Automation Framework for Flight Dynamics Products Generation; Product Operations Status Summary Metrics; Mars Terrain Generation; Application-Controlled Parallel Asynchronous Input/Output Utility; Planetary Image Geometry Library; Propulsion Design With Freeform Fabrication (PDFF); Economical Fabrication of Thick-Section Ceramic Matrix Composites; Process for Making a Noble Metal on Tin Oxide Catalyst; Stacked Corrugated Horn Rings; Refinements in an Mg/MgH2/H2O-Based Hydrogen Generator; Continuous/Batch Mg/MgH2/H2O-Based Hydrogen Generator; Strain System for the Motion Base Shuttle Mission Simulator; Ko Displacement Theory for Structural Shape Predictions; Pyrotechnic Actuator for Retracting Tubes Between MSL Subsystems; Surface-Enhanced X-Ray Fluorescence; Infrared Sensor on Unmanned Aircraft Transmits Time-Critical Wildfire Data; and Slopes To Prevent Trapping of Bubbles in Microfluidic Channels.

Source record↗

NASA NTRS2004

THz Hot-Electron Photon Counter

We present a concept for the hot-electron transition-edge sensor capable of counting THz photons. The main need for such a sensor is a spectroscopy on future space telescopes where a background limited NEP approx. 10(exp -20) W/H(exp 1/2) is expected at around 1 THz. Under these conditions, the rate of photon arrival is very low and any currently imaginable detector with sufficient sensitivity will operate in the photon counting mode. The Hot-Electron Photon Counter based on a submicron-size Ti bridge has a very low heat capacity which provides a high enough energy resolution (approx.140 GHz) at 0.3 K. With the sensor time constant of a few microseconds, the dynamic range would be approx. 30 dB. The sensor couples to radiation via a planar antenna and is read by a SQUID amplifier or by a 1-bit RSFQ ADC. A compact array of the antenna-coupled counters can be fabricated on a silicon wafer without membranes.

radiation detectors↗

NASA NTRS2004

Validation of Mars-GRAM and Planned New Features

For altitudes below 80 km, Mars Global Reference Atmospheric Model (Mars-GRAM 2001) is based on output climatology from NASA Ames Mars General Circulation Model (MGCM). At COSPAR 2002, results were presented of validation tests of Mars-GRAM versus data from Mars Global Surveyor Thermal Emission Spectrometer (TES) and Radio Science (RS) experiment. Further validation tests are presented comparing Mars- GRAM densities with those from the European Mars Climate Database (MCD), and comparing densities from both Mars-GRAM and MCD against TES observations. Throughout most of the height and latitude range of TES data (040 km and 70s to 70N), good agreement is found between atmospheric densities from Mars-GRAM and MCD. However, at the season and latitude zone for Mars Phoenix arrival and landing (Ls = 65 to 80 degrees and latitude 65 to 75N), Mars-GRAM densities are about 30 to 45 percent higher than MCD densities near 40 km altitude. Further evaluation is warranted concerning potential impact of these model differences on planning for Phoenix entry and descent. Three planned features for Mars-GRAM update are also discussed: (1) new MGCM and Thermospheric General Circulation Model data sets to be used as a revised basis for Mars-GRAM mean atmosphere, (2) a new feature to represent planetary-scale traveling waves for upper altitude density variations (such as found during Mars Odyssey aerobraking), and (3) a new model for effects of high resolution topographic slope on winds near the surface (0 to 4.5 km above MOLA topography level). Mars-GRAM slope winds will be computed from a diagnostic (algebraic) relationship based on Ye, Segal, and Pielke (1990). This approach differs from mesoscale models (such as MRAMS and Mars MM5), which use prognostic, full-physics solutions of the time- and space-dependent differential equations of motion. As such, slope winds in Mars-GRAM will be consistent with its "engineering-level" approach, and will be extremely fast and easy to evaluate, compared with mesoscale model solutions. Mars-GRAM slope winds are not being suggested as a replacement for sophisticated, full-physics Mars mesoscale models, but may have value, particularly for preliminary screening of large numbers of candidate landing sites for future Mars missions, such as Phoenix and Mars Science Laboratory. Test output is presented from Mars-GRAM slope winds in the area of Gusev Crater and Valles Marineris.

Justus, C. G.↗

NASA NTRS1992

Non-relativistic solar electron events during December 1990 - Results from Ulysses

Several groups of impulsive flare accelerated nonrelativistic solar electron events occurred in November and December 1990. In a total of 18 separate events, most show the characteristic dispersion in arrival times at the Ulysses spacecraft corresponding to travel time for the various particle energy groups. After maximum development, the electron intensities generally decay smoothly with characteristic times of 10 to 15 hours. In a few cases there are marked departures from this 'classic' behavior. On 15 December 1990, these departures are associated with a structure in the interplanetary magnetic field having a width of about 4 x 10 exp 6 km at 1.37 AU. The particle intensities inside this structure varied greatly with spatial position. Some of the changes occurred over distances as small as 3 x 10 exp 4 km. It is believed that this interplanetary structure had its origin in the complex magnetic fields that overlay the solar active region in which the electron accelerating flares occurred, and that it is these fields near the sun that determine access of the flare accelerated electrons to interplanetary field lines. A solar electron event on 11 December 1990 is similar in many respects to the one on 15 December. Neither of these events is directly related to an interplanetary shock wave.

Anderson, K. A.↗

NASA NTRS2006

An Ultrasensitive Hot-Electron Bolometer for Low-Background SMM Applications

We are developing a hot-electron superconducting transition-edge sensor (TES) that is capable of counting THz photons and operates at T = 0.3K. The main driver for this work is moderate resolution spectroscopy (R approx. 1000) on the future space telescopes with cryogenically cooled (approx. 4 K) mirrors. The detectors for these telescopes must be background-limited with a noise equivalent power (NEP) approx. 10(exp -19)-10(exp -20) W/Hz(sup 1/2) over the range v = 0.3-10 THz. Above about 1 THz, the background photon arrival rate is expected to be approx. 10-100/s), and photon counting detectors may be preferable to an integrating type. We fabricated superconducting Ti nanosensors with a volume of approx. 3x10(exp -3) cubic microns on planar substrate and have measured the thermal conductance G to the thermal bath. A very low G = 4x10(exp -14) W/K, measured at 0.3 K, is due to the weak electron-phonon coupling in the material and the thermal isolation provided by superconducting Nb contacts. This low G corresponds to NEP(0.3K) = 3x10(exp -19) W/Hz(sup 1/2). This Hot-Electron Direct Detector (HEDD) is expected to have a sufficient energy resolution for detecting individual photons with v > 0.3 THz at 0.3 K. With the sensor time constant of a few microseconds, the dynamic range is approx. 50 dB.

bolometers↗

NASA NTRS1992

Hydrogen leak detection in the Space Shuttle

This study focuses on a helium gas jet flowing into room air. Measurements of helium concentration and velocity in the jet-air mixture are reported. The objective is to learn about jet characteristics so that dynamically similar hydrogen leaks may be located in the Space Shuttle. The hazardous gas detection system (HGDS) in the mobile launch pad uses mass spectrometers to monitor the shuttle environment for leaks. The mass spectrometers are fed by long sample tubes which draw gas from the payload bay, mid body, aft engine compartment and external tank. The overall purpose of this study is to improve the HGDS especially in its potential for locating hydrogen leaks. A rapid-response leak detection experiment was designed, built, and tested, following on the work done in this program last summer. The apparatus included a Perkin Elmer MGA-1200 mass spectrometer and air velocity transducer, both monitored by a Macintosh IIFX computer using LabVIEW software. A jet of helium flowing into the lab air simulated a gas leak. Steady helium or hydrogen-nitrogen jets were logged for concentration and velocity, and the power spectral density of each was computed. Last year, large eddies and vortices were visually seen with Schlieren imaging, and they were detected in the time plots of the various instruments. The response time of the MGA-1200 was found in the range of 0.05 to 0.1 sec. Pulsed concentration waves were clearly detected at 25 cycles per sec by spectral analysis of MGA data. No peaks were detected in the power spectrum, so in the present study, 10 Hz bandwidth-averaged power levels were examined at regular frequency intervals. The practical consequences of last year's study are as follows: sampling frequency should be increased above the present rate of 1 sample per second so that transients could be observed and analyzed with frequency response methods. Many more experiments and conditions were observed in this second summer, including the effects of orifice diameter, jet velocity, sample tube design, radial effects, vertical flow, and low hydrogen concentrations (1 percent). A frequent observation was that the power spectrum, calculated from the Fourier transform of concentration fluctuations, gives a separate piece of information from concentration. Many of the tests suggest that power is high where mixing occurs at the helium-air interface. This fact is apparently independent of the concentration level, which could be high or low, but depends on the sample location relative to the jet (leak) origin, whereas high concentration may be due to a strong leak far away or a small leak close to the sample tube. If the power is low for any concentration level, this would signify helium is arriving at the sample tube by diffusion, not chaotic mixing caused by the jet interaction with air. The practical result is to propose a modification of the HGDL mass spectrometer data sampling and software so that sampling rates could be capable of observing at least 25 Hz fluctuations.

Barile, Ronald G↗

NASA NTRS2018

Juno at Jupiter: The Mission and Its Path to Unveiling Secrets of the History of the Solar System

The Juno mission is described, focusing on its orbits at Jupiter, how the plan evolved, and science return so far. Juno is a NASA New Frontiers spacecraft in a near-polar highly elliptical 53-day orbit at Jupiter. Since arrival in July 2016, it has used 9 science investigations to study the planet’s atmospheric composition and structure, magnetic and gravity fields, and polar and extended magnetosphere. A radiation monitoring investigation contributes to our understanding of Jupiter’s environment. Juno’s primary science goal is to understand the origin and evolution of Jupiter, to shed light on how the Earth and other planets formed. Baseline objectives will be satisfied with 32 science orbits, a spin-stabilized solar powered spacecraft, an electronics vault for radiation shielding, and a robust payload with microwave receivers, X- and Ka-band radio science hardware, vector magnetometers, high- and low-energy charged particle detectors, radio and plasma wave antennas, UV and IR spectroscopic imagers, and a visible light camera for public outreach. Observations are made in a limited number of orientations, including Gravity Science (spin axis and main antenna pointing to Earth), and microwave atmospheric sounding (spin plane passing through Jupiter’s center). Prime science data are collected near closest approach (perijove), plus calibrations, occasional remote sensing, and continued magnetospheric observations in the outer parts of the orbit. Juno’s mission plan has evolved since the 2005 proposal due to design and ops choices, e.g., mission design (cruise or early orbital trajectory), orbit period (11, 14, then 53 days), perijove attitudes (2 or more), and DSN coverage (34- and 70-m stations). Choices were partly motivated by the effect on science return. Selected preliminary science results are summarized, including the benefits of decisions as the plan evolved. Juno has begun to unveil Jupiter – peeling apart its interior by measuring gravity and magnetic fields, using microwaves to probe its atmosphere down to 100s of km, exploring its polar and extended magnetosphere, and imaging the poles for the first time. In doing so, it is revealing secrets of the history of the Earth and solar system.

Stephens, Stuart K.↗

NASA NTRS2009

On the Importance of Small Ice Crystals in Tropical Anvil Cirrus

In situ measurements of ice crystal concentrations and sizes made with aircraft instrumentation over the past two decades have often indicated the presence of numerous relatively small (< 50 m diameter) crystals in cirrus clouds. Further, these measurements frequently indicate that small crystals account for a large fraction of the extinction in cirrus clouds. The fact that the instruments used to make these measurements, such as the Forward Scattering Spectrometer Probe (FSSP) and the Cloud Aerosol Spectrometer (CAS), ingest ice crystals into the sample volume through inlets has led to suspicion that the indications of numerous small ]crystals could be artifacts of large ]crystal shattering on the instrument inlets. We present new aircraft measurements in anvil cirrus sampled during the Tropical Composition, Cloud, and Climate Coupling (TC4) campaign with the 2 ] Dimensional Stereo (2D ]S) probe, which detects particles as small as 10 m. The 2D ]S has detector "arms" instead of an inlet tube. Since the 2D ]S probe surfaces are much further from the sample volume than is the case for the instruments with inlets, it is expected that 2D ]S will be less susceptible to shattering artifacts. In addition, particle inter ]arrival times are used to identify and remove shattering artifacts that occur even with the 2D ]S probe. The number of shattering artifacts identified by the 2D ]S interarrival time analysis ranges from a negligible contribution to an order of magnitude or more enhancement in apparent ice concentration over the natural ice concentration, depending on the abundance of large crystals and the natural small ]crystal concentration. The 2D ]S measurements in tropical anvil cirrus suggest that natural small ]crystal concentrations are typically one to two orders of magnitude lower than those inferred from CAS. The strong correlation between the CAS/2D ]S ratio of small ]crystal concentrations and large ]crystal concentration suggests that the discrepancy is likely caused by shattering of large crystals on the CAS inlet. We argue that past measurements with CAS in cirrus with large crystals present may contain errors due to crystal shattering, and past conclusions derived from these measurements may need to be revisited. Further, we present correlations between CAS spurious concentration and 2D ]S large ]crystal mass from spatially uniform anvil cirrus sampling periods as an approximate guide for estimating quantitative impact of large ]crystal shattering on CAS concentrations in previous datasets. We use radiative transfer calculations to demonstrate that in the maritime anvil cirrus sampled during TC4, small crystals indicated by 2D ]S contribute relatively little cloud extinction, radiative forcing, or radiative heating in the anvils, regardless of anvil age or vertical location in the clouds. While 2D ]S ice concentrations in fresh anvil cirrus may often exceed 1 cm.3, and are observed to exceed 10 cm.3 in turrets, they are typically ~0.1 cm.3 and rarely exceed 1 cm.3 (<1.4% of the time) in aged anvil cirrus. We hypothesize that isolated occurrences of higher ice concentrations in aged anvil cirrus may be caused by ice nucleation driven by either small ]scale convection or gravity waves. It appears that the numerous small crystals detrained from convective updrafts do not persist in the anvil cirrus sampled during TC ]4.

Jensen, E. J.↗

NASA NTRS2023

High-Energy (> 40 MeV) Proton Intensity Enhancements Associated with the Passage of Interplanetary Shocks at 1 au

We analyze periods with elevated >40 MeV proton intensities observed near Earth over a time span of 43 years (1973-2016) that coincide with the passage of interplanetary shocks. Typically, elevated proton intensities result from large solar energetic particle (SEP) events. The interplanetary shocks observed during these elevated-intensity periods may or may not be related to the origin of the SEP events. By choosing those cases when the shocks can be confidently associated with the solar eruption that generated the SEP event, we analyze the components of these SEP events that are localized in the vicinity of the shock (so-called “energetic storm particles (ESPs)"), focusing on those events where the ESP component exceeds 40 MeV. We examine the interdependence of these high-energy ESPs with (i) the properties of the solar eruptions that generated the shocks and the SEP events, and (ii) the parameters of the shocks at their arrival at 1 au. The solar eruptions at the origin of the shocks producing >40 MeV proton ESP intensity enhancements are within ±50° longitude of central meridian and are associated with fast coronal mass ejections (plane-of-sky speeds ≳1000 km s -1 ). The ESP events with the largest >40 MeV proton intensity increases tend to occur when there are structures such as intervening interplanetary coronal mass ejections and other unrelated shocks present in the solar wind through which the shock is propagating. Among the various local shock parameters considered, only the shock speed shows a certain degree of correlation with the observed ESP intensity increase.

Solar energetic particles↗

NASA NTRS2004

Application of Simulated Annealing and Related Algorithms to TWTA Design

Simulated Annealing (SA) is a stochastic optimization algorithm used to search for global minima in complex design surfaces where exhaustive searches are not computationally feasible. The algorithm is derived by simulating the annealing process, whereby a solid is heated to a liquid state and then cooled slowly to reach thermodynamic equilibrium at each temperature. The idea is that atoms in the solid continually bond and re-bond at various quantum energy levels, and with sufficient cooling time they will rearrange at the minimum energy state to form a perfect crystal. The distribution of energy levels is given by the Boltzmann distribution: as temperature drops, the probability of the presence of high-energy bonds decreases. In searching for an optimal design, local minima and discontinuities are often present in a design surface. SA presents a distinct advantage over other optimization algorithms in its ability to escape from these local minima. Just as high-energy atomic configurations are visited in the actual annealing process in order to eventually reach the minimum energy state, in SA highly non-optimal configurations are visited in order to find otherwise inaccessible global minima. The SA algorithm produces a Markov chain of points in the design space at each temperature, with a monotonically decreasing temperature. A random point is started upon, and the objective function is evaluated at that point. A stochastic perturbation is then made to the parameters of the point to arrive at a proposed new point in the design space, at which the objection function is evaluated as well. If the change in objective function values (Delta)E is negative, the proposed new point is accepted. If (Delta)E is positive, the proposed new point is accepted according to the Metropolis criterion: rho((Delta)f) = exp((-Delta)E/T), where T is the temperature for the current Markov chain. The process then repeats for the remainder of the Markov chain, after which the temperature is decremented and the process repeats. Eventually (and hopefully), a near-globally optimal solution is attained as T approaches zero. Several exciting variants of SA have recently emerged, including Discrete-State Simulated Annealing (DSSA) and Simulated Tempering (ST). The DSSA algorithm takes the thermodynamic analogy one step further by categorizing objective function evaluations into discrete states. In doing so, many of the case-specific problems associated with fine-tuning the SA algorithm can be avoided; for example, theoretical approximations for the initial and final temperature can be derived independently of the case. In this manner, DSSA provides a scheme that is more robust with respect to widely differing design surfaces. ST differs from SA in that the temperature T becomes an additional random variable in the optimization. The system is also kept in equilibrium as the temperature changes, as opposed to the system being driven out of equilibrium as temperature changes in SA. ST is designed to overcome obstacles in design surfaces where numerous local minima are separated by high barriers. These algorithms are incorporated into the optimal design of the traveling-wave tube amplifier (TWTA). The area under scrutiny is the collector, in which it would be ideal to use negative potential to decelerate the spent electron beam to zero kinetic energy just as it reaches the collector surface. In reality this is not plausible due to a number of physical limitations, including repulsion and differing levels of kinetic energy among individual electrons. Instead, the collector is designed with multiple stages depressed below ground potential. The design of this multiple-stage collector is the optimization problem of interest. One remaining problem in SA and DSSA is the difficulty in determining when equilibrium has been reached so that the current Markov chain can be terminated. It has been suggested in recent literature that simulating the thermodynamic properties opecific heat, entropy, and internal energy from the Boltzmann distribution can provide good indicators of having reached equilibrium at a certain temperature. These properties are tested for their efficacy and implemented in SA and DSSA code with respect to TWTA collector optimization.

Radke, Eric M.↗