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At least 451 records · Page 25

Elasticity of two-dimensional ferroelectrics across their paraelectric phase transformation

The mechanical behavior of two-dimensional (2D) materials across 2D phase changes is unknown, and the finite temperature (T) elasticity of paradigmatic SnSe monolayers—ferroelectric 2D materials turning paraelectric as their unit cell turns from a rectangle into a square—is described here in a progressive manner. To begin with, their zero–T total energy landscape gives way to (Boltzmann-like) averages from which the elastic behavior is determined. Furthermore, these estimates are complemented with results from the strain-fluctuation method, which employs the energy landscape or ab initio molecular dynamics data. All approaches capture the coalescence of elastic moduli < C 11 (T) > = < C 22 (T) > due to the structural transformation. The broad evolution and sudden changes of elastic parameters < C 11 (T) >, < C 22 (T) >, and < C 12 (T) > of these atomically thin phase-change membranes establishes a heretofore overlooked connection among 2D materials and soft matter.

2-dimensional systems↗

Modeling the partitioning of amphiphilic molecules and co-solvents in biomembranes

We report amphiphilic co-solvents can have a significant impact on the structure, organization and physical properties of lipid bilayers. Describing the mutual impact of partitioning and induced structure changes is therefore a crucial consideration for a range of topics such as anesthesia and other pharmacokinetic effects, as well as microbial solvent tolerance in the production of biofuels and other fermentation products, where molecules such as ethanol, butanol or acetic acid might be generated. Small-angle neutron scattering (SANS) is a key method for studying lipid and polymer bilayer structures, with many models for extracting bilayer structure (thickness, area per lipid etc.) from scattering data in use today. However, the molecular details of co-solvent partitioning are conflated with induced changes to bilayer structure, making interpretation and modeling of the scattering curves a challenge with the existing set of models. To address this, a model of a bilayer structure is presented which invokes a two-term partition constant accounting for the localization of the co-solvent within the bilayer. This model was validated using a series of SANS measurements of lipid vesicles in the presence of the co-solvent tetrahydrofuran (THF), showing several strategies of how to deploy the two-parameter partition constant model to describe scattering data and extract both structure and partitioning information from the data. Molecular dynamics simulations are then used to evaluate assumptions of the model, provide additional molecular scale details and illustrate its complementary nature to the data fitting procedure. This approach results in estimates of the partition coefficient for THF in 1,2-dimyristoyl-sn-glycero-3-phosphocholine at 35°C, along with an estimate of the fraction of THF residing in the hydrophobic core of the membrane. The authors envision that this model will be applicable to a wide range of other bilayer/amphiphile interactions and provide the associated code needed to implement this model as a fitting algorithm for scattering data in the SasView suite.

59 BASIC BIOLOGICAL SCIENCES↗

Results of CO2 Storage Efficiency in Deep Saline Formations – Stage 2

Conference paper presented at 14th International Conference on Greenhouse Gas Control Technologies (GHGT-14), Melbourne, Australia, October 12–25, 2018. Previous dynamic simulations indicate that it may take hundreds of years and an unrealistic number of wells to approach a static volumetrically derived estimate of storage capacity and efficiency for an actual large-scale CO 2 storage development. This study shows how efficiency factors may be influenced by key parameters of practical project development, such as a 50-year injection period, number of wells and drilling sequence, onshore vs. offshore conditions, and increasing unit storage cost as development intensifies. Two potential storage formations were investigated: the Minnelusa Formation of the Powder River Basin and the Bunter Sandstone of the North Sea Basin.

58 GEOSCIENCES↗

Evaluation of dynamically downscaled extreme temperature using a spatially-aggregated generalized extreme value (GEV) model

The Weather Research and Forecast (WRF) model downscaling skill in extreme maximum daily temperature is evaluated by using the generalized extreme value (GEV) distribution. While the GEV distribution has been used extensively in climatology and meteorology for estimating probabilities of extreme events, accurately estimating GEV parameters based on data from a single pixel can be difficult, even with fairly long data records. This work proposes a simple method assuming that the shape parameter, the most difficult of the three parameters to estimate, does not vary over a relatively large region. This approach is applied to evaluate 31-year WRF-downscaled extreme maximum temperature through comparison with North American Regional Reanalysis (NARR) data. Uncertainty in GEV parameter estimates and the statistical significance in the differences of estimates between WRF and NARR are accounted for by conducting bootstrap resampling. Despite certain biases over parts of the United States, overall, WRF shows good agreement with NARR in the spatial pattern and magnitudes of GEV parameter estimates. Both WRF and NARR show a significant increase in extreme maximum temperature over the southern Great Plains and southeastern United States in January and over the western United States in July. The GEV model shows clear benefits from the regionally constant shape parameter assumption, for example, leading to estimates of the location and scale parameters of the model that show coherent spatial patterns.

Wang, Jiali↗

THE SAMI GALAXY SURVEY: TOWARD A UNIFIED DYNAMICAL SCALING RELATION FOR GALAXIES OF ALL TYPES

We take advantage of the first data from the Sydney-AAO Multi-object Integral field Galaxy Survey to investigate the relation between the kinematics of gas and stars, and stellar mass in a comprehensive sample of nearby galaxies. We find that all 235 objects in our sample, regardless of their morphology, lie on a tight relation linking stellar mass (M {sub *}) to internal velocity quantified by the S {sub 0.5} parameter, which combines the contribution of both dispersion (σ) and rotational velocity (V {sub rot}) to the dynamical support of a galaxy (S{sub 0.5}=√(0.5 V{sub rot}{sup 2}+σ{sup 2})). Our results are independent of the baryonic component from which σ and V {sub rot} are estimated, as the S {sub 0.5} of stars and gas agree remarkably well. This represents a significant improvement compared to the canonical M {sub *} versus V {sub rot} and M {sub *} versus σ relations. Not only is no sample pruning necessary, but also stellar and gas kinematics can be used simultaneously, as the effect of asymmetric drift is taken into account once V {sub rot} and σ are combined. Our findings illustrate how the combination of dispersion and rotational velocities for both gas and stars can provide us with a single dynamical scaling relation valid for galaxies of all morphologies across at least the stellar mass range 8.5 <log (M {sub *}/M {sub ☉}) < 11. Such relation appears to be more general and at least as tight as any other dynamical scaling relation, representing a unique tool for investigating the link between galaxy kinematics and baryonic content, and a less biased comparison with theoretical models.

79 ASTRONOMY AND ASTROPHYSICS↗

Prices in Frequency Regulation Markets: Impacts of Natural Gas Prices and Variable Renewable Energy

Increasing wind and solar penetration and low natural gas prices have reduced electricity prices in competitive power markets in recent years, while also increasing the relative importance of ancillary services in balancing short-term net load variability. As a result, ancillary service markets are providing a valuable alternative revenue stream for many market participants. Yet the price dynamics in these markets are still not very well understood. In this work, we incorporate unit-level ancillary service offer prices and quantities into a production cost model and examine how prices for frequency regulation are impacted by relatively extreme perturbations of several system parameters. Initial offers are first estimated on the basis of limited available public data and are then iteratively calibrated against historic market outcomes. Through a case study of the PJM Interconnection, we find that doubling the natural gas price increases the average annual regulation price by 36%, while replacing all coal generation with natural gas decreases the average price by 42%. Increasing the wind penetration from 2% to 30% in isolation increases the average regulation price by 32%, while further doubling the regulation requirement results in an 84% increase. These price increases can be mitigated by introducing additional battery storage capacity or by increasing offer quantities from hydro and thermal units. Finally, we discuss a number of modeling challenges that are faced when incorporating ancillary services into traditional production cost models. These include poor data availability, inconsistent product definitions across markets, and complex market rules.

02 PETROLEUM↗

Heavy-Duty Vehicle Air Drag Coefficient Estimation: From an Algebraic Perspective

When a heavy-duty vehicle (HDV) operates at the nominal highway speed, over two-thirds of its total resistive force comes from the air drag, contributing to more than half of its fuel consumption. One effective countermeasure to reduce the fuel consumption of HDVs is platooning, which employs connectivity and automated driving technologies to link two or more HDVs in convoy. Platooning allows HDVs to drive closer together and yields improved fuel economy and less CO2 emission thanks to the reduced air drag. Maximizing the energy benefits of an HDV platoon requires quantifying the drag interaction between vehicles. In practice, modeling the drag reduction in a platoon boils down to identifying the relationship between the air drag coefficient C d and the inter-vehicle distance d. Existing approaches to identify C d (d) include vehicle field tests, wind tunnel experiments, and computational fluid dynamics simulation, which can howbeit be time-consuming and cost prohibitive. In contrast, this paper proposes an algebraic approach, which relies on onboard-measurable variables, to estimate the air drag coefficient of an HDV in a platoon. Its algebraic nature avoids the classical persistence of excitation condition for parameter identification and can yield the identified parameter almost instantaneously. Simulation results demonstrate its effectiveness and the improved estimation speed over a recursive least squares identifier.

Wang, Zejiang↗

Multiplexed Anodic Stripping Voltammetry Detection of Heavy Metals in Water Using Nanocomposites Modified Screen-Printed Electrodes Integrated With a 3D-Printed Flow Cell

In this study, we present multiplexed anodic stripping voltammetry (ASV) detection of heavy metal ions (HMIs)—As(III), Cd(II), and Pb(II)—using a homemade electrochemical cell consisting of dual working, reference and counter screen-printed electrodes (SPE) on polyimide substrate integrated with a 3D-printed flow cell. Working and counter electrodes were fabricated by the screen-printing of graphite paste while the Ag/AgCl paste was screen-printed as a reference electrode (Ag/AgCl quasi-reference electrode). The working electrodes were modified with (BiO) 2 CO 3 -reduced graphene oxide (rGO)-Nafion [(BiO) 2 CO 3 -rGO-Nafion] and Fe 3 O 4 magnetic nanoparticles (Fe 3 O 4 MNPs) decorated Au nanoparticles (AuNPs)-ionic liquid (IL) (Fe 3 O 4 -Au-IL) nanocomposites separately to enhance HMIs sensing. Electrochemical detection was achieved using square wave ASV technique. The desired structure of the flow electrochemical cell was optimized by the computational fluid dynamic (CFD). Different experimental parameters for stripping analysis of HMIs were optimized including deposition time, deposition potential and flow rate. The linear range of calibration curves with the sensing nanocomposites modified SPE for the three metal ions was from 0–50 μg/L. The limits of detection (S/N = 3) were estimated to be 2.4 μg/L for As(III), 1.2 μg/L for Pb(II) and 0.8 μg/L for Cd(II). Furthermore, the homemade flow anodic stripping sensor platform was used to detect HMIs in simulated river water with a 95–101% recovery, indicating high selectivity and accuracy and great potential for applicability even in complex matrices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Parameter space for magnetization effects in high-energy-density plasmas

Magnetic fields are well known to affect the evolution of fluids via the J × B force, where J is the current density and B is the magnetic field. This force leads to the influence of magnetic fields on hydrodynamics (magnetohydrodynamics). Magnetic fields are often neglected in modeling of high-energy-density plasmas, since J × B is very small compared with the plasma pressure gradients. However, many experiments lie in a separate part of parameter space where the plasma is indirectly affected via magnetization of the heat flux and charged particle transport. This is true even for initially unmagnetized plasmas, since misaligned density and temperature gradients can self-generate magnetic fields. By comparing terms in the induction equation, we go on to estimate the regions of parameter space where these self-generated fields are strong enough to affect the hydrodynamics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

THE KEPLER-19 SYSTEM: A TRANSITING 2.2 R{sub Circled-Plus} PLANET AND A SECOND PLANET DETECTED VIA TRANSIT TIMING VARIATIONS

We present the discovery of the Kepler-19 planetary system, which we first identified from a 9.3 day periodic transit signal in the Kepler photometry. From high-resolution spectroscopy of the star, we find a stellar effective temperature T{sub eff} = 5541 {+-} 60 K, a metallicity [Fe/H] = -0.13 {+-} 0.06, and a surface gravity log(g) = 4.59 {+-} 0.10. We combine the estimate of T{sub eff} and [Fe/H] with an estimate of the stellar density derived from the photometric light curve to deduce a stellar mass of M{sub *} = 0.936 {+-} 0.040 M{sub Sun} and a stellar radius of R{sub *} = 0.850 {+-} 0.018 R{sub Sun} (these errors do not include uncertainties in the stellar models). We rule out the possibility that the transits result from an astrophysical false positive by first identifying the subset of stellar blends that reproduce the precise shape of the light curve. Using the additional constraints from the measured color of the system, the absence of a secondary source in the high-resolution spectrum, and the absence of a secondary source in the adaptive optics imaging, we conclude that the planetary scenario is more than three orders of magnitude more likely than a blend. The blend scenario is independently disfavored by the achromaticity of the transit: we measure a transit depth with Spitzer at 4.5 {mu}m of 547{sup +113}{sub -110} ppm, consistent with the depth measured in the Kepler optical bandpass of 567 {+-} 6 ppm (corrected for stellar limb darkening). We determine a physical radius of the planet Kepler-19b of R{sub p} = 2.209 {+-} 0.048 R{sub Circled-Plus }; the uncertainty is dominated by uncertainty in the stellar parameters. From radial velocity observations of the star, we find an upper limit on the planet mass of 20.3 M{sub Circled-Plus }, corresponding to a maximum density of 10.4 g cm{sup -3}. We report a significant sinusoidal deviation of the transit times from a predicted linear ephemeris, which we conclude is due to an additional perturbing body in the system. We cannot uniquely determine the orbital parameters of the perturber, as various dynamical mechanisms match the amplitude, period, and shape of the transit timing signal and satisfy the host star's radial velocity limits. However, the perturber in these mechanisms has a period {approx}< 160 days and mass {approx}< 6 M{sub Jup}, confirming its planetary nature as Kepler-19c. We place limits on the presence of transits of Kepler-19c in the available Kepler data.

79 ASTRONOMY AND ASTROPHYSICS↗

Gas and dust dynamics in γ Cephei-type disks

Context. Giant planets are observed orbiting the primary stars of close binary systems. Such planets may have formed in compact circumprimary disks, which once surrounded these stars, under conditions much different than those encountered around single stars. Aims. In order to quantify the effects of the strong gravitational perturbations exerted on circumprimary disk material, the three-dimensional (3D) dynamics of gas and dust in orbit around the primary star of a compact and eccentric binary system was modeled by applying the stellar and orbital parameters of γ Cephei, a well-known system that can be representative of a class of close binaries. Methods. Circumprimary gas was approximated as an Eulerian viscous and compressible fluid and modeled by means of 3D hydrodynamical simulations, assuming locally isothermal conditions in the medium around the primary star. Dust grains were modeled as Lagrangean particles, subjected to gravity and aerodynamic drag forces. Models that include a giant planet were also considered. Results. Models indicate that spiral density waves excited around pericenter passage propagate toward the inner boundary of the disk, through at least a few pressure scale-heights from the mid-plane, inducing radial and vertical mixing in the gas. However, perturbations imparted to gas, both in terms of eccentricity and precession, are far weaker than previously estimated by two-dimensional (2D) simulations. Models predict small eccentricities, ≲0.03, and slow retrograde precession. The addition of a giant planet does not change the low eccentricity state of the disk. The parameters applied to the disk would lead to the formation of a massive planet, many times the mass of Jupiter, in agreement with some observations. Micron to mm-size dust grains are well coupled to the gas, resulting in similar dynamics and statistically similar distributions of orbital elements. The planet only affects the dust distributions locally. In agreement with outcomes of recent 2D models, the lifetime of an isolated circumprimary disk would be brief, ~10 5 years, because of its compact nature, requiring a long-term external supply of mass to allow for the in situ formation of a giant planet.

79 ASTRONOMY AND ASTROPHYSICS↗

The giant molecular cloud environments of infrared dark clouds

We study giant molecular cloud (GMC) environments surrounding 10 infrared dark clouds (IRDCs), using {sup 13}CO(1−0) emission from the Galactic Ring Survey. We measure physical properties of these IRDCs/GMCs on a range of scales extending to radii, R, of 30 pc. By comparing different methods for defining cloud boundaries and for deriving mass surface densities and velocity dispersions, we settle on a preferred “CE,τ,G” method of “Connected Extraction” in position–velocity space plus Gaussian fitting to opacity-corrected line profiles for velocity dispersion and mass estimation. We examine how cloud definition affects measurements of the magnitude and direction of line-of-sight velocity gradients and velocity dispersions, including associated dependencies on size scale. CE,τ,G-defined GMCs show velocity dispersion versus size relations σ ∝ s{sup 1/2}, which are consistent with the large-scale gradients being caused by turbulence. However, IRDCs have velocity dispersions that are moderately enhanced above those predicted by this scaling relation. We examine the dynamical state of the clouds, finding mean virial parameters α-bar {sub vir}≃1.0 for GMCs and 1.6 for IRDCs, broadly consistent with models of magnetized virialized pressure-confined polytropic clouds, but potentially indicating that IRDCs have more disturbed kinematics. CE,τ, G-defined clouds exhibit a tight correlation of σ/R{sup 1/2}∝Σ{sup n}, with n ≃ 0.7 for GMCs and 1.3 for IRDCs (cf. a value of 0.5 expected for a population of virialized clouds). We conclude that while GMCs show evidence for virialization over a range of scales, IRDCs may be moderately supervirial. Alternatively, IRDCs could be virialized but have systematically different {sup 13}CO gas-phase abundances, i.e., owing to freeze-out, affecting mass estimations.

79 ASTRONOMY AND ASTROPHYSICS↗

Chlorophyll- a dynamics in the lower Amazon River: insights from in situ and hyperspectral remote sensing using OCI-PACE

Chlorophyll-a concentration (Chla) is a key indicator of phytoplankton biomass and aquatic trophic status. However, satellite-derived Chla in sediment-rich waters, such as those found in the Lower Amazon River, remains challenging. The present study characterizes in situ Chla levels and their relationships with geographic, physical, and biogeochemical parameters in the Lower Amazon. Data collected between 2014 and 2017 across four hydrological seasons included measurements of Chla, remote sensing reflectance, and water quality parameters such as total suspended sediment, conductivity, water surface temperature, dissolved oxygen, pH, dissolved organic carbon and coloured dissolved organic matter. An empirical model was developed to estimate Chla using simulated hyperspectral bands from NASA’s PACE mission, achieving high performance (R 2 = 0.76; RMSE = 0.11 μg·L −1 ). Red bands proved particularly effective for Chla retrieval, while the addition of ultraviolet bands further enhanced model accuracy. The application of the developed model to satellite imagery yielded results consistent with in situ observations for the same hydrologic season. Seasonal variation and geographic location were major factors influencing Chla dynamics. This study provides a novel contribution to Chla estimation in optically complex, highly turbid waters and highlights the potential of the PACE mission to enhance global aquatic ecosystem monitoring. In conclusion, by offering freely available hyperspectral data with high radiometric resolution, PACE represents a significant advancement in the realm of remote sensing of aquatic environments.

Amazon River↗

Quantification of early nonpharmaceutical interventions aimed at slowing transmission of Coronavirus Disease 2019 in the Navajo Nation and surrounding states (Arizona, Colorado, New Mexico, and Utah)

During an early period of the Coronavirus Disease 2019 (COVID-19) pandemic, the Navajo Nation, much like New York City, experienced a relatively high rate of disease transmission. Yet, between January and October 2020, it experienced only a single period of growth in new COVID-19 cases, which ended when cases peaked in May 2020. The daily number of new cases slowly decayed in the summer of 2020 until late September 2020. In contrast, the surrounding states of Arizona, Colorado, New Mexico, and Utah all experienced at least two periods of growth in the same time frame, with second surges beginning in late May to early June. Here, we investigated these differences in disease transmission dynamics with the objective of quantifying the contributions of non-pharmaceutical interventions (NPIs) (e.g., behaviors that limit disease transmission). We considered a compartmental model accounting for distinct periods of NPIs to analyze the epidemic in each of the five regions. We used Bayesian inference to estimate region-specific model parameters from regional surveillance data (daily reports of new COVID-19 cases) and to quantify uncertainty in parameter estimates and model predictions. Our results suggest that NPIs in the Navajo Nation were sustained over the period of interest, whereas in the surrounding states, NPIs were relaxed, which allowed for subsequent surges in cases. Our region-specific model parameterizations allow us to quantify the impacts of NPIs on disease incidence in the regions of interest.

60 APPLIED LIFE SCIENCES↗

Studying of multi-shell gas-puff Z-pinches using x-ray spectroscopy with spatial resolution

Dynamics and parameters of gas-puff Z-pinch plasmas at stagnation were studied using x-ray spectroscopic diagnostics. In experiments on a 1 MA pulsed power generator, multilayer coaxial loads were made using a triple-nozzle gas-puff valve. High-luminosity spectrographs with spherically bent crystals made it possible to record spectra with high spatial resolution along the pinch axis and to record two-dimensional plasma images in separate spectral lines. Using various combinations of gases in the nozzles and adding small amounts of a gas tracer, the final structure and composition of the compressed plasma were determined. Furthermore, plasma parameters were estimated by modeling the spectra using the PrismSPECT program, but with the limitation that the spectra were time-integrated, so that spectra from different gases and at different positions may have been emitted at different times.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Penumbra: A spatially distributed, mechanistic model for simulating ground-level incident solar energy across heterogeneous landscapes

Landscape solar energy is a significant environmental driver, yet it remains complicated to model well. Several solar radiation models simplify the complexity of light by estimating it at discrete point locations or by averaging values over larger areas. These modeling approaches may be useful in certain cases, but they are unable to provide spatially distributed and temporally dynamic representations of solar energy across entire landscapes. We created a landscape-scale ground-level shade and solar energy model called Penumbra to address this deficiency. Penumbra simulates spatially distributed ground-level shade and incident solar energy at user-defined timescales by modeling local and distant topographic shading and vegetative shading. Spatially resolved inputs of a digital elevation model, a normalized digital surface model, and landscape object transmittance are used to estimate spatial variations in solar energy at user-defined temporal timesteps. The research goals for Penumbra included: 1) simulations of spatiotemporal variations of shade and solar energy caused by both objects and topographic features, 2) minimal user burden and parameterization, 3) flexible user defined temporal parameters, and 4) flexible external model coupling. We test Penumbra’s predictive skill by comparing the model’s predictions with monitored open and forested sites, and achieve calibrated mean errors ranging from -17.3 to 148.1 μmoles/m 2 /s. Penumbra is a dynamic model that can produce spatial and temporal representations of shade percentage and ground-level solar energy. Outputs from Penumbra can be used with other ecological models to better understand the health and resilience of aquatic, near stream terrestrial, and upland ecosystems.

54 ENVIRONMENTAL SCIENCES↗

Data Assimilation for Robust UQ Within Agent-Based Simulation on HPC Systems

Agent-based simulation provides a powerful tool for in silico system modeling. However, these simulations do not provide built-in methods for uncertainty quantification (UQ). Within these types of models a typical approach to UQ is to run multiple realizations of the model then compute aggregate statistics. This approach is limited due to the compute time required for a solution. When faced with an emerging biothreat, public health decisions need to be made quickly and solutions for integrating near real-time data with analytic tools are needed. We propose an integrated Bayesian UQ framework for agent-based models based on sequential Monte Carlo sampling. Given streaming or static data about the evolution of an emerging pathogen this Bayesian framework provides a distribution over the parameters governing the spread of a disease through a population. These estimates of the spread of a disease may be provided to public health agencies seeking to abate the spread. By coupling agent-based simulations with Bayesian modeling in a data assimilation, our proposed framework provides a powerful tool for modeling dynamical systems in silico. We propose a method which reduces model error and provides a range of realistic possible outcomes. Moreover, our method addresses two primary limitations of ABMs: the lack of UQ and an inability to assimilate data. Our proposed framework combines the flexibility of an agent-based model with UQ provided by the Bayesian paradigm in a workflow which scales well to HPC systems. We provide algorithmic details and results on a simulated outbreak with both static and streaming data.

Spannaus, Adam [ORNL] (ORCID:0000000225213657)↗

Consequences of bounds on longitudinal emittance growth for the design of recirculating linear accelerators

Recirculating linear accelerators (RLAs) are a cost-effective method for the acceleration of muons for a muon collider in energy ranges from a couple GeV to a few 10s of GeV. Muon beams generally have longitudinal emittances that are large for the RF frequency that is used, and it is important to limit the growth of that longitudinal emittance. This has particular consequences for the arc design of the RLAs. I estimate the longitudinal emittance growth in an RLA arising from the RF nonlinearity. Given an emittance growth limitation and other design parameters, one can then compute the maximum momentum compaction in the arcs. I describe how to obtain an approximate arc design satisfying these requirements based on the deisgn in [1]. Longitudinal dynamics also determine the energy spread in the beam, and this has consequences on the transverse phase advance in the linac. This in turn has consequences for the arc design due to the need to match beta functions. I combine these considerations to discuss design parameters for the acceleration of muons for a collider in an RLA from 5 to 63 GeV.

43 PARTICLE ACCELERATORS↗