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NASA NTRS2011

The Legacy of Space Shuttle Flight Software

The initial goals of the Space Shuttle Program required that the avionics and software systems blaze new trails in advancing avionics system technology. Many of the requirements placed on avionics and software were accomplished for the first time on this program. Examples include comprehensive digital fly-by-wire technology, use of a digital databus for flight critical functions, fail operational/fail safe requirements, complex automated redundancy management, and the use of a high-order software language for flight software development. In order to meet the operational and safety goals of the program, the Space Shuttle software had to be extremely high quality, reliable, robust, reconfigurable and maintainable. To achieve this, the software development team evolved a software process focused on continuous process improvement and defect elimination that consistently produced highly predictable and top quality results, providing software managers the confidence needed to sign each Certificate of Flight Readiness (COFR). This process, which has been appraised at Capability Maturity Model (CMM)/Capability Maturity Model Integration (CMMI) Level 5, has resulted in one of the lowest software defect rates in the industry. This paper will present an overview of the evolution of the Primary Avionics Software System (PASS) project and processes over thirty years, an argument for strong statistical control of software processes with examples, an overview of the success story for identifying and driving out errors before flight, a case study of the few significant software issues and how they were either identified before flight or slipped through the process onto a flight vehicle, and identification of the valuable lessons learned over the life of the project.

Hickey, Christopher J.↗

NASA NTRSDate not supplied

Thermal Vacuum and Vibration Testing of the Differential Thermal Expansion Thermal Switch

The Extended Stroke, Reverse Operation, Differential Expansion Thermal Switch for Extreme Variable Environments uses materials with both positive and negative coefficients of thermal expansion (CTE) arranged in concentric cylinders so that the thermal switch (TS) operates passively, opening a gap between interfaces to create a low thermal contact when cold, and closing the gap between interfaces to create a high thermal contact when hot. This paper details the testing of the TS at Marshall Space Flight Center including the pre-vibe thermal vacuum cycle test, vibration test, post-vibe thermal vacuum cycle test, and long duration thermal vacuum cycle test. The pre- and post-vibe thermal cycle and the long duration cycle test tested to hot and cold plateau initial temperatures of 40 °C, and -173 °C, respectively. The pre- and post-vibe tests required plateau holds of at least 2 hours, whereas the long duration cycle test required plateau holds of at least 20 hours. The tests each used a rate of temperature change of < 2 °C/min when transitioning between plateaus. The data collected from each thermal test is compared to show the operation of the TS both before and after the vibration test to GEVS levels, and throughout the long duration cycle test. From the data collected, the total conductance through the TS interfaces is calculated for both on (TS closed – during hot plateau) and off (TS open – during cold plateau) configurations, and the turndown ratio is also calculated. Challenges and lessons learned from the testing are also discussed.

thermal control technology↗

NASA NTRS2003

Exploring Asteroid Interiors: The Deep Interior Mission Concept

Deep Interior is a mission to determine the geophysical properties of near-Earth objects, including the first volumetric image of the interior of an asteroid. Radio reflection tomography will image the 3D distribution of complex dielectric properties within the ~1 km rendezvous target and hence map structural, density or compositional variations. Laser altimetry and visible imaging will provide high-resolution surface topography. Smart surface pods culminating in blast experiments, imaged by the high frame rate camera and scanned by lidar, will characterize active mechanical behavior and structure of surface materials, expose unweathered surface for NIR analysis, and may enable some characterization of bulk seismic response. Multiple flybys en route to this target will characterize a diversity of asteroids, probing their interiors with non-tomographic radar reflectance experiments. Deep Interior is a natural follow-up to the NEARShoemaker mission and will provide essential guidance for future in situ asteroid and comet exploration. While our goal is to learn the interior geology of small bodies and how their surfaces behave, the resulting science will enable pragmatic technologies required of hazard mitigation and resource utilization.

Asphaug, E.↗

NASA NTRS2004

Space-Based Telemetry And Range Safety Flight Demonstration #1

The basic ability of STARS to maintain a satellite communications link with TDRSS satellites during dynamic aircraft flights was successfully demonstrated during FD 1. The Range Safety and Range User systems' link margins were measured. The ability to acquire/reacquire and maintain lock between a high-dynamic vehicle and a satellite-based system was demonstrated. The Range Safety system simultaneously received and processed command links from space and ground transmitters and provided near real-time Range Safety telemetry to DFRC, which then sent it in near real time to KSC, GSFC, and WFF for monitoring. The GPS receiver maintained track except during extremely dynamic maneuvers. The Range User system sent data at three different data rates. There were excellent cooperation and support from the different Centers, contractors, and Ranges. A large amount of data was recorded and extensive post-flight analysis was performed. The Range User TDRSS link margin met or exceeded the predicted performance at three different data rates. The Range Safety launch-head link margins generally agreed with the predicted performance. The UPS positions and velocities agreed with those from tracking radar to within about 20 m and a few rn/s. The link margins for the Range Safety TDRSS telemetry link were less than expected. The link margin for one TDRSS command link LPT channel was occasionally much less than the other. Additional post-flight testing has yet to identify the root causes of these results. There were many lessons learned from this first set of test flights. The most important one is that more time and testing are needed for each step to deal with the inevitable problems. It is vital that these lessons be among the primary areas of study that will carry over from FD#1 to FD#2, which is currently scheduled for early FY05 at DFRC and will use a specially designed Ku-band phased array antenna for the Range User system. The next series of flight demonstrations scheduled for late 2004 at DFRC will incorporate many lessons learned from FD#1. A specially designed Ku-band phased array antenna will be used with the Range User system. A test flight on a hypersonic vehicle is planned by the end of 2006.

Demspm. Erol↗

NASA NTRS2014

Engineering Antifragile Systems: A Change In Design Philosophy

While technology has made astounding advances in the last century, problems are confronting the engineering community that must be solved. Cost and schedule of producing large systems are increasing at an unsustainable rate and these systems often do not perform as intended. New systems are required that may not be achieved by current methods. To solve these problems, NASA is working to infuse concepts from Complexity Science into the engineering process. Some of these problems may be solved by a change in design philosophy. Instead of designing systems to meet known requirements that will always lead to fragile systems at some degree, systems should be designed wherever possible to be antifragile: designing cognitive cyberphysical systems that can learn from their experience, adapt to unforeseen events they face in their environment, and grow stronger in the face of adversity. Several examples are presented of on ongoing research efforts to employ this philosophy.

Jones, Kennie H.↗

NASA NTRS2016

Reliability and Maintainability Analysis for the Amine Swingbed Carbon Dioxide Removal System

I have performed a reliability & maintainability analysis for the Amine Swingbed payload system. The Amine Swingbed is a carbon dioxide removal technology that has gone through 2,400 hours of International Space Station on-orbit use between 2013 and 2016. While the Amine Swingbed is currently an experimental payload system, the Amine Swingbed may be converted to system hardware. If the Amine Swingbed becomes system hardware, it will supplement the Carbon Dioxide Removal Assembly (CDRA) as the primary CO2 removal technology on the International Space Station. NASA is also considering using the Amine Swingbed as the primary carbon dioxide removal technology for future extravehicular mobility units and for the Orion, which will be used for the Asteroid Redirect and Journey to Mars missions. The qualitative component of the reliability and maintainability analysis is a Failure Modes and Effects Analysis (FMEA). In the FMEA, I have investigated how individual components in the Amine Swingbed may fail, and what the worst case scenario is should a failure occur. The significant failure effects are the loss of ability to remove carbon dioxide, the formation of ammonia due to chemical degradation of the amine, and loss of atmosphere because the Amine Swingbed uses the vacuum of space to regenerate the Amine Swingbed. In the quantitative component of the reliability and maintainability analysis, I have assumed a constant failure rate for both electronic and nonelectronic parts. Using this data, I have created a Poisson distribution to predict the failure rate of the Amine Swingbed as a whole. I have determined a mean time to failure for the Amine Swingbed to be approximately 1,400 hours. The observed mean time to failure for the system is between 600 and 1,200 hours. This range includes initial testing of the Amine Swingbed, as well as software faults that are understood to be non-critical. If many of the commercial parts were switched to military-grade parts, the expected mean time to failure would be 2,300 hours. Both calculated mean times to failure for the Amine Swingbed use conservative failure rate models. The observed mean time to failure for CDRA is 2,500 hours. Working on this project and for NASA in general has helped me gain insight into current aeronautics missions, reliability engineering, circuit analysis, and different cultures. Prior my internship, I did not have a lot knowledge about the work being performed at NASA. As a chemical engineer, I had not really considered working for NASA as a career path. By engaging in interactions with civil servants, contractors, and other interns, I have learned a great deal about modern challenges that NASA is addressing. My work has helped me develop a knowledge base in safety and reliability that would be difficult to find elsewhere. Prior to this internship, I had not thought about reliability engineering. Now, I have gained a skillset in performing reliability analyses, and understanding the inner workings of a large mechanical system. I have also gained experience in understanding how electrical systems work while I was analyzing the electrical components of the Amine Swingbed. I did not expect to be exposed to as many different cultures as I have while working at NASA. I am referring to both within NASA and the Houston area. NASA employs individuals with a broad range of backgrounds. It has been great to learn from individuals who have highly diverse experiences and outlooks on the world. In the Houston area, I have come across individuals from different parts of the world. Interacting with such a high number of individuals with significantly different backgrounds has helped me to grow as a person in ways that I did not expect. My time at NASA has opened a window into the field of aeronautics. After earning a bachelor's degree in chemical engineering, I plan to go to graduate school for a PhD in engineering. Prior to coming to NASA, I was not aware of the graduate Pathways program. I intend to apply for the graduate Pathways program as positions are opened up. I would like to pursue future opportunities with NASA, especially as my engineering career progresses.

Dunbar, Tyler↗

NASA NTRS2018

The Zwicky Transient Facility: Data Processing, Products, and Archive

The Zwicky Transient Facility (ZTF) is a new robotic time-domain survey currently in progress using the Palomar 48-inch Schmidt Telescope. ZTF uses a 47 square degree field with a 600 megapixel camera to scan the entire northern visible sky at rates of ∼3760 square degrees/hour to median depths of g ~ 20.8 and r ~ 20.6 mag (AB, 5σ in 30 sec). We describe the Science Data System that is housed at IPAC, Caltech. This comprises the data-processing pipelines, alert production system, data archive, and user interfaces for accessing and analyzing the products. The real-time pipeline employs a novel image-differencing algorithm, optimized for the detection of point-source transient events. These events are vetted for reliability using a machine-learned classifier and combined with contextual information to generate data-rich alert packets. The packets become available for distribution typically within 13 minutes (95th percentile) of observation. Detected events are also linked to generate candidate moving-object tracks using a novel algorithm. Objects that move fast enough to streak in the individual exposures are also extracted and vetted. We present some preliminary results of the calibration performance delivered by the real-time pipeline. The reconstructed astrometric accuracy per science image with respect to Gaia DR1 is typically 45 to 85 milliarcsec. This is the RMS per-axis on the sky for sources extracted with photometric S/N ≥10 and hence corresponds to the typical astrometric uncertainty down to this limit. The derived photometric precision (repeatability) at bright unsaturated fluxes varies between 8 and 25 millimag. The high end of these ranges corresponds to an airmass approaching ∼2—the limit of the public survey. Photometric calibration accuracy with respect to Pan-STARRS1 is generally better than 2%. The products support a broad range of scientific applications: fast and young supernovae; rare flux transients; variable stars; eclipsing binaries; variability from active galactic nuclei; counterparts to gravitational wave sources; a more complete census of Type Ia supernovae; and solar-system objects.

Frank J. Masci↗

NASA NTRSDate not supplied

Laser Beam Welding Advancements for In-Space Servicing, Assembly, and Manufacturing

NASA is currently working to develop in-space servicing, assembly, and manufacturing (ISAM) capabilities for low Earth orbit and the lunar surface. One crucial technology for this effort is laser beam welding. Laser systems can perform joining, cleaning, cutting, and repair activities, which will enable the construction of large in-space structures that could not fit on a single launch vehicle, such as trusses for solar panels, radiators, or communications infrastructure. Multiple projects studying laser welding for space applications are currently underway at NASA Marshall Space Flight Center. One of these, the DIsk-Shaped Configurable and Modular vAcuum uNit (DISCMAN), is a compact vacuum chamber designed to support parameter development for laser welding in microgravity. It contains a rotating platen with weld samples made from aluminum, steel, and titanium, a high-power infrared laser, and integrated pumps for pulling vacuum inside the sample cartridge. The DISCMAN payload is planned to launch to the International Space Station, where welds will be performed under sustained microgravity inside the Bishop Airlock. Another effort underway at Marshall is the Lunar Assembly and Servicing by Autonomous Robotics (LASAR) initiative. This project uses a space-rated robotic arm equipped with a laser weld head, wire feeder, and multiple cameras to perform welds in a thermal vacuum chamber simulating the lunar surface environment. Some of these welds are done on snowflake joints, which are specially designed to slot together to join segments of trussN structures, allowing for the construction of tall surface infrastructure. DISCMAN, LASAR, and other projects are being carried out to advance the technological maturity of in-space laser beam welding, collect data to inform computational models, and learn reliable processes for creating weld joints in space. This work supports NASA’s greater goals to expand humanity’s presence in low Earth orbit, establish a permanent moon base, and eventually send crewed missions to Mars and beyond.

Manufacturing↗

NASA NTRSDate not supplied

Laser Beam Welding Advancements for In-Space Servicing, Assembly, and Manufacturing

Robotics↗

NASA NTRS1998

Mars Atmospheric Dynamics

The Martian atmosphere is dynamically similar to the Earth's. Its spin-axis rotation rate is only minutes longer than Earth's so the Coriolois force is nearly identical to Earth's. The inclination of its spin axis is also similar to Earth's giving it similarity in seasonal change. And the Martian atmosphere is nearly transparent to solar radiation (except during dust periods) such that it is heated primarily by upwelling infrared radiation from the surface. These characteristics make Mars an ideal laboratory for studying the dynamics of rapidly rotating differentially heated atmospheres. This talk reviews what we have learned about Mars atmospheric dynamics and how if compares with Earth. The source of information to make such a comparison comes from observations and models. The former are sparse and that the latter have played a major role in shaping our thinking about the general circulation on Mars. However, the models need validation. Fortunately, the first two orbiters in NASA's Mars Surveyor Program have instrumentation to address many of the issues related to the general circulation and climate of Mars. The first, Mars Global Surveyor, is already at Mars gathering data. The second, the Mars 98 Orbiter to be launched later this year, carries a dedicated atmospheric sounder. Thus, much will be learned about Mars' atmosphere in the next few years.

Haberle, Robert↗

NASA NTRS2002

Flight Evaluation of the Army/NASA Variable Stability Fly-by-Wire Rotorcraft Aircrew Systems Concept Airborne Laboratory (RASCAL) JUH-60A

NASA Ames Research Center and the U.S. Army Aeroflight dynamics Directorate (AFDD) have performed initial flight evaluations of the Research Flight Control System (RFCS) integrated into the Army/NASA Rotorcraft Aircrew Systems Concepts Airborne Laboratory (RASCAL) JUH-GOA. The highly modified JUH-GOA Black Hawk helicopter is a full authority, high bandwidth, variable stability, in-flight simulator designed to support development of advanced flight control, sensor, and integrated display and control technologies in a fail safe environment. Preparation for flight test required an extensive hazard analysis and ground testing to ensure proper system operation. A hardware in the loop development facility was utilized to evaluate control law stability following software changes, assess servo hardover upset conditions during manual and monitor disengagements and provide pilot familiarization of test techniques and software changes prior to flight. First engagement of the RFCS was conducted on 31 Aug 2001. RFCS transfer system operation, envelope expansion and a limited rate monitor evaluation have been completed with low bandwidth and model following control laws. The presentation will discuss the following - System overview including aircraft modifications and integrated development facilities used with the RASCAL facility. - Preliminary hazard identification and mitigation prior to flight test. - Ground testing used to qualify the RFCS transfer system and verify fault monitor operation. - Flight test results of low-bandwidth and model following control law evaluations including maneuver agility, control limitations, fault monitor reliability, and recovery from manual and monitor disengagement. - Lessons learned including test techniques using a passive three-axis sidearm controller, the value of the development facility in reducing risk and crew coordination issues related to the operation of a full authority, variable stability platform. - Future research and modifications planned for the RASCAL aircraft.

Dave Arterburn↗

NASA NTRS1986

What have we learned about galaxies through large computations?

Numerical models permit modelling processes within galaxies that are seemingly beyond the reach of physical contact or close-up viewing from different angles. N-body equations permit simple computations of the interactions of individual stars within galaxies, but the motions of these objects feature nonlinear characteristics because of the forces exerted by the complex as a whole which are not amenable to examination with Newtonian laws of force. The models have, however, revealed that thin disk galactic are not stable forms, that barlike structures rotating end-over-end are more stable structures, and that galactic contraction occurs during collisions between galaxies. Internal effects have been successfully predicted for galaxies which are part of clusters, growth rate disturbances due to the expansion of the Universe have been quantified as 2-3 percent and dynamical friction has been shown to damage galaxies which are sliding into background material.

Miller, R. H.↗

NASA NTRS2008

Object Recognition using Feature- and Color-Based Methods

An improved adaptive method of processing image data in an artificial neural network has been developed to enable automated, real-time recognition of possibly moving objects under changing (including suddenly changing) conditions of illumination and perspective. The method involves a combination of two prior object-recognition methods one based on adaptive detection of shape features and one based on adaptive color segmentation to enable recognition in situations in which either prior method by itself may be inadequate. The chosen prior feature-based method is known as adaptive principal-component analysis (APCA); the chosen prior color-based method is known as adaptive color segmentation (ACOSE). These methods are made to interact with each other in a closed-loop system to obtain an optimal solution of the object-recognition problem in a dynamic environment. One of the results of the interaction is to increase, beyond what would otherwise be possible, the accuracy of the determination of a region of interest (containing an object that one seeks to recognize) within an image. Another result is to provide a minimized adaptive step that can be used to update the results obtained by the two component methods when changes of color and apparent shape occur. The net effect is to enable the neural network to update its recognition output and improve its recognition capability via an adaptive learning sequence. In principle, the improved method could readily be implemented in integrated circuitry to make a compact, low-power, real-time object-recognition system. It has been proposed to demonstrate the feasibility of such a system by integrating a 256-by-256 active-pixel sensor with APCA, ACOSE, and neural processing circuitry on a single chip. It has been estimated that such a system on a chip would have a volume no larger than a few cubic centimeters, could operate at a rate as high as 1,000 frames per second, and would consume in the order of milliwatts of power.

Duong, Tuan↗

NASA NTRSDate not supplied

Validation of Fitness for Duty Standards Using Pre- and Post-Flight Capsule Egress and Suited Functional Performance Tasks in Simulated Reduced Gravity

The transition between gravity environments will involve one of the most complex, high-risk phases of any mission. For example, the reduced functional capacity caused by physiological deconditioning adaptations in microgravity coupled with the stressors of re-entry into partial gravity environments will increase risks to crew, even with rigorous adherence to inflight countermeasures. Quantification of the astronauts’ post-landing functional performance is necessary to design ConOps for exploration missions. Specifically, these two high-risk scenarios may be required to be performed soon after gravity transitions: • Nominal and/or emergency unassisted capsule egress task after return to Earth • Planetary extravehicular activity (EVA) soon after landing on Mars or the Moon This study is broken down into two phases. Phase 1: A feasibility study that will assess the overall feasibility and demonstrate the capability to do these tasks shortly after landing. Phase 2: the full Egress Fitness study, which is part of the CIPHER complement. This study uses a task-based approach to characterize functional performance of these high-risk scenarios in long-duration ISS crewmembers before flight and shortly after return to Earth. Prior to any testing, each astronaut subject completes a suit fit check to ensure adequate sizing and a mobility assessment to confirm completion of the EVA tasks. Pilot Egress Fitness pre-flight and post-flight testing includes an Earth-based emergency egress out of a functional capsule mockup and a short Mars gravity EVA simulation including suit donning, hatch egress, ladder descent, task board cable operations, baggage transfer over sand/rocky regolith, alignment with a rear entry port, and suit egress. Pre-flight testing will occur at any time point prior to flight. Post-flight assessment is much more critical with the capsule egress test that will occur 1–4 hours after landing and the planetary EVA approximately 18–36 hours after landing. The CIPHER study will incorporate additional pre-flight sessions, longer EVA tasks that include traverse and geology sampling, and post-flight sessions on R+1, 4, and 8 to characterize the timeframe of recovery. Data collected for both tasks include task completion time, photo, and video. The EVA portion also includes collection of metabolic and heart rate. Pilot Egress Fitness study has completed both baseline and post-flight testing on four astronaut subjects, with all four able to complete post-flight EVA testing and three able to complete postflight capsule egress testing. Preliminary results observe individual physiological variations, which were to be expected but also suggest the need to carefully track the timeline from undock to landing to testing. Furthermore, some task performance instructions and equipment may need to be adjusted to ensure results are primarily physiological. These and other lessons learned will be addressed with minor protocol changes in the full CIPHER Egress Fitness study.

J R Norcross↗

NASA NTRS2012

Thermostructural Analysis of the SOFIA Fine Field and Wide Field Imagers Subjected to Convective Thermal Shock

The Stratospheric Observatory For Infrared Astronomy (SOFIA) is a highly modified Boeing 747-SP with a 17- ton infrared telescope installed in the aft portion of the aircraft. Unlike ground- and space-based platforms, SOFIA can deploy to make observations anytime, anywhere, in the world. The originally designed aircraft configuration included a ground pre-cool system, however, due to various factors in the history of the project, that system was not installed. This lack of ground pre-cooling was the source of the concern about whether or not the imagers would be exposed to a potentially unsafe thermostructural environment. This concern was in addition to the already-existing concern of some project members that the air temperature rate of change during flight (both at the same altitude as well as ascent or descent) could cause the imagers to be exposed to an unsafe thermostructural environment. Four optical components were identified as the components of concern: two of higher concern (one in each imager), and two of lower concern (one in each imager). The analysis effort began by analyzing one component, after which the analyses for the other components was deemed unnecessary. The purpose of this report is to document these findings as well as lessons learned from the effort.

Kostyk, Christopher B.↗

NASA NTRS2010

NASA Astronauts on Soyuz: Experience and Lessons for the Future

The U. S., Russia, and, China have each addressed the question of human-rating spacecraft. NASA's operational experience with human-rating primarily resides with Mercury, Gemini, Apollo, Space Shuttle, and International Space Station. NASA s latest developmental experience includes Constellation, X38, X33, and the Orbital Space Plane. If domestic commercial crew vehicles are used to transport astronauts to and from space, Soyuz is another example of methods that could be used to human-rate a spacecraft and to work with commercial spacecraft providers. For Soyuz, NASA's normal assurance practices were adapted. Building on NASA's Soyuz experience, this report contends all past, present, and future vehicles rely on a range of methods and techniques for human-rating assurance, the components of which include: requirements, conceptual development, prototype evaluations, configuration management, formal development reviews (safety, design, operations), component/system ground-testing, integrated flight tests, independent assessments, and launch readiness reviews. When constraints (cost, schedule, international) limit the depth/breadth of one or more preferred assurance means, ways are found to bolster the remaining areas. This report provides information exemplifying the above safety assurance model for consideration with commercial or foreign-government-designed spacecraft. Topics addressed include: U.S./Soviet-Russian government/agency agreements and engineering/safety assessments performed with lessons learned in historic U.S./Russian joint space ventures

Source record↗

NASA NTRS2023

A Regional Map of Mangrove Extent for Myanmar, Thailand, and Cambodia Shows Losses of 44% By 1996

Southeast Asia is home to some of the planet’s most carbon-dense and biodiverse mangrove ecosystems. There is still much uncertainty with regards to the timing and magnitude of changes in mangrove cover over the past 50 years. While there are several regional to global maps of mangrove extent in Southeast Asia over the past two decades, data prior to the mid-1990s is limited due to the scarcity of Earth Observation data of sufficient quality and the historical limitations to publicly available EO. We present a classification of mangrove extent using Landsat 1-2 MSS Tier 2 data from 1972-1977 for three Southeast Asian countries: Myanmar, Thailand, and Cambodia. Mangrove extent land cover maps were generated using a Random Forest machine learning algorithm that effectively mapped a total of 15,420.51 km2. Accuracy assessments indicated that the classification for the mangrove and non-mangrove class had a producer’s accuracy of 79.63 % and 98.24 %a user’s accuracy of 89.58 % and 96.21 %, and an overall accuracy of 95.26 % . We found a decline of 6,830 km2 between the 1970’s and 2020, showing that44.29% of the mangrove area in these countries has been lost in the past 48 years. Most of this loss occurred between the 1970’s and 1996; rates of deforestation declined dramatically after 1996. This study also urges that these results be considered within the context of the local need for these coastal resources that helped them endure the political and financial challenges of their coastal homes.

Priscilla Baltezar↗

NASA NTRS1989

Choice of gauge in 2-photon 1s-2s transition in atomic hydrogen and pseudostate expansions

The problem of gauge choice in multiphoton transitions in connection with the proper choice of the unperturbed wave functions require to insure gauge invariance was considered. J. Bassani, J. J. Forney, and A. Quattropani considered the case of 2-photon 1s-2s transition rate for hydrogen, using gauges vector E x vector r and vector A x vector p. Exactly the same results were obtained for the two gauges, but the findings indicate that the vector E x vector r interaction tends to the final result with a small number of intermediate states and is therefore the one to be used in any approximate calculation. Whether the so-called pseudostate expansion method works equally well with either gauge was tested. To accomplish this task, in addition to researching the problem, the FORTRAN programming was learned and a FORTRAN program was constructed for the calculation of the dimensionless 2-photon transition probability amplitude D(v) for 1s-2s transition in Hydrogen as a function as a function of the incident photon frequency v in gauge vector E x vector p at certain values of v, using the pseudostate method. However, some puzzling unresolved difficulties were experienced in the calculation. Then should the pseudostate calculations prove successful for gauge vector E x vector r the method will be applied to gauge vector A x vector p. If successful, then the problem is complete.

Shabazz, Abdulalim A.↗