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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

Cassini Information Management System in Distributed Operations Collaboration and Cassini Science Planning

Launched on October 15, 1997, the Cassini-Huygens spacecraft began its ambitious journey to the Saturnian system with a complex suite of 12 scientific instruments, and another 6 instruments aboard the European Space Agencies Huygens Probe. Over the next 6 1/2 years, Cassini would continue its relatively simplistic cruise phase operations, flying past Venus, Earth, and Jupiter. However, following Saturn Orbit Insertion (SOI), Cassini would become involved in a complex series of tasks that required detailed resource management, distributed operations collaboration, and a data base for capturing science objectives. Collectively, these needs were met through a web-based software tool designed to help with the Cassini uplink process and ultimately used to generate more robust sequences for spacecraft operations. In 2001, in conjunction with the Southwest Research Institute (SwRI) and later Venustar Software and Engineering Inc., the Cassini Information Management System (CIMS) was released which enabled the Cassini spacecraft and science planning teams to perform complex information management and team collaboration between scientists and engineers in 17 countries. Originally tailored to help manage the science planning uplink process, CIMS has been actively evolving since its inception to meet the changing and growing needs of the Cassini uplink team and effectively reduce mission risk through a series of resource management validation algorithms. These algorithms have been implemented in the web-based software tool to identify potential sequence conflicts early in the science planning process. CIMS mitigates these sequence conflicts through identification of timing incongruities, pointing inconsistencies, flight rule violations, data volume issues, and by assisting in Deep Space Network (DSN) coverage analysis. In preparation for extended mission operations, CIMS has also evolved further to assist in the planning and coordination of the dual playback redundancy of highvalue data from targets such as Titan and Enceladus. This paper will outline the critical role that CIMS has played for Cassini in the distributed ops paradigm throughout operations. This paper will also examine the evolution that CIMS has undergone in the face of new science discoveries and fluctuating operational needs. And finally, this paper will conclude with theoretical adaptation of CIMS for other projects and the potential savings in cost and risk reduction that could potentially be tapped into by future missions.

Equils, Douglas J.↗
NASA NTRS2012

MAVEN Relay Operations Concept

The Mars Atmosphere and Volatile EvolutioN (MAVEN) mission will launch in late 2013 and following a 10 month cruise to Mars, will study the upper atmosphere of the planet. In addition to the science instruments, the MAVEN spacecraft is equipped with an Electra UHF transceiver to support relay communication with landed assets. This paper describes how UHF relay service is provisioned by MAVEN. The discussion includes a description of the Electra payload, the process by which relay activities are coordinated and accounted for, the process of a typical relay session, including uplink and downlink, as well as special commands to calibrate and verify relay performance. The operational processes for providing these services are inherited largely from prior Mars missions and take advantage of existing infrastructure and lessons learned from those missions. Preliminary data volume return capabilities using adaptive data rates and low-density parity check channel coding are presented.

Electra↗
NASA NTRS1995

Turbulence in the solar wind: Kinetic effects

Although a casual look at the fluctuating magnetic and velocity fields in the solar wind may be reminiscent of a chaotic and disordered flow, there is, nonetheless. considerable organization and structure in the temporal and spatial evolution of those fluctuations. Much of that evolution is controlled by processes operating on rather large scales for example, in the inner heliosphere, the fluctuations in magnetic and velocity are highly correlated in the sense of outward propagating Alfven waves. This correlation can be destroyed both in time and distance by the velocity gradients present between fast and slow streams and by other nonlinear processes which stir the medium, producing a turbulent cascade of energy from large to small scales. Many aspects of this turbulent evolution can be described using fluid models; however, at some scale the fluid approximation breaks down and a more detailed paradigm is necessary. The breakdown is evident in the power spectrum of magnetic fluctuations at scales approaching the wavelength of ion cyclotron waves. At those scales, as evident in Mariner 10 and other magnetometer data, the spectrum bends over and the fluctuations damp, possibly heating the ambient plasma. Some evidence for heating of the solar wind is present in the Voyager data. Fluid models can be modified to some extent to incorporate aspects of a kinetic treatment. This is done by modifying the dissipation terms in the fluid equations and by including extra terms, such as the Hall term. As the scale lengths of phenomena shrink further and approach the spatial and temporal scales characteristic of electron phenomena, the fluid description must be abandoned altogether and a fully kinetic treatment is required. One example is the generation of Langmuir solitons produced by the electron beams that generate type 3 solar radio bursts.

Goldstein, M. L.↗
DOE OSTI2022

Strengthening the Security of Operational Technology: Understanding Contemporary Bill of Materials

The evolution of cyber-physical infrastructure has made its security more challenging. The last few years have witnessed a convergence of hardware and software segments in various domains, including operational technology (OT) which is responsible for carrying out critical tasks such as monitoring and controlling power grids, nuclear plants, transportation, and emergency services. Both hardware and software encapsulate numerous open source and proprietary subcomponents, making it crucial for end-users to understand the composition of the products they are using. For example, wind turbines incorporate thousands of lines of code (software) used for the turbine's design, planning, operation, and analytics in addition to the numerous hardware subcomponents that construct it. Due to the highly complex nature of software and hardware, knowledge of the components and subcomponents is required to mitigate cyber vulnerabilities and defend against cyberattacks. There has also been a transformation from a traditional linear supply chain into a global, dynamic, diverse, and interconnected system. The digitization of the supply chain makes it easier to find and exploit vulnerabilities. Critical infrastructures (e.g., power grids, oil, natural gas, water, and wastewater) rely on OT to function, and if the OT is compromised, equipment damage and potential interruption of services could result. A significant security measure to protect OT systems from disruption is to develop a supply chain bill of materials (BoM) corresponding to the software and hardware used in OT, along with attestations amongst vendors and asset owners. A supply chain BoM is a proactive way to understand the inherent vulnerabilities in the system and mitigate them in advance of being exploited. BoMs bolster the trust placed in the digital infrastructure and enhance software supply chain security by sustaining the management of component obsolescence and compliance, along with the seclusion of unsafe segments of a specific product. Adopting BoM tools is becoming increasingly important across various government sectors, as evidenced by the recent U.S. executive order on cybersecurity (NIST 2021). This paper aims to classify BoMs based on structure, functionality, component type, and architecture. The work also discusses case studies to further highlight the benefits of BoMs. In addition, it identifies missing pieces in existing BoM implementations so that future research may identify bounds on where it could expect to make improvements and directly enable researchers to identify promising areas for exploration. Further, the authors provide valuable recommendations to tool developers, researchers, and standardizing organizations (policymakers), additionally benefitting critical infrastructure owners and government executives. This aids in paving a path for future work, thereby, providing suggestions to determine a tool for consumers that best suit their needs.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2016

Predicting Real-Time Safety of the National Airspace System

To gain the situational awareness necessary for informed decision making regarding avoidance of airspace hazards, each operator must consolidate operations-relevant information from disparate sources and apply extensive domain knowledge to correctly interpret not just the current state of the NAS but forecast its (combined) evolution over the duration of the operation. This time- and workload-intensive process is periodically repeated throughout the operation so that changes can be managed in a timely manner.The imprecision, inaccuracies, inconsistency, and incompleteness of the incoming data further challenges the process. To facilitate informed decision making, this paper presents a model-based framework for the textitautomated real-time monitoring and prediction of possible effects of airspace hazards on the safety of the National Airspace System (NAS). First, hazards to flight are identified and transformed into sms, that is, quantities of interest that could be evaluated based on available data and are predictive of an unsafe event. The sms and associated thresholds that specify when an event transitions from emphsafe to emphunsafe are combined with models of airspace operations and aircraft dynamics. The framework can include any hazard to flight that can be modeled quantitatively. Models can be detailed and complex, or they can be considerably simplifed, as appropriate to the application. Real-time NAS safety monitoring and prediction begins with an estimate of the state of the NAS using the dynamic models. Given the state estimate and a probability distribution of future inputs to the NAS, we can then predict the evolution of the NAS - the future state - and the occurrence of hazards and unsafe events. The entire probability distribution of airspace sms is computed, not just point estimates, without significant assumptions regarding the distribution type andor parameters. We demonstrate our overall approach through a simulated scenario in which we predict the occurrence of some unsafe events and show how these predictions evolve in time as flight operations progress. Predictions accounting for common sources of uncertainty are included and it is shown how the predictions improve in time, become more confident, and change dynamically as new information is made available to the prediction algorithm.

safety↗
DOE OSTI2022

Development of an Open-source Alloy Selection and Lifetime Assessment Tool for Structural Components in CSP

Lack of sufficient data on high temperature mechanical and corrosion behavior of structural materials is a huge barrier in the technological maturity of current and future Concentrating Solar Power (CSP) technologies. Rapid development and selection of materials cannot be achieved by expensive and time-consuming acquisition of experimental data. The goal of the proposed work is development of an open-source alloy selection and lifetime prediction tool that will integrate validated physics-based models to describe influence of temperature, alloy composition, environment and component geometry (thickness) on mechanical and corrosion behavior of Ni and Fe-based alloys employed in molten salts/sCO 2 heat exchangers. This one-year project leveraged the extensive dataset on the creep\corrosion behavior of candidate materials generated at ORNL through past projects and input from current collaborations with industrial partners. Based on previous experience and the feedback provided by industry (Brayton Energy and Echogen), three candidate materials of interest, Ni-based alloys 740H, 282 and 625 and application-specific operating conditions (max. temperature of 730 °C and stress of 150 MPa) were identified for the heat exchanger. An extensive corrosion and creep dataset was assimilated for the relevant operating conditions and was supported by detailed characterization of about 100 metallographic cross-sections. The corrosion dataset consisted of scanning electron microscopy images (secondary electron and backscatter electron), measured concentration profiles of alloying elements using energy dispersive X-ray spectroscopy (EDS), widths of denuded zones (dissolution of strengthening phases) and depths of attack in molten KCl-MgCl 2 mixtures using image analyses. The creep dataset comprised of creep rupture data and creep strain curves (for 740H and 282). Coupled thermodynamic-kinetic microstructure-based models were employed to predict the stress-corrosion induced compositional and phase evolutions in the alloy during operation under the identified operating conditions. Reduced order models were developed from advanced physics-based models and were integrated in a user-friendly alloy selection tool. The corrosion model was able to predict the time to a critical Cr concentration at the oxide/alloy interface (chemical lifetime) within ±10% (1 standard deviation) of typical statistical variation in corrosion tests and EDS measurement errors (±0.5 wt%). The initial scope of the project was limited to predict creep rupture times (Larson-Miller parameter). Based on the input provided by industry, the mechanical lifetime of the heat exchanger is governed by accumulated creep strains (2%) rather than creep rupture. To be able to predict the times to specific creep strains, a more extensive creep model development was undertaken largely beyond the initial scope of the project. The continuum damage mechanics creep model was able to predict times to 2% creep strain, t 2% with an accuracy of ±500h. Ultimately, a screening protocol for SiC was generated to demonstrate the pathway for integration of one of the currently immature materials from a commercial adoption standpoint in the current material evaluation tool. The modeling tool developed here is accessible to the science community and stakeholders and lays the foundation for methods that will enable a rapid evaluation of optimum materials for CSP applications and reliable prediction of material degradation thereby considerably reducing operational costs, improving reliability and increasing overhaul intervals. However, the complete potential of such a tool to include a wider range of materials and test conditions can only be realized with a more concentrated combined experimental-characterization-computation effort.

14 SOLAR ENERGY↗
NASA NTRS1989

Space shuttle avionics system

The Space Shuttle avionics system, which was conceived in the early 1970's and became operational in the 1980's represents a significant advancement of avionics system technology in the areas of systems and redundacy management, digital data base technology, flight software, flight control integration, digital fly-by-wire technology, crew display interface, and operational concepts. The origins and the evolution of the system are traced; the requirements, the constraints, and other factors which led to the final configuration are outlined; and the functional operation of the system is described. An overall system block diagram is included.

Hanaway, John F.↗
NASA NTRS2009

The Evolution and Development of the Lunar Regolith and Implications for Lunar Surface Operations and Construction

The lunar regolith consists of about 90% submillimeter particles traditionally termed lunar soil. The remainder consists of larger particles ranging up to boulder size rocks. At the lower size end, soil particles in the 10s of nanometer sizes are present in all soil samples. Lunar regolith overlies bedrock which consists of either lava flows in mare regions or impact-produced megaregolith in highland regions. Lunar regolith has been produced over billions of years by a combination of breaking and communition of bedrock by meteorite bombardment coupled with a variety of complex space weathering processes including solar wind implantation, solar flare and cosmic ray bombardment with attendant radiation damage, melting, vaporization, and vapor condensation driven by impact, and gardening and turnover of the resultant soil. Lunar regolith is poorly sorted compared to most terrestrial soils, and has interesting engineering properties including strong grain adhesion, over-compacted soil density, an abundance of agglutinates with sharp corners, and a variety of properties related to soil maturity. The NASA program has supported a variety of engineering test research projects, the production of bricks by solar or microwave sintering, the production of concrete, the in situ sintering and glazing of regolith by microwave, and the extraction of useful resources such as oxygen, hydrogen, iron, aluminum, silicon and other products. Future requirements for a lunar surface base or outpost will include construction of protective berms, construction of paved roadways, construction of shelters, movement and emplacement of regolith for radiation shielding and thermal control, and extraction of useful products. One early need is for light weight but powerful digging, trenching, and regolith-moving equipment.

McKay, David↗
NASA NTRS2017

Discovery Deep Space Optical Communications (DSOC) transceiver

NASA’s 22 cm diameter Deep Space Optical Communications (DSOC) Transceiver is designed to provide a bi-directional optical link between a spacecraft in the inner solar system and an Earth-based optical ground station. This design, optimized for operation across a wide range of illumination conditions, is focused on minimizing blinding from stray light, and providing reliable, accurate attitude information to point its narrow communication beam accurately to the future location of the ground terminal. Though our transceiver will transmit in the 1550 nm waveband and receive in the 1064 nm waveband, the system design relies heavily on reflective optical elements, extending flexibility to be modified for use at different wavebands. The design makes use of common path propagation among transmit, receive and pointing verification optical channels to maintain precise alignment among its components, and to naturally correct for element misalignment resulting from launch or thermal element perturbations. This paper presents the results of trade studies showing the evolution of the design, unique operational characteristics of the design, elements that help to maintain minimal stray light contamination, and preliminary results from development and initial testing of a functional aluminum test model.

Roberts, W. Thomas↗
NASA NTRS2010

Anatomy of a Security Operations Center

Many agencies and corporations are either contemplating or in the process of building a cyber Security Operations Center (SOC). Those Agencies that have established SOCs are most likely working on major revisions or enhancements to existing capabilities. As principle developers of the NASA SOC; this Presenters' goals are to provide the GFIRST community with examples of some of the key building blocks of an Agency scale cyber Security Operations Center. This presentation viII include the inputs and outputs, the facilities or shell, as well as the internal components and the processes necessary to maintain the SOC's subsistence - in other words, the anatomy of a SOC. Details to be presented include the SOC architecture and its key components: Tier 1 Call Center, data entry, and incident triage; Tier 2 monitoring, incident handling and tracking; Tier 3 computer forensics, malware analysis, and reverse engineering; Incident Management System; Threat Management System; SOC Portal; Log Aggregation and Security Incident Management (SIM) systems; flow monitoring; IDS; etc. Specific processes and methodologies discussed include Incident States and associated Work Elements; the Incident Management Workflow Process; Cyber Threat Risk Assessment methodology; and Incident Taxonomy. The Evolution of the Cyber Security Operations Center viII be discussed; starting from reactive, to proactive, and finally to proactive. Finally, the resources necessary to establish an Agency scale SOC as well as the lessons learned in the process of standing up a SOC viII be presented.

Wang, John↗
NASA NTRS1990

Space Station Freedom altitude strategy

The Space Station Freedom (SSF) altitude strategy provides guidelines and assumptions to determine an altitude profile for Freedom. The process for determining an altitude profile incorporates several factors such as where the Space Shuttle will rendezvous with the SSF, when reboosts must occur, and what atmospheric conditions exist causing decay. The altitude strategy has an influence on all areas of SSF development and mission planning. The altitude strategy directly affects the micro-gravity environment for experiments, propulsion and control system sizing, and Space Shuttle delivery manifests. Indirectly the altitude strategy influences almost every system and operation within the Space Station Program. Evolution of the SSF altitude strategy has been a very dynamic process over the past few years. Each altitude strategy in turn has emphasized a different consideration. Examples include a constant Space Shuttle rendezvous altitude for mission planning simplicity, or constant micro-gravity levels with its inherent emphasis on payloads, or lifetime altitudes to provide a safety buffer to loss of control conditions. Currently a new altitude strategy is in development. This altitude strategy will emphasize Space Shuttle delivery optimization. Since propellant is counted against Space Shuttle payload-to-orbit capacity, lowering the rendezvous altitude will not always increase the net payload-to-orbit, since more propellant would be required for reboost. This altitude strategy will also consider altitude biases to account for Space Shuttle launch slips and an unexpected worsening of atmospheric conditions. Safety concerns will define a lower operational altitude limit, while radiation levels will define upper altitude constraints. The evolution of past and current SSF altitude strategies and the development of a new altitude strategy which focuses on operational issues as opposed to design are discussed.

Mcdonald, Brian M.↗
DOE OSTI2024

Operando Freezing Cryogenic Electron Microscopy of Active Battery Materials

Abstract Understanding structural and chemical evolution of battery materials during operation is critical to achieving safe, efficient, and long-lasting energy storage. Cryogenic electron microscopy (cryo-EM) has become a valuable tool in battery characterization, leveraging low temperatures to improve stability of sensitive materials under electron beam irradiation. However, typical cryo-EM sample preparations leave extended time between the electrochemical point of interest and ex situ freezing of samples, during which active structures may relax, degrade, or otherwise evolve. Here, we detail a method for operando freezing cryo-EM to preserve and characterize native electrode and interfacial structures that arise during battery cycling, based on an operando plunge freezer and cold sample removal process. We validate the method on multiple electrode materials and quantify and discuss the freezing rate achieved. Operando freezing cryo-EM can be used to directly visualize transient features that arise at active electrochemical interfaces, to enable deeper understanding of structural evolution and interfacial chemistry in batteries and other electrochemical systems.

25 ENERGY STORAGE↗
DOE OSTI2024

Chemical Doppelgangers in GALAH DR3: The Distinguishing Power of Neutron-capture Elements among Milky Way Disk Stars

The observed chemical diversity of Milky Way stars places important constraints on Galactic chemical evolution and the mixing processes that operate within the interstellar medium. Recent works have found that the chemical diversity of disk stars is low. For example, the Apache Point Observatory Galactic Evolution Experiment (APOGEE) "chemical doppelganger rate," or the rate at which random pairs of field stars appear as chemically similar as stars born together, is high, and the chemical distributions of APOGEE stars in some Galactic populations are well-described by two-dimensional models. However, limited attention has been paid to the heavy elements (Z > 30) in this context. In this work, we probe the potential for neutron-capture elements to enhance the chemical diversity of stars by determining their effect on the chemical doppelganger rate. We measure the doppelganger rate in GALactic Archaeology with HERMES DR3, with abundances rederived using The Cannon, and find that considering the neutron-capture elements decreases the doppelganger rate from ~2.2% to 0.4%, nearly a factor of 6, for stars with –0.1 < [Fe/H] < 0.1. While chemical similarity correlates with similarity in age and dynamics, including neutron-capture elements does not appear to select stars that are more similar in these characteristics. Our results highlight that the neutron-capture elements contain information that is distinct from that of the lighter elements and thus add at least one dimension to Milky Way abundance space. This work illustrates the importance of considering the neutron-capture elements when chemically characterizing stars and motivates ongoing work to improve their atomic data and measurements in spectroscopic surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2013

Evolving Systems: Nonlinear Adaptive Key Component Control with Persistent Disturbance Rejection

This paper presents an introduction to Evolving Systems, which are autonomously controlled subsystems that self-assemble into a new Evolved System with a higher purpose. Evolving Systems of aerospace structures often require additional control when assembling to maintain stability during the entire evolution process. This is the concept of Adaptive Key Component Control which operates through one specific component to maintain stability during the evolution. In addition this control must overcome persistent disturbances that occur while the evolution is in progress. We present theoretical results for the successful operation of Nonlinear Adaptive Key Component control in the presence of such disturbances and an illustrative example.

adaptive control↗
NASA NTRSDate not supplied

MOC Automation with GMSEC and the Generic Extendable Message Utility (GEMU)

Automation has become critical for ground systems, improving efficiency and reliability while reducing costs across mission operations. The Goddard Mission Services Evolution Center (GMSEC) software suite has played a significant role in enabling this automation, leveraging its publish/subscribe paradigm through a message bus architecture to facilitate seamless communication and data flow. Historically, the GMSEC suite, through components like Criteria Action Table (CAT) has been pivotal in automating ground system capabilities. However, as technology advances, limitations in automation with CAT have emerged, creating an opportunity to enhance ground system automation through the introduction of GEMU. This new GMSEC component brings new capabilities and addresses specific automation constraints that CAT could not overcome, allowing for more sophisticated, flexible, and efficient message processing. GEMU, at its core, is designed to accelerate the development of custom GMSEC-compliant applications. It enables users to construct automated message processing pipelines quickly, supporting both drag-and-drop web-based configuration and scripting through a simple domain-specific language. This advancement not only simplifies the process but also reduces the time needed for implementing automated solutions. This presentation will outline GEMU’s potential value in improving mission operations automation. It will highlight the benefits of transitioning from CAT to GEMU and offer insights into how GEMU can drive operational efficiencies. We will also provide an overview of the automation capabilities of GEMU and its potential impact on mission operations centers (MOCs).

GMSEC↗
DOE OSTI2021

Synergistic epistasis enhances the co-operativity of mutualistic interspecies interactions

Abstract Early evolution of mutualism is characterized by big and predictable adaptive changes, including the specialization of interacting partners, such as through deleterious mutations in genes not required for metabolic cross-feeding. We sought to investigate whether these early mutations improve cooperativity by manifesting in synergistic epistasis between genomes of the mutually interacting species. Specifically, we have characterized evolutionary trajectories of syntrophic interactions of Desulfovibrio vulgaris (Dv) with Methanococcus maripaludis (Mm) by longitudinally monitoring mutations accumulated over 1000 generations of nine independently evolved communities with analysis of the genotypic structure of one community down to the single-cell level. We discovered extensive parallelism across communities despite considerable variance in their evolutionary trajectories and the perseverance within many evolution lines of a rare lineage of Dv that retained sulfate-respiration (SR+) capability, which is not required for metabolic cross-feeding. An in-depth investigation revealed that synergistic epistasis across pairings of Dv and Mm genotypes had enhanced cooperativity within SR− and SR+ assemblages, enabling their coexistence within the same community. Thus, our findings demonstrate that cooperativity of a mutualism can improve through synergistic epistasis between genomes of the interacting species, enabling the coexistence of mutualistic assemblages of generalists and their specialized variants.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1987

On Lipschitz continuity of nonlinear differential operators

In connection with approximations for nonlinear evolution equations, it is standard to assume that nonlinear terms are at least locally Lipschitz continuous. However, it is shown here that f = f(X,del sub u(X)) is Lipschitz continuous from the subspace W sup 1, infinity is a subset of L sub 2 into W sup 1,2, and maps W sup 2, infinity into W sup 1, infinity, if and only if f is affine with W sup 1, infinity coefficients. In fact, a local version of this claim is proved.

Keeling, Stephen L.↗
DOE OSTI2022

Quark and gluon helicity evolution at small x: revised and updated

We revisit the problem of small Bjorken-x evolution of the gluon and flavor-singlet quark helicity distributions in the shock wave (s-channel) formalism. Earlier works on the subject in the same framework resulted in an evolution equation for the gluon field-strength F 12 and quark “axial current” $\overline{\psi}\gamma$ + γ 5 ψ operators (sandwiched between the appropriate light-cone Wilson lines) in the double-logarithmic approximation (summing powers of α s ln 2 (1/x) with α s the strong coupling constant). In this work, we observe that an important mixing of the above operators with another gluon operator, ${}_D{}^{\leftarrow i} {}_D{}^{i}$, also sandwiched between the light-cone Wilson lines (with the repeated transverse index i = 1, 2 summed over), was missing in the previous works. This operator has the physical meaning of the sub-eikonal (covariant) phase: its contribution to helicity evolution is shown to be proportional to another sub-eikonal operator, ${}_D{}^{i} {}_D{}^{\leftarrow i}$, which is related to the Jaffe-Manohar polarized gluon distribution. In this work we include this new operator into small-x helicity evolution, and construct novel evolution equations mixing all three operators (${}_D{}^{i} {}_D{}^{\leftarrow i}$, F 12 , and $\overline{\psi}\gamma$ + γ 5 ψ), generalizing the results of . We also construct closed double-logarithmic evolution equations in the large-N c and large-N c &N f limits, with N c and N f the numbers of quark colors and flavors, respectively. Solving the large-N c equations numerically we obtain the following small-x asymptotics of the quark and gluon helicity distributions ΔΣ and ΔG, along with the g 1 structure function, $$ \Delta \Sigma \left(x,{Q}^2\right)\sim \Delta G\left(x,{Q}^2\right)\sim {g}_1\left(x,{Q}^2\right)\sim {\left(\frac{1}{x}\right)}^{3.66\sqrt{\frac{\alpha_s{N}_c}{2\pi }}} $$ in complete agreement with the earlier work by Bartels, Ermolaev and Ryskin.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗