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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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Final Design of the Material Plasma Exposure eXperiment

The Material Plasma Exposure eXperiment (MPEX) has completed its design phase. MPEX will be a unique facility to investigate plasma material interactions (PMIs) under fusion prototypic divertor conditions in steady state. This includes plasma exposure conditions expected in a fusion reactor divertor. Materials to be investigated will include solids, liquids, and neutron pre-irradiated materials. Electron and ion heating will allow for a large operational domain ranging from erosion-dominated PMI conditions to deposition-dominated PMI conditions. An overview of the final design for all MPEX systems is given. Here, in particular, it is shown how mission-driven project requirements have led to detailed design choices with innovative solutions. Examples are the water-cooled helicon window, the electron cyclotron heating launcher, the target holder and manipulator, and the autonomous decouplers.

Fusion reactor↗
DOE OSTI2020

5G Enabled Energy Innovation: Advanced Wireless Networks for Science (Workshop Report)

Rapidly expanding, new telecommunications infrastructure based on 5G technologies will disrupt and transform how we design, build, operate, and optimize scientific infrastructure and the experiments and services enabled by that infrastructure, from continental-scale sensor networks to centralized scientific user facilities, from intelligent Internet of Things devices to supercomputers. Concurrently, 5G will introduce, or exacerbate, challenges related to protecting infrastructure and associated scientific data as well as to fully leveraging opportunities related to expanded infrastructure scale and complexity. The U.S. Department of Energy (DOE) Office of Science operates scientific infrastructure, supporting some of the nation’s most advanced intellectual discoveries, spanning the country and including 30 world-class user facilities from supercomputers to accelerators. Along with field experiments and remote observatories, every aspect of DOE’s scientific enterprise will be affected by 5G, which amounts to a complete renovation of the underpinnings of the nation’s information infrastructure. In this report we explore the scientific opportunities and new research challenges associated with 5G, ranging from scalability to heterogeneity to cybersecurity. The rapid commercial deployment of 5G opens the opportunity to rethink and reinvent DOE’s scientific infrastructure and experimentation, from intelligent sensor networks at unprecedented scales to a digital continuum of cyberinfrastructure spanning low-power sensors, high-performance computing embedded within and at the edge of the network, and DOE’s large-scale user instrument and computing facilities. New programming paradigms, workflow and data frameworks, and AI-based system design, operation, and autonomous adaptation and optimization will be necessary in order to exploit these new opportunities. Field deployments and centralized scientific instruments can also be revolutionized, moving (without traditional performance penalties) from wired to wireless connectivity for data and control systems, improving flexibility, and opening new sensing modalities, including the use of the 5G electromagnetic spectrum itself as an environmental probe. For DOE science, in contrast to commercial 5G applications and settings, devices will be deployed in extreme environments such as cryogenically cooled instrument control systems and in remote settings with harsh conditions, requiring the design of new materials for RF communication and edge processing to operate in these regimes. Concurrently, 5G infrastructure comprises both hardware and sophisticated software systems - currently closed and proprietary. The cybersecurity challenges to 5G-empowered reinvention mirror the complexity and variety of new 5G features, from virtualization to private network slices to ubiquitous access. Research is also needed in order to accelerate the development of secure and open 5G software infrastructure, reducing reliance on hardware and software produced outside the United States and providing the transparency and rigorous evaluation and testing afforded through open software. Twelve broad research thrusts are laid out in four chapters, with a companion fifth chapter (and three additional research thrusts) underscoring the needs and opportunities for an aggressive testbed program co-designed by networking experts and scientists involved in the 15 research thrusts. The urgency of undertaking this research is fueled by a global, accelerating deployment of new telecommunications infrastructure that is designed for entertainment and commercial applications - barely scratching the surface of what 5G can do to extend U.S. leadership in scientific discovery.

42 ENGINEERING↗
DOE OSTI2020

Energy Impact of Connected and Automated Vehicle Technologies. Final report

The overarching goal of this project is to understand the potential impact of connected and automated vehicles. The goal was achieved through data collection, model development, algorithm designs, simulations, and limited field tests. The main outcomes from this project include: (1) we collected energy consumption and GPS data from 500 vehicles over one year, with a total mileage of 8 million miles; (2) Based on the collected data and other datasets collected at the University of Michigan, we developed a calibrated Ann Arbor model in Polaris (model developed by ANL), and the fuel economy accuracy was found to be around 3.9% by comparison with field collected data; (3) An open-source SUMO model of Ann Arbor was developed; (4) Eco-Routing algorithms in Ann Arbor using the SUMO model shows 6% fuel saving potential; (5) Experiments conducted at the Mcity test facility shows that human drivers roughly follow the Eco-driving suggestions roughly 70% of the time; (6) Based in the Ann Arbor travel patterns, we found that each shared automated vehicle can replace around 4 individually owned vehicles; and (7) Adaptive Traffic Signal Control Algorithm developed through this project has been validated both in simulations and preliminary test results. For connected and automated vehicles, on average the performance is 13% delay reduction, and 10% fuel reduction. While connected and automated vehicles are in their early stage of deployment, the results from this project confirm that there is significant potential for energy saving if the technologies are developed and used properly. The three main technologies studied in this project include eco-routing, shared autonomous rides, and adaptive traffic signal controls. The data collected and model developed through the project can be used to study many other connected and automated vehicle technologies.

02 PETROLEUM↗
DOE OSTI2015

Viewpoint: Exorcizing Maxwell’s demon

Here, physicists have been haunted by the idea of Maxwell's demon for almost 150 years. The beast, conjured in a thought experiment by James Clerk Maxwell, sorts particles in a gas according to their speeds, thus transferring heat from the colder, evenly mixed gas to the region containing the hotter, high-speed particles. At first sight, the demon appears to violate the second law of thermodynamics. But the paradox can be resolved by realizing that work must be performed on the demon for it to do its job properly. This description isn’t entirely satisfying, however, as it introduces an external—not necessarily physical—entity to do work on the demon. Jukka Pekola and colleagues of Aalto University in Finland [1] have now exorcised such nonphysical beings by realizing a nanodevice equivalent to a Maxwell's demon (Fig. 1), but one whose operation doesn’t depend on an external entity. This so-called autonomous device, also known as an information machine, is completely self-contained. So far, autonomous demons have been a purely theoretical concept; this new experimental system provides a way to test formulations of fundamental axioms of thermodynamics and descriptions of information processing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A Data-Fusion Method using Bayesian Approach to Enhance Raw Data Accuracy of Position and Distance Measurements for Connected Vehicles

Accurate positioning of vehicles is a critical element of autonomous and connected vehicle systems. Most of other studies heavily focused on enhancing simultaneous localization and mapping (SLAM) methods, i.e., constructing or updating a map of an unknown environment and tracking an object within the map. This paper provides a method that can, in addition to existing SLAM or relevant methods, enhance the raw measurements of position and distance. The basic idea of this study is to identify and update the error distribution of each data source by combining all available information. A Bayesian approach was incorporated to estimate and update the error distribution of individual data sources or sensors. The proposed method can be conducted in real-time environments, and a self-learning scheme determines whether enough data has been collected to further improve the accuracy of such measurements. The simulated experiments show that the proposed model noticeably improves the accuracy of position and distance measurements. Especially, the estimated biases of position coordinates and distance measures are very close to the biases of true error distributions, with the R-squared over 0.98. A similar approach can also be utilized to enhance accuracy of other sensors or measurements in connected vehicle or relevant systems, where multi-data sources are available.

Lim, Hyeonsup↗
DOE OSTI2024

Anomaly Detection in Connected and Autonomous Vehicle Trajectories Using LSTM Autoencoder and Gaussian Mixture Model

Connected and Autonomous Vehicles (CAVs) technology has the potential to transform the transportation system. Although these new technologies have many advantages, the implementation raises significant concerns regarding safety, security, and privacy. Anomalies in sensor data caused by errors or cyberattacks can cause severe accidents. To address the issue, this study proposed an innovative anomaly detection algorithm, namely the LSTM Autoencoder with Gaussian Mixture Model (LAGMM). This model supports anomalous CAV trajectory detection in the real-time leveraging communication capabilities of CAV sensors. The LSTM Autoencoder is applied to generate low-rank representations and reconstruct errors for each input data point, while the Gaussian Mixture Model (GMM) is employed for its strength in density estimation. The proposed model was jointly optimized for the LSTM Autoencoder and GMM simultaneously. The study utilizes realistic CAV data from a platooning experiment conducted for Cooperative Automated Research Mobility Applications (CARMAs). The experiment findings indicate that the proposed LAGMM approach enhances detection accuracy by 3% and precision by 6.4% compared to the existing state-of-the-art methods, suggesting a significant improvement in the field.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

Interconnection and Interoperability Requirements of Hydrogen Assets to Enable Grid Integration

Traditionally, the inverters used for distributed energy resources (DERs) including solar, energy storage and hydrogen fuel cells are grid following assets. Grid following assets track real power and reactive power setpoints decided by either a local autonomous controller or a remote controller like a microgrid controller. In the past five years, multiple challenges have increased the need for grid forming inverters that can interface to a wide variety of energy resources. These grid forming inverters are becoming critical assets for power systems to enable the replacement of existing rotational machines and provide grid services such as grid resiliency services and black-start. Hydrogen assets (fuel cells) have the potential to successfully replace rotating machines and act as voltage and frequency master by leveraging the long-duration and seasonal energy storage capabilities of hydrogen technologies. This poster presents the progress made in budget period 1 of the proposed work. We will leverage an existing ARIES platform experimental setup to run power-hardware-in-the-loop and controller-hardware-in-the-loop experiments with grid forming fuel cell inverters to develop and document the standardization requirements.

electrolyzer↗
DOE OSTI2025

Invariant discovery of features across multiple length scales: Applications in microscopy and autonomous materials characterization

Physical imaging is a foundational characterization method in areas from condensed matter physics and chemistry to astronomy and spans length scales from atomic to universe. Images encapsulate crucial data regarding atomic bonding, materials microstructures, and dynamic phenomena such as microstructural evolution and turbulence, among other phenomena. The challenge lies in effectively extracting and interpreting this information. Variational Autoencoders (VAEs) have emerged as powerful tools for identifying the underlying factors of variation in image data, providing a systematic approach to distilling meaningful patterns from complex data sets. However, a significant hurdle in their application is the definition and selection of appropriate descriptors reflecting local structures. Here, we introduce the scale-invariant VAE approach (SI-VAE) based on the progressive training of the VAE with the descriptors sampled at different length scales. The SI-VAE allows the discovery of the length scale-dependent factors of variation in the system. Here, we illustrate this approach using the ferroelectric domain images and generalize it to the movies of the electron-beam induced phenomena in graphene and topography evolution across combinatorial libraries. This approach can further be used to initialize the decision making in automated experiments including structure–property discovery and can be applied across a broad range of imaging methods. This approach is universal and can be applied to any spatially resolved data including both experimental imaging studies and simulations, and can be particularly useful for exploration of phenomena such as turbulence and scale-invariant transformation fronts.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Control System of Multi-Port Autonomous Reconfigurable Solar Power Plant (MARS) & HIL Platforms for Design

Multi-port autonomous reconfigurable solar power plant (MARS) provides an attractive alternative to connect photovoltaic (PV) and energy storage systems (ESSs) to high-voltage direct current (HVdc) links and high-voltage alternating current (ac) grids. In this paper, a unique hierarchical control system of MARS is proposed and evaluated. To evaluate the control system and associated algorithms in early-stage research of complex architectures like MARS, it is important to develop unique suitable hardware-in-the-loop (HIL) platforms. In this paper, the HIL platforms for MARS to evaluate the performance of the hierarchical control system and the control algorithms implemented are presented. Further, they help with the design process of control systems. The real-time simulation models and algorithms that are utilized for MARS in the HIL platforms are also discussed in the paper. The HIL experiments of the control system of MARS showcase the capability to provide continuity of operation under faults and frequency support to the power grid during loss of generation. They also showcase the stability of the proposed hierarchical control system of MARS.

14 SOLAR ENERGY↗
DOE OSTI2022

A perspective on Bayesian methods applied to materials discovery and design

For more than two decades, there has been increasing interest in developing frameworks for the accelerated discovery and design of novel materials that could enable promising and transformative technologies. The Integrated Computational Materials Engineering (ICME) program called for integrating computational tools to establish linkages along process-structure-property-performance (PSPP) chains. The Materials Genome Initiative called for integrating experiments and computations within data science frameworks as a strategy to accelerate the materials development cycle. While these frameworks and paradigms have been quite influential, traditional ICME or data science-based approaches tend to have some limitations, mainly when querying the materials space is costly and very little information is available. Bayesian methods are more suitable in this context due to their efficiency gains. To this end, the materials discovery problem is framed as a Bayesian Optimization (BO). Different examples in which BO has been applied to solve materials discovery problems are presented. The methods/examples discussed include BO under model uncertainty, multi-information source BO, multi-objective and multi-constraint BO, and batch BO. Bayesian Materials Discovery is a promising area of research that is likely to become more influential as more attention is put on autonomous materials discovery platforms. Therefore, a discussion is provided on the potential development of such methods to increase the ability of existing platforms in materials discovery. Here, the ultimate goal is to pave the way to autonomous materials discovery.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Temporal Characterization of Hydrates System Dynamics beneath Seafloor Mounds. Integrating Time-Lapse Electrical Resistivity Methods and In Situ Observations of Multiple Oceanographic Parameters

This study was designed to investigate temporal variations in hydrate system dynamics by measuring changes in volumes of hydrate beneath hydrate-bearing mounds on the continental slope of the northern Gulf of Mexico, the landward extreme of hydrate occurrence in this region. Direct Current Resistivity (DCR) measurements were made contemporaneously with measurements of oceanographic parameters at Woolsey Mound, a carbonate-hydrate complex on the mid-continental slope, where formation and dissociation of hydrates are most vulnerable to variations in oceanographic parameters affected by climate change, and where changes in hydrate stability can readily translate to loss of seafloor stability, impacts to benthic ecosystems, and venting of greenhouse gases to the water-column, and eventually, the atmosphere. We focused our study on hydrate within seafloor mounds because the structurally-focused methane flux at these sites likely causes hydrate formation and dissociation processes to occur at higher rates than at sites where the methane flux is less concentrated and we wanted to maximize our chances of witnessing association/dissociation of hydrates. We selected a particularly well-studied hydrate-bearing seafloor mound near the landward extent of the hydrate stability zone, Woolsey Mound (MC118). This mid-slope site has been studied extensively and the project was able to leverage considerable resources from the team’s research experience at MC118. The site exhibits seafloor features associated with gas expulsion, hydrates have been documented at the seafloor, and changes in the outcropping hydrates have been documented, photographically, to have occurred over a period of months. We conducted observatory-based, in situ measurements to 1) characterize, geophysically, the sub-bottom distribution of hydrate and its temporal variability, and 2) contemporaneously record relevant environmental parameters (temperature, pressure, salinity, turbidity, bottom currents) to detect short-term changes within the hydrates system, identify relationships/impacts of local oceanographic parameters on the hydrates system, and improve our understanding of how seafloor instability is affected by hydrates-driven changes. A 2009 DCR survey of MC118 demonstrated that we could image resistivity anomalies to a depth of 75m below the seafloor in water depths of 1km. We reconfigured this system to operate autonomously on the seafloor in a pre-programmed mode, for periods of months. We designed and built a novel seafloor lander and deployment capability that would allow us to investigate the seafloor at potential deployment sites and deploy instruments only when conditions met our criteria. This lander held the DCR system, controlling computers, and battery power supply, as well as instruments to record oceanographic parameters. During the first of two cruises to the study site, we conducted resistivity surveying, selected a monitoring site, and deployed the instrumented lander and DCR, centered on what appeared to be the most active locations within the site, programmed to collect a DCR profile, weekly. After a 4.5-month residence on the seafloor, the team recovered all equipment. Unfortunately, several equipment failures occurred prior to recovery of the instrument packages. Prior to the failures, however, two resistivity profiles were collected together with oceanographic data. Results show, unequivocally, that significant changes can occur in both hydrate volume and distribution during time periods as brief as one week. Occurrences appear to be controlled by both deep and near-surface structure. Results have been integrated with seismic data from the area and show correspondence in space of hydrate and structures, including faults and gas chimneys.

58 GEOSCIENCES↗
DOE OSTI2026

Programmable hydrogels by combining persistent and transient dynamic bonds

Out-of-equilibrium chemistry is currently being applied to polymer systems to mimic the autonomous behavior of biological materials. In this study, hydrogels with self-healing properties were developed that combine persistent crosslinks from dynamic metal-ligand coordination with transient crosslinks from dynamic anhydride bonds. Polymers containing terpyridine ligands and carboxylic acid groups were synthesized and crosslinked with divalent metal ions (Fe 2+ , Ni 2+ , Co 2+ , Zn 2+ , Cu 2+ ). The coordination bonds from terpyridine–metal coordination impart persistent stability, while transient anhydrides formed on treatment with 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide hydrochloride (EDC) temporarily increase crosslink density. Distinct behaviors are observed depending on the choice of metal, with Ni 2+ forming robust, stable networks; Zn 2+ creating moderately dynamic gels; and Cu 2+ yielding highly dynamic, soft materials. Treatment with EDC increased storage moduli significantly, with transient effects lasting up to 280 min depending on the metal ion. Self-healing experiments demonstrated independent contributions from metal coordination and transient anhydrides, enabling recovery of stress and strain under varying conditions. Additionally, complex and reversible 2D stiffness patterns were generated by spatially controlled EDC treatment of Zn 2+ and Cu 2+ hydrogel films, demonstrating programmability and reusability.

Rajawasam, Chamoni W. H. [Miami University, Oxford↗
DOE OSTI2025

Integrating Machine-learning-assisted Computer Vision with RICH System

Developments in artificial intelligence have vastly expanded the capabilities of robots. Currently, the Spallation Neutron Source (SNS) beamlines at Oak Ridge National Lab (ORNL) have robotic sample loaders to increase the efficiency of running experiments. However, they require retraining if anything about the situation changes, e.g., where the samples are, and cannot notice if errors occur. So, the viability of using computer vision and machine learning to enhance these sample loaders’ functionality was investigated. In this project, the RICH system with a Dobot CR3 6-axis robot present at the VULCAN beamline assisted by an Intel Realsense D435i camera, a unique camera that enables convenient translation of 2D pixel coordinates to 3D world points, was programmed to load ceramic crucibles into a thermogravimetric analyzer (TGA) furnace. An algorithm was constructed in Python with three major phases planned: (1) obtaining a sample, (2) moving it to the target location, and then (3) bringing the sample back to its original location once the experiment finished. In the first phase, the algorithm would dynamically detect sample locations using ArUco markers to recognize the samples’ general location and a custom-trained yolov5 object detection model to locate the crucibles’ centers. Afterward, the robot would be directed to pick up samples based on the crucibles’ calculated positions. In the second phase, the robot would move the sample to a secondary point, reorient its grip, and place the sample at the target location. In the final phase, the robot would determine whether the sample was intact and would bring it back to its original place if it was or raise an alarm. Using this algorithm, the robot was able to pick up different types of crucibles at varying positions. These results indicate that integrating machine-learning-assisted computer vision with robotic sample loaders can result in effective autonomous detection of samples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A Vision–based Robust $\mathcal{H}$ ∞ Gain Scheduling Longitudinal and Lateral Following Controller for Autonomous Vehicles on Urban Curved Roads

Implementing advanced driver assistance systems (ADAS) in congested and intricate urban traffic scenarios poses significant challenges. To address the frequent stop–and–go motions exhibited by autonomous vehicles (AVs) navigating urban roads with changes in curvature, we propose a vision–based robust $\mathcal{H}$ ∞ adaptive cruise control system (ACC) for longitudinal control, plus a lane keeping assist system (LKAS) for lateral control. For the vision-based ACC, a weighted probability objective function for the vehicle following behavior is formulated. We incorporate $\mathcal{H}$ ∞ performance and gain scheduling techniques to mitigate the impact of uncertainty in visual sensor measurements. Furthermore, the optimal time headway is scheduled based on the velocity to ensure traffic flow efficiency and safety during the vehicle following process. For the LKAS, we introduce a road curvature estimation method that integrates lane and vehicle dynamics information to obtain the lateral and heading offsets. Next, the design criterion of the observer–based robust gain scheduling lateral motion controller is established by linear matrix inequality (LMI). Here, a series of experiments conducted within a camera–in–loop platform validate the proposed method.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2021

Harnessing autocatalytic reactions in polymerization and depolymerization

Abstract Autocatalysis and its relevance to various polymeric systems are discussed by taking inspiration from biology. A number of research directions related to synthesis, characterization, and multi-scale modeling are discussed in order to harness autocatalytic reactions in a useful manner for different applications ranging from chemical upcycling of polymers (depolymerization and reconstruction after depolymerization), self-generating micelles and vesicles, and polymer membranes. Overall, a concerted effort involving in situ experiments, multi-scale modeling, and machine learning algorithms is proposed to understand the mechanisms of physical and chemical autocatalysis. It is argued that a control of the autocatalytic behavior in polymeric systems can revolutionize areas such as kinetic control of the self-assembly of polymeric materials, synthesis of self-healing and self-immolative polymers, as next generation of materials for a sustainable circular economy. Graphic Abstract

36 MATERIALS SCIENCE↗
DOE OSTI2023

Optimizing Perovskite Thin‐Film Parameter Spaces with Machine Learning‐Guided Robotic Platform for High‐Performance Perovskite Solar Cells

Abstract Simultaneously optimizing the processing parameters of functional thin films remains a challenge. The design and utilization of a fully automated platform called SPINBOT is presented for the engineering of solution‐processed functional thin films. The SPINBOT is capable of performing experiments with high sampling variability through the unsupervised processing of hundreds of substrates with exceptional experimental control. Through the iterative optimization process enabled by the Bayesian optimization (BO) algorithm, the SPINBOT explores an intricate parameter space, continuously improving the quality and reproducibility of the produced thin films. This machine learning (ML)‐guided reliable SPINBOT platform enables the acceleration of the optimization process of perovskite solar cells via a simple photoluminescence characterization of films. As a result, this study arrives at an optimal film that, when processed into a solar cell in an ambient atmosphere, immediately yields a champion power conversion efficiency (PCE) of 21.6% with satisfactory performance reproducibility. The unsealed devices retain 90% of their initial efficiency after 1100 h of continuous operation at 60–65 °C under metal‐halide lamps. It is anticipated that the integration of robotic platforms with the intelligent algorithm will facilitate the widespread adoption of effective autonomous experimentation to address the evolving needs and constraints within the materials science research community.

14 SOLAR ENERGY↗
DOE OSTI2024

A Neural Network-Based Power Mismatch Elimination Strategy for Integrated Solar and ESS AC/DC Systems (MARS)

The multiport autonomous reconfigurable solar power plant (MARS) is a promising concept for the integration of photovoltaic (PV) and energy storage system (ESS) to the transmission ac grid and a high-voltage direct current (HVdc) link. The presence of PV and ESS in each arm of the MARS results in uneven distribution of active power among different submodules (SMs), thereby leading to unbalanced SM capacitor voltages and potentially compromising the system stability. Moreover, in the case of partial shadings, shaded PV SMs will suffer from decreased power injections causing power mismatch in the MARS system. To address this issue, a neural-network-based power mismatch elimination (NNPME) strategy is proposed in this article. The proposed NNPME strategy optimizes ESS usage and leverages both dc and ac circulating currents to facilitate power transfer among the SMs, arms, and phases of the MARS system. Simulation and control hardware-in-the-loop (cHIL) experiments demonstrate the effectiveness of the proposed NNPME strategy. Compared with the traditional approaches, the proposed NNPME strategy can significantly enhance system efficiency and ensure stable and continuous operation, even in the presence of uneven power distribution within the MARS system.

14 SOLAR ENERGY↗
DOE OSTI2023

Evolution of coupled weakly driven waves in a dissipative plasma

The nonlinear collisional dynamics of coupled driven plasma waves in the presence of background dissipation is studied analytically within kinetic theory. Sufficiently near marginal stability, phase space correlations are poorly preserved and time delays become unimportant. The system is then shown to be governed by two first-order coupled autonomous differential equations of cubic order for the wave amplitudes and two complementary first-order equations for the evolution of their phases. That system of equations can be decoupled and further simplified to a single second-order differential equation of Liénard's type for each amplitude. Numerical solutions for this equation are obtained in the general case, while analytic solutions are obtained for special cases in terms of parameters related to the spacing of the resonances of the two waves in frequency space, e.g., wave lengths and oscillation frequencies. These parameters are further analyzed to find classes of quasi-steady saturation and pulsating scenarios. To classify equilibrium points, local stability analysis is applied, and bifurcation conditions are determined. When the two waves saturate at similar amplitude levels, their combined signal is shown to invariably exhibit amplitude beating and phase jumps of nearly π. In conclusion, the obtained analytical results can be used to benchmark simulations and to interpret eigenmode amplitude measurements in fusion experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗