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DOE OSTI2016

A critical appraisal of the zero-multipole method: Structural, thermodynamic, dielectric, and dynamical properties of a water system

We performed extensive and strict tests for the reliability of the zero-multipole (summation) method (ZMM), which is a method for estimating the electrostatic interactions among charged particles in a classical physical system, by investigating a set of various physical quantities. This set covers a broad range of water properties, including the thermodynamic properties (pressure, excess chemical potential, constant volume/pressure heat capacity, isothermal compressibility, and thermal expansion coefficient), dielectric properties (dielectric constant and Kirkwood-G factor), dynamical properties (diffusion constant and viscosity), and the structural property (radial distribution function). We selected a bulk water system, the most important solvent, and applied the widely used TIP3P model to this test. In result, the ZMM works well for almost all cases, compared with the smooth particle mesh Ewald (SPME) method that was carefully optimized. In particular, at cut-off radius of 1.2 nm, the recommended choices of ZMM parameters for the TIP3P system are α ≤ 1 nm{sup −1} for the splitting parameter and l = 2 or l = 3 for the order of the multipole moment. We discussed the origin of the deviations of the ZMM and found that they are intimately related to the deviations of the equilibrated densities between the ZMM and SPME, while the magnitude of the density deviations is very small.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2011

FIRST SEASON QUIET OBSERVATIONS: MEASUREMENTS OF COSMIC MICROWAVE BACKGROUND POLARIZATION POWER SPECTRA AT 43 GHz IN THE MULTIPOLE RANGE 25 {<=} l {<=} 475

The Q/U Imaging ExperimenT (QUIET) employs coherent receivers at 43 GHz and 94 GHz, operating on the Chajnantor plateau in the Atacama Desert in Chile, to measure the anisotropy in the polarization of the cosmic microwave background (CMB). QUIET primarily targets the B modes from primordial gravitational waves. The combination of these frequencies gives sensitivity to foreground contributions from diffuse Galactic synchrotron radiation. Between 2008 October and 2010 December, over 10,000 hr of data were collected, first with the 19 element 43 GHz array (3458 hr) and then with the 90 element 94 GHz array. Each array observes the same four fields, selected for low foregrounds, together covering Almost-Equal-To 1000 deg{sup 2}. This paper reports initial results from the 43 GHz receiver, which has an array sensitivity to CMB fluctuations of 69 {mu}K{radical}s. The data were extensively studied with a large suite of null tests before the power spectra, determined with two independent pipelines, were examined. Analysis choices, including data selection, were modified until the null tests passed. Cross-correlating maps with different telescope pointings is used to eliminate a bias. This paper reports the EE, BB, and EB power spectra in the multipole range l = 25-475. With the exception of the lowest multipole bin for one of the fields, where a polarized foreground, consistent with Galactic synchrotron radiation, is detected with 3{sigma} significance, the E-mode spectrum is consistent with the {Lambda}CDM model, confirming the only previous detection of the first acoustic peak. The B-mode spectrum is consistent with zero, leading to a measurement of the tensor-to-scalar ratio of r = 0.35{sup +1.06}{sub -0.87}. The combination of a new time-stream 'double-demodulation' technique, side-fed Dragonian optics, natural sky rotation, and frequent boresight rotation leads to the lowest level of systematic contamination in the B-mode power so far reported, below the level of r = 0.1.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Increasing the power of weak lensing data with multipole-based intrinsic alignment estimators

ABSTRACT It has long been known that galaxy shapes align coherently with the large-scale density field. Characterizing this effect is essential to interpreting measurements of weak gravitational lensing, the deflection of light from distant galaxies by matter overdensities along the line of sight, as it also produces coherent galaxy alignments that we wish to interpret in terms of a cosmological model. Existing direct measurements of intrinsic alignments using galaxy samples with high-quality shape and redshift measurements typically use well-understood but sub-optimal projected estimators, which do not make good use of the information in the data when comparing those estimators to theoretical models. We demonstrate a more optimal estimator, based on a multipole expansion of the correlation functions or power spectra, for direct measurements of galaxy intrinsic alignments. We show that even using the lowest order multipole alone increases the significance of inferred model parameters using simulated and real data, without any additional modelling complexity. We apply this estimator to measurements of parameters of the non-linear alignment model using data from the Sloan Digital Sky survey, demonstrating consistent results with a factor of ∼2 greater precision in parameter fits to intrinsic alignments models. This result is functionally equivalent to quadrupling the survey area, but without the attendant costs – thereby demonstrating the value in using this new estimator in current and future intrinsic alignments measurements using spectroscopic galaxy samples.

Astronomy & Astrophysics↗

DOE OSTI2016

Effect of higher-order multipole moments on the Stark line shape

Spectral line shapes are sensitive to plasma conditions and are often used to diagnose electron density of laboratory plasmas as well as astrophysical plasmas. Stark line-shape models take into account the perturbation of the radiator’s energy structure due to the Coulomb interaction with the surrounding charged particles. Solving this Coulomb interaction is challenging and is commonly approximated via a multipole expansion. Yet, most models include only up to the second term of the expansion (the dipole term). While there have been studies on the higher-order terms due to one of the species (i.e. either ions or electrons), there is no model that includes the terms beyond dipole from both species. Here, we investigate the importance of the higher-order multipole terms from both species on the Hβ line shape. First, we find that it is important to include higher order terms consistently from both ions and electrons to reproduce measured line-shape asymmetry. Next, we study the line shape convergence with the higher-order terms at 1017, 1018, and 1019 e/cc. We discover that the line shape calculated with the dipole-only approximation becomes inaccurate as density increases. It is necessary to include only up to the third (quadrupole) term to compute the line-shape accurately within 2%. Since most existing models include only the dipole terms, the densities inferred with such models are in question. Finally, we investigate the impact of neglecting the quadrupole terms on density diagnostics. We find that the model without the quadrupole term slightly underestimates the density, and the discrepancy becomes as large as 12% at high densities. Although the case of study is limited to Hβ , we expect similar impact on other lines.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

Multipole responses in fissioning nuclei and their uncertainties

Electromagnetic multipole responses are key inputs to model the structure, decay, and reactions of atomic nuclei. With the introduction of the finite amplitude method (FAM), large-scale calculations of the nuclear linear response in heavy deformed nuclei have become possible. This work provides a detailed study of multipole responses in actinide nuclei with Skyrme energy density functionals. We quantify both systematic and statistical uncertainties induced by the functional parametrization in FAM calculations. We also extend the FAM formalism to perform blocking calculations with the equal filling approximation for odd-mass and odd-odd nuclei, and analyze the impact of blocking configurations on the response. In conclusion, by examining the entire plutonium isotopic chain from the proton to the neutron drip line, we find a large variability of the response with the neutron number and study how it correlates with the deformation of the nuclear ground state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

Chiral NNLO sat descriptions of nuclear multipole resonances within the random-phase approximation

We study nuclear multipole resonances in the framework of the random-phase approximation by using the chiral potential NNLO sat . This potential includes two- and three-body terms that have been simultaneously optimized to low-energy nucleon-nucleon scattering data and selected nuclear structure data. Our main focuses have been the isoscalar monopole, isovector dipole, and isoscalar quadrupole resonances of the closed-shell nuclei, 4 He, 16,22,24 O, and 40,48 Ca. These resonance modes have been widely observed in experiment. In addition, we use a renormalized chiral potential Vlow-k, based on the N 3 LO two-body potential by Entem and Machleidt [Phys. Rev. C 68, 041001 (2011)]. This introduces a dependency on the cutoff parameter used in the normalization procedure as reported in previous works by other groups. While NNLO sat can reasonably reproduce observed multipole resonances, it is not possible to find a single cutoff parameter for the V low-k potential that simultaneously describes the different types of resonance modes. The sensitivity to the cutoff parameter can be explained by missing induced three-body forces in the calculations. Our results for neutron-rich 22,24 O show a mixing nature of isoscalar and isovector resonances in the dipole channel at low energies. We predict that 22 O and 24 O have low-energy isoscalar quadrupole resonances at energies lower than 5 MeV.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2011

Forecasting the cosmological constraints with anisotropic baryon acoustic oscillations from multipole expansion

Baryon acoustic oscillations imprinted in the galaxy power spectrum can be used as a standard ruler to determine the angular diameter distance and Hubble parameter from high-redshift galaxies. Combining redshift distortion effect which apparently distorts the galaxy clustering pattern, we can also constrain the growth rate of large-scale structure formation. Usually, future forecasts for constraining these parameters from galaxy redshift surveys are made with the full 2D power spectrum characterized as a function of wave number k and directional cosine {mu} between line-of-sight direction and wave vector, i.e., P(k,{mu}). Here, we apply the multipole expansion to the full 2D power spectrum, and discuss how much cosmological information can be extracted from the lower-multipole spectra, taking a proper account of the nonlinear effects on gravitational clustering and redshift distortion. Fisher matrix analysis reveals that compared to the analysis with the full 2D spectrum, using only the partial information from the monopole and quadrupole spectra generally degrades the constraints by a factor of {approx}1.3 for each parameter. The additional information from the hexadecapole spectrum helps to improve the constraints, leading to a result that is almost comparable to the one expected from the full 2D spectrum.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2017

Measurement of higher-order multipole amplitudes in ψ ( 3686 ) → γ χ c 1 , 2 with χ c 1 , 2 → γ J / ψ and search for the transition η c ( 2 S ) → γ J / ψ

Using 106 ×10 6 ψ (3686) events collected with the BESIII detector, we measure multipole amplitudes for the decay ψ (3686) → γχ c1,2 → γγ J/ψ beyond the dominant electric-dipole amplitudes. The normalized magnetic-quadrupole (M2) amplitude for ψ (3686) → γχ c1,2 → γγ J/ψ and the normalized electric-octupole amplitudes for ψ ( 3686 ) → γχ c2 , χ c2 → γJ/ψ are determined. The M2 amplitudes for ψ (3686) → γ χ c1 and χ c1,2 → γ J / ψ are found to differ significantly from zero and are consistent with theoretical predictions. We also obtain the ratios of M2 contributions of ψ ( 3686 ) and J /ψ decays to χ c1,2 , b$1\atop{2}$/ b$2\atop{2}$ = 1.35 ± 0.72 and a$1\atop{2}$/a$2\atop{2}$ = 0.617 ± 0.083 , which agree well with theoretical expectations. By considering the multipole contributions of χ c 1 , 2 , we measure the product branching fractions for the cascade decays ψ ( 3686 ) → γχ c0,1,2 → γγJ/ψ and search for the process η c (2S) → γJ/ψ through ψ ( 3686 ) → γη c (2S). The product branching fraction for ψ (3686) → γχ c0 → γγJ/ψ is 3σ larger than published measurements, while those of ψ (3686) → γχ c1,2 → γγJ/ψ are consistent. In conclusion, no significant signal for the decay ψ ( 3686 ) → γη c (2S) → γγJ/ψ is observed, and the upper limit of the product branching fraction at the 90% confidence level is determined.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

DESI DR2 Baryon Acoustic Oscillations from the Lyman Alpha Forest Multipoles

We present an alternative measurement of the Baryon Acoustic Oscillation (BAO) using the Legendre multipole representation of the Ly$α$ forest correlation functions from the second data release (DR2) of the Dark Energy Spectroscopic Instrument survey. Compressing the auto- and cross-correlation functions into Legendre multipoles yields a positive-definite covariance matrix without any smoothing -- unlike the baseline DR2 analysis -- thanks to a significantly reduced data vector size. We introduce the statistical corrections required to debias the finite-sample covariance matrix estimate and demonstrate that monopole and quadrupole terms for both auto- and cross-correlations can be used even when the correlation functions are distorted by continuum errors and contaminated by metals. This formalism has slightly diminished the constraining power of the BAO scale, while considerably weakening constraints on nuisance parameters. We measure the isotropic BAO scale with $0.93\%$ precision at $z_\mathrm{eff}=2.35$, the Hubble parameter $H(z_\mathrm{eff})=(239.5\pm3.4)~(147.09~\mathrm{Mpc}/r_d) ~\mathrm{km~s}^{-1}~\text{Mpc}^{-1}$, and the transverse comoving distance $D_M(z_\mathrm{eff})=(5.80 \pm 0.10)~(r_d/147.09~\mathrm{Mpc})$~Gpc for a given value of the sound horizon ($r_d$). Our BAO results are entirely consistent with the baseline DR2 analysis.

Karaçaylı, Naim Göksel [Chicago U., KICP; Ohio Sta↗

DOE OSTI2021

Topological Magnets: Functions Based on Berry Phase and Multipoles

Macroscopic responses of magnets are often governed by magnetization and, thus, have been restricted to ferromagnets. However, such responses are strikingly large in the newly developed topological magnets, breaking the conventional scaling with magnetization. Taking the recently discovered antiferromagnetic (AF) Weyl semimetals as a prime example, we highlight the two central ingredients driving the significant macroscopic responses: the Berry curvature enhanced because of nontrivial band topology in momentum space, and the cluster magnetic multipoles in real space. The combination of large Berry curvature and multipoles enables large macroscopic responses such as the anomalous Hall and Nernst effects, the magneto-optical effect, and the novel magnetic spin Hall effect in antiferromagnets with negligible net magnetization, but also allows us to manipulate these effects by electrical means. Furthermore, nodal-point and nodal-line semimetallic states in ferromagnets may provide the strongly enhanced Berry curvature near the Fermi energy, leading to large responses beyond the conventional magnetization scaling. These significant properties and functions of the topological magnets lay the foundation for future technological development such as spintronics and thermoelectric technology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Green's function fast multipole method for continuum mechanics (SM-FMM)

Solid Mechanics Fast Multipole Method based on elastic Green's function and accelerated using FFTs The code calculates the mechanical fields (stress and strain) for a heterogeneous elasto-plastic material unit cell under quasi-static conditions (no dynamic effects). The fields are calculated using a Green's function method, where the strain field is given by a discrete convolution of Green's operator with an auxiliary stress field. The convolution is calculated using the fast multipole method.

Zecevic, Miroslav↗

DOE OSTI2014

Space Charge Simulation in COSY using The Fast Multipole Method

A method is implemented in COSY Infinity that allows the computation of space charge effects of arbitrary and large distributions of particles in an efficient and accurate way based on a variant of the Fast Multipole Method (FMM). It relies on an automatic multigrid-based decomposition of charges in near and far regions and the use of high-order differential algebra methods to obtain decompositions of far fields that lead to an error that scales with a high power of the order. Given an ensemble of N particles, the method allows the computation of the self-fields of all particles on each other with a computational expense that scales as O(N). Further- more, the method allows the computation of all high-order multipoles of the space charge fields that are necessary for the computation of high-order transfer maps and all resulting aberrations. Space charge effects are crucial in modeling the latter stages of the six-dimensional (6D) cooling channel for the Muon Collider. Results of simulating the 6D cooling channel for the Muon Collider using the FMM method and other tools and improvements implemented for ionization cooling lattices are presented.

Loseth, B.↗

DOE OSTI2019

Higher Multipoles in 3rd Integer Resonance Extraction

The efficiency of slow extraction is becoming a limiting factor, as the demand for delivered beam power is constantly growing. New methods for improving extraction efficiency include folding the extraction separatrix using the higher multipoles. In this report we discuss a simple and effective approach to determine an optimal placement of those multipoles in the storage ring. This allows reduction of the beam losses and therefore, the level of prompt and residual radioactivity in the accelerator components and surrounding buildings by as much as 40% or more. We also explore here manipulating the higher order effects produced in the pure sextupole configurations for the same purpose and demonstrate that similar results can be achieved by only rearranging the sextupole magnets in the lattice.

43 PARTICLE ACCELERATORS↗

DOE OSTI2020

Diffusion Models to Construct a First Principles Multipole-Based Cable Braid Model for Conducting Wires in the Time Domain

We describe here diffusion models apt to construct a multipole-based, cable braid time domain model for conducting wires. Implementation details of both a ladder network valid for time-domain signals with all frequency content and an approximate single-stage circuit valid for low-frequency dominated time signals (such as electromagnetic pulses) are reported. This time domain model can be leveraged to treat system-generated electromagnetic pulse events, as well as used to further confirm the correctness of the multipole-based, cable braid frequency domain model.

42 ENGINEERING↗

DOE OSTI2018

Fast multipole methods for multiparticle simulations

The fast multipole method (FMM) reduces the computation cost of the pairwise non-oscillating interaction between N particles from O(N^2) to O(N). In the FMM, the contribution from a source particle is represented as a multipole expansion, while the contributions from multiple faraway sources can be combined into a local expansion around an objective particle. Without the dependence on a grid covering the whole domain under study, the FMM treats any charge distribution and geometry in a natural way. It avoids artificial smoothing due to the grid size and redundant computation on the free space grids. We will introduce the concept of the FMM using the Coulomb interaction as an example and then explain how the FMM can be extended to arbitrary non-oscillating interactions. Examples and discussions on how the FMM can be used in scientific simulations, especially in accelerator physics will also be provided.

Zhang, He↗

DOE OSTI2024

Higher Order Multipole Analysis of Beam Crabbing Mode at 197 MHz for Electron-Ion Collider

In the local crabbing scheme for Electron Ion Collider interaction region, beam rotation is initiated by one set of crab cavities at a high beta region with near 90 deg phase advance to the interaction point (IP), and ceased by an identical set of cavities on the symmetrically opposite side. The fundamental mode of all crab cavities is designed to apply a momentum kick to the particle bunches to complete this half cycle of rotation in the horizontal plane, meanwhile the electromagnetic (EM) field can be expanded into a series of harmonics. Despite the lowest dipole mode, higher harmonics cause instabilities during beam operation and loss of particles. We used SimTrack, which is the 6-d symplectic element-by-element tracking code developed at Brookhaven National Laboratory in 2015, to study the threshold of each higher-order harmonic multipolar mode with the criteria of maintaining a dynamic aperture of 6 σ or greater for the Hadron Storage Ring (HSR). In this paper, we showed the threshold for each higher harmonic multipole and their comparison with the multipole strength for the current crab cavity design.

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

Magnetic Properties of Cables with Meandering Wires through a Multipole-based Cable Braid Electromagnetic Penetration Model

In this paper, we employ our first principles multipole-based cable braid electromagnetic penetration model to evaluate the transfer inductance of cables exhibiting meandering wires. We concentrate on a cable structure with two wires, and consider the dependence on the transfer inductance as a function of braid angle and amplitude of the meandering. We compare the results from the first principles model to analytical estimations, confirming the accuracy and correctness of our model. In turn, this makes the multipole-based model readily available for the modeling of realistic cable geometries by accounting for the full dependence on the actual cable geometry.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Multipole-based Cable Braid Magnetic Penetration Model for Conducting Wires

In this report, we investigate the effects of conductor losses in a multipole-based cable braid magnetic penetration model. Our multipole model uses a mesh of the actual cable geometry, which enables us to model more complicated structures. After summarizing the first principles model formulation, we consider a one-dimensional array of wires, for which an analytical solution is known in the lossless case. We extend this solution to the lossy case by using a complex-valued radius. We also model this structure analytically using a conformal-mapping solution. We then compare both the self-impedance and the transfer impedance results from our first principles cable braid electromagnetic penetration model to those obtained using the analytical solutions. An analysis for various frequencies (and skin depths) usually encountered in cable modeling is reported. These results are found in good agreement up to a radius to half spacing ratio of about 0.7, demonstrating a robustness needed for many commercial and non-commercial cables.

36 MATERIALS SCIENCE↗