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DOE OSTI2021

WaterTAP3 (The Water Technoeconomic Assessment Pipe-Parity Platform)

The Water Technoeconomic Assessment Pipe-Parity Platform (WaterTAP3) was developed under the National Alliance for Water Innovation (NAWI) to facilitate consistent technoeconomic assessments of desalination treatment trains. The WaterTAP3 is an analytically robust modeling tool that can be used to evaluate water technology cost, energy, environmental, and resiliency tradeoffs across different water sources, sectors, and scales. The model simulates steady-state water treatment train performance and costs including flow and constituent mass balance across unit processes, based on source water conditions, configurations of treatment technologies, and system-level techno-economic assumptions. Users can build a new treatment train by connecting any number of unit processes, specific for their context and system, or selecting a train from the treatment train library. The model contains various technical and cost parameter options for a range of treatment processes and a library of influent water quality characteristics for a variety of source waters and case studies. Users can customize water quality parameters to evaluate the technology performance in their context. The model can be set up for different assessment needs including simulation, optimization, and uncertainty and sensitivity analyses. The results from WaterTAP3 can help identify trade-offs among the different system performance metrics, with insight on how particular technologies or systems promote pipe-parity. The flexibility and comprehensive scope of the tool makes it a promising solution to industry-wide water technoeconomic evaluations, leading to more informed water investment decisions and technologies. As a user-friendly, open-source platform, WaterTAP3 can be used by industry, academia, policymakers, planners, and those with or without extensive analytical experience.

Miara, Ariel↗

DOE OSTI2021

Water Technoeconomic Assessment Pipe-Parity Platform (WaterTAP3)

Miara, Ariel↗

DOE OSTI2025

The Effect of Flow on CO2 Corrosion of Self-Healing Metallic Coatings

Internal corrosion is an issue that affects natural gas pipelines, a significant part of the United States’ energy infrastructure. Over time, this corrosion has worn away longstanding pipelines due to the original construction materials used for the lines and impurities in the gas and liquid streams flowing through them. The main impurities in natural gas are H2O, CO2, H2S, and O2. One of the leading causes of corrosion is the CO2 dissolved in water, giving rise to carbonic acid formation, which can further dissolve the steel pipe. The National Energy Technology Laboratory (NETL) has been studying different solutions to this problem. One potential answer is a self-healing sacrificial metallic coating applied by a novel cold spray technique. This study explored the impact of flow on corrosion with this coating and carbon steel when exposed to a saturated CO2 environment by simulating the pipeline flow profile in a small-scale lab setting. The samples were evaluated using multiple electrochemical techniques that found corrosion rates and were backed up with surface analysis to conclude the behavior of the corrosion mechanisms. The cold spray coating exhibited steel corrosion protection under flow conditions. This study has significantly advanced our understanding of CO2 corrosion, particularly in the context of natural gas pipelines and coating design.

carbon steel↗

DOE OSTI2025

The Effect of Flow on CO2 Corrosion of Self-Healing Metallic Coatings

Internal corrosion is an issue that affects natural gas pipelines, a significant part of the United States energy infrastructure. Over time, this corrosion has worn away longstanding pipelines due to the original construction materials used for the lines and impurities in the gas and liquid streams flowing through them. The main impurities in natural gas are H2O, CO2, H2S, and O2. One of the leading causes of corrosion is the CO2 dissolved in water, giving rise to carbonic acid formation, which can further dissolve the steel pipe. The National Energy Technology Laboratory (NETL) has been studying different solutions to this problem. One potential answer is a self-healing sacrificial metallic coating applied by a novel cold spray technique. Previous studies at NETL have shown that the zinc-rich self-healing coating can withstand corrosion through passivation and create a barrier to the diffusion of corrosive species. This study explored the impact of flow on corrosion with this coating and carbon steel when exposed to a saturated CO2 environment by simulating the pipeline flow profile in a small-scale lab setting. The samples were evaluated using multiple electrochemical techniques that found corrosion rates and were backed up with surface analysis to conclude the behavior of the corrosion mechanisms.

CO2 corrosion↗

DOE OSTI2023

Asymptotic hydrogen redistribution analysis in yttrium-hydride-moderated heat-pipe-cooled microreactors using DireWolf

Yttrium hydride (YH x ) is one of the materials being considered for moderating thermal and epithermal nuclear microreactors. One potential issue with YH x use is that the hydrogen redistributes in the hydride when thermal and concentration gradients are present. This hydrogen redistribution leads to spatial gradients in the hydrogen concentration, thus affecting neutron transport in the reactor. Here, by building upon observations in prior works, this paper aims to gain a better understanding of the reactivity feedback associated with such hydrogen redistributions. In particular, we wish to understand the sign (+/–) of the hydrogen redistribution neutronic feedback, its order of magnitude, and its underlying physical causes. To achieve this goal, the DireWolf multiphysics software driver was used to solve the coupled radiation transport, heat transfer, heat pipe two-phase flow, and hydrogen redistribution equations for the Simplified Microreactor Benchmark Assessment (SiMBA) problem, a full-core microreactor numerical benchmark developed at Idaho National Laboratory.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Development of a Testbed for Pipeline Flushing - 20425

Pipelines which carry high-level waste within the DOE complex should be properly flushed in the cases where stationary or moving beds of solid sediment occur, or lines are prone to hydrogen gas buildup. Present guidelines establish a minimum for the amount of water (flush volume) and flush velocity values used for post-transfer flushing operations to achieve satisfactory cleaning of pipelines. However, further studies are needed to find optimal operating velocity modes/values in order to minimizing the flush volume and consequent downstream waste. These efforts are significantly helpful to DOE waste remediation sites by preserving tank storage, preventing additional waste processing, and minimizing dilution and changes in waste chemistry. An experimental test loop was recently developed for study of non-Newtonian slurry flushing at the Florida International University (FIU). This loop was designed to create sediment beds of various materials and bed heights and investigate parameters that effect the efficiency of flushing operations. The objective is to find flush velocity values/modes which lead to satisfactory cleaning of transport lines with a minimum amount of water usage. A 165 ft experimental test loop made of 3-inch carbon steel pipes was constructed and used in initial testing campaigns. This pipe loop was equipped with real-time monitoring instruments to record variation of pressure, density, mass flow rate, and temperature during testing. Post-flush in-situ no-flow evaluations were performed using ultrasonic, endoscopy, and visual inspection. Additional post-flush evaluations were conducted using filtration and density monitoring of residuals within a designated circulations loop. These provisions enable comparison of pipeline cleanness before the start and after termination of flushing operations for efficiency evaluation. This paper presents efforts associated with flushing of kaolin-water mixtures at different concentrations and with various flush volume and flush velocity values/modes. In initial testing, efforts focused on creating repeatable sediment beds inside the pipeline in both fully-flooded (no pre-flush drainage) and gravity-drained (pre-flush drained) systems. Bed characterization (i.e., measurement of sediment height and solids concentration) was conducted to ensure about consistency of initial conditions between tests. Preliminary results for flushing study of 10% vol. kaolin-water mixtures starting from a fully-flooded initial condition showed that flushing with 1-line volume (65 gallons) could remove up to 72 percent of solids from the pipeline. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

Surface Treatment Strategies for Mitigating Gas Hydrate & Asphaltene Formation, Growth, and Deposition in Flowloops

Abstract Numerous solids including gas hydrates, waxes, and asphaltenes have the potential to form in the production lines of gas and oil fields. This creates a highly non-ideal scenario as the accumulation of said species leads to flow assurance issues, especially with long-term processes like deposition. Since an ever-increasing amount of material is deposited in place at the pipe surface, production stoppage or active mitigation efforts become inevitable. The latter production issues result in increased safety risks and operational expenditures. Therefore, a cost-effective, passive deposition mitigation technology, such as a pipeline coating or surface treatment is especially appealing. The ability to address multiple pipeline flow assurance issues simultaneously without actively disrupting production would represent a dramatic step forward in this area. This study is part of a long-term ongoing effort that evaluates the performance and application of an omniphobic surface treatment for solids deposition prevention in industrially relevant systems. In particular, this specific work concentrates on the efficacy and robustness of the treatment under fully flowing conditions. The apparatuses utilized for this include two flowloops: a lab-scale, high-pressure flowloop for gas hydrate and surface treatment durability studies, and a bench-scale, atmospheric pressure loop for crude oil and asphaltene experiments. Film growth in high-pressure flowloop tests corroborated previous reports of delayed gas hydrate nucleation observed in rocking cells. Without the aid of the memory effect, treated oil-dominated experiments never experienced hydrate formation, spending upwards of a week in the hydrate stability zone (at the subcooled/fluid test conditions). Subsequent tests which utilized the memory effect then revealed that the hydrate formation rate reduced in the presence of the surface treatment compared to a bare stainless-steel surface. This testing was part of a larger set of trials conducted in the flowloop, which lasted about one year. The surface treatment durability under flowing conditions was evaluated during this time. Even after experiencing ∼4000 operating hours and 2 full pressure cycles, no evidence of delamination or damage was detected. Finally, as part of an extension to previous work, corroded surface asphaltene deposition experiments were performed in a bench-top flowloop. Treated experiments displayed an order of magnitude reduction in both total oil (all fractions of crude oil) and asphaltene fraction deposited.

03 NATURAL GAS↗

DOE OSTI2020

Development of the INL Thermal Energy Distribution System (TEDS) in the Modelica Eco-System for Validation and Verification

This report provides an overview on the development of the Thermal Energy Distribution System (TEDS) in the Modelica process model eco-system at Idaho National Laboratory as part of the integrated energy system initiative. Model development has led to the creation of a dynamic process model of the experimental TEDS facility housed within the Engineering Science Laboratory (ESL) at INL. The model was then used during the pre-construction phase of the experimental effort to inform experimental design (insulation requirements, bypass line placement, expected performance of components) and to test innovative control schemes prior to the initial operation. The TEDS model developed in Modelica includes the primary components of the TEDS experimental unit including: a 200kW Chromalox heater, a single-tank packed bed thermal energy storage system filled with 0.125 inch Alumina (Al 2 O 3 ), an ethylene-glycol to Therminol-66 heat exchanger, system piping, six control valves, and all associated temperature, pressure, and mass flow sensors. The model does not include nitrogen fill gas tanks, or associated overfill tanks, as these are not part of standard system control. Two simulation sets were run. The first is a five-hour test that operates as a shakedown test for the facility. This simulation puts the facility through all five potential operating modes and showcases the ability of valving, control sensors, and component controllers to meet the system demands. The second case imposes a typical summer day demand on the system from a region with mixed commercial and residential electrical needs where the generator alone cannot meet peak demand but instead requires the thermal storage unit to act as a peaking unit. Over the course of the fifteen-hour discharge cycle heat losses account for a heat loss of approximately 15°C in outlet temperature. Such heat losses would lead to a decrease in overall system efficiency and may lead to additional design changes for such designs in the future that may include a topping heater. Through commencement of this work, a systems level model of TEDS with associated control systems, sensors, piping diameters, and component capabilities has been created. This model has been utilized in the pre-experimental phase to inform system design, insulation thicknesses, and potential control schemes to operate the system effectively and safely. Once TEDS begins operation, this model will be refined, tuned, and used for validation and verification purposes.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Reducing Ohmic Resistances in Membrane Capacitive Deionization Using Micropatterned Ion-Exchange Membranes, Ionomer Infiltrated Electrodes, and Ionomer-Coated Nylon Meshes

Membrane capacitive deionization (MCDI) is an emerging water desalination platform that is compact, electrified, and does not require high-pressure piping. Herein, highly conductive poly(phenylene alkylene) ion-exchange membranes (IEMs) are micropatterned with different surface geometries for MCDI. The micropatterned membranes increase the interfacial area with the liquid stream leading to a 700 mV reduction in cell voltage when operating at constant current (2 mA cm -2 ; 2000 ppm NaCl feed) while improving the energy normalized adsorbed salt (ENAS) value by 1.4 times. Combining the micropatterned poly(phenylene alkylene) IEMs with poly(phenylene alkylene) ionomer-filled electrodes reduces the cell voltage by 1000 mV and improves the ENAS values by 2.3 times relative to the base case. This reduction in cell voltage allows for higher current density operation (i.e., 3–4 mA cm -2 ) . The reduction in cell voltage is ascribed to the ameliorating ohmic resistances related to ion transport at the membrane-process stream interface and in the carbon cloth electrode. Finally, porous ionic conductors are implemented into the spacer channel with flat and micropatterned IEM configurations and ionomer infiltrated electrodes. For the configuration with flat IEMs, the porous ionic conductor improves ENAS values across the current density regime (2–4 mA cm -2 ), while for micropatterned IEMs it gets improved only at 4 mA cm -2 .

42 ENGINEERING↗

DOE OSTI2020

Radiative heat transfer in FLiBe molten salt participating medium in a vertical heated tube under forced and mixed convection laminar flows

The contribution of radiative heat transfer (RHT) to convective heat transfer in a heated vertical pipe with laminar flow and constant wall temperature, for FLiBe molten salt, is investigated computationally. The combined effects of conduction in the fluid, forced convection, buoyancy, temperature-dependent physical properties, and thermal radiation are investigated. The P1 approximation is employed in the discretization of the Radiative Transfer Equation (RTE). The COMSOL Multiphysics software is used to generate the numerical solutions. The theoretical analysis developed here demonstrates that only for intermediate values of the optical thickness, i.e. τ D ~ O 1 , the participating media effects are expected to be important. This analysis is confirmed computationally and a value of τ D ≈ 4 is shown to lead to the highest increase in overall heat transfer behavior. Under forced convection, the Nusselt ratio N u total / N u no - rad reaches a peak value of 1.76 at τ D = 4 and z/D = 200 , and is less than 1.1 for τ D < 0 . 1 and τ D > 60 . Under aiding-flow mixed convection, N u total / N u no - rad reaches a peak of 1.34 at τ D = 4 . 2 and is less than 1.1 for τ D < 0 . 4 and τ D > 36 . Under opposing-flow mixed convection, Nu total / Nu no - rad reaches a peak of 1.81 at τ D = 4 . 2 and is less than 1.1 for τ D < 0 . 2 and τ D > 50 . RHT effects on the overall heat transfer are most pronounced in opposing mixed convection, where N u total / N u no - rad is 2.26 observed at z/D = 50 . The sensitivity to wall emissivity is evaluated; in forced convection, the peak N u total / N u no - rad is 1.66 at ε = 0 (reflective wall) and 2.04 at ε = 1 (absorptive wall). Finally, the sensitivity to pipe diameter is also discussed. Overall, for a vertical heated tube, radiative heat transfer effects lead to enhancement of heat transfer by as high as a factor of two, and they depend on the optical thickness of the flow, mixed convection environment ( Gr / R e 2 and direction of flow relative to the gravitational force), surface emissivity, and entrance effects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Spallation Neutron Source Hydrogen Relief Analysis for the Cryogenic Moderator System

The Spallation Neutron Source at Oak Ridge National Laboratory operates the Cryogenic Moderator System (CMS) which provides hydrogen cooling at 20K to three neutron moderators. Each hydrogen loop is protected by multiple burst discs and reclosing relief valves. As a result of the Proton Power Upgrade project, the CMS moderator loops will hold more hydrogen and thus require piping modifications. Operational experience has demonstrated that transient pressure increases in these hydrogen loops occasionally result in the rupture of the burst discs. The causes for pressure transients in the system that might lead to hydrogen venting are varied and complex, for example loss of vacuum or cooling. Dynamic simulation and analysis of the parameters considered as the worst-case relief venting scenario were performed and will be presented.

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

Key Nuclear Data Impacting Reactivity in Advanced Reactors

Advanced reactor concepts currently being developed throughout the industry are significantly different from light water reactor (LWR) designs with respect to geometry, materials, and operating conditions, and consequently, with respect to their reactor physics behavior. Given the limited operating experience with non-LWRs, the accurate simulation of reactor physics and the quantification of associated uncertainties are critical for ensuring that advanced reactor concepts operate within the appropriate safety margins. Nuclear data are a major source of input uncertainties in reactor physics analysis. As part of an ongoing project at Oak Ridge National Laboratory (ORNL), the effects of nuclear data uncertainties on key figures of merit associated with advanced reactor safety are being assessed for selected advanced reactor technologies. Key nuclear data relevant for reactor safety analysis for each selected advanced reactor technology were identified, and their impact on important key figures of merit was assessed. Available advanced reactor specifications were reviewed, results from studies performed at ORNL and other research institutions were consulted, and available evaluated nuclear data libraries were analyzed. This report summarizes the key nuclear data for nuclides in the fuel, as well as other significant data, including scattering and neutron capture in various materials for the moderator, coolant, and structure of the considered advanced reactors. For the considered advanced reactors that use low-enriched uranium (LEU) fuel, results from LWR studies provided insight into relevant nuclear data given the lack of available studies specifically addressing these new systems. The major nominal missing data that were identified consist of thermal scattering data and 135m Xe cross section data for molten salt reactor (MSR) analysis. The identified major gaps with respect to nuclear data uncertainties are missing uncertainties of thermal scattering data for high temperature gas-cooled reactors and moderated MSR systems, and incomplete uncertainties on angular distributions in particular for fast spectrum systems, such as sodiumcooled fast reactors, fast molten salt reactors, and heat pipe reactors. Furthermore, it was found that special attention should be paid to cross section and uncertainty differences between different evaluated nuclear data library releases, because significant differences in nuclear data that can lead to major differences in reactivity calculations were found, even for well-known nuclides.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2025

Unraveling the ecological success of Iodidimonas in a bioreactor treating oil and gas produced water

Iodidimonas sp., a bacterium found in bioreactors treating oil and gas produced water as well as iodide-rich brines, has garnered attention for its unique ability to oxidize iodine. However, little is known about the metabolic capabilities that enable Iodidimonas sp. to thrive in certain unique ecological niches. In this study, we isolated, characterized, and sequenced three strains belonging to the Iodidimonas genus from the sludge of a membrane bioreactor used for produced water treatment. We investigated the genomic features of these isolates and compared them with the four publicly available isolate genomes from this genus, as well as a metagenome-assembled genome from the source bioreactor. Our Iodidimonas isolates had several genes associated with mitigating salinity, heavy metal, and organic compound stress, which likely help these bacteria to survive in produced water. Phenotyping tests revealed that while the isolates could utilize a wide variety of simple carbon substrates, they failed to degrade aliphatic or aromatic hydrocarbons, consistent with the lack of genes associated with common hydrocarbon degradation pathways in their genomes. We hypothesize that these microbes may lead a scavenging lifestyle in the bioreactor and similar iodide-rich brines. IMPORTANCE: Occupying a niche habitat and having few representative isolates, the genus Iodidimonas is a relatively understudied alphaproteobacterial group. Its ability to corrode pipes in iodine production facilities has economic implications, and its ability to generate potentially carcinogenic iodinated organic compounds during treatment of oil and gas produced water may cause environmental and health concerns with the recycling of treated water. Therefore, detailed characterization of the metabolic potential of the Iodidimonas isolates in this study both sheds light on their adaptation to the environmental conditions they inhabit and has environmental and economic significance.

Acharya, Shwetha M↗

DOE OSTI2020

Connecting particle interactions to agglomerate morphology and rheology of boehmite nanocrystal suspensions

Rheology imposes significant challenges on processing of complex suspensions such as nuclear waste slurries at the Hanford and Savannah River sites. Understanding rheology connecting to microstructures and underlying particle interactions in complex slurries is therefore important for both fundamental knowledge and practical applications. Here, we use suspensions of aluminum oxyhydroxide minerals in the form of boehmite as an analog of the radioactive waste slurry to gain physical insights on the correlation between particle interactions, microstructures, and slurry rheology. Specifically, we use a combination of Couette rheometry and small-angle scattering techniques (independently and simultaneously) to understand how the slurry microstructure changes under flow and how these structural changes manifest themselves in the bulk rheology of the suspensions. Our experiments show that the boehmite slurries are thixotropic, with the rheology and structure of the suspensions changing with increasing exposure to flow. In the slurries, particle aggregates begin as loose, system-spanning clusters, but exposure to moderate shear rates causes the aggregates to irreversibly consolidate into denser clusters of finite size. The microstructural changes directly influence the rheological properties of the slurries such as viscosity and viscoelasticity. More importantly, our study shows that solution pH affects the amount of structural rearrangement and the kinetics of the rearrangement process, with an increase in pH leading to faster and more dramatic changes in the bulk rheology. Such dynamic microstructural changes and resultant rheology are understood via correlations between particle interactions and strength of particle network, coupled with surface chemistry and anisotropic nature of particle interactions. Nearly identical structural changes are also observed in Poiseuille flow geometries, implying that the observed changes are relevant in the pipe flow conditions present during waste processing.

Weston, Javen S.↗

DOE OSTI2024

Integrated positron emission particle tracking (PEPT) and X-ray computed tomography (CT) imaging of flow phenomena in twisted tape swirl flow

Abstract A combined positron emission particle tracking (PEPT) and X-ray computed tomography (CT) technique is presented, and its utility is demonstrated through investigation of flow in a pipe with twisted tape swirl insert with varying flow conditions (diameter-based Reynolds numbers 16,300–63,300). A description of this technique is given, as well as data handling practices used to relate geometric information captured by CT to fluid flow data gathered via PEPT. It is found that the CT component is readily capable of capturing the stainless steel insert geometry in this present system, but the use of combined plastic and metal materials leads to artifacts in imaging of the plastic surface. Nonetheless, CT data are related to PEPT flow measurements, and average velocity fields are calculated via a pseudo-framing and interpolation scheme and used to visualize and interrogate key flow phenomena within the system. Radial velocity profiles of the mean flow characteristics are seen to collapse to a nearly common form across all flow conditions considered. Helical vortices are seen propagating through the flow field, generated by bypass flow around the gap between the insert and pipe wall, with additional coherent secondary flow structures seen in the higher Reynolds number cases. These findings enhance the understanding of the mixing mechanisms in these swirl flows and encourage the continued development of PEPT-CT methodologies for 3D flow measurements in optically inaccessible systems.

42 ENGINEERING↗

DOE OSTI2021

Development of an Innovative Inspection Tool for Superheater Tubes in Fossil Fuel Power Plants

Fossil fuel power plants are complex systems containing multiple components that require periodic health monitoring. Failures in these systems can lead to increased downtime for the plant, reduction of power, and significant cost for repairs. Inspections of the plant’s superheater tubes are typically manual, laborious, and extremely time-consuming. This is due to their small diameter size (between 1.3 and 7.6 cm) and the coiled structure of the tubing. In addition, the tubes are often stacked close to each other, limiting access for external inspection. This paper presents the development and testing of an electrically powered pipe crawler that can navigate inside 5 cm diameter tubes and provide an assessment of their health. The crawler utilizes peristaltic motion within the tubes via interconnected modules for gripping and extending. The modular nature of the system allows it to traverse through straight sections and multiple 90° and 180° bends. Additional modules in the system include an ultrasonic sensor for tube thickness measurements, as well as environmental sensors, a light detecting and ranging (LiDAR) sensor, and camera. Furthermore, these modules utilize a gear system that allows for 360° rotation and provides a means to inspect the entire internal circumference of the tubes.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Combined modeling and experiments to predict corrosion and embrittlement in dual-phase stainless steels within the MARMOT framework

Extending service of Light Water Reactors (LWRs) to beyond 60 years will demand high integrity of materials and components in the reactors. The accurate evaluation and prediction of materials performance under anticipated operating conditions are of particular importance for ensuring the safety of nuclear power plants over their extended lifetime. Stainless steels are extensively used as structural alloys in light water reactor (LWR) systems because of their excellent combination of mechanical properties and corrosion resistance. Austenitic stainless steel welds and cast austenitic stainless steels (CASS) contain significant amounts of ferrite ~5-30% and are ubiquitous in LWR piping (elbows, pump casings, valves) and internal structural components. During their lifetime, these components are subjected to thermal aging at the temperature range of 288-327°C for pressurized water reactors (PWR). A phase transformation within the ferrite phase of these materials leads to embrittlement and degradation in corrosion resistance, which undermines the materials selection criteria.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Space charge fields in azimuthally symmetric beams: Integrated Green's function approach

Electromagnetic fields induced by the space charge in relativistic beams play an important role in Accelerator Physics. They lead to emittance growth, slice energy change, and the microbunching instability. Typically, these effects are modeled numerically since simple description exists only inthe limits of large- or small-scale current variations. In this paper we consider an axially symmetric charged beam inside a round pipe and find the solution of the space charge problem that is valid in the full range of current variations. We express the solution for the field components in terms of Green’s functions, which are fully determined by just a single function. We then find that this function is an on-axis potential from a charged disk in a round pipe, with transverse charge density ρ⊥(r), and it has a compact analythical expression. We finally provide an integrated Green’s function based approach for efficient numerical evaluation in the case when the transverse charge density stays the same along the beam

43 PARTICLE ACCELERATORS↗