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

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A nanoscale photonic thermal transistor for sub-second heat flow switching

Abstract Control of heat flow is critical for thermal logic devices and thermal management and has been explored theoretically. However, experimental progress on active control of heat flow has been limited. Here, we describe a nanoscale radiative thermal transistor that comprises of a hot source and a cold drain (both are ~250 nm-thick silicon nitride membranes), which are analogous to the source and drain electrodes of a transistor. The source and drain are in close proximity to a vanadium oxide (VO x )-based planar gate electrode, whose dielectric properties can be adjusted by changing its temperature. We demonstrate that when the gate is located close ( < ~1 µm) to the source-drain device and undergoes a metal-insulator transition, the radiative heat transfer between the source and drain can be changed by a factor of three. More importantly, our nanomembrane-based thermal transistor features fast switching times ( ~ 500 ms as opposed to minutes for past three-terminal thermal transistors) due to its small thermal mass. Our experiments are supported by detailed calculations that highlight the mechanism of thermal modulation. We anticipate that the advances reported here will open new opportunities for designing thermal circuits or thermal logic devices for advanced thermal management.

42 ENGINEERING↗
DOE OSTI2026

AGR-5/6/7 Thermal Model with Non-uniform Gas Gaps

The daily as-run thermal analysis for the Advanced Gas Reactor (AGR)-5/6/7 experiment was documented in ECAR-5633 (Hawkes 2021). A finite element model was created for the entire test train, which consisted of five capsules. The fuel compacts, graphite holders, stainless-steel capsule walls, and all other major components were individually modeled, including all thermocouples (TCs). Daily heat rates for each compact and component in the model were input from daily as-run physics analyses. Daily gas compositions for each capsule were also input. The thermal conductivity of the compacts and graphite holders varied with fast neutron fluence. Gas mixture thermal conductivity was implemented using experimentally attained values from the literature. Fluence and temperature-dependent thermal conductivity was used for the graphite components and the fuel compacts. Radiation heat transfer was implemented. The model was tuned in an attempt to match the TC readings during the first cycle by adjusting the Neolube (graphite lubricant) thickness.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2010

Study of Fabry-Perot Etalon Stability and Tuning for Spectroscopic Rayleigh Scattering

The Fabry-Perot interferometer is a commonly employed instrument for resolving the spectrum of molecular Rayleigh scattered light for the purpose of evaluating flow properties such as gas velocity and temperature. Rayleigh scattered light from a focused laser beam can be directly imaged through a solid Fabry-Perot etalon onto a CCD detector to provide the spectral content of the scattered light. The spatial resolution of the measurements is governed by the locations of interference fringes. The location of the fringes can be changed by altering the etalon?s physical characteristics, such as thickness and index of refraction. For a fused silica solid etalon the physical properties can be adjusted by changing the etalon temperature; hence changing the order of the interference pattern and the physical fringe locations. Controlling the temperature of the etalon can provide for a slow time-response spatial scanning method for this type of etalon system. A custom designed liquid crystal Fabry-Perot (LCFP) can provide for a fast time-response method of scanning the etalon system. Voltage applied to the liquid crystal interface sets the etalon?s properties allowing Rayleigh measurements to be acquired at varying spatial locations across the image of the laser beam over a very short time period. A standard fused silica etalon and a tunable LCFP etalon are characterized to select the system that is best suited for Rayleigh scattering measurements in subsonic and supersonic flow regimes. A frequency-stabilized laser is used to investigate the apparent frequency stability and temperature sensitivity of the etalon systems. Frequency stability and temperature sensitivity data of the fused silica and LCFP etalon systems are presented in this paper, along with measurements of the LCFP etalon?s tuning capabilities. Rayleigh scattering velocity measurements with both etalon systems are presented, in an effort to determine which etalon is better suited to provide optical flow measurements of velocity, temperature, and density.

Clem, Michelle M.↗
DOE OSTI2019

A high performance UV–visible dual-band photodetector based on an inorganic Cs 2 SnI 6 perovskite/ZnO heterojunction structure

Inorganic metal halide (IMH) perovskites have recently emerged as highly promising optoelectronic materials due to their excellent material properties, including tunable direct bandgap, long carrier diffusion length, high carrier mobility and outstanding environmental stabilities. However, the performance of photodetectors fabricated from IMH perovskites so far is limited as compared to their counterparts based on organic–inorganic hybrid perovskites. In this work, we demonstrate a high performance ultraviolet–visible (UV–Vis) dual-band photodetector based on a Cs 2 SnI 6 /ZnO heterojunction structure. Therefore, by adjusting the polarity of the applied bias voltage, the photodetector can switch between two operation modes: (1) UV–Vis dual-band detection mode and (2) visible-blind UV detection mode. High detectivity in both the UV (1.39 × 10 12 Jones) and visible (5.88 × 10 11 Jones) regions is achieved. In addition, this photodetector demonstrated a fast response speed with a rise and fall time on the order of milliseconds and a large linear dynamic range of 119 dB. The excellent performance of this photodetector originates from efficient charge separation at the heterojunction interfaces, which will be discussed in detail in terms of the energy band diagrams and carrier dynamics of the device. Our study demonstrates the great application potential of inorganic vacancy-ordered perovskites in high-performance heterojunction photodetectors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1992

Dynamic interactions between hypersonic vehicle aerodynamics and propulsion system performance

Described here is the development of a flexible simulation model for scramjet hypersonic propulsion systems. The primary goal is determination of sensitivity of the thrust vector and other system parameters to angle of attack changes of the vehicle. Such information is crucial in design and analysis of control system performance for hypersonic vehicles. The code is also intended to be a key element in carrying out dynamic interaction studies involving the influence of vehicle vibrations on propulsion system/control system coupling and flight stability. Simple models are employed to represent the various processes comprising the propulsion system. A method of characteristics (MOC) approach is used to solve the forebody and external nozzle flow fields. This results in a very fast computational algorithm capable of carrying out the vast number of simulation computations needed in guidance, stability, and control studies. The three-dimensional fore- and aft body (nozzle) geometry is characterized by the centerline profiles as represented by a series of coordinate points and body cross-section curvature. The engine module geometry is represented by an adjustable vertical grid to accommodate variations of the field parameters throughout the inlet and combustor. The scramjet inlet is modeled as a two-dimensional supersonic flow containing adjustable sidewall wedges and multiple fuel injection struts. The inlet geometry including the sidewall wedge angles, the number of injection struts, their sweepback relative to the vehicle reference line, and strut cross-section are user selectable. Combustion is currently represented by a Rayleigh line calculation including corrections for variable gas properties; improved models are being developed for this important element of the propulsion flow field. The program generates (1) variation of thrust magnitude and direction with angle of attack, (2) pitching moment and line of action of the thrust vector, (3) pressure and temperature distributions throughout the system, and (4) performance parameters such as thrust coefficient, specific impulse, mass flow rates, and equivalence ratio. Preliminary results are in good agreement with available performance data for systems resembling the NASP vehicle configuration.

Flandro, G. A.↗
DOE OSTI2021

Simplified tuning of long-range corrected density functionals for use in symmetry-adapted perturbation theory

Long considered a failure, second-order symmetry-adapted perturbation theory (SAPT) based on Kohn–Sham orbitals, or SAPT0(KS), can be resurrected for semiquantitative purposes using long-range corrected density functionals whose asymptotic behavior is adjusted separately for each monomer. Here, as in other contexts, correct asymptotic behavior can be enforced via “optimal tuning” based on the ionization energy theorem of density functional theory, but the tuning procedure is tedious, expensive for large systems, and comes with a troubling dependence on system size. Here, we show that essentially identical results are obtained using a fast, convenient, and automated tuning procedure based on the size of the exchange hole. In conjunction with “extended” (X)SAPT methods that improve the description of dispersion, this procedure achieves benchmark-quality interaction energies, along with the usual SAPT energy decomposition, without the hassle of system-specific tuning.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Design of the EIC hadron storage ring stripline injection kicker with a novel impedance tuning capability

The Electron-Ion Collider (EIC), to be built at Brookhaven National Laboratory, will be a high luminosity (~10 34 cm –2 s –1 ) nuclear science facility. To facilitate EIC experiments, the existing yellow ring of the Relativistic Heavy Ion Collider (RHIC) will be reconfigured to serve as the Hadron Storage Ring (HSR). Designing a stripline injection kicker for the HSR beams, with high magnetic rigidity (~ 82 Tm), poses some technical challenges due to the required large pulsed voltage with long flattop duration, very fast rise time, expected shorter bunch spacing, and potential heating due to higher peak current. In addition, minimizing impedance mismatch in the transition region between the feedthrough and the stripline electrode is challenging. This paper focuses on the mechanical design and optimization of the HSR injection kicker, highlighting a novel impedance tuning capability achieved through an innovative kicker aperture adjustment mechanism. We comprehensively cover the design, including impedance optimization (both beam coupling and characteristic), beam-induced heating, and thermal analysis, and investigation of the maximum electric field due to high voltage signal excitation to ensure safe and reliable operation.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Thermal Model Heat Rate Predictions of the AGR-5/6/7 Experiment

Several fuel and material irradiation experiments have been planned for the U.S. Department of Energy Advanced Gas Reactor Fuel Development and Qualification Program, which supports the development and qualification of tristructural isotropic (TRISO) coated particle fuel for use in high-temperature gas-cooled reactors. The goals of these experiments are to provide irradiation performance data to support fuel process development, qualify fuel for normal operating conditions, support development of fuel performance models and codes, and provide irradiated fuel and materials for post-irradiation examination and safety testing. Originally planned and named as separate fuel experiments, but subsequently combined into a single test train. AGR-5/6/7 will test low-enriched uranium oxycarbide (UCO – a heterogeneous mixture of uranium oxide and uranium carbide) TRISO fuel. The AGR-5/6 portion of the experiment will provide data to support qualification of the selected reference fuel design, while the AGR-7 portion will serve as a margin test, irradiating the fuel beyond normal operating conditions. During irradiation, the temperature in each capsule is controlled by varying the helium / neon gas mixture flowing through the capsule until the desired thermocouple temperature is reached. Further adjustments can be made by changing the lobe power and the neutron filter. Three neutron filters are available to use as the experiment burns up the fissionable fuel. A thermal finite element model has been created for the five capsules comprising the AGR-5/6/7 experiment. Heat rates from a physics analysis are imported into the model along with fast neutron fluence. Graphite shrinkage due to the fast neutron fluence is incorporated into the model. Gas gaps change as a function of fast neutron fluence. Radiation heat transfer is a major contributor in this model. This is a large model with more than 1 million finite element brick elements. More than 150 different parts are modeled in the finite element model and communicate with each other from a heat transfer sense. More than 50 thermocouples are used in the experiment and are compared to actual measurements. The experiment is composed of five separate stainless steel capsules all welded together. This paper presents a method used to predict the gas mixture in the event that all of the thermocouples fail in a particular capsule. Curve fitting of heat rates from previous cycles and projecting them into the future is the basis of the method.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Origin of short- and medium-range order in supercooled liquid Ge 3 Sb 2 Te 6 from ab initio molecular dynamics simulations

Phase-change materials such as Ge–Sb–Te compounds have attracted much attention due to their potential value in electrical data storage. In contrast to the amorphous and crystalline phases, supercooled liquids are far from being deeply understood despite their inevitable role in both amorphization and crystallization processes. To this end, we have studied the dynamics properties and structural characteristics of liquid and supercooled liquid Ge 3 Sb 2 Te 6 during the fast cooling process. As the temperature decreases, chemical bonds become more homogeneous, but coordination numbers of Ge, Sb and Te atoms change very little. Meanwhile, the structural order of short-range configuration is obviously enhanced. Further studies suggest that Ge-centered, Sb-centered and Te-centered configurations change to the more ordered defective octahedrons mainly by adjusting the bond-angle relationship and bond length, rather than just by changing the coordination environment. It is the more ordered octahedrons that promote the formation of medium-range order. Our findings provide a deep insight into the origin of local structural order in supercooled liquid Ge 3 Sb 2 Te 6 , which is of great importance for the comprehensive understanding of amorphization and crystallization processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Neutral gas analysis for JET DT operation

Neutral gas analysis, the measurement and evaluation of total and partial pressures, is a key technique to study the impact of neutral gas dynamics on retention, recycling and release processes of fuel or impurity species in fusion devices. At JET, the experiment closest to ITER in terms of operating parameters and size, various detectors and techniques for partial pressure and total pressure measurements are deployed together to characterise neutral gas dynamics during and after plasma operation on various toroidal and poloidal locations. An extensive modification of JET's sub-divertor neutral gas diagnostic system aims at retaining and extending established measurement capabilities in the forthcoming Deuterium-Tritium (DT) experiments (DTE2). To achieve DT compatibility, a separation of radiation-sensitive electronics from the sensor and adequate radiation shielding is required, as well as utilisation of a DT compatible differential pumping system with adjustable throughput to account for the strong pressure variation in the sub-divertor region. Finally, the sub-divertor neutral gas diagnostic will be equipped with multiple Residual Gas Analysers (RGAs), utilising quadrupole mass spectrometry and electrostatic ion-trap-principles, all operating with remote electronics located behind the biological radiation shield. These RGAs will record data in a fast selected discrete mass mode during plasma pulses (cycle ~2 s) and will automatically switch back to continuous data recording (cycle ~100 s) afterwards. They will be complemented by a newly improved Penning gauge spectroscopy configuration in particular supporting the He and D 2 separation relevant for DT operation. The distance between these devices and their associated control unit is typically 15m . A newly developed RGA with a cable length of 80 m, compatible with the ITER environment, will also be employed for the first time. Finally, this set-up and its operation in DTE2 will provide vital input to the development of the ITER divertor RGA in the most relevant environment currently available.

47 OTHER INSTRUMENTATION↗
NASA NTRS1990

Calibration For On-Machine Inspections

Permanent calibration setup on numerically-controlled machine tool enables fast and reliable calibration of automated probes for inspection of workpieces while still mounted on machine. Setup includes one or more artifacts, dimensions and locations known precisely and stored in memory of computer controlling machine. Before probes used to inspect newly machined part, used to check artifacts. Probe measurements compared with values in memory to determine whether probe readings need adjustment.

Haymaker, Carlton L., Jr.↗
DOE OSTI2021

Development and experimental qualification of novel disruption prevention techniques on DIII-D

Novel disruption prevention solutions spanning a range of control regimes are being developed and tested on DIII-D to enable ITER success. First, a new real-time control algorithm has been developed and tested for regulating nearness to stability limits and maintaining safety-margins. Its first application has been for reliable prevention of vertical displacement events (VDEs) by adjusting plasma elongation (κ) and the inner-gap between the plasma and inner-wall in response to real- time open-loop VDE growth rate (γ) estimators. VDEs were robustly prevented up to average open-loop growth rates of 800 rad/s with initial tunings, with only applying shape modification when near safety limits. Second, the disruption risk during fast, emergency shutdown after large tearing and locked modes can be significantly improved by transitioning to a limited topology during shutdown. More than 50% of emergency limited shutdowns after locked modes reach a final normalized current I_N < 0.3 before terminating, scaling to the 3 MA ITER requirement. Furthermore, this is in contrast to diverted shutdowns, the majority of which disrupt at I_N > 0.8. Despite improvements, these results highlight the critical importance of early prevention. Third, a novel emergency shut down method has been developed which excites instabilities to form a warm, helical core post-thermal quench. The current quench extends to ~100ms and avoids VDEs and runaway electron generation. Novel real-time machine learning disruption prediction has been integrated with the DIII-D proximity controller, and a real- time compatible multi-mode MHD spectroscopy technique has been developed. Results presented here were enabled by a focused effort, the Disruption Free Protocol, in DIII-D’s 2019-20 campaign to complement disruption prevention experiments with a large piggy-back program. In addition to testing novel techniques, it is estimated to have helped avoid 32 potential disruptions in piggyback operations with rapid, early shutdowns after large rotating n=1 or locked modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Aerosol size distribution changes in FIREX-AQ biomass burning plumes: the impact of plume concentration on coagulation and OA condensation/evaporation

Abstract. The evolution of organic aerosol (OA) and aerosol size distributions within smoke plumes is uncertain due to the variability in rates of coagulation and OA condensation/evaporation between different smoke plumes and at different locations within a single plume. We use aircraft data from the FIREX-AQ campaign to evaluate differences in evolving aerosol size distributions, OA, and oxygen to carbon ratios (O:C) between and within smoke plumes during the first several hours of aging as a function of smoke concentration. The observations show that the median particle diameter increases faster in smoke of a higher initial OA concentration (>1000 µg m−3), with diameter growth of over 100 nm in 8 h – despite generally having a net decrease in OA enhancement ratios – than smoke of a lower initial OA concentration (<100 µg m−3), which had net increases in OA. Observations of OA and O:C suggest that evaporation and/or secondary OA formation was greater in less concentrated smoke prior to the first measurement (5–57 min after emission). We simulate the size changes due to coagulation and dilution and adjust for OA condensation/evaporation based on the observed changes in OA. We found that coagulation explains the majority of the diameter growth, with OA evaporation/condensation having a relatively minor impact. We found that mixing between the core and edges of the plume generally occurred on timescales of hours, slow enough to maintain differences in aging between core and edge but too fast to ignore the role of mixing for most of our cases.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Development and experimental qualification of novel disruption prevention techniques on DIII-D

Novel disruption prevention solutions spanning a range of control regimes are being developed and tested on DIII-D to enable ITER success. First, a new real-time control algorithm has been developed and tested for regulating nearness to stability limits and maintaining safety-margins. Its first application has been for reliable prevention of vertical displacement events (VDEs) by adjusting plasma elongation (κ) and the inner-gap between the plasma and inner-wall in response to real- time open-loop VDE growth rate (γ) estimators. VDEs were robustly prevented up to average open-loop growth rates of 800 rad/s with initial tunings, with only applying shape modification when near safety limits. Second, the disruption risk during fast, emergency shutdown after large tearing and locked modes can be significantly improved by transitioning to a limited topology during shutdown. More than 50% of emergency limited shutdowns after locked modes reach a final normalized current I N < 0.3 before terminating, scaling to the 3 MA ITER requirement. This is in contrast to diverted shutdowns, the majority of which disrupt at I N > 0.8. Despite improvements, these results highlight the critical importance of early prevention. Third, a novel emergency shut down method has been developed which excites instabilities to form a warm, helical core post-thermal quench. The current quench extends to ~100ms and avoids VDEs and runaway electron generation. Novel real-time machine learning disruption prediction has been integrated with the DIII-D proximity controller, and a real- time compatible multi-mode MHD spectroscopy technique has been developed. Results presented here were enabled by a focused effort, the Disruption Free Protocol, in DIII-D’s 2019-20 campaign to complement disruption prevention experiments with a large piggy-back program. In addition to testing novel techniques, it is estimated to have helped avoid 32 potential disruptions in piggyback operations with rapid, early shutdowns after large rotating n=1 or locked modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Reinforcement learning based automated history matching for improved hydrocarbon production forecast

History matching aims to find a numerical reservoir model that can be used to predict the reservoir performance. An engineer and model calibration (data inversion) method are required to adjust various parameters/properties of the numerical model in order to match the reservoir production history. In this study, we develop deep neural networks within the reinforcement learning framework to achieve automated history matching that will reduce engineers’ efforts, human bias, automatically and intelligently explore the parameter space, and remove the need of large set of labeled training data. To that end, a fast-marching-based reservoir simulator is encapsulated as an environment for the proposed reinforcement learning. The deep neural-network-based learning agent interacts with the reservoir simulator within reinforcement learning framework to achieve the automated history matching. Reinforcement learning techniques, such as discrete Deep Q Network and continuous Deep Deterministic Policy Gradients, are used toth, used to train the learning agents. The continuous actions enable the Deep Deterministic Policy Gradients to explore more states at each iteration in a a learning episode; consequently, a better history matching is achieved using this algorithm as compared to Deep Q Network. For simplified dual-target composite reservoir models, the best history-matching performances of the discrete and continuous learning methods in terms of normalized root mean square errors are 0.0447 and 0.0038, respectively. Furthermore, our study shows that continuous action space achieved by the deep deterministic policy gradient drastically outperforms deep Q network.

42 ENGINEERING↗
DOE OSTI2025

Evaluation of E3SM Simulated Aerosols and Aerosol‐Cloud Interactions Across GCM and Convection‐Permitting Scales

This paper introduces an Earth system modeling testbed for predicting aerosols and aerosol‐cloud interactions (ACIs) at convection‐permitting scales. Using the Energy Exascale Earth System Model (E3SM) version 2 with a four‐mode Modal Aerosol Module, we conduct simulations at 3.25 km resolution on a regionally refined mesh (RRM) across four regions with distinct aerosol and cloud regimes. Results are compared with the standard 100 km E3SM configuration and evaluated against satellite, aircraft, and ground‐based observations. We find that increasing model resolution improves heavy precipitation simulation but amplifies positive bias in light drizzle at coarse resolution. These resolution‐induced changes affect cloud and aerosol properties to varying degrees across regions. Generally, cloud cover and liquid water path (LWP) show better agreement with satellite retrievals at 3.25 km, though surface‐based comparisons suggest otherwise. Aerosol composition remains poorly represented at both resolutions. The RRM increases Aitken mode aerosol number concentrations via enhanced new particle formation. However, accumulation mode aerosols are decreased at higher resolution as aerosol removals become more efficient. This partially contributes to fewer cloud condensation nuclei (CCN) and lower cloud droplet number concentrations (N d ), which produces larger model biases in some scenarios. These findings suggest that solely increasing horizontal resolution to kilometer scales is insufficient to broadly improve aerosol and cloud predictions without concurrent advancements in physical and chemical process representations. Nonetheless, the RRM moderately improves key ACI relationships such as CCN‐N d correlation, reflecting enhanced aerosol activation representation. The LWP‐N d relationship is also better captured by RRM, suggesting a better characterization of LWP adjustment.

Huang, Meng [Pacific Northwest National Laboratory↗
DOE OSTI2025

Surrogate Modelling of 3rd Integer Resonant Extraction at Fermilab Delivery Ring

We present an ongoing work in which a surrogate model is being developed to reproduce the response dynamics of the third-integer resonant extraction process in the Delivery Ring (DR) at Fermilab. This effort is in pursuit of smoothly extracting circulating beam to the Mu2e Experiment s production target, wherein the goal is to extract a uniform slice of the circulating $1e12$ protons in the DR over 25,000 turns (43~ms). The DR contains 3 harmonic sextupoles which excite a third-integer resonance as well as three fast, tune-ramping quadrupole magnets which drive the horizontal tune towards the $29/3$ resonance. In our initial work the surrogate model trains on a semi-analytical simulation provided in the same format as live data. Using Reinforcement Learning (and other potential ML methods), the trained surrogate acts as the environment in which a simple ML control agent could learn to dynamically adjust the quadrupole ramp at 430 break points within the 43 microsecond spill window. The control agent will be hosted on a dedicated Arria 10 FPGA, introducing its own requirements on control agent architecture. In this work we report the accuracy and fidelity of surrogate models in comparison to the response dynamics of the physics simulator.

Narayanan, Aakaash [Fermilab] (ORCID:0000000157944↗
DOE OSTI2023

ESR Dipole Power Supply Current Ripple and Noise Specifications

This note presents key findings for the ESR main magnet dipole power supplies (PS), where we find the current ripple specification to be close to or beyond the state-of-the-art. These specifications originate from beam-beam considerations, with the requirement to limit the ripple-induced hadron emittance growth to below 10%/hour. Beam dynamics that drive this PS ripple specification arise from the beam motions at the Interaction Point (IP). The frequency of the motions can be separated into "low", compared to the betatron frequency, and "high", i.e. around the betatron frequency and harmonics. In terms of the driving frequency, "low" implies ƒ<<ƒ 0 v x,y and "fast" means ƒ≈{ƒ 0 v x,y , ƒ 0 (1- v x,y , etc.}, where ƒ 0 =1/ T 0 =78.2 kHz is the revolution frequency, and v x,y are the fractional parts of the betatron tunes. Frequencies higher than ƒ 0 /2 will be folded back due to the particles sampling the field once per turn. To provide flexibility for future lattice adjustments and working point variations, we do not consider the tunes as fixed. Instead, we assume a certain margin and allow them to potentially fall within the range of 0.1< v x,y <0.5. In other words, the high-frequency region spans approximately from 8kHz to 40 kHz. Consequently,, we definte the dipole PS ripple in two distinct frequency ranges: the low-frequency range of [1-8000] Hz and the high-frequency range of [8-40] kHz. For the physics effects we analyzed in this note, there is no distinction between the ripple (which can be approximately reproduced in the frequency domain) and the random noise if both have some power within the frequency bandwidth of interest. Therefore, while we will use the term "ripple" for short, it should always be understood that we are referring to "ripple plus noise." Except for the lower end of the low-frequency range, the impact of the rippling PS current on the beam will be considerably reduced due to the eddy currents induced in the walls of the vacuum chamber. We will account for this effect in the PS ripple specifications to follow. The remaining sections of this note are structure as follows: Section II outlines the beam-beam physics requirements for the positional stability of the beam at the IP. Section III describes the anticipated shielding effect of the eddy currents induced in the vacuum chamber. Section IV derives the ripple requirement for the low-frequency range by propagating the closed orbit ripple resulting from the rippling dipoles to the IP (relevant lattice simulation results are summarized in the Appendix). In Section V, we present the analytical criterion for the ripple in the high-frequency range by considering resonant oscillations of the electron beam around a stable closed orbit near the betatron frequency. Finally, Section VI provides a summary of our findings and discusses related work.

43 PARTICLE ACCELERATORS↗