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Development and Implementation of a Small Satellite Systems Engineering Webinar Series: A Collaboration Between United Nations Office for Outer Space Affairs and National Aeronautics and Space Administration

The United Nations Office for Outer Space Affairs (UNOOSA) in collaboration with the National Aeronautics and Space Administration (NASA) established a webinar series on NASA systems engineering standards and practices for the purpose of sharing knowledge in this area through UNOOSA’s “Access to Space for All” which provides free and accessible educational content. Through NASA’s Small Spacecraft Systems Virtual Institute (S3VI), the four-part series was designed to cover basic systems engineering and project management skills that are fundamental for planning, developing, and implementing an experiment or a space project, and that serve as critical knowledge for those engaged in space activities, whether as a designer, builder, or manager of space infrastructure and services. This first series of webinars was convened over the course of November 2023 through February 2024. The webinar series was segmented into four one and a half hour webinars which covered topics related to the Fundamentals of Systems Engineering, Requirements and Systems Engineering, System Assembly, Integration and Test, and Spacecraft Handling, as well as an Introduction to the Small Spacecraft Systems Virtual Institute (S3VI). The agendas for the first three webinars focused on addressing a number of questions relevant to a particular topic. Examples of these questions include: What is systems engineering and what does a systems engineer do? Why does NASA use systems engineering? How do you define requirements for a small spacecraft mission? Why are requirements important to space missions? How are trade studies used to determine parts selection and why are they important? The final webinar of the first series provided interactive discussions and demonstrations of the S3VI tools; shared information on additional webinar opportunities offered by the S3VI; and reviewed databases curated by the S3VI that include the Small Satellite Reliability Initiative (SSRI) Knowledge Base Tool, Mission Design Tools, Small Spacecraft Information Search, and the State-of-the-Art (SoA) Small Spacecraft Report. Future webinar series will be conducted with topics are to be determined. The presenter will discuss details related to the first webinar series and future plans for additional series.

systems engineering↗

TIE02. IGARSS’2024 Townhall on “Digital Twins for Earth Science

NASA, ESA, NOAA, CNES and several other international organizations have started programs to design and develop Digital Twins of the Earth and/or Earth systems. Earth Systems Digital Twins (ESDTs) are dynamic and interactive information systems for understanding, forecasting, and conjecturing the complex interconnections among Earth systems, including anthropomorphic forcings and impacts to humanity. Organized around interconnected, multi-domain, high-scale modeling capabilities, the three major components of an Earth System Digital Twin are a continuously updated Digital Replica of the Earth System of interest (or “What Now”), dynamic Forecasting models (or “What Next”), and Impact Assessment capabilities (or “What If”). ESDTs provide unified, comprehensive representations and predictions that can be utilized for monitoring the health of the Planet, as well as for developing actionable information to support decision making. More generally, Digital Twins will help researchers better understand the fundamental Earth systems that impact everything from wildfires to climate change. This Townhall will provide a status of Destination Earth as well as ESA’s, NASA’s, CNES’s and NOAA’s current independent and common efforts in Digital Twins; then the four organizations will provide information about community building before engaging a dialogue about Digital Twins of the Earth with the IGARSS community.

Earth Science Remote Sensing; Information Systems;↗

Atomic oxygen interaction with spacecraft materials: Relationship between orbital and ground-based testing for materials certification

The effects of atomic oxygen on boron nitride (BN), silicon nitride (Si3N4), Intelsat 6 solar cell interconnects, organic polymers, and MoS2 and WS2 dry lubricant, were studied in Low Earth Orbit (LEO) flight experiments and in a ground based simulation facility. Both the inflight and ground based experiments employed in situ electrical resistance measurements to detect penetration of atomic oxygen through materials and Electron Spectroscopy for Chemical Analysis (ESCA) analysis to measure chemical composition changes. Results are given. The ground based results on the materials studied to date show good qualitative correlation with the LEO flight results, thus validating the simulation fidelity of the ground based facility in terms of reproducing LEO flight results. In addition it was demonstrated that ground based simulation is capable of performing more detailed experiments than orbital exposures can presently perform. This allows the development of a fundamental understanding of the mechanisms involved in the LEO environment degradation of materials.

Cross, Jon B.↗

Broad-Band Measurements of Cen X-3 With XTE and CGRO

Centaurus X-3 has played a key role in the development of our understanding of galactic x-ray binary sources. Timing analysis of the UHURU x-ray observations for the luminous Cen X-3 source (L approximately 10(exp 38) erg/s) revealed the first evidence for coherent x-ray pulsations from an object in a binary system (Giaconni 1971; Schreier 1972). It was quickly understood that the luminous pulsed x-ray emission could be generated by the accretion of matter from a companion star onto a rotating neutron star and led to the adoption of binary star models as the fundamental model for galactic x-ray sources (e.g. Pringle and Rees 1972; Lamb 1973). Based on modeling and refined observations since the original measurements, we now believe that Cen X-3 is a high mass x-ray binary system that contains a disk-fed pulsar with a period of 4.84 seconds that is in a 2.087 day orbit around an O-star companion. Since the pulsar discovery, its period has been intermittently monitored and those studies show a long term spin-up of the pulsar punctuated by short intervals of spin-down (e.g. Finger 1994). The implied torques are thought to originate from the interaction of an accretion disk with the magnetic field of a neutron star (Ghosh and Lamb 1979).

Vestrand, W. Thomas↗

Propagation of Interplanetary Disturbances in the Outer Heliosphere

Contents include the following: 1. We have developed a one-dimensional, spherically symmetric, multi-fluid MHD model that includes solar wind protons and electrons, pickup ions, and interstellar neutral hydrogen. This model advances the existing solar wind models for the outer heliosphere in two important ways: one is that it distinguishes solar wind protons from pickup ions, and the other is that it allows for energy transfer from pickup ions to the solar wind protons. Model results compare favorably with the Voyager 2 observations. 2. 2. Solar wind slowdown and interstellar neutral density. The solar wind in the outer heliosphere is fundamentally different from that in the inner heliosphere since the effects of interstellar neutrals become significant. 3. ICME propagation from the inner to outer heliosphere. Large coronal mass ejections (CMEs) have major effects on the structure of the solar wind and the heliosphere. The plasma and magnetic field can be compressed ahead of interplanetary CMEs. 4. During the current solar cycle (Cycle 23), several major CMEs associated with solar flares produced large transient shocks which were observed by widely-separated spacecraft such as Wind at Earth and Voyager 2 beyond 60 AU. Using data from these spacecraft, we use the multi-fluid model to investigate shock propagation and interaction in the heliosphere. Specifically, we studied the Bastille Day 2000, April 2001 and Halloween 2003 events. 5. Statistical properties of the solar wind in the outer heliosphere. In a collaboration with L.F. Burlaga of GSFC, it is shown that the basic statistical properties of the solar wind in the outer heliosphere can be well produced by our model. We studied the large-scale heliospheric magnetic field strength fluctuations as a function of distance from the Sun during the declining phase of a solar cycle, using our numerical model with observations made at 1 AU during 1995 as input. 6. Radial heliospheric magnetic field events. The heliospheric magnetic field (HMF) direction, on average, conforms well to the Parker spiral.

Wang, Chi↗

Direct Analysis of Early Solar System Aqueous Fluids

We lack fundamental information on early solar system aqueous fluids. Fluid inclusions are present in carbonates, sulfides and halides in astro materials, whose characterization is finally becoming feasible. The ordinary chondrite regolith breccias Monahans 1998 (H5) and Zag (H3-6)contain fluid inclusion-bearing halite (NaCl) crystals dated at~4.5 billion years old. Freezing studies to measure the eutectic temperature demonstrated that the brines likely contain divalent cations(Ca, Mg, Fe). Halite is effective at preservation (at least 250 MY) of organic phases and structures. Thus, compositional data on fluid inclusions in halite will reveal unique information on the origin and activity of aqueous fluids in the early solar system, and interactions with organics. To measure fluid compositions from individual fluid inclusions we performed TOF-SIMS depth profiling a tultra-high vacuum at ~110 Kusing a 30 kVBi+analysis ion beam and a1 kVO2+sputtering ion beam. Halite fluid inclusion FI1 contains H2O, K,Na,Cl and NaCl•2H2O.FI2 contains H2O, K, Na, Cl, Al, Fe,Ca,NaCl•2H2O and C-N-O-H species originating from organic molecules. Mass overlap with NaOH species prevented definitive identification of Cain FI1.

M. E Zolensky↗

Engineering of Novel Biocolloid Suspensions

Colloidal suspensions are materials with a variety of uses from cleaners and lubricants to food, cosmetics, and coatings. In addition, they can be used as a tool for testing the fundamental tenets of statistical physics. Colloidal suspensions can be synthesized from a wide variety of materials, and in the form of monodisperse particles, which can self-assemble into highly ordered colloidal crystal structures. As such they can also be used as templates for the construction of highly ordered materials. Materials design of colloids has, to date, relied on entropic self-assembly, where crystals form as result of lower free energy due to a transition to order. Here, our goal is to develop a completely new method for materials fabrication using colloidal precursors, in which the self-assembly of the ordered colloidal structures is driven by a highly controllable, attractive interaction. This will greatly increase the range of potential structures that can be fabricated with colloidal particles. In this work, we demonstrate that colloidal suspensions can be crosslinked through highly specific biological crosslinking reactions. In particular, the molecules we use are protein-carbohydrate interactions derived from the immune system. This different driving force for self-assembly will yield different and novel suspensions structures. Because the biological interactions are heterotypic (A binding to B), this chemical system can be used to make binary alloys in which the two colloid subpopulations vary in some property - size, density, volume fraction, magnetic susceptibility, etc. An additional feature of these molecules which is unique - even within the realm of biological recognition - is that the molecules bind reversibly on reasonable time-scales, which will enable the suspension to sample different configurations, and allow us to manipulate and measure the size of the suspension dynamically. Because of the wide variety of structures that can be made from these novel colloids, and because the suspension structure can be altered dynamically, we believe this biocolloid system will yield a novel set of materials with many technological applications, including sensors (both biological and non-biological), optical filters and separation media.

Hammer, D. A.↗

Measured Activities of Al and Ni in gamma-(Ni) and gamma'-(Ni)3Al in the Ni-Al-Pt System

Adding Pt to Ni-Al coatings is critical to achieving the required oxidation protection of Ni-based superalloys, but the nature of the Pt effect remains unresolved. This research provides a fundamental part of the answer by measuring the influence of Pt on the activities of Al and Ni in gamma-(Ni), gamma prime-(Ni)3Al and liquid in the Ni-Al-Pt system. Measurements have been made at 25 compositions in the Ni-rich corner over the temperature range, T = 1400-1750 K, by the vapor pressure technique with a multiple effusion-cell mass spectrometer (multi-cell KEMS). These measurements clearly show adding Pt (for X(sub Pt) less than 0.25) decreases a(Al) while increasing a(Ni). This solution behavior supports the idea that Pt increases Al transport to an alloy / Al2O3 interface and also limits the interaction between the coating and substrate alloys in the gamma-(Ni) + gamma prime-(Ni)3Al region. This presentation will review the progress of this study.

Copland, Evan↗

Cloud Uniformity Measurement from NASA's 2nd Fundamental Ice Crystal Icing Test - Part 2 (Temperature and Humidity)

This paper provides a characterization of the temperature and humidity variations within icing cloud flows generated during the second Fundamental Ice Crystal Icing Physics test conducted in NASA’s Propulsion Systems Laboratory, in June of 2018. The tests were conducted at airflow velocities of 85, 135, and 185 m/s, a static pressure of 44.8 kPa, and a total temperature of 7.2 ⁰C. A custom rearward facing probe and commercial total air temperature probe were used to obtain temperature and humidity profiles of the icing cloud flow leaving the exit duct plane. Additional background humidity measurements were also obtained from a commercial total water content probe. The probes captured the changes in temperature and humidity that took place at the test section after the cloud was activated. As the main altitude airflow interacts with the icing cloud, their thermodynamic properties undergo substantial changes. Due to the particle nature of the icing cloud, the droplets and ice crystals tend to redistribute within the cloud as it propagates with the main flow. Data will be presented that shows how these factors affect the thermodynamic property distribution within the icing cloud. A discussion is given of the thermal balances in the icing cloud, between the evaporating spray droplets and the airflow, as a basis for interpreting the measured results.

Crystal Icing↗

A Break In the Size-Stellar Mass Relation: Evidence for Quenching and Feedback in Dwarf Galaxies

Mapping stars and gas in nearby galaxies is fundamental for understanding their growth and the impact of their environment. This issue is addressed by comparing the stellar ‘edges’ of galaxies D stellar, defined as the outermost diameter where in situ star formation significantly drops, with the gaseous distribution parameterized by the neutral atomic hydrogen diameter measured at 1M⊙/pc2,DHI. By sampling a broad HI mass range 105M⊙< MHI<1011M⊙, we find several dwarf galaxies withMHI<109M⊙from the field and Fornax Cluster which are distinguished by D stellar>> DHI. For the cluster dwarfs, the average HI surface density near D stellar is∼0.3M⊙/pc2, reflecting the impact of quenching and outside-in gas removal from ram pressure and tidal interactions. In comparison, D stellar/DHI ranges between 0.5–2 in dwarf field galaxies, consistent with the expectations from stellar feedback. Only more massive disk galaxies in the field can thus be characterized by the common assumption that D stellar≲DHI. We discover a break in the D stellar−M⋆relation atm break∼4×108M⊙that potentially differentiates the low mass regime where the influence of stellar feedback and environmental processes more prominently regulates the sizes of nearby galaxies. Our results highlight the importance of combining deep optical and HI imaging for understanding galaxy evolution.

Scaling relations↗

Climate Lecture 20: The Educational Global Climate Model (EdGCM)

Climate change will profoundly impact Earth's environmental health as well as the world's economic and geopolitical landscape over the coming decades. The impacts of climate change are, in fact, already beginning to be experienced and have the potential to affect every living plant and animal on Earth within decades. Given this reality, every citizen of this planet should have the right to knowledge about the Earth's climate system and have the option to adapt to, or help mitigate the profound changes that are coming. In addition, a portion of the workforce needs to be capable of interpreting and analyzing climate information because, since the impacts of climate change will be widespread, pervasive, and continue to change over time, more professions will be interacting with climate data. We are already at, or past, the point where educators and their students require access to the scientific and technological resources - computer models, data, and visualization tools - that scientists use daily in the study of climate change. Although scientists use many methods to study Earth's climate system, global climate models (GCMs) have become the primary tools for exploring the complex interactions between components of the entire system: atmosphere, oceans, and land. GCMs are used to make projections of future climate change, to simulate climates of the past, and even to help scientists look for life on other planets. Like any model, a GCM can help people evaluate actions before they are taken. Like Business Intelligence software, they are Climate Intelligence tools. Unfortunately, GCMs are black boxes to most people. A previous chapter in this book by Gary Russell, entitled Building a Climate Model, is one example of the growing body of literature aimed at the general public describing the inner workings of global climate models. This literature goes a long way toward explaining climate model fundamentals. However, it will not be enough to alleviate their black-box nature unless people are afforded hands-on, authentic learning experiences as well.

Chandler, Mark A.↗

Crystal growth of device quality GaAs in space

The present program has been aimed at solving the fundamental and technological problems associated with Crystal Growth of Device Quality in Space. The initial stage of the program was devoted strictly to ground-based research. The unsolved problems associated with the growth of bulk GaAs in the presence of gravitational forces were explored. Reliable chemical, structural and electronic characterization methods were developed which would permit the direct relation of the salient materials parameters (particularly those affected by zero gravity conditions) to the electronic characteristics of single crystal GaAs, in turn to device performance. These relationships are essential for the development of optimum approaches and techniques. It was concluded that the findings on elemental semiconductors Ge and Si regarding crystal growth, segregation, chemical composition, defect interactions, and materials properties-electronic properties relationships are not necessarily applicable to GaAs (and to other semiconductor compounds). In many instances totally unexpected relationships were found to prevail.

Gatos, H. C.↗

Interactive displays for trajectory planning and proximity operations

Rendezvous, docking, and other Space Station proximity operations (PROX OPS) will be conducted routinely in space. Real-time interactive visual aids and planning tools will be helpful, if not necessary, for future missions both in preflight training and on orbit. Two such displays, eivaN and Navie, are currently available for examination and human factors testing. A study was conducted in which data were collected from eight test subjects. Solution times for both devices decreased rapidly with experience. Neither fuel usage nor the number of waypoints (burns) decreased with experience. With Navie, medians of solution time and fuel consumption totaled over all subjects peaked at one of two starting points above the V-bar with monotonically decreasing values in both directions. This pattern did not appear with eivaN values. Since the docking tasks were fundamentally different with each device, and because Navie imposed more constraints on the users than eivaN did, the orbital mechanics effects had a more pronounced effect on the Navie results than on the eivaN data.

Brody, Adam R.↗

Characterization of Magnetoacoustic Emission Related to Structural Properties of Ferromagnets

An extensive study of magnetoacoustic emission (MAE) properties has been performed over the past several years. As a result, the dependence of the spectral characteristics of MAE on certain microstructural variations and uniaxially applied stress in a particular type of low carbon steel are now well known. The embrittlement-causing concentration of certain atomic species, e. g., tin, sulphur, phosphorous etc., at the grain boundaries of this steel creates strong potential barriers resisting the motion of non-180 domain walls which is the source of MAE. (Since the only type of non-180 domain walls in this material are 90 domain walls, the term 90 domain wall will be used throughout this paper in place of non-180 domain wall.) An MAE burst produced during one-half cycle of a hysteresis loop at a low AC magnetic field frequency (e. g., 0.7 Hz) shows two sub-peaks; the leading peak is usually sharp and short-lived, while the trailing peak is usually smooth and long-lasting. It has been shown that the enhanced domain wall-defect interaction, due to the strengthened potential barriers, causes an increase in the asymmetry of the MAE signal by suppressing the leading sub-peak and amplifying the trailing sub-peak. This phenomena is due to the delayed motion of the 90 domain walls. The effect of a tensile stress applied parallel to the external AC magnetic field is to diminish the MAE. On the other hand, the amplitude of the MAE burst has been shown to be a non-monotonic function of the stress amplitude. Recently, our study has concentrated on obtaining quantitative values for parameters computed from the MAE spectra averaged over a sufficient number of cycles to achieve statistical stability. Nevertheless, certain fundamental elements of the MAE characteristics remain unexplained.

Namkung, M.↗

A Deeper Look at the Fundamentals of Heterodyne Detection Requirements

We generally accept the experimentally observed criteria for heterodyne detections that the two waves that are mixed must (i) be collinear, (ii) have matched wave fronts and (iii) cannot be orthogonally polarized. We have not found in the literature adequate physical explanations for these requirements. The purpose of this paper is to find deeper physical understanding of the coherent heterodyne detection processes that could lead to better coherent laser radar system designs1. We find that there are a number of unresolved paradoxes in classical and quantum optics regarding the definitions and understanding of the "interference" and "coherence" properties of light, which are attributed as essentially due to inherent properties of the EM waves. A deeper exploration indicates that it is the various quantum mechanical properties of the detecting material dipoles that make light detectable (visible, or measurable) to us. Accordingly, all the properties that we generally attribute to only light, are in reality manifestations of collective properties of dipole-light interactions. "Interference" and "coherence" can be better understood in terms of this mutual interaction, followed by energy absorption by the dipoles from EM wave fields, manifesting in some measurable transformation of the detecting dipoles. Light beams do not interfere by themselves. The superposition effects due to light beams become manifest through the response characteristics of the detecting dipoles. In this paper, we will show some preliminary expe rimental results that clearly demonstrate that the heterodyning wave fronts have quantitative degradation in signal generation as the angle between them deviates from perfect collinearity. Subsequently, we will propose a hypothesis for this behavior. We will present experimental data establishing that the so called incoherent light can be detected through heterodyne mixing as long as the pulse length contained in the "incoherent" light is longer than the response time of the detector. We will also present a correspondingly better interpretation of two distinguishable coherence properties, temporal coherence and spectral coherence. Our investigation provides a deeper insight into how to rela x various system requirements for heterodyne detection and accordingly develop systems that are simpler, more reliable and lower in cost. Also, we believe that engineering of detector architecture by appropriately modifying dipole behavior using emerging nanotechnology to optimize heterodyne efficiency will be advantageous.

Roychoudhuri, Chandrasekhar↗

Laboratory studies of the newly discovered infrared band at 4705.2 cm-1 (2.1253 micrometers) in the spectrum of Io: the tentative identification of CO2

We discuss over 120 laboratory experiments pertaining to the identification of the new absorption band discovered by Trafton et al. (1991) at 4705.2 cm-1 (2.1253 micrometers) in the spectrum of Io. It is shown that this band is not due to overtones or combinations of the fundamental bands associated with the molecules (or their chemical complexes) already identified on Io, namely, SO2, H2S, and H2O. Thus, this band is due to a new, previously unidentified, component of Io. Experiments also demonstrate that the band is not due to molecular H2 frozen in SO2 frosts. Since the frequency of this band is very close to the first overtone of the nu 3 asymmetric stretching mode of CO2, we have investigated the spectral behavior of CO2 under a variety of conditions appropriate for Io. The profile of the Io band is not consistent with the rotational envelope expected for single, freely rotating, gaseous CO2 under Io-like conditions. It was found that pure, solid CO2 and CO2 intimately mixed in a matrix of solid SO2 and H2S produce bands with similar widths (5-10 cm-1), but that these bands consistently fall at frequencies about 10-20 cm-1 (approximately 0.007 micrometer) lower than the Io band. CO2 in SO2 : H2S ices also produces several additional bands that are not in the Io spectra. The spectral fit improves, however, as the CO2 concentration in SO2 increases, suggesting that CO2-CO2 interactions might be involved. A series of Ar : CO2 and Kr : CO2 matrix isolation experiments, as well as laboratory work done elsewhere, show that CO2 clustering shifts the band position to higher frequencies and provides a better fit to the Io band. Various laboratory experiments have shown that gaseous CO2 molecules have a propensity to cluster between 80 and 100 K, temperatures similar to those found on the colder regions of Io. We thus tentatively identify the newly discovered Io band at 4705.2 cm-1 (2.1253 micrometers) with CO2 multimers or "clusters" on Io. Whether these clusters are buried within an SO2 frost, reside on the surface, or are in a residual, steady-state "atmospheric aerosol" population over local coldtraps is not entirely clear, although we presently favor the latter possibility. The size of these clusters is not well defined, but evidence suggests groups of more than four molecules are required. The absorption strength of the 2 nu 3 CO2 cluster overtone determined in the laboratory, in conjunction with the observed strength of the Io band, suggests that the disk-integrated abundance of CO2 is less than 1% that of the SO2. Studies of the sublimation behavior of CO2 indicate that it probably resides predominantly in the cooler areas (< 100 K) of Io. The relative constancy of the Io feature over a variety of orbital phases suggests that the polar regions may contain much of the material. Some consequences of the physical properties of CO2 under conditions pertinent to Io are discussed. The presence of CO2 clusters on Io could be verified by the detection of any one of several other infrared bands associated with the CO2 molecule, of which the strongest are the nu 3 12CO2 asymmetric stretch fundamental near 2350 cm-1 (4.25 micrometers) and the nu 2 bending mode fundamental near 660 cm-1 (15.1 micrometers). Weaker bands that may also be detectable include the nu 3 13CO2 asymmetric stretch fundamental near 2280 cm-1 (4.39 micrometers), the 2 nu 2 + nu 3 combination/overtone band near 3600 cm-1 (2.78 micrometers), and the nu 1 + nu 3 combination band near 3705 cm-1 (2.70 micrometers).

NASA Center ARC↗

Physics of planetary ionospheres

The fundamental physical and chemical processes in an idealized planetary ionosphere are considered as a general abstraction, with actual planetary ionospheres representing special cases. After describing the structure of the neutral atmospheres (the barosphere, the thermosphere, and the exosphere) and noting the principal ionizing radiations responsible for the formation of planetary ionospheres, a detailed study is made of the thermal structure of these ionospheres and of the chemical processes and plasma-transport processes occurring in them. The features of equilibrium and realistic models of planetary ionospheres are discussed, and an attempt is made to determine the extent of these ionospheres. Considering the ionosphere as a plasma, a plasma kinetic approach is developed for determining the effects of interactions between individual particles and waves in this plasma. The use of remote-sensing radio techniques and direct measurement or in situ techniques is discussed. Finally, the observed properties of the ionospheres of the Earth, Mars, Venus, and Jupiter are reviewed.

Bauer, S. J.↗

Does the resistive tearing instability nonlinearly evolve to a fast reconnection mode

A fundamental problem in applying linear tearing instability theory to the rapid processes (particle acceleration, heating) in flares was the characteristically slow rate of reconnection. This problem can be at least partially overcome if the tearin mode nonlinearly evolves to a regime in which the reconnection rate is substantially enhanced, such as that for the Petschek configuration. This possibility was often suggested, and some numerical simulations appear to provide support for such a view. Numerical simulation are used to study the nonlinear evolution of the tearing stability and show that a fast Petschek-like regime may not be achieved. This conclusion follows when there are sufficient grid points within the diffusion region to completely resolve the nonlinear dynamic interactions in the diffusion layer. When the numerical resolution is not adequate, the solution does appear to approach a Petschek configuration. The resolved solution contains reverse flow vortices and current sheets, terminated with a current reversal, similar to those obtained by Syrovatsky (JEPT, 33, 933, 1971).

Steinolfson, R. S.↗