Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Power system stability”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 991 records · Page 55

Identifying Suitable Front Contacts for High‐Efficiency Cd(Se,Te) Solar Cells on Space‐Qualified Cover Glass

Deployment of photovoltaics in space requires devices that combine high-efficiency, low areal mass, and resilience to harsh environments. Historically, high-efficiency multijunction III–V materials have dominated space power systems; however, their high cost and limited manufacturing throughput motivate the exploration of scalable alternatives. While CdTe-based thin-film photovoltaics offer an attractive option, their performance on non-conventional substrates can suffer from front contact instability under higher-temperature processing. Here, the role of front contact chemistry in limiting cell performance is investigated using CdTe-based devices fabricated on 150 μm thick Ceria-doped space-qualified 0214 Corning glass. A matrix of four transparent conducting oxides (TCOs: CTO, AZO, ITO, IZO) combined with two n-type emitters (MZO, IGO) reveals chemical stability at the front interface—rather than absorber composition alone—governs recombination losses, voltage deficits, and device reproducibility. Chemically stable front contact combinations suppress elemental diffusion and interfacial degradation, resulting in significantly improved carrier lifetimes and junction quality. These insights are validated through record-certified Cd(Se,Te) cell efficiencies of 18.4% under AM1.5G and 16.2% under AM0 illumination on ultra-thin glass. Beyond CdTe, this work provides a general framework for the rational selection of TCO/emitter interfaces in superstrate thin-film photovoltaics, including emerging technologies like metal halide perovskites, while enabling high-efficiency, lightweight photovoltaics for space applications.

14 SOLAR ENERGY↗

Voltage Service Limits Smart Contract Using Distributed Ledger Technology for Electrical Utility Grid with Customer-Owned Generator

Modern electrical grids face growing stability risks from customer-owned generators, especially at points of common couplings (PCCs). Disruptive behavior from power-electronic sources can cause protective relays to isolate problematic generators, making measurement integrity critical. This article presents a distributed ledger technology (DLT) approach that uses smart contracts to evaluate PCC voltage measurements and trigger backup breaker operations. The approach is framed as a verifiable, multi-organization attestation and audit layer, not as a real-time control security mechanism. In the proposed architecture, voltage measurements from a hardware protective relay are anchored on a DLT through the Cyber Grid Guard (CGG) system for attestation by both the grid utility and customer-owned generator. A Voltage Service Limits (VSLs) smart contract evaluates the on-chain measurements against allowable phase-voltage limits derived from the ANSI C84.1 standard. The framework is validated in a hardware-relay-in-the-loop test bed under sustained-undervoltage, sustained-overvoltage, and transient line-to-line fault scenarios. The results show that the VSL smart contract can process these measurements and issue backup breaker actions consistent with the defined service-limit criteria, demonstrating the DLT potential as a verifiable audit layer at the PCC that complements primary protection.

cyber security↗

Polyphenol-Sensitized Atomic Layer Deposition for Membrane Interface Hydrophilization

Improvements in energy-water systems will necessitate fabrication of high-performance separation membranes. To this end, interface engineering is a powerful tool for tailoring properties, and atomic layer deposition (ALD) has recently emerged as a promising and versatile approach. However, most non-polar polymeric membranes are not amenable to ALD processing due to the absence of nucleation sites. Here, a sensitization strategy for ALD-coating is presented, illustrated by membrane interface hydrophilization. Facile dip-coating with polyphenols effectively sensitizes hydrophobic polymer membranes to TiO2 ALD coating. Tannic acid-sensitized ALD-coated membranes exhibit outstanding underwater crude oil repulsion and rigorous mechanical stability through bending and rinsing tests. As a result, these membranes demonstrate outstanding crude oil-in-water separation and reusability compared to untreated membranes or those treated with ALD without polyphenol pretreatment. A possible polyphenol-sensitized ALD mechanism is proposed involving initial island nucleation followed by film intergrowth. This polyphenol sensitization strategy enriches the functionalization toolbox in material science, interface engineering, and environmental science.

36 MATERIALS SCIENCE↗

Characterizing different motility-induced regimes in active matter with machine learning and noise

Here we examine motility-induced phase separation (MIPS) in two-dimensional run-and-tumble disk systems using both machine learning and noise fluctuation analysis. Our measures suggest that within the MIPS state there are several distinct regimes as a function of density and run time, so that systems with MIPS transitions exhibit an active fluid, an active crystal, and a critical regime. The different regimes can be detected by combining an order parameter extracted from principal component analysis with a cluster stability measurement. The principal component-derived order parameter is maximized in the critical regime, remains low in the active fluid, and has an intermediate value in the active crystal regime. We demonstrate that machine learning can better capture dynamical properties of the MIPS regimes compared to more standard structural measures such as the maximum cluster size. The different regimes can also be characterized via changes in the noise power of the fluctuations in the average speed. In the critical regime, the noise power passes through a maximum and has a broad spectrum with a 1/f 1.6 signature, similar to the noise observed near depinning transitions or for solids undergoing plastic deformation.

97 MATHEMATICS AND COMPUTING↗

Tech-X contributions to the Center for Tokamak Transients (CTTS) Scientific Discovery through Advanced Computing (SciDAC) project (Final Report)

The Center for Tokamak Transients Simulations (CTTS) consists of computational plasma physicists, computer scientists, and applied mathematicians who are together developing and applying simulation software to improve our understanding of and ability to predict and control transient events in tokamak discharges, particularly those that lead to violent disruptions. We have major simulation activities concerning disruptions that are caused by violating ideal MHD stability criteria, vertical displacement events, resistive wall modes, and tearing modes. We are performing comprehensive modeling of disruption mitigation techniques, particularly by shattered pellet injection (SPI). The Center is built around two mature extended MHD codes: NIMROD and M3D-C1. These codes are being extended in a number of ways as required by the demands of disruption modeling, and are being optimized to work well for larger problem size and modern computer architectures as required to model tokamak plasmas with realistic parameters over the required timescales. The codes will be coupled to the FronTier code for state-of-the-art modeling of SPI. Validation with experimental data on DIII-D, NSTX, and JET is being facilitated by rigorous uncertainty quantification (UQ). The high-level objectives of the center are to: (1) Develop better understanding and improved predictive capability of when crossing a linear stability boundary will likely lead to a disruption, (2) Provide a tool for calculating vessel forces, both axisymmetric and non-axisymmetric, for worst case VDE and other disruptions in tokamaks, (3) Develop increased understanding and improved predictive capability for locked mode disruptions and how best to avoid them, (4) Develop, verify, and validate 3D models for disruption mitigation by shattered pellets that can be used to design and optimize a system for future tokamaks, and (5) Increase the efficiency and scalability of the M3D-C1 and NIMROD codes so that they can model disruptions in ITER scale devices using the most powerful DOE HPC hardware, and (6) Demonstrate code-coupling via FronTier coupling with NIMROD and M3D-C1 and by interfacing these codes within a WDM framework.

97 MATHEMATICS AND COMPUTING↗

Exploring mounting solutions for cryogenically cooled thin crystal optics in high power density x-ray free electron lasers

This study investigates three mounting methods—clamping, soldering, and a hybrid clamping–soldering approach—for cryogenically cooled thin diamond crystals crucial to stable operation of X-ray Free Electron Laser (XFEL) systems. While clamping methods exhibit temperature resilience and flexibility, meticulous design is required to prevent stress-induced warping and reduce thermal contact area. Soldering methods offer reliable mechanical and thermal bonding but encounter challenges due to the coefficient of thermal expansion mismatch at cryogenic temperatures. The hybrid method, integrating clamping and soldering with strain relief cuts, effectively mitigates overall distortion caused by mounting and XFEL thermal loads. These findings offer a novel mounting solution for high-performance x-ray optics in XFEL research and applications, ensuring stability and optimal functionality in cryogenic conditions.

Instruments & Instrumentation↗

Empirically-calibrated H100 node power models for accurate AI training energy estimation

Accurately quantifying the energy use of artificial intelligence (AI) training is critical for infrastructure planning, carbon accounting, and sustainable data center operation, but few studies have directly measured the power consumption of production workloads on contemporary hardware. By combining empirical measurements from Brookhaven National Laboratory during AI training on 8-graphics-processing-unit H100 systems with open-source benchmarking data, we develop statistical models relating computational intensity to node-level power consumption. We measure the gap between manufacturer-rated thermal design power (TDP) and actual power demand during AI training. Our analysis reveals that even computationally intensive workloads operate at only 76% of the 10.2 kW TDP rating. Our architecture-specific model, calibrated to floating-point operations, predicts energy consumption with 11.4% mean absolute percentage error, significantly outperforming TDP-based approaches (27%–37% error). We identified distinct power signatures between transformer and convolutional neural network architectures, with transformers showing characteristic fluctuations that may impact grid stability. These results provide a measurement-grounded basis for improving AI training energy estimates, enabling more reliable infrastructure sizing, cost projections, and environmental impact assessments.

Newkirk, Alex C↗

Toward fusion plasma scenario planning for NSTX-U using machine-learning-accelerated models

One of the most promising devices for realizing power production through nuclear fusion is the tokamak. To maximize performance, it is preferable that tokamak reactors achieve advanced operating scenarios characterized by good plasma confinement, improved magnetohydrodynamic (MHD) stability, and a largely non-inductively driven plasma current. Such scenarios could enable steady-state reactor operation with high \emph{fusion gain} --- the ratio of produced fusion power to the external power provided through the plasma boundary. Precise and robust control of the evolution of the plasma boundary shape as well as the spatial distribution of the plasma current, density, temperature, and rotation will be essential to achieving and maintaining such scenarios. The complexity of the evolution of tokamak plasmas, arising due to nonlinearities and coupling between various parameters, motivates the use of model-based control algorithms that can account for the system dynamics. In this work, a learning-based accelerated model trained on data from the National Spherical Torus Experiment Upgrade (NSTX-U) is employed to develop planning and control strategies for regulating the density and temperature profile evolution around desired trajectories. The proposed model combines empirical scaling laws developed across multiple devices with neural networks trained on empirical data from NSTX-U and a database of first-principles-based computationally intensive simulations. The reduced execution time of the accelerated model will enable practical application of optimization algorithms and reinforcement learning approaches for scenario planning and control development. An initial demonstration of applying optimization approaches to the learning-based model is presented, including a strategy for mitigating the effect of leaving the finite validity range of the accelerated model. The approach shows promise for actuator planning between experiments and in real-time.

machine learning↗

Membrane-based Carbon Capture Process Optimization using CFD Modeling

Carbon capture is a promising option to mitigate CO2 emissions from existing coal-fired power plants, cement and steel industries, and petrochemical complexes. Among the available technologies, membrane-based carbon capture presents the lowest energy consumption, operating costs, and carbon footprint. In addition, membrane processes have important operational flexibility and response times. On the other hand, the major challenges to widespread application of this technology are related to reducing capital costs and improving membrane stability and durability. To upscale the technology into stacked flat sheet configurations, high fidelity computational fluid dynamics (CFD) that describes the separation process accurately are required. High fidelity simulations have been shown to be effective in studying the complex transport phenomena in membrane systems. In addition, obtaining high CO2 recovery percentages and product purity re-quires a multi-stage membrane process, where the optimal network configuration of the mem-brane modules must be studied in a systematic way. In order to address the design problem at process scale, we formulate a superstructure for the membrane-based carbon capture, including up to three separation stages. In the formulation of the optimization problem, we include reduced models, based on rigorous CFD simulations of the membrane modules.

Pedrozo, Hector A.↗

Membrane-based carbon capture process optimization using CFD modeling

Carbon capture is a promising option to mitigate CO2 emissions from existing coal-fired power plants, cement and steel industries, and petrochemical complexes. Among the available technologies, membrane-based carbon capture presents the lowest energy consumption, operating costs, and carbon footprint. In addition, membrane processes have important operational flexibility and response times. On the other hand, the major challenges to widespread application of this technology are related to reducing capital costs and improving membrane stability and durability. To upscale the technology into stacked flat sheet configurations, high fidelity computational fluid dynamics (CFD) that describes the separation process accurately are required. High fidelity simulations have been shown to be effective in studying the complex transport phenomena in membrane systems. In addition, obtaining high CO2 recovery percentages and product purity requires a multi-stage membrane process, where the optimal network configuration of the membrane modules must be studied in a systematic way. In order to address the design problem at process scale, we formulate a superstructure for the membrane-based carbon capture, including up to three separation stages. In the formulation of the optimization problem, we include reduced models, based on rigorous CFD simulations of the membrane modules. Numerical results indicate that the optimal design includes three membrane stages, and the capture cost is 45.4 $/t-CO2.

Pedrozo, Hector A.↗

Dispatching Grid-Forming Inverters in Grid-Connected and Islanded Mode

This paper explores the dispatchability of grid-forming (GFM) inverters in grid-connected and islanded mode. An innovative concept of dispatching GFM sources (inverters and synchronous generators) is proposed to output the target power by adjusting their droop intercepts. The fundamental principle is that the GFM inverter's active and reactive power is dictated by its frequency and voltage, and thus dispatching the active and reactive power of a GFM inverter can be achieved through dispatching its frequency and voltage. The concept is validated with an example microgrid system with two GFM inverters, one diesel generator, one GFL inverter, and the load in both grid-connected and islanded mode. This pioneering work results in practical guidance for the development of energy management systems for future electric grids with GFM and GFL inverters. The key findings are summarized as follows: 1) The GFM inverters can be dispatched through frequency and voltage droop intercepts to output the target power; 2) The dispatch rule for grid-connected and islanded mode is slightly different.

dispatch GFM inverter↗

Experimental Comparison of Elastomeric Materials for Hydraulic Seal Durability under Reciprocating Conditions

Wave Energy Converters (WECs) rely on hydraulic Power Take-Off (PTO) systems to transform the kinetic energy of ocean waves into electricity, where hydraulic seals play a critical role in preventing fluid leakage and ensuring watertight operation under harsh marine conditions. However, seal degradation due to wear, fatigue, and corrosion remains a key challenge limiting system reliability and increasing maintenance costs. In this study, the tribological performance of elastomeric materials for hydraulic sealing applications that are based on commercial polyurethane and custom-compounded Ethylene Propylene Diene Monomer (EPDM) is investigated. Using a CSM tribometer, reciprocating wear tests were conducted in accordance with ASTM G133 under dry sliding conditions, with normal loads ranging from 3 to 10 N, and sliding speeds of 10 to 30 mm/s. Coefficient of friction (COF), specific wear rate, and worn surface morphology are evaluated to understand how load, velocity, and material composition affect seal durability. Improved wear stability and high Shore A hardness (93–94) were demonstrated by the commercial thermoplastic polyurethane (Duralast 4203 and 4758). EPDM-based compounds showed different filler-dependent behaviors, formulations filled with carbon black (E3) had the lowest wear rate (1.45 × 10?4 mm³ N?¹ m?¹) and increased load-bearing capacity, while samples modified with silica and plasticizer (E4, E5) had better conformability and damping but less hardness. Compounded EPDMs showed wider deformation zones because of their lower modulus and filler-matrix interfacial fluctuations, while commercial grades exhibited shallower wear scars (= 380 µm), according to optical profilometry. The Archard model-based lifetime estimation showed that, under 10 N and 30 mm/s, operational endurance ranged from 3.1 to 6.2 years. Because of its low wear rate and steady interfacial behavior, E3 had the longest anticipated life. For medium-load hydraulic sealing applications, these results demonstrate the possibility of customized EPDM formulations as affordable substitutes for commercial polyurethanes. They also offer a quantitative foundation for material selection and lifespan prediction.

Durability↗

A review of Geological Thermal Energy Storage for seasonal, grid-scale dispatching

Energy storage is essential for the decarbonization of the U.S. energy grid, especially with the increasing deployment of variable renewable energy sources like solar and wind. Geological thermal energy storage (GeoTES) has emerged as a promising long duration, grid scale solution, providing stability and security through flexible operations and valuable grid services. GeoTES utilizes subsurface reservoirs to store thermal energy for power generation and direct-use heating and cooling. This approach significantly enhances the use of low-temperature reservoirs, which would otherwise be unsuitable for geothermal power plants. It also aligns well with depleted oil and gas reservoirs, concentrating solar power, non-flexible renewables (photovoltaic and wind), and geothermal-related power cycles. Given the favorable marginal costs of GeoTES as storage duration increases, it becomes particularly competitive for seasonal, grid-scale dispatch, where few technologies are viable. This paper provides a comprehensive review of GeoTES systems and the research underpinning itsr development. This analysis begins by defining and categorizing the unique characteristics of thermal energy storage techniques, setting GeoTES apart from other technologies. The various components, configurations, subsurface characteristics, and modeling efforts that guide GeoTES development are then explored. Finally, challenges in GeoTES research, development, and deployment are discussed, along with mitigation strategies and lessons from related technologies. Beyond their economic benefits, GeoTES systems support grid resilience and decarbonize industrial processes. Their scalability, broad distribution, seasonal storage potential, and flexible dispatch capacity make GeoTES a valuable tool for expanding renewable energy deployment and addressing climate change.

15 - GEOTHERMAL ENERGY↗

Computation-guided optimization of split protein systems

Splitting bioactive proteins into conditionally reconstituting fragments is a powerful strategy for building tools to study and control biological systems. However, split proteins often exhibit a high propensity to reconstitute, even without the conditional trigger, limiting their utility. Current approaches for tuning reconstitution propensity are laborious, context-specific or often ineffective. Here, we report a computational design strategy grounded in fundamental protein biophysics to guide experimental evaluation of a sparse set of mutants to identify an optimal functional window. We hypothesized that testing a limited set of mutants would direct subsequent mutagenesis efforts by predicting desirable mutant combinations from a vast mutational landscape. This strategy varies the degree of interfacial destabilization while preserving stability and catalytic activity. We validate our method by solving two distinct split protein design challenges, generating both design and mechanistic insights. Furthermore, this new technology will streamline the generation and use of split protein systems for diverse applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Protection and Restoration Solutions to Reliable and Resilient Integration of Grid-connected PV Installations and Distributed Energy Resources: Design, Testbed, Proof of Work and Impact Studies (Final Report)

To gain a better understanding of the complex transients in a utility grid with a large number of solar PV installations coupled by PWM inverters during the protection and restoration period of the power grid, in this project a kW-level experimental system with dominating inverter-based resources and a hardware-in-loop simulation system with transmission and distribution models, as well as several SEL protective relays have been built and used. The major research findings of the project are summarized below in two perspectives: Experimental research: A self-organized ultra-high frequency solitary waveform is discovered and demonstrated in the hardware experimental system. Despite the familiarities, such a solitary waveform is distinct from any harmonics, transient, or resonance waves in that, it is 1) non-dispersive over time and space, 2) not associated with any active source or the linear superposition of sources, 3) half-cycle asymmetric, 4) not responding to filters or change of system characteristic resonance frequency, 5) ubiquitous as it occurs simultaneously everywhere in the system from DC supply, power lines, and the utility grid, and 6) explosive through tripping the protection or damaging susceptible devices or circuits. Analytical study: The nature of such a new waveform and an analytical explanation of its formation are studied based on related physics and non-linear science principles, with the following highlights: 1) such a new waveform follows the solutions to the Non-linear Schrödinger equation, so the classic linear perturbation theory is unable to explain or predict such a unique waveform as confirmed with the research team of RTDS; 2) the critical condition of occurrence of such a waveform is derived, which indicates that the breakings of solitary wave is a system synchronous issue between the utility grid in the 60Hz phasor domain and duty-ratio modulation of DC sources in the inverter switching frequency domain; 3) such a waveform carries energy mass so it could be detrimental; 4) such a waveform is deceiving as it is not readily detectable in the energy propagation direction by the primary protection equipment, while it is detrimental in the perpendicular direction of energy propagation, i.e. voltage direction. Thus, it has more likely challenges to the second primary equipment and devices, particularly at the weakest link and point such as aging insulation and inappropriate setting of susceptible devices. Therefore, such a waveform can be easily ignored in the aftermath investigation. The intellectual merits: The experimental discovery reveals certain unfamiliar transient phenomena that could challenge the integration of large-scale grid-connected solar PV installation during the group ride-through period of solar PV installations, commissioning of large-solar farms, or dramatic change of solar radiation conditions. Particularly, the research findings suggest that the occurrence of the unfamiliar transient phenomena is uniquely associated with the inverter-based solar PV installation, which is less likely to happen for rotary energy systems. The physics and non-linear science-based research work laid down an analytical path to the challenging transient stability problems including those that have been observed currently and future calls. Both experimental and analytical research results explain the limitation of many current research effects including some DoE research undertakings as well as possible solutions. The broader impacts: The research outcome of the project advances the understanding of the possible transient problems for the integration of inverter-based solar PV installation. It also highlights the theoretical and technical barriers for applying the conventional theory and technology to design and implement countermeasures against their adverse impacts of the large-scale solar PV installation and operation on grid reliability and security. More broadly, the research outcomes have shed some light on the open, fundamental challenges in the integration of large-scale solar photovoltaic energy into current and next-generation power grids across the country, and worldwide. The advanced physics and non-linear science-based analysis open up a path to harmonization of the renewables for societal energy needs via building a resilient and sustainable electric power infrastructure.

14 SOLAR ENERGY↗

Electrochemical CO 2 Utilization: Scalable System Operation for Formic Acid Production

In recent years, research into the electrochemical reduction of CO 2 has grown exponentially. Formic acid (FA) has become a particular value product from CO 2 due to its versatility [1], optimal atom economy [2], and thermodynamic favorable [3]. FA can be produced electrochemically via a direct two-electron transfer process involving CO 2 with a proton source, requiring less energy input and fewer reaction steps than the conventional Kemira process. However, product selectivity, electrode stability, and low faradic efficiency due to increased resistance under constant current, remain key issues for CO 2 reduction to FA [4]. University of Kentucky’s Center for Applied Energy Research (UK CAER) is currently investigating reactor designs to address the challenges associated with electrochemical CO 2 conversion to FA [5]. The current reactor system employs: (1) an organic-based charge carrier which shuttles charge directly to the catalyst to enable CO 2 reduction to FA; (2) novel electrode materials to mitigate large voltages and improve conductivity; and (3) a flow system which not only allows for the volumetric scale-up of both charge carrier and catalyst, but also decouples the charger carrier re-energized and FA production processes to protect the catalyst’s stability due to overpotential. Through careful adjustment of electrode, charge carrier, and electrolyte selection, cell resistances have decreased by over 15%, facilitating conduction necessary for effective CO 2 reduction to FA. The system uses a highly specific engineered catalyst, which has produced over 100 mM FA at a rate of over 10 mM FA/hour following the aforementioned electrode/charge carrier changes. System design considerations (flow rate, bulk volume) and modeling of the system will also be discussed.

20 FOSSIL-FUELED POWER PLANTS↗

Design and Analysis of Liquid Lithium Plasma Facing Components

In this study, liquid metal (LM) on plasma-facing components (PFCs) creates a renewable protective cover enhancing power exhaust and protecting the solid substrate. Additionally, energy confinement improvement through particle pumping can be achieved in the case of liquid lithium (LL). A new variant of PFCs was recently introduced at Princeton Plasma Physics Laboratory (PPPL) where a porous wall is used to stabilize the LM surface, while using magnetohydrodynamic (MHD) drive to push the LM flow inside the component. This arrangement allows efficient heat exhaust, and enhanced control of the LM surface temperature, leading to spatial control of evaporation and condensation of LL on the plasma interface. This feature is particularly attractive when vapor shielding is introduced to allow heat flux redistribution. This system has the advantage that as the heat flux increases, the evaporation rate will increase, while decreasing heat flux will decrease the evaporation rate of lithium, ideally creating a feedback effect which could self-regulate the amount of lithium evaporated. Analytical and numerical models for LL PFCs were developed in PPPL. To calculate the target temperature distribution for the case of evaporation from the divertor, we apply an iterative process allowing two-way coupling between the fluid-kinetic analysis of plasma using SOLPS-ITER code and the flow and heat transfer analysis of the PFC using an analytical model. In the last stage, the results are validated using computational fluid dynamics (CFD) analysis with customized version of the CFX code from ANSYS. CFX was modified at PPPL to allow MHD analysis at the high magnetic field typical for fusion applications. Results of the analysis for NSTX-U tokamak conditions will be presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Eddy Current Shielding of the Magnetic Field Ripple in the EIC Electron Storage Ring Vacuum Chambers

The EIC electron storage ring (ESR) has very tight tolerances for the beam position and size stability at the interaction point. The oscillations at the proton betatron frequency and its harmonics are the most dangerous because, for instance, they could lead to unacceptable proton emittance growth from the oscillating beam-beam kick from the electrons at the amplitude of the positional oscillations as low as 10 -4 of the beam size. Even at much lower frequencies, down to the single Hz range, the position oscillations at a few percent level of the nominal beam size were found to be dangerous. These oscillations could have different causes including magnet power supply ripple, mag net vibration, noise in the main and crab RF systems, and some collective instabilities. To specify the acceptable level of the current ripple and noise of the magnet power supplies we need to accurately account for the eddy current shielding by the vacuum chamber, as well as, potentially, by the laminated magnet yokes (considered elsewhere). With some ap proximations, the chamber shielding can be described analytically. The main objective of this note is to derive these analytical expressions and to document the resulting shielding performance of the ESR chamber.

43 PARTICLE ACCELERATORS↗