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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Fast Multipole Method for Coulomb Interaction Based on Traceless Totally Symmetric Tensor

The fast multipole method (FMM) is widely used to calculate the Coulomb interaction between a huge amount of charged particles. The efficiency of FMM scales with O(N) for N particles with any arbitrary distribution. Hence it is apposite for problems with complicated charge distribution or geometry. Under the same FMM framework, there are different approaches, such as using spherical harmonic functions or Maxwell Cartesian tensors. Here we will present a version using traceless totally symmetric Maxwell Cartesian tensor. The previous Maxwell Cartesian tensor based FMM uses totally symmetric tensor. There are (n+1)(n+2)/2 independent elements in a rank n totally symmetric tensor. However, there are only 2n+1 independent elements in a rank n traceless totally symmetric tensor, due to which the efficiency of the traceless version is highly improved compared with the old version, especially when high accuracy is needed and high rank tensors are used.

Huang, He↗
DOE OSTI2015

Traceless Totally Symmetric Tensor Based Fast Multipole Method for Space Charge Field Calculation

The fast multipole method (FMM) is widely used to calculate the Coulomb interaction between a huge amount of charged particles. The efficiency of FMM scales with $O(N)$ for $N$ particles with any arbitrary distribution. Hence it is apposite for problems with complicated charge distribution or geometry. We developed a new FMM code for Coulomb interaction. In the new code the Coulomb potential is expressed as traceless totally symmetric tensors in Cartesian coordinates, in which the number of independent element is only $2n+1$ for the $n^{\mathrm{th}}$ rank, while it is $3^{n}$ for a general Cartesian tensor. The significant reduce of independent element number in Cartesian tensor helps to achieve high efficiency in the new algorithm. Result of test runs for space charge field calculation and multi-particle tracking using the new algorithm will be presented.

Zhang, He↗
DOE OSTI2024

Implementation of Windowed Multipole into MCNP6.3

This work details the implementation of the Windowed MultiPole(WMP) method of generating cross sections into the monte carlo code MCNP6.3, the verification and validation performed, and potential future improvements to be implemented. Further, this work contextualizes WMP within the broader changes to how nuclear data is stored, iterated upon, and used that have been developing over the past decade.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Critically evaluated theoretical energies, lifetimes, hyperfine constants, and multipole polarizabilities in {sup 87}Rb

Systematic study of Rb atomic properties is carried out using a high-precision relativistic all-order method. Excitation energies of the ns, np, nd, and nf (n{<=}10) states in neutral rubidium are evaluated. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for the levels up to n=8. Recommended values and estimates of their uncertainties are provided for a large number of electric-dipole transitions. Electric-dipole (5s-np, n=5-26), electric-quadrupole (5s-nd{sub j}, n=4-26), and electric-octupole (5s-nf{sub j}, n=4-26) matrix elements are calculated to obtain the ground state E1, E2, and E3 static polarizabilities. Scalar polarizabilities of the ns, np, and nd states, and tensor polarizabilities of the np{sub 3/2} and nd excited states of Rb are evaluated. The hyperfine A and B values in {sup 87}Rb are determined for the first low-lying levels up to n=9. These calculations provide recommended values critically evaluated for their accuracy for a number of Rb atomic properties useful for a variety of applications.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2015

Corrigendum: The creation, destruction, and transfer of multipole moments in electron- and proton-impact ionization of atoms and ions (2013 J. Phys. B: At. Mol. Opt. Phys. 46 245202)

The present corrigendum is dedicated to correcting unfortunate errors made in certain equations of our paper [1]. We should first stress the point that those errors have no serious consequences on the main results of the paper and most derived equations remain valid. This is a follow-up to the first corrigendum which was reported in reference [2] to correct errors of a similar nature in another previously reported work [3]. The source of all those errors resides in the treatment of charged-particle scattering and the subtle manipulations made to obtain some of the equations in both references [1, 3]. All equation numbers cited here correspond to those of [1] unless specified otherwise.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Joint Planck and WMAP assessment of low CMB multipoles

The remarkable progress in cosmic microwave background (CMB) studies over past decade has led to the era of precision cosmology in striking agreement with the ΛCDM model. However, the lack of power in the CMB temperature anisotropies at large angular scales (low-ℓ), as has been confirmed by the recent Planck data also (up to 0ℓ=4), although statistically not very strong (less than 3σ), is still an open problem. One can avoid to seek an explanation for this problem by attributing the lack of power to cosmic variance or can look for explanations i.e., different inflationary potentials or initial conditions for inflation to begin with, non-trivial topology, ISW effect etc. Features in the primordial power spectrum (PPS) motivated by the early universe physics has been the most common solution to address this problem. In the present work we also follow this approach and consider a set of PPS which have features and constrain the parameters of those using WMAP 9 year and Planck data employing Markov-Chain Monte Carlo (MCMC) analysis. The prominent feature of all the models of PPS that we consider is an infra-red cut off which leads to suppression of power at large angular scales. We consider models of PPS with maximum three extra parameters and use Akaike information criterion (AIC) and Bayesian information criterion (BIC) of model selection to compare the models. For most models, we find good constraints for the cut off scale k{sub c}, however, for other parameters our constraints are not that good. We find that sharp cut off model gives best likelihood value for the WMAP 9 year data, but is as good as power law model according to AIC. For the joint WMAP 9 + Planck data set, Starobinsky model is slightly preferred by AIC which is also able to produce CMB power suppression up to 0ℓ≤3 to some extent. However, using BIC criteria, one finds model(s) with least number of parameters (power law model) are always preferred.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Multipoles and Force on External Points for a Two-layered Spheroidal Liquid Mass Rotating Differentialy

We recently reported on a series of equilibrium figures for a self-gravitating heterogeneous liquid body, consisting of two concentric distorted spheroids, “nucleus” and “atmosphere,” each endowed with its own internal motion of differential rotation. In our current work, we calculate the body’s force at external points and obtain a multipolar expansion of the potential. We also give an account of figures with prolate nuclei, which remained unnoticed by us in our former paper.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Dual AC Dipole Excitation for the Measurement of Magnetic Multipole Strength from Beam Position Monitor Data

An experiment was conducted at Jefferson Lab's Continuous Electron Beam Accelerator Facility to develop a technique for characterizing the nonlinear fields of the beam transport system. Two air-core dipole magnets were simultaneously driven at two different frequencies to provide a time-dependent transverse modulation of the electron beam. Fourier decomposition of beam position monitor data was then used to measure the amplitude of these frequencies at different positions along the beamline. For a purely linear transport system one expects to find solely the frequencies that were applied to the dipoles with amplitudes that depend on the phase advance of the lattice. In the presence of nonlinear fields one expects to also find harmonics of the driving frequencies that depend on the order of the nonlinearity. The technique was calibrated using one of the sextupole magnets in a CEBAF beamline and then applied to a dipole to measure the sextupole and octupole strength of the magnet. A comparison is made between the beam-based measurements, results from TOSCA and data from our Magnet Measurement Facility.

43 PARTICLE ACCELERATORS↗
DOE OSTI2018

Characterization of Harmonic Signal Acquisition with Parallel Dipole and Multipole Detectors

Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) is a powerful instrument for the study of complex biological samples due to its high resolution and mass measurement accuracy. However, the relatively long signal acquisition periods needed to achieve high resolution can serve to limit applications of FTICR-MS. The use of multiple pairs of detector electrodes enables detection of harmonic frequencies present at integer multiples of the fundamental cyclotron frequency, and the obtained resolving power for a given acquisition period increases linearly with the order of harmonic signal. However, harmonic signal detection also increases spectral complexity and presents challenges for interpretation. In the present work, ICR cells with independent dipole and harmonic detection electrodes and preamplifiers are demonstrated. A benefit of this approach is the ability to independently acquire fundamental and multiple harmonic signals in parallel using the same ions under identical conditions, enabling direct comparison of achieved performance as parameters are varied. Spectra from harmonic signals showed generally higher resolving power than spectra acquired with fundamental signals and equal signal duration. In addition, the maximum observed signal to noise (S/N) ratio from harmonic signals exceeded that of fundamental signals by 50 to 100%. Finally, parallel detection of fundamental and harmonic signals enables deconvolution of overlapping harmonic signals since observed fundamental frequencies can be used to unambiguously calculate all possible harmonic frequencies. Thus, the present application of parallel fundamental and harmonic signal acquisition offers a general approach to improve utilization of harmonic signals to yield high-resolution spectra with decreased acquisition time. .

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2013

Energies, wavelengths, and multipole transition probabilities for B-like Fe and Ga ions

Energy levels, transition probabilities, oscillator strengths, line strengths, and lifetimes have been calculated for transitions in B-like Fe and Ga ions. The configurations 2s{sup 2}2p, 2s2p{sup 2}, 2p{sup 3}, 2s2p3ℓ, and 2p{sup 2}3ℓ were used in the calculations and 125 fine-structure levels were obtained. The fully relativistic GRASP code has been adopted, and results are reported for all electric dipole, electric quadrupole, magnetic dipole, and magnetic quadrupole transitions among the lowest 125 levels of Fe XXII and Ga XXVII, belonging to the n≤3 configurations. Comparisons are made with earlier available theoretical results.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2013

Approximate recalculation of the {alpha}(Z{alpha}){sup 5} contribution to the self-energy effect on hydrogenic states with a multipole expansion

A contribution of virtual electron states with large wave numbers to the self-energy of an electron bound in the weak Coulomb field is analyzed in the context of the evaluation method suggested in the previous paper. The contribution is of the order {alpha}(Z{alpha}){sup 5}. The same value for this contribution is found here as the one found in the previous calculations using different evaluation methods. When we add the remaining terms of the order {alpha}(Z{alpha}){sup 5} to the calculation of the self-energy effect in hydrogen-like ions presented in the previous paper we find a very good agreement with numerical evaluations. The relative difference between present and numerical evaluations ranges from 2 parts in 10{sup 6} for Z=1 up to 6 parts in 10{sup 4} for Z=10. - Highlights: Black-Right-Pointing-Pointer The complete terms of the order {alpha}(Z{alpha}){sup 5} are identified. Black-Right-Pointing-Pointer The accuracy of the result for the ground state of the hydrogen is 2 ppm. Black-Right-Pointing-Pointer The separation into the low and high energy regions and their matching is avoided.

74 ATOMIC AND MOLECULAR PHYSICS↗
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↗