Effects Of Multipoles Research Articles

High-Order Multipole and Binary Love Number Universal Relations

Using a data set of approximately 2 million phenomenological equations of state consistent with observational constraints, we construct new equation-of-state-insensitive universal relations that exist between the multipolar tidal deformability parameters of neutron stars, Λl, for several high-order multipoles (l=5,6,7,8), and we consider finite-size effects of these high-order multipoles in waveform modeling. We also confirm the existence of a universal relation between the radius of the 1.4M⊙ NS, R1.4 and the reduced tidal parameter of the binary, Λ˜, and the chirp mass. We extend this relation to a large number of chirp masses and to the radii of isolated NSs of different mass M, RM. We find that there is an optimal value of M for every M such that the uncertainty in the estimate of RM is minimized when using the relation. We discuss the utility and implications of these relations for the upcoming LIGO O4 run and third-generation detectors.

Effects of higher-order multipoles of the lunar disturbing potential on elongated orbits in cislunar space

For an Earth satellite in cislunar space, the effects of the third or higher-order harmonics in the solar disturbing function are negligible. For lunar perturbations, however, these terms become increasingly important as the semimajor axis increases. We investigate the effects of these higher-order multipole moments on circular, moderate, and highly elliptical orbits, where the semimajor axis is a relatively large fraction (~20%) of the Moon’s one. We specifically characterize the regions of cislunar space where the octupole-order approximation, often used in celestial and astrophysical dynamics for studying the stability and fates of hierarchical planetary systems, is actually a valid truncation of the gravitational interactions.

Relativistic effects in the non-resonant two-photon K-shell ionization of neutral atoms

Relativistic effects in the non-resonant two-photon K-shell ionization of neutral atoms are studied theoretically within the framework of second-order perturbation theory. The non-relativistic results are compared with the relativistic calculations in the dipole and no-pair approximations as well as with the complete relativistic approach. The calculations are performed in both velocity and length gauges. Our results show a significant decrease of the total cross section for heavy atoms as compared to the non-relativistic treatment, which is mainly due to the relativistic wavefunction contraction. The effects of higher multipoles and negative continuum energy states counteract the relativistic contraction contribution, but are generally much weaker. While the effects beyond the dipole approximation are equally important in both gauges, the inclusion of negative continuum energy states visibly contributes to the total cross section only in the velocity gauge.

Partial cross sections for radiative recombination of bare ions : effects of relativity and radiation multipoles

SynopsisWe derived an original expression for the partial cross sections for radiative recombination (RR) of highly charged bare ions in the nonrelativistic electric-dipole approach. Three sets of cross sections for RR to individual magnetic sublevels of the excited levels of various recombined H-like ions were computed: the first two in the electric-dipole approximation with the nonrelativistic and relativistic electron wavefunctions and the third one in the exact relativistic method including all multipole orders of the radiation field.

Circular polarization of the Lyman-α 1 line radiation emitted by longitudinally-polarized electron impact excitation: effects of Breit interaction and radiation multipoles

Detailed calculations are carried out for the longitudinally-polarized electron impact excitation cross sections from the ground state 1s 1/2 to the individual magnetic sublevels of the excited state 2p 3/2 of highly charged H-like ions using a fully relativistic distorted-wave method. The influence of the Breit interaction and radiation multipoles on the circular polarization of X-ray radiation are investigated systematically. Our results show that the Breit interaction, as the dominant correction to the Coulomb interaction, may lead to a considerable change in the magnetic sublevels cross sections and circular polarizations of Lyman-α 1 (2p 3/2 → 1s 1/2) line radiation with a more pronounced effect at higher incident energies and/or atomic numbers. Moreover, the interference between the electric dipole (E1) decay and the magnetic quadrupole (M2) decay may significantly alter the circular polarizations of the emitted X-rays. The circular polarizations of the Lyman-α 1 line are exhibit a different behavior than the linear polarizations for the same transition line regarding the radiative electron capture [Weber et al., Phys. Rev. Lett. 105, 243002 (2010)], radiative recombination [Bettadj et al., J. Phys. B 47, 105205 (2014)], and electron-impact excitation processes [Chen et al., Phys. Rev. A. 90, 012703 (2014)].

Polarization of the Lyman line emission following radiative recombination of bare ions: effects of relativity and radiation multipoles

We have calculated the degree of linear polarization of the Ly-α1 (2p3/2 → 1s1/2) and Ly-β1 (3p3/2 → 1s1/2) lines emitted after radiative recombination of spinless bare nuclei with unidirectional, unpolarized electrons. These calculations have been performed for various recombined H-like ions with atomic numbers in the range 10 ⩽ Z ⩽ 92. Several incident-electron kinetic energies ε0 ranging from 0.01 to 10 times the electron binding energy in the 1s1/2 ground state were considered and the radiative cascades following recombination into states with principal quantum number up to n = 6 were included. Three sets of cross sections for radiative recombination to individual magnetic sublevels of the excited levels of the recombined H-like ions were computed: the first two in the electric-dipole approximation with the nonrelativistic and relativistic electron wavefunctions and the third one in the exact relativistic method including all multipole orders of the radiation field. Results for the polarization calculated using these three sets of cross-section data were compared in order to stress the relative importance of relativistic and multipole effects as Z or ε0 increases.

Electric toroidal dipole response in split-ring resonator metamaterials

Toroidal dipoles are usually masked by other stronger effects of classical electric and magnetic multipoles, such as dipoles, quadrupoles, octupoles and so forth. So observation of the toroidal response is extremely rare. For the first time we present an electric toroidal dipole model based on metamaterials, which is composed of split-ring resonators. The transmission and reflection spectra show that there are two resonances at the frequency of 5.0 GHz and 11.2 GHz. Calculated radiated power dispersion for various multipole moments derived from the current density proved that these two resonances are electric dipole response and elusive electric toroidal dipole response respectively. Our experimental evidence of electric toroidal dipole response brings attentions to the often ignored toroidal multipoles.

Effects of higher-order multipoles on the performance of a two-plate quadrupole ion trap mass analyzer

We report on the effects of varying higher-order multipole components on the performance of a novel radiofrequency quadrupole ion-trap mass analyzer, named the planar Paul trap. The device consists of two parallel ceramic plates, the opposing surfaces of which are lithographically imprinted with 24 concentric metal rings. Using this device, the magnitude and sign of different multipole components, including octopole and dodecapole, can be independently adjusted through altering the voltages applied to each ring. This study presents a systematic investigation of the effects of the octopole and dodecapole field components on the mass resolution and signal intensity of the planar Paul trap. Also, the effect of dipole amplitude and scan speed under both forward and reverse scan modes have been investigated for various combinations of octopole and dodecapole. A trapping field in which the magnitudes of the octopole and dodecapole are, respectively, set to 0% and +8% of the magnitude of the quadrupole yields the highest mass resolution under the conditions studied. A small threshold voltage for dipole resonance ejection is observed for positive octopole, and to a lesser extent for positive dodecapole, but not for negative poles. When both octopole and dodecapole are negative, a reverse scan produces higher resolution, but this effect is not observed when only one of the components is negative.

Differential Cross Section and Polarization of Radiative Recombination

The formulae of photon angular distribution and polarization degree for radiative recombination are presented to include the contribution of multipoles and their correlations. A fully relativistic code is then developed to calculate the photon angular distribution and polarization. The calculated polarization degree and differential cross-sections agree well with that of Scofield's results within 10%. The effects of multipoles on polarization and angular distribution are investigated. The polarization and the angular distribution become asymmetric when the multipoles are accounted as the electron energy increases.

Mathematical formulation to predict the harmonics of the superconducting Large Hadron Collider magnets. II. Dynamic field changes and scaling laws

A superconducting particle accelerator like the LHC (Large Hadron Collider) at CERN, can only be controlled well if the effects of the magnetic field multipoles on the beam are compensated. The demands on a control system solely based on beam feedback may be too high for the requirements to be reached at the specified bandwidth and accuracy. Therefore, we designed a suitable field description for the LHC (FIDEL) as part of the machine control baseline to act as a feed-forward magnetic field prediction system. FIDEL consists of a physical and empirical parametric field model based on magnetic measurements at warm and in cryogenic conditions. The performance of FIDEL is particularly critical at injection when the field decays, and in the initial part of the acceleration when the field snaps back. These dynamic components are both current and time dependent and are not reproducible from cycle to cycle since they also depend on the magnet powering history. In this paper a qualitative and quantitative description of the dynamic field behavior substantiated by a set of scaling laws is presented.

Thermal transport in sheared electro- and magnetorheological fluids

Thermal energy transport in sheared electrorheological and magnetorheological (ER and MR) fluids is analyzed. Although energy production by viscous dissipation can be significant, energy transport on the particle length scale can be analyzed by ignoring viscous dissipation. For typical situations, energy transport normal to the flow direction is dominated by conduction. Particle-level simulations were employed to determine the suspension structure as a function of Mason number and volume fraction. A self-consistent mean-field dipole model is used to estimate the effective thermal conductivities for these simulated structures. The field-induced chain-like aggregates that form at small Mason number result in a larger effective thermal conductivity at small Mason number than at large Mason number. Effects of higher-order multipoles are estimated by analyzing effective thermal conductivities of model structures. For highly conducting particles, the effective thermal conductivity of a sheared ER or MR suspension is predicted to roughly double as the Mason number is decreased from the large to the small Mason number limits.

Effects of higher rank multipoles on relaxation of an I = 3 spin system.

Magnetic multipoles of rank higher than one become active in spin systems with I > 1/2 and their contribution to relaxation depends on dynamics. The appearance of multipole terms complicates the relaxation description and supports the multiexponential behavior of relaxation. In this paper the effects of high-rank multipoles on lineshape and longitudinal relaxation of I = 3 spin systems are presented. Results obtained from both numerical simulation and experimental data show that longitudinal and transverse relaxation are strongly influenced by these multipole terms, especially at lower temperature where, due to lower molecular mobility, the extreme narrowing condition is not fulfilled.

Effects of high-order multipoles on the extinction spectra of dispersive bispheres

Extinction spectra of randomly oriented pairs of dispersive spheres are calculated by the T-matrix method. The number of multipoles, L, that have to be included in the calculation in order to achieve convergence was studied for a wide range of sphere radii and inter-sphere separations. For a given sphere size, L increases with decreasing separation between the spheres. For the most severe case, i.e., touching spheres, convergence becomes more difficult to achieve as the sphere size is reduced.

Neptune radio emission in dipole and multipole magnetic fields

We study Neptune's smooth radio emission in two ways: we simulate the observations and we then consider the radio effects of Neptune's magnetic multipoles. A procedure to deduce the characteristics of radio sources observed by the Planetary Radio Astronomy experiment minimizes limiting assumptions and maximizes use of the data, including quantitative measurement of circular polarization. Study of specific sources simulates time variation of intensity and apparent polarization of their integrated emission over an extended time period. The method is applied to Neptune smooth recurrent emission (SRE). Time series are modeled with both broad and beamed emission patterns, and at two frequencies which exhibit different time variation of polarization. These dipole‐based results are overturned by consideration of more complex models of Neptune's magnetic field. Any smooth emission from the anticipated auroral radio source is weak and briefly observed. Dominant SRE originates in complex fields at midlatitude. Possible SRE source locations overlap that of “high‐latitude” emission (HLE) between +(out) and −(in) quadrupoles. This is the first identification of multipolar magnetic structure with a major source of planetary radio emission.

Effects of Higher-Rank Multipoles on Spectral Lineshapes of Higher Quadrupolar Nuclei near the Null Point in Inversion-Recovery Experiments

The effects of higher-rank multipoles on the spectral lineshape of I = 52 and 72 quadrupolar nuclei have been examined near the null point in the inversion-recovery measurements. 27Al (I = 52) and 133Cs (I = 72) NMR inversion-recovery experiments were performed in D2O/glycerol-d8 solutions. The longitudinal and transverse relaxational matrix elements using state multipole formalism for spin-52, -72, and -92 have been derived. It is found that the null-point spectra of spin-52, -72, and -92 are similar to those of the spin-32 system. This indicates that the direct coupling between rank-one and rank-three elements plays the key role in the generation of fine structure in null-point spectra.

Some Recent Developments in NMR Approaches for Studying Liquid Molecular Dynamics and Their Biological Applications

AbstractTwo aspects of NMR relaxation are reviewed and their use in studying molecular dynamics in the liquid state and their application to biological systems are discussed. The first aspect concerns the use of ‘null‐point spectra’ for observing the effects of higher rank multipoles (tensors) in the relaxation of quadrupolar nuclei. The second aspect concerns the effects of cross‐correlation in homo‐ and heteronuclear spin systems. The application of null point spectral analysis to study cross‐correlation in homonuclear spin systems is also discussed. Analysis of the effects of higher rank multipoles and of cross‐correlation effects are shown to provide substantially more structural and motional information about spin systems than that available from traditional relaxation measurements. While similar in information content to multiple quantum techniques, the null point technique is experimentally less demanding. Over the past several years, work in this laboratory has been heavily involved in the theoretical formulation and the application of these techniques to biological systems. Illustrations of the use of these techniques to biological systems are drawn from our recent work.

Effects of higher-rank multipoles on spectral lineshapes of [formula omitted] quadrupolar nuclei near the null point in inversion-recovery experiments

The effects of higher-rank multipoles on the spectral lineshape of I = 3 2 quadrupolar nuclei have been examined near the null point in inversion-recovery measurements. 7Li NMR inversion-recovery experiments were performed on LiCl dissolved in isopropanol- d 8/D 2O solution at 225 K. The state multipole formalism approach was applied to interpret relaxation processes and analyze lineshapes. The experimental spectra could be simulated using a correlation time of 1.1 ns for the fluctuation of the direction of the electric field gradient at the 7/Li nucleus and a quadrupolar coupling constant of 42.7 kHz. The excellent agreements between observed and simulated spectra demonstrate that analysis of spectral lineshapes derived from inversion-recovery experiments provides a convenient way of determining the quadrupolar coupling constant and the fluctuation correlation time of the electric field gradient at the nucleus and of observing the dynamic frequency shift.

Theoretical shell-model signatures in heavy-ion, coherent pion production

A comprehensive summary of a many-body, microscopic, particle–hole formalism is presented that describes coherent, subthreshold, pion production in peripheral, heavy-ion collisions. The formalism uses a new separable model transition interaction that produces Δ-hole states in either the projectile or target nucleus. Shell-model states described by harmonic oscillator functions are used in the calculation of Δ formation and decay and Lorentz-contraction effects of the nucleus not at rest are included. An analytical expression to lowest multipole order for the differential cross section is examined. The sensitivity of the theoretical results to the shell-model states is determined with preliminary shape results compared with data. The effects of higher multipoles are examined with attention paid to the second-order multipole value.

Symmetry characterization in molecular multiphoton spectroscopy

In this paper it is shown how simple application of irreducible tensor calculus provides a powerful method for the symmetry characterization of a wide range of multiphoton transitions in solids, liquids or gases. These methods provide for a systematic classification of distinct symmetry classes for any multiphoton process and facilitate devising suitable polarization studies for spectroscopic application. General results for multiphoton processes up to and including those involving four-photon interactions are presented in the tables for all the common molecular and crystallographic point groups. A new symmetry class labelling scheme is also introduced. Applications are illustrated by reference to two-, three- and four-photon absorption, resonance and non-resonance Raman scattering and hyper-Raman scattering. Whilst the examples principally involve electric dipole coupling, it is demonstrated how the effects of higher multipoles may be incorporated into the results.

The effects of higher rank multipoles on relaxation measurements in isotropic high spin systems

The nuclear spin relaxation in isotropic spin systems with I = 3 2 , I = 5 2 , and I = 7 2 in the nonextreme narrowing regime is analyzed. The effect of the higher rank multipoles (rank ⩾3) of the spin density operator on a 180°- τ i - Θ pulse experiment is twofold. The recorded NMR lineshape is τ 1 and φ dependent. The multiexponentiality of the spin-lattice relaxation may be exaggerated by recording the amplitudes of the Lorentzian-like signals, instead of the full integrated signal. The influence of the detection pulse angle φ is discussed and we suggest that by choosing the detection angle φ = 63° the effects of the higher multipoles may be diminished.