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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

McMillan map and nonlinear Twiss parameters

In this article we consider two dynamical systems: the McMillan sextupole and octupole integrable mappings originally introduced by Edwin McMillan; the second one is also known as canonical McMillan map. Both of them are simplest symmetric McMillan maps with only one intrinsic parameter, the trace of the Jacobian at the fixed point. While these dynamical systems have numerous of applications and are used in many areas of math and physics, some of their dynamical properties have not been described yet. We fulfill the gap and provide complete description of all stable trajectories including parametrization of invariant curves, Pioncaré rotation numbers and canonical action-angle variables. In the second part we relate these maps with general chaotic map in McMillan-Turaev form. We show that McMillan sextupole and octupole mappings are first order approximations of dynamics around the fixed point, in a similar way as linear map and quadratic invariant (Courant-Snyder invariant in accelerator physics) is the zeroth order approximation (known as linearization). Finally we suggest the new formalism of nonlinear Twiss parameters which incorporate dependence of rotation number as a function of amplitude, in contrast to e.g. betatron phase advance used in accelerator physics which is independent of amplitude. Specifically in application to accelerator physics this new formalism is capable of predicting dynamical aperture around 1-st, 2-nd, 3-rd and 4-th order resonances for flat beams, which is critical for beam injection/extraction.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Design of double- and multi-bend achromat lattices with large dynamic aperture and approximate invariants

A numerical method to design nonlinear double- and multi-bend achromat (DBA and MBA) lattices with approximate invariants of motion is investigated. The search for such nonlinear lattices is motivated by Fermilab’s Integrable Optics Test Accelerator (IOTA), whose design is based on an integrable Hamiltonian system with two invariants of motion. While it may not be possible to design an achromatic lattice for a dedicated synchrotron light source storage ring with one or more exact invariants of motion, it is possible to tune the sextupoles and octupoles in existing DBA and MBA lattices to produce approximate invariants. In our procedure, the lattice is tuned while minimizing the turn-by-turn fluctuations of the Courant-Snyder actions J x and J y at several distinct amplitudes, while simultaneously minimizing diffusion of the on-energy betatron tunes. The resulting lattices share some important features with integrable ones, such as a large dynamic aperture, trajectories confined to invariant tori, robustness to resonances and errors, and a large amplitude-dependent tune-spread. Compared to the nominal NSLS-II lattice, the single- and multi-bunch instability thresholds are increased and the bunch-by-bunch feedback gain can be reduced.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Dynamics of McMillan mappings I. McMillan multipoles

In this article, we consider two dynamical systems: the McMillan sextupole and octupole integrable mappings, originally proposed by Edwin McMillan. Both represent the simplest symmetric McMillan maps, characterized by a single intrinsic parameter. While these systems find numerous applications across various domains of mathematics and physics, some of their dynamical properties remain unexplored. We aim to bridge this gap by providing a comprehensive description of all stable trajectories, including the parametrization of invariant curves, Poincaré rotation numbers, and canonical action–angle variables. In the second part, we establish connections between these maps and general chaotic maps in standard form. Our investigation reveals that the McMillan sextupole and octupole serve as first-order approximations of the dynamics around the fixed point, akin to the linear map and quadratic invariant (known as the Courant–Snyder invariant in accelerator physics), which represents zeroth-order approximations (referred to as linearization). Furthermore, we propose a novel formalism for nonlinear Twiss parameters, which accounts for the dependence of rotation number on amplitude. This stands in contrast to conventional betatron phase advance used in accelerator physics, which remains independent of amplitude. Notably, in the context of accelerator physics, this new formalism demonstrates its capability in predicting dynamical aperture around low-order resonances for flat beams, a critical aspect in beam injection/extraction scenarios.

43 PARTICLE ACCELERATORS↗
DOE OSTI2026

Fabrication of freeform potassium dihydrogen phosphate crystals by belt-on-wheel polishing for spatially tailored polarization control in high-power lasers

Large-aperture (>30 cm) optical components that provide spatially tailored control of the properties of a laser beam, such as phase, polarization, and amplitude, have been the focus of much research and development in recent years. Such optics can improve energy throughput and target implosion efficiency in high-power laser systems conducting inertial confinement fusion research. Here, a method is demonstrated for fabricating freeform surface topographies into the birefringent crystalline material, potassium dihydrogen phosphate (KDP). Belt-on-wheel polishing with an oil-based fluid, developed to mitigate the deliquescent properties of KDP, is used to deterministically polish a freeform topography into KDP, enabling the fabrication of a wave plate with spatially arbitrary retardance. Testing of the laser-induced damage threshold of belt-on-wheel polished KDP was conducted at a wavelength of 351 nm and a pulse duration of 1 ns. The results revealed that the polished surfaces are highly resistant to laser-induced damage, making them suitable for large-aperture, high-power laser applications.

Urban, Nathaniel D. [Univ. of Rochester, NY (Unite↗
DOE OSTI2024

Relating Hydro–Mechanical and Elastodynamic Properties of Dynamically Stressed Tensile–Fractured Rock in Relation to Applied Normal Stress, Fracture Aperture, and Contact Area

We exploit nonlinear elastodynamic properties of fractured rock to probe the micro-scale mechanics of fractures and understand the relation between fluid transport and fracture aperture under dynamic stressing. Experiments were conducted on rough, tensile-fractured Westerly granite subject to triaxial stresses. We measure fracture permeability for steady-state fluid flow with deionized water. Pore pressure oscillations are applied at amplitudes ranging from 0.2 to 1 MPa at 1 Hz frequency. During dynamic stressing we transmit ultrasonic signals through the fracture using an array of piezoelectric transducers (PZTs) to monitor evolution of interface properties. We examine the influence of fracture aperture and contact area by conducting measurements at effective normal stresses of 10–20 MPa. Additionally, the evolution of contact area with stress is characterized using pressure sensitive film. These experiments are conducted separately with the same fracture and map contact area at stresses from 9 to 21 MPa. The measurements are a proxy for “true” contact area for the fracture surface and we relate them to elastic properties using the calculated PZT sensor footprints via numerical modeling of Fresnel zones. We compare the elastodynamic response of the fracture using the stress-induced changes in ultrasonic wave velocities for transmitter-receiver pairs to image spatial variations in contact properties. We show that nonlinear elasticity and permeability enhancement decrease with increasing normal stress. Additionally, post-oscillation wave velocity and permeability exhibit quick recoveries toward pre-oscillation values. Estimates of fracture contact area (global and local) demonstrate that the elastodynamic and permeability responses are dominated by fracture topology.

58 GEOSCIENCES↗
DOE OSTI2026

Practical Three-Dimensional Curvilinear Aperture Monopulse Synthetic Aperture Radar

When collected over a curved path, Synthetic Aperture Radar (SAR) contains information about the three-dimensional content of a scene that can aid interpretation of this difficult imaging modality. In a point scatterer simulation with amplitudes and heights derived from a real SAR image pair, we supplement confocal processing with a monopulse-based algorithm to compute heights of certain bright points, which we find automatically. In SAR, bright points often reflect man-made infrastructure central to scene interpretation.

Story, Mark [ORNL] (ORCID:0000000289148911)↗
DOE OSTI2023

Groundwater Volume Loss in Mexico City Constrained by InSAR and GRACE Observations and Mechanical Models

Abstract Groundwater withdrawal can cause localized and rapid poroelastic subsidence, spatially broad elastic uplift of low amplitude, and changes in the gravity field. Constraining groundwater loss in Mexico City, we analyze data from the Gravity Recovery and Climate Experiment and its follow‐on mission (GRACE/FO) and Synthetic Aperture Radar (SAR) Sentinel‐1A/B images between 2014 and 2021. GRACE/FO observations yield a groundwater loss of 0.85–3.87 km 3 /yr for a region of ∼300 × 600 km surrounding Mexico City. Using the high‐resolution interferometric SAR data set, we measure >35 cm/yr subsidence within the city and up to 2 cm/yr of uplift in nearby areas. Attributing the long‐term subsidence to poroelastic aquifer compaction and the long‐term uplift to elastic unloading, we apply respective models informed by local geology, yielding groundwater loss of 0.86–12.57 km 3 /yr. Our results suggest Mexico City aquifers have been depleting at faster rates since 2015, exacerbating the socioeconomic and health impacts of long‐term groundwater overdrafts.

58 GEOSCIENCES↗
DOE OSTI2025

Sextupole reduction via chaos suppression at NSLS-II

We revisit the nonlinear lattice design approach for the National Synchrotron Light Source II (NSLS-II) storage ring. By suppressing chaos, we identify alternative sextupole configurations to the original design, which relied on the conventional approach of simultaneously minimizing Resonance Driving Terms (RDTs) and Amplitude-Dependent Detuning (ADD). These alternatives achieve comparable performance while requiring fewer sextupoles. A detailed comparison of two representative solutions is presented and supported by experimental validation. Our results indicate that dynamic aperture correlates more strongly with global chaos than with individual RDTs, and that the importance of minimizing ADD may have been overstated in earlier design approach.

43 PARTICLE ACCELERATORS↗
DOE OSTI2026

Sextupole reduction via chaos suppression at the National Synchrotron Light Source II

We revisit the nonlinear lattice design approach for the National Synchrotron Light Source II (NSLS-II) storage ring. By suppressing chaos, we identify alternative sextupole configurations to the original design, which relied on the conventional strategy of simultaneously minimizing resonance driving terms (RDTs) and amplitude-dependent detuning (ADD). These alternatives achieve comparable performance while requiring fewer sextupoles. A detailed comparison of two representative solutions is presented and supported by experimental validation. Our results show that the dynamic aperture correlates more strongly with global chaos than with individual RDTs, and that the importance of minimizing ADD may have been overstated in earlier design strategies.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Parasitic Modulation of Microwave Signals by a Hypersonic Plasma Layer

During hypersonic flight, compressional and viscous heating of the air can form a plasma layer which encases the aircraft. If the boundary layer becomes turbulent, then the electron density fluctuations can effect a parasitic modulation in microwave signals transmitted through the plasma. We developed an approach for studying the interaction of microwave signals with a turbulent, hypersonic plasma layer. The approach affords a great deal of flexibility in both the plasma layer model and the antenna configuration. We then analyzed a situation in which microwaves, transmitted from a rectangular aperture antenna, propagate through a turbulent plasma layer to a distant receiver. We characterized the first-and second-order statistics of the computed parasitic modulation and quantified the depolarization of the signal. The amplitude fluctuations are lognormally distributed at low frequencies and Rice-distributed at high frequencies. Fluctuations in the copolarized phase and amplitude of the far-field signal are strongly anticorrelated. Here, we used a multioutput Gaussian process (MOGP) to model these quantities. The efficacy of the MOGP model is demonstrated by recovering the time evolution of the copolarized phase given the copolarized amplitude and occasional measurements of the phase.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Simons Observatory: characterizing the Large Aperture Telescope Receiver with radio holography

Here, we present near-field radio holography measurements of the Simons Observatory Large Aperture Telescope Receiver optics. These measurements demonstrate that radio holography of complex millimeter-wave optical systems comprising cryogenic lenses, filters, and feed horns can provide detailed characterization of wave propagation before deployment. We used the measured amplitude and phase, at 4 K, of the receiver near-field beam pattern to predict two key performance parameters: 1) the amount of scattered light that will spill past the telescope to 300 K and 2) the beam pattern expected from the receiver when fielded on the telescope. These cryogenic measurements informed the removal of a filter, which led to improved optical efficiency and reduced sidelobes at the exit of the receiver. Holography measurements of this system suggest that the spilled power past the telescope mirrors will be less than 1%, and the main beam with its near sidelobes are consistent with the nominal telescope design. This is the first time such parameters have been confirmed in the lab prior to deployment of a new receiver. This approach is broadly applicable to millimeter and submillimeter instruments.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Introducing a New Spitzer Master BLISS Map to Remove the Instrument Systematic Phase-curve-parameter Degeneracy, as Demonstrated by a Reanalysis of the 4.5 μm WASP-43b Phase Curve

While Spitzer Infrared Array Camera (IRAC) systematics are generally well understood, each data set can provide its own challenges that continue to teach us about the underlying functional form of these systematics. Multiple groups have analyzed the phase curves of WASP-43b with varying detrending techniques, each obtaining different results. In this work, we take another look at WASP-43b while exploring the degenerate relation between Bilinearly Interpolated Subpixel Sensitivity (BLISS) mapping, point response function (PRF)–FWHM detrending, and phase curve parameters. We find that there is a strong correlation between the detrending parameters in the two models, and best-fit phase curve amplitudes vary strongly when the data are temporally binned. To remove this degeneracy, we present a new Gaussian centroided intrapixel sensitivity map (hereafter fixed sensitivity map), generated using 3,712,830 exposures spanning 5 yr, for a variety of aperture sizes at 4.5 μm. We find evidence for time variability in the sensitivity at 3.6 μm and do not generate a visit-independent map for this channel. With the fixed 4.5 μm intrapixel sensitivity map, the best fits for WASP-43b no longer vary strongly with bin size and PRF–FWHM detrending is no longer required to remove correlated noise. For data sets that do not fall completely within the sweet spot, temporal binning should not be used in the analysis of Spitzer phase curves. We confirm nightside emission for WASP-43b with a disk-integrated nightside temperature of 806 ± 48 K at 4.5 μm. The 4.5 μm maps are available at github.com/kevin218/POET.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Super-resolution surface slope metrology of x-ray mirrors

We present experimental, analytical, and numerical methods developed for reconstruction (deconvolution) of one-dimensional (1D) surface slope profiles over the spatial frequency range where the raw data are significantly perturbed due to the limited resolution of the measurement instrument. We characterize the spatial resolution properties of a profiler with the instrument's transfer function (ITF). To precisely measure the ITF, we apply a recently developed method utilizing test surfaces with 1D linear chirped height profiles of constant slope amplitude. Based on the results of the ITF calibration, we determine parameters of an analytical model for the ITF that is used in the original reconstruction software. Here, we treat surface slope metrology data obtained with the Optical Surface Measuring System (OSMS), using as a sensor an electronic autocollimator (AC) ELCOMAT-3000. The spatial resolution of the OSMS is limited by the size of the AC light-beam-collimating aperture. For the purposes of this investigation, the OSMS is equipped with a circular aperture with a diameter of 2.5 mm. This is a typical arrangement of most AC-based slope profilers developed for surface slope metrology of state-of-the-art x-ray mirrors. Using the example of surface slope metrology of two state-of-the-art elliptically shaped x-ray focusing mirrors, we demonstrate that the developed data reconstruction procedure allows us to significantly improve the accuracy of surface slope metrology with the OSMS over the spatial wavelength range from ~1.6 mm to 7 mm. Thus, the amplitude of the quasi-periodic error characteristic of the deterministic polishing process used appears to be higher by a factor of~2 than is apparent from the rough metrology data. Underestimation of the surface slope errors in this spatial wavelength range can lead to serious errors in the expected performance of x-ray mirrors in synchrotron beamlines, especially at modern light sources utilizing coherent x rays, where the perturbations can lead to increased speckle-like intensity variation.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Optical Characterization of the Keck Array and BICEP3 CMB Polarimeters from 2016 to 2019

The BICEP/Keck experiment (BK) is a series of small-aperture refracting telescopes observing degree-scale cosmic microwave background (CMB) polarization from the South Pole in search of a primordial B-mode signature. This B-mode signal arises from primordial gravitational waves interacting with the CMB and has amplitude parametrized by the tensor-to-scalar ratio r. Since 2016, BICEP3 and the Keck Array have been observing with 4800 total antenna-coupled transition-edge sensor detectors, with frequency bands spanning 95, 150, 220, and 270 GHz. Here we present the optical performance of these receivers from 2016 to 2019, including far-field beams measured in situ with an improved chopped thermal source and instrument spectral response measured with a field-deployable Fourier transform spectrometer. As a pair differencing experiment, an important systematic that must be controlled is the differential beam response between the co-located, orthogonally polarized detectors. We generate per-detector far-field beam maps and the corresponding differential beam mismatch that is used to estimate the temperature-to-polarization leakage in our CMB maps and to give feedback on detector and optics fabrication. The differential beam parameters presented here were estimated using improved low-level beam map analysis techniques, including efficient removal of non-Gaussian noise as well as improved spatial masking. These techniques help minimize systematic uncertainty in the beam analysis, with the goal of constraining the bias on r induced by temperature-to-polarization leakage to be subdominant to the statistical uncertainty. This is essential as we progress to higher detector counts in the next generation of CMB experiments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Quantitative agreement between dynamical rocking curves in ultrafast electron diffraction for x-ray lasers

Electron diffraction through a thin patterned silicon membrane can be used to create complex spatial modulations in electron distributions. By precisely varying parameters such as crystallographic orientation and wafer thickness, the intensity of reflections in the diffraction plane can be controlled and by placing an aperture to block all but one spot, we can form an image with different parts of the patterned membrane, as is done for bright-field imaging in microscopy. The patterned electron beams can then be used to control phase and amplitude of subsequent x-ray emission, enabling novel coherent x-ray methods. Furthermore, the electrons themselves can also be used for femtosecond time resolved diffraction and microscopy. As a first step toward patterned beams, we demonstrate experimentally and through simulation the ability to accurately predict and control diffraction spot intensities. We simulate MeV transmission electron diffraction patterns using the multislice method for various crystallographic orientations of a single crystal Si(001) membrane near beam normal. The resulting intensity maps of the Bragg reflections are compared to experimental results obtained at the Accelerator Structure Test Area Ultrafast Electron Diffraction (ASTA UED) facility at SLAC. Furthermore, the fraction of inelastic and elastic scattering of the initial charge is estimated along with the absorption of the membrane to determine the contrast that would be seen in a patterned version of the Si(001) membrane.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Experimental 3-dimensional tracking of the dynamics of a single electron in the Fermilab Integrable Optics Test Accelerator (IOTA)

We present the results of experimental studies on the transverse and longitudinal dynamics of a single electron in the IOTA storage ring. IOTA is a flexible machine dedicated to beam physics experiments with electrons and protons. A method was developed to reliably inject and circulate a controlled number of electrons in the ring. A key beam diagnostic system is the set of sensitive high-resolution digital cameras for the detection of synchrotron light emitted by the electrons. With 60–130 electrons in the machine, we measured beam lifetime and derived an absolute calibration of the optical system. At exposure times of 0.5 s, the cameras were sensitive to individual electrons. Camera images were used to reconstruct the time evolution of oscillation amplitudes of a single electron in all 3 degrees of freedom. The evolution of amplitudes directly showed the interplay between synchrotron-radiation damping, quantum excitations, and scattering with the residual gas. From the distribution of measured single-electron oscillation amplitudes, we deduced transverse emittances, momentum spread, damping times, and beam energy. Estimates of residual-gas density and composition were calculated from the measured distributions of vertical scattering angles. Combining scattering and lifetime data, we also provide an estimate of the aperture of the ring. To our knowledge, this is the first time that the dynamics of a single electron are tracked in all three dimensions with digital cameras in a storage ring.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Mapping the gas density with the kinematic Sunyaev-Zel’dovich and patchy screening effects: A self-consistent comparison

The secondary anisotropies of the cosmic microwave background (CMB) provide a wealth of astrophysical and cosmological information. Pairing measurements of the CMB temperature map obtained by DR5 of the Atacama Cosmology Telescope (ACT) with the imaging survey conducted by the Dark Energy Spectroscopic Instrument for the purposes of target selection, DECaLS DR9, we investigate two effects that are sensitive to the gas density 𝜏: kinematic Sunyaev-Zel’dovich (kSZ) and patchy screening or anisotropic screening (resulting from the Thomson scattering of CMB photons away from the line-of-sight by free electrons). In particular, we measure the stacked profiles of the gas density around luminous red galaxies (LRGs) at a mean redshift of 𝑧 ≈ 0.7. We detect the kSZ signal at 7.2⁢𝜎, and we find a signal at ∼ 4.1⁢𝜎 for the patchy screening estimator, which is in excess relative to the kSZ signal. We attribute this excess to contamination from CMB lensing. Here, we demonstrate the effect of lensing using 𝑁-body simulations, and we show that the screening signal is dominated by it. Accounting for lensing, our measurement places a 95% upper bound on the optical depth of the Extended DESI LRG sample of 𝜏 < 2.5 10 −4 for a mean value of the sample of 𝜏 ≈ 1.6 10 −4 . Furthermore, via hydro simulations, we show that the underlying optical depth signal measured by both effects (after removing the CMB lensing contribution) is in perfect agreement when adopting either a compensated aperture photometry (CAP) filter or a high-pass filter. Consistent with previous measurements, we see evidence for excess baryonic feedback around DESI LRGs in the patchy screening measurement. In the future, when both effects can be measured with high signal-to-noise, one can measure the amplitude ratio between them, which is proportional to the root-mean-square velocity of the host halo sample, and even place constraints on velocity-sensitive models such as modified gravity and phantom dark energy.

Astrophysical & cosmological simulations↗
DOE OSTI2021

A Frequency-Domain-Based Algorithm for Detecting Microseismicity Using Dense Surface Seismic Arrays

We propose a new frequency-domain-based algorithm for detecting small-magnitude seismic events using dense surface seismic arrays. Our proposed method takes advantage of the high energy carried by S waves, and approximate known source locations, which are used to rotate the horizontal components to obtain the maximum amplitude. By surrounding the known source area with surface geophones, we achieve a favorable geometry for locating the detected seismic events with the backprojection method. To test our new detection method, we used a dense circular array, consisting of 151 5 Hz three-component geophones, over a 5 km aperture that was in operation at the Utah Frontier Observatory for Research in Geothermal Energy (FORGE) in southcentral Utah. We apply the new detection method during a small-scale test injection phase at FORGE, and during an aftershock sequence of an Mw 4.1 earthquake located ~30 km north of the geophone array, within the Black Rock volcanic field. We are able to detect and locate microseismic events (Mw<0) during injections, despite the high level of anthropogenic activity, and several aftershocks that are missing from the regional catalog. By comparing our method with known algorithms that operate both in the time and frequency domain, we show that our proposed method performs better in the case of the FORGE injection monitoring, and equally well for the off-array aftershock sequence. Our new method has the potential to improve microseismic event detections even in extremely noisy environments, and the proposed location scheme serves as a direct discriminant between true and false detections.

Geochemistry & Geophysics↗