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At least 649 records · Page 36

Nickel-incorporated Oxide Composites for Fiber-Optic Based Gas Sensing

Numerous high-value applications within the energy sector involve environmental conditions that are incompatible with traditional sensor technology due to degradation of electrical interconnects, packaging, or the sensors themselves. These can include chemically harsh conditions, high temperature operation, or the presence of electromagnetic interference due to high voltage. The fiber optic platform, constructed of robust, electrically insulating glass or single crystal oxides, offers a versatile and often low cost per node solution to this problem, especially with the integration of distributed sensing techniques such as optical time-domain and frequency-domain reflectometry (OTDR, OFDR). A major challenge of gas and chemical sensing on the optical fiber platform is the fabrication of robust and stable sensing materials that interact quickly and reversibly to the presence of the target analytes. In this work, we discuss the utilization of nickel-incorporated oxides on evanescent-field optical fiber sensors for gas sensing under harsh conditions relevant to multiple energy infrastructure applications. This paper will discuss a Ni/GDC (Ni / Gd-doped ceria) based sensing layer targeting conditions relevant for high-temperature (up to at least 800 oC) hydrogen sensing applications (e.g., for operation within a solid oxide fuel cell or electrolyzer). The impact of hydrogen at elevated temperatures on the optical properties of Ni/GDC will be shown and the material mechanisms for the optical response will be discussed.

gas sensors↗

A note on efficiently generating ionic configurations for opacity calculations

When calculating the spectral opacity of hot dense plasmas one often encounters the need to generate a list of detailed ionic configurations of bound states for each ion stage in the plasma. Here we present here a non-recursive algorithm for the efficient construction of such a list of states.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Transition metal vacancy and position engineering enables reversible anionic redox reaction for sodium storage

Triggering the anionic redox reaction is an effective approach to boost the capacity of layered transition metal (TM) oxides. However, the irreversible oxygen release and structural deterioration at high voltage remain conundrums. Herein, a strategy for Mg ion and vacancy dual doping with partial TM ions pinned in the Na layers is developed to improve both the reversibility of anionic redox reaction and structural stability of layered oxides. Both the Mg ions and vacancies (□) are contained in the TM layers, while partial Mn ions (~1.1%) occupy the Na-sites. The introduced Mg ions combined with vacancies not only create abundant nonbonding O 2p orbitals in favor of high oxygen redox capacity, but also suppress the voltage decay originated from Na–O–□ configuration. The Mn ions pinned in the Na layers act as “rivets” to restrain the slab gliding at extreme de-sodiated state and thereby inhibit the generation of cracks. The positive electrode, Na 0.67 Mn 0.011 [Mg 0.1 □ 0.07 Mn 0.83 ]O 2 , delivers an enhanced discharge capacity and decent cyclability. This study provides insights into the construction of stable layered oxide positive electrode with highly reversible anionic redox reaction for sodium storage.

Cai, Congcong [Wuhan Univ. of Technology (China)]↗

New principles of self‐organization created through the interplay of DNA condensates, microtubules, and motors

Bioinspired design—which holds great promise for a new generation of materials that are robust to defects, scalable under green manufacture, environmentally responsive, and programmably reconfigurable—requires mastery over molecular self-organization. Yet, from its specific mechanisms to most general architectures, the principles governing self-organization remain poorly understood and not even fully enumerated. For living systems, one obvious architectural principle is the modular reuse of a few simple molecular components in myriad combinations to achieve more complex phenomena. For example, the mechanical tasks of a cell are driven by the nonequilibrium dynamics of cytoskeletal filaments and molecular motors—the same filaments and motors, reprogrammed by a variety of modulators, perform tasks ranging from cell movement to division. Similarly, many compartmentalization tasks are performed by liquid-like condensates of simple components, which act as membraneless organelles to localize particular molecules in space and time (e.g. for gene regulation or RNA processing). In a few cases, condensates combine and interact with the cytoskeleton to create still more complex phenomena, e.g. the nucleation of microtubule asters from the centrosome (a protein condensate) to form the mitotic spindle during cell division. Very little is known about the fundamental mechanisms of such filament-plus-condensate phenomena. Despite few examples, the landscape of behaviors that can be achieved through the combination of condensates, filaments, and motors appears vast. However, exploration has been hindered by a lack of systems that have sufficiently programmable and dynamically tunable interactions between component condensates, filaments, and motors. We proposed to combine programmable DNA condensates, filamentous microtubules, and light-controlled motors into self-organizing systems whose principles go beyond those that have been observed in nature. In one limit, our systems will use microtubules and motors to create the molecular analog of a network of roads, which will organize droplets of DNA condensates capable of carrying molecular cargo. DNA condensates coupled to motors will flow from one microtubule aster hub to another, with their direction and timing controlled by DNA circuits. In another limit, microtubules will swim through bulk DNA condensates and exhibit strong interactions with boundaries between different types of condensates. Microtubule swimmers will reflect, get trapped, or refract at boundaries, under a mechanical analog of the classical optical index of refraction. DNA condensates having different mechanical indexes of refraction will be used to construct the analog of optical lenses, so that microtubule swimmers can be manipulated like light—collimated, diffracted, focused, and sorted based on properties analogous to wavelength. These two limits define two new architectures, within which multiple new mechanistic principles for self-organization will be discovered and explored. To explore these architectures, the motor-based coupling between DNA condensates and filaments will be controlled in time and space through the use of opto-proteins that create reversible links between DNA condensates and motors upon illumination. For each principle of interest, patterns of light will create virtual experiments by defining patterns of activity where DNA condensates walk along filaments, or filaments swim through condensates, and patterns of inactivity which will serve either as controls, or as boundary conditions vital to create the desired phenomena. This research serves the goals of Basic Energy Sciences Biomolecular Material Program by elucidating the principles by which the emergent, nonequilibrium behavior of collections of DNA condensates, motors, and microtubules can be programmed by environmental light patterns to create complex motion and materials transport. Because DNA condensates can be readily coupled to virtually any high performance nanomaterial, from carbon nanotubes, to metal nanoparticles, to light harvesting systems, this work provides a path to the construction, self-maintenance and reconfiguration of materials relevant to the Department of Energy.

60 APPLIED LIFE SCIENCES↗

Identifying Opportunities and Recommendations for the Integration of Advanced Reactors for Industrial Heat and Electricity Users

Nuclear power in the United States has been used traditionally to provide baseload electric power to the grid. Advancements in nuclear power to create smaller and safer reactors have renewed interest in nuclear as a source of both heat and electricity for a variety of applications. There is great interest in coupling nuclear reactors with industrial applications because nuclear power is a low carbon energy source that can be utilized for process heating, hydrogen generation, on-site electricity demand, and more. Idaho National Laboratory is developing guidelines to identify and assist industrial heat and electricity decarbonization by integrating with nuclear power plants (NPPs) to provide clean, abundant, and dispatchable energy. Considerations include specific industrial hazards which impact NPP siting, heat transport requirements and associated technologies, and implementation feasibility based on site-specific demand profiles. To assess integration feasibility, facility process models are developed based on real data obtained from a survey of baseline requirements and process information from industrial facilities in the United States. An assessment of safety and siting requirements is also performed to determine how nuclear industrial pairings could meet licensing requirements for NPPs. In addition, site characterization of an industrial plant is essential to determining the feasibility and suitable integration methods for each industry. Characterization includes facility distance from the nearest population center, site size, rail or water transport availability, and proximity to undeveloped land. These characteristics are important to determine reactor- or industry-side design requirements for safe, efficient operation. The siting and technical data assessment will reveal opportunities for single-use nuclear integration and co-location opportunities for industries to share benefits from a single reactor. In addition to existing facilities, this “energy-park” style cooperation could include new construction like data centers which can cost-share energy investments or provide a stable demand-and-revenue stream to the investor. Deliverables will contain a library of documents and models to guide various industries toward understanding nuclear technologies based on their users’ needs. This paper is a summary of the current project status, and provides insights on suitable pairings for specific industries and reactor technologies

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

The Mu2e crystal calorimeter

The Mu2e experiment at Fermilab will search for the charged-lepton flavour violating conversion of negative muons into electrons in the coulomb field of an Al nucleus, planning to reach a single event sensitivity of about $3\cdot10^{−17}$, four orders of magnitude beyond the current best limit.The conversion electron has a clear monoenergetic signature at 104.967 MeV, slightly below the muon rest mass, and will be identified by a complementary measurement carried out by a high-resolution tracker and an electromagnetic calorimeter (EMC). The calorimeter is composed of 1348 pure CsI crystals, each read by two custom UV-extended SiPMs, that are arranged in two annular disks. The EMC should achieve better than 10% energy resolution and 500 ps timing resolution for 100 MeV electrons and maintain extremely high levels of reliability and stability and in a harsh operating environment with high vacuum, 1 T B-field and radiation exposures up to 100 krad and $10^{12} \rm{n}_\rm{1MeVeq}/\rm{cm}^{2}$.The calorimeter technological choice, along with the design of the custom front-end electronics, cooling and mechanical systems were validated through an electron beam test on a large-scale 51-crystals prototype (Module-0) and extensive test campaigns that characterised and verified the performance of crystals, photodetectors, analogue and digital electronics. This included hardware stress tests and irradiation campaigns with neutrons, protons, and photons.The production and QC phases of all calorimeter components is completed apart for the digital electronics that has been revised for improving its resilience to SEU and SEL. A series of vertical slice tests with the final electronics is being carried out on the Module-0 at LNF along with the implementation and validation of the calibration procedures. The first disk has been assembled in 2022 while the second disk is under assembly at the moment of writing. Status of construction will be summarised, along with plans for commissioning and first calibration of the fully assembled disks.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

A Comparison of the Environmental Effects of Open-Loop and Closed-Loop Pumped Storage Hydropower

Pumped storage hydropower (PSH) capabilities are generally characterized as either open-loop or closed-loop. The U.S. Department of Energy (DOE) defines open-loop PSH as “continuously connected to a naturally flowing water feature,” and closed-loop PSH as “not continuously connected to a naturally flowing water feature.” All the PSH projects constructed in the United States to date are open-loop, so the potential environmental effects of closed-loop systems are not as well documented as the effects of open-loop systems. To address this knowledge gap, the DOE Water Power Technologies Office, under its HydroWIRES Initiative, has prepared this report to: (1) compare the potential environmental effects of open-loop PSH projects with those of closed-loop PSH projects; (2) describe how these effects are being avoided, minimized, or mitigated at existing projects in other countries and proposed projects in the United States; and (3) discuss the relative significance of the environmental issues. The report begins with a brief introduction on the current status of PSH development in the United States. Next, the report describes the current Federal Energy Regulatory Commission (FERC) hydropower licensing process, emphasizing some recent regulatory changes that affect closed-loop PSH development. The report then provides a summary comparison of the environmental effects of constructing and operating open-loop and closed-loop PSH systems and discusses the relative significance of those issues. This comparison and discussion are based on the results of a literature review and a review of FERC licensing records. The literature review includes journal articles, technical reports, and presentations on the environmental effects of PSH systems. It includes literature from the United States as well as countries where closed-loop PSH projects have been constructed. The FERC records review examines the FERC licensing record (e.g., National Environmental Policy Act documents and license orders) to identify the environmental effects anticipated and mitigation measures proposed for six of the closed-loop PSH projects currently licensed or permitted in the United States. For comparison, the FERC records review also discusses the environmental effects and mitigation measures for four open-loop PSH projects proposed or currently operating in the United States. The comparison of effects between open-loop and closed-loop projects is relative; that is, it characterizes the impacts of each project type as generally lower or higher than another project type. The comparison reflects general trends among project types because there are sometimes exceptions to the examples cited. The comparison is based on both spatial (location) and temporal (duration) factors and reflects both the severity and likelihood of effects. The report concludes that the environmental effects of closed-loop PSH projects are generally lower (i.e., more localized and of shorter duration) than those of open-loop PSH projects because they are located “off-stream,” minimizing aquatic and terrestrial impacts, and often have greater siting flexibility than open-loop PSH projects. For certain closed-loop project designs, however, impacts to groundwater may be higher relative to open-loop projects and should be considered in any environmental review.

13 HYDRO ENERGY↗

Activationof Oxygen Evolution Electrocatalysis viaReduced Ruthenium–Oxygen–Ruthenium Coordination

Noble metal oxides such as RuO2 are the state-of-the-art electrocatalysts for anodic reactions in acidic electrolytes, but their scarcity and moderate activity greatly limit emerging renewable energy technologies. Here, we show that oxidized overlayers of ruthenium on earth-abundant manganese oxide (MnO2/o-RuOx) nanocrystal supports exhibit Ru chemical states associated with reduced Ru–O–Ru coordination that enable dynamic switching of hydrogen bonding, with *OH intermediates hydrogen bonding to surface O and *OOH intermediates bonding to protruding RuOx clusters. The resulting electrocatalysts exhibit an overpotential of 218.9 ± 0.3 mV at 10 mA cm–2 for the oxygen evolution reaction in acid, corresponding to a 2425% increase in Ru mass activity compared to RuO2, enabling the construction of electrolyzers that achieved 3 A cm–2 at 1.646 V, 5.54 A cm–2 at 1.8 V, and exhibited over 3000-h stability at 100 mA cm–2. These findings motivate further efforts to develop nanomaterials that harness reduced Ru–O–Ru coordination to enable emerging renewable energy technologies.

58 GEOSCIENCES↗

DEM analysis of the effect of interface transition zone on dynamic splitting tensile behavior of high-strength concrete based on multi-phase model

Highlights: • Crushable aggregates with the real geometry shape are generated by using clump-cluster method. • Flat-Joint Model is adopted as the constitutive law. • The tensile strength is almost not affected by ITZ strength when its strength exceeds 0.8 times that of mortar. • A modified formula that can reflect the functional relationship between the ITZ strength and the TDIF is proposed. The tensile strength is one of the main parameters in the design of concrete structures and has an important influence on the cracking performance and durability of concrete materials. As the weak region in concrete, the strength of the interface transition zone (ITZ) directly affects the dynamic mechanical response of concrete. Meanwhile, considering that the tensile performance of concrete is far weaker than its compressive performance, the study of the strength of ITZ is of great significance to the dynamic tensile fracture characteristics and mechanical properties of concrete. In this paper, a method combining 3D scanning technology and Clump-Cluster was proposed to generate a real geometry shape model of crushable aggregate. On this basis, the 3D discrete element model (DEM) of high-strength concrete was constructed using the Flat-Joint Model (FJM). The effects of the ITZ strength on the failure mode, number of microcracks, tensile strength and strain rate effect of high-strength concrete under strain rates from 0.01/s to 100/s were studied by splitting tensile test. The simulation results indicate that the number of microcracks generated decreases with the increase of ITZ strength, and the proportion of ITZ cracks decreases obviously. When the ITZ strength exceeds the critical value of 0.8 times that of mortar, the tensile strength is almost not affected by ITZ strength. In addition, based on the numerical simulation results, a modified formula that can reflect the functional relationship between the ITZ strength and the dynamic increasing factor of the concrete tensile strength (TDIF) is proposed, and the rationality of the TDIF modified formula is verified.

36 MATERIALS SCIENCE↗

Metabolic multireactor: Practical considerations for using simple oxygen sensing optodes for high-throughput batch reactor metabolism experiments

We present a system for carrying out small batch reactor oxygen consumption experiments on water and sediment samples for environmental questions. In general, it provides several advantages that can help researchers achieve impactful experiments at relatively low costs and high data quality. In particular, it allows for multiple reactors to be operated and their oxygen concentrations to be measured simultaneously, providing high throughput and high time-resolution data, which can be advantageous. Most existing literature on similar small batch-reactor metabolic studies is limited to either only a few samples, or only a few time points per sample, which can restrict the ability for researchers to learn from their experiments. The oxygen sensing system is based very directly on the work of Larsen, et al. [2011], and similar oxygen sensing technology is widely used in the literature. As such we do not delve deeply into the specifics of the fluorescent dye sensing mechanism. Instead, we focus on practical considerations. We describe the construction and operation of the calibration and experimental systems, and answer many of the questions likely to come up when other researchers choose to build and operate a similar system themselves (questions we ourselves had when we first built the system). In this way, we hope to provide an approachable and easy to use research article that can help other researchers construct and operate a similar system that can be tailored to ask their own research questions, with a minimum of confusion and missteps along the way.

3D printing↗

Simultaneous Discovery of Positive and Negative Interactions Among Rhizosphere Bacteria Using Microwell Recovery Arrays

Understanding microbe-microbe interactions is critical to predict microbiome function and to construct communities for desired outcomes. Investigation of these interactions poses a significant challenge due to the lack of suitable experimental tools available. Here we present the microwell recovery array (MRA), a new technology platform that screens interactions across a microbiome to uncover higher-order strain combinations that inhibit or promote the function of a focal species. One experimental trial generates 10 4 microbial communities that contain the focal species and a distinct random sample of uncharacterized cells from plant rhizosphere. Cells are sequentially recovered from individual wells that display highest or lowest levels of focal species growth using a high-resolution photopolymer extraction system. Interacting species are then identified and putative interactions are validated. Using this approach, we screen the poplar rhizosphere for strains affecting the growth of Pantoea sp. YR343, a plant growth promoting bacteria isolated from Populus deltoides rhizosphere. In one screen, we montiored 3,600 microwells within the array to uncover multiple antagonistic Stenotrophomonas strains and a set of Enterobacter strains that promoted YR343 growth. The later demonstrates the unique ability of the platform to discover multi-membered consortia that generate emergent outcomes, thereby expanding the range of phenotypes that can be characterized from microbiomes. This knowledge will aid in the development of consortia for Populus production, while the platform offers a new approach for screening and discovery of microbial interactions, applicable to any microbiome.

59 BASIC BIOLOGICAL SCIENCES↗

An Initial Evaluation of the Elevated-Temperature Cyclic Properties of Optimized 316H Stainless Steel Fabricated by Powder Metallurgy Hot Isostatic Pressing

Powder metallurgy hot isostatic pressing (PM-HIP) is a mature advanced manufacturing technology, which can consolidate metallic powder under high temperature and pressure to generate near-net shape components. This process can lower production costs and reduce component lead times for nuclear reactor construction and can be readily deployed in the near term for microreactor components because of their smaller size. The purpose of this work is to continue the evaluation of elevated-temperature cyclic material properties for PM-HIP 316H stainless steel. Prior scoping results have shown that the commercially procured PM-HIP stainless-steel materials have reduced creep-fatigue performance compared to wrought 316 stainless steels. To better understand how PM-HIP processed material properties compare to traditional manufacturing methods, additional billets of PM-HIP 316H stainless steel were procured and tested. This testing is necessary to understand how elevated-temperature properties are influenced by the PM-HIP process and what data are needed for incorporating PM HIP 316H into the American Society of Mechanical Engineers Boiler Pressure Vessel Code, Section III, Division 5 for high temperature reactor construction. Specifically, an additional PM-HIP 316H stainless steel billet with lower oxygen and nitrogen concentrations was fabricated by the Nuclear Advanced Manufacturing Research Centre of the United Kingdom and tested to understand if elevated-temperature cyclic properties can be improved. The creep-fatigue resistance of the material from this new billet did not show appreciable improvement compared to prior testing.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Empowering Lineworkers: The Case for Active Exoskeletons in Utility Work

Exoskeletons have evolved from early medical prototypes to advanced systems capable of addressing physical demands in various industries. This report explores the potential of active exoskeleton technology within the utility sector, focusing on its application for linemen who face significant risks of work-related musculoskeletal disorders (WMSDs). By analyzing existing literature on exoskeletons across industries such as construction, manufacturing, and military, the study identifies a gap in utility-specific applications. Task-specific design features like gravity compensation, limb support, and advanced safety measures, improve exoskeletons’ potential to alleviate physical strain, reduce workplace injuries, and enhance productivity. This review emphasizes the need for targeted research and development to optimize exoskeleton designs for the utility sector to provide benefits for workers, companies, and the broader community.

60 APPLIED LIFE SCIENCES↗

Efficient Reinforcement Learning for Real-Time Hardware-Based Energy System Experiments: Preprint

In the context of urgent climate challenges and the pressing need for rapid technology development, Reinforcement Learning (RL) stands as a compelling data-driven method for controlling real-world physical systems. However, RL implementation often entails time-consuming and computationally intensive data collection and training processes, rendering them inefficient for real-time applications that lack non-real-time models. To address these limitations, real-time emulation techniques have emerged as valuable tools for the lab-scale rapid prototyping of intricate energy systems. While emulated systems offer a bridge between simulation and reality, they too face constraints, hindering comprehensive characterization, testing, and development. In this research, we construct a surrogate model using limited data from simulated systems, enabling an efficient and effective training process for a Double Deep Q-Network (DDQN) agent for future deployment. Our approach is illustrated through a hydropower application, demonstrating the practical impact of our approach on climate-related technology development.

deep Q-learning↗

Human Factors and Technologies Design to Improve User Acceptance of Pooled Rideshare for Increasing Transportation System Energy Efficiency

This multi-year project delivered a comprehensive, human-factors-driven framework to understand, model, and improve pooled rideshare (PR) adoption in the United States. Through three large-scale national survey studies involving more than 16,000 participants across multiple cities and demographic groups, the research established one of the most extensive datasets to date on user perceptions, behavioral barriers, and service expectations related to pooled rideshare. These data revealed key human factors barriers of user acceptance of PR and suggested potential actionable experience optimizations that could lead to increased PR usage. This foundational knowledge guided the development of novel human-factors models and behavioral choice models that quantify how psychological, demographic, and trip-level factors influence willingness to pool. Building on these empirical insights, the project developed advanced behavioral modeling tools, including mixed logit and integrated choice and latent variable models, to capture both observable and latent influences on PR adoption. These models significantly improved the ability to predict riders’ acceptance of pooled trips, explaining choice heterogeneity through latent constructs such as safety, service experience, privacy concerns, time sensitivity, and environmental attitudes. Together, these models provide a robust analytical foundation for designing PR systems that more effectively meet user needs. The project translated human-factors insights and behavioral models into actionable technology innovations by extending POLARIS—an agent-based, activity-based travel simulation platform—into a fully functional pooled rideshare simulation environment. New PR modules, acceptance models, and regional scenarios were implemented for Greenville, SC and Austin, TX, enabling high-fidelity validation of algorithmic strategies under realistic demand and traffic conditions. The simulation platform supported the development and evaluation of adaptive discount-based assignment algorithms, enhanced willingness-to-pay formulations, demographic-aware incentive mechanisms, and a proactive joint assignment and repositioning strategy. Simulation results demonstrated substantial gains in pooling uptake, average vehicle occupancy, energy efficiency, and fleet profitability. In Greenville, pooling adoption more than doubled, while reductions in vehicle-miles traveled and energy consumption were significant. In Austin, pooling improvements were achieved with minimal service-quality trade-offs, and profitability increased across all fleet sizes. Through this research, we developed a comprehensive understanding of the human factors barriers that limit user acceptance of pooled rideshare services. These insights enabled the design of human-factors-aware pooled rideshare technologies that more effectively address user concerns and improve adoption rates. By integrating these models into an advanced agent-based simulation framework, we demonstrated that higher adoption of pooled rideshare can lead to measurable improvements in energy efficiency and system performance. Together, these contributions establish a validated pathway from human-centered analysis to technology development and energy-saving outcomes, supporting national goals for more sustainable and efficient mobility systems.

Jia, Yunyi↗

Decisions and coordination of retailer-led low-carbon supply chain under altruistic preference

A low-carbon supply chain formed by a dominant retailer and a small and medium-sized manufacturer (SMM) is considered. Because the SMM faces the high cost pressure of adopting carbon emission reduction (CER) technologies, the retailer may take an altruistic preference for the long-term sustainability of the chain. Three decision-making models, centralized, decentralized without altruistic preference, and decentralized with altruistic preference, are constructed to compare decisions and profits of both parties. Since neither decentrailized models can lead to a coordinated solution that is incentive compitable, a coordination contract, referred to as the cost sharing contract with altruistic preference, is proposed. Numerical study shows that the altruistic preference can help increase the SMM's profit and system efficiency but decrease the retailer's profit. The coordination contract requires the retailer to adjust the unit profit and share more than half of the CER cost. Finally, it is found that the wholesale price is the lowest in the coordination contract and the comparison of unit profit depends on the coefficient of CER cost.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

An unconditionally stable, time-implicit algorithm for solving the one-dimensional Vlasov–Poisson system

The development of an implicit, unconditionally stable, numerical method for solving the Vlasov–Poisson system in one dimension using a phase-space grid is presented. The algorithm uses the Crank–Nicolson discretization scheme and operator splitting allowing for direct solution of the finite difference equations. This method exactly conserves particle number, enstrophy and momentum. A variant of the algorithm which does not use splitting also exactly conserves energy but requires the use of iterative solvers. This algorithm has no dissipation and thus fine-scale variations can lead to oscillations and the production of negative values of the distribution function. We find that overall, the effects of negative values of the distribution function are relatively benign. We consider a variety of test cases that have been used extensively in the literature where numerical results can be compared with analytical solutions or growth rates. We examine higher-order differencing and construct higher-order temporal updates using standard composition methods.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗