Higher-order Multipole Contributions Research Articles

Post-Newtonian Lagrangian of an N -body system with arbitrary mass and spin multipoles

The present paper derives the post-Newtonian Lagrangian of translational motion of N arbitrary-structured bodies with all mass and spin multipoles in a scalar-tensor theory of gravity. The multipoles depend on time and evolve in accordance with their own dynamic equations of motion. The Lagrangian is retrieved from the post-Newtonian equations of motion by solving the inverse problem of the Lagrangian mechanics and generalizes a well-known Lagrangian of pole-dipole-quadrupole massive particles to the particles of higher multipolarity. Analytic treatment of the higher-order multipole contributions is important for more rigorous computation of gravitational waveform of inspiralling compact binaries at the latest stage of their orbital evolution before merger when tidal and rotational deformations of stars are no longer small and rapidly change in time. The Lagrangian of an N-body system with arbitrary mass and spin multipoles is instrumental for formulation of the post-Newtonian conservation laws of energy, momenta and the integrals of the center of mass.

SELF-TRAPPING OF DISKOSEISMIC CORRUGATION MODES IN NEUTRON STAR SPACETIMES

ABSTRACT We examine the effects of higher-order multipole contributions of rotating neutron star (NS) spacetimes on the propagation of corrugation (c-)modes within a thin accretion disk. We find that the Lense–Thirring precession frequency, which determines the propagation region of the low-frequency fundamental corrugation modes, can experience a turnover allowing for c-modes to become self-trapped for sufficiently high dimensionless spin j and quadrupole rotational deformability α. If such self-trapping c-modes can be detected, e.g., through phase-resolved spectroscopy of the iron line for a high-spin low-mass accreting neutron star, this could potentially constrain the spin-induced NS quadrupole and the NS equation of state.

Towards an optical far-field measurement of higher-order multipole contributions to the scattering response of nanoparticles

We experimentally show an all-optical multipolar decomposition of the lowest-order eigenmodes of a single gold nanoprism using azimuthally and radially polarized cylindrical vector beams. By scanning the particle through these tailored field distributions, the multipolar character of the eigenmodes gets encoded into 2D-scanning intensity maps even for higher-order contributions to the eigenmode that are too weak to be discerned in the direct far-field scattering response. This method enables a detailed optical mode analysis of individual nanoparticles.

Experimental evaluation of micro-ion trap mass spectrometer geometries

We describe a new fabrication method, simulations, and experimental results for micromachined cylindrical ion trap (μ-CIT) arrays for use in miniaturized mass spectrometers. The micromachined μ-CIT arrays were fabricated in a silicon-on-insulator (SOI) substrate, and a variety of trap geometries were incorporated into a single μ-CIT array chip to allow fast iterative measurements of the differences in the mass spectra from μ-CITs with different ratios of half-axial to half-radial dimensions (z0/r0). The chip dimensions were approximately 1.0cm×1.5cm×0.1cm. A series of z0/r0 were chosen in incremental steps of 3% for each array by changing r0 from 308 to 392μm while keeping z0 fixed at 355μm, resulting in a range of z0/r0 from 1.16 to 0.92 (nine geometries in total). Simulations were performed in SIMION 7.0 to determine the optimum range of μ-CIT z0/r0 to be fabricated and tested, by producing simulated mass spectra from μ-CITs with a variety of z0/r0 to evaluate predicted mass resolution. Following the simulations, we fabricated the arrays of μ-CIT geometries in SOI wafers using deep reactive ion etching (DRIE) to create the cylindrical structures and surface metallization to create ion trap electrodes. Symmetrical arrays of half-CITs were fabricated, diced, and bonded back-to-back to obtain complete μ-CIT array chips containing all nine geometrical ratios (z0/r0), which are referred to in this paper as the “gradient arrays”. The bonding process provided approximately 5-μm alignment accuracy between the two arrays of half-CITs, and the resulting arrays had flat μ-CIT endplate electrodes with <3μm upwards bow. We discuss several critical issues encountered during process development such as delamination of the buried oxide layer, excessive wafer bow, high capacitance, and ring-electrode wall verticality, along with solutions to mitigate these issues. Mass spectra were obtained experimentally from each trap geometry, and μ-CIT performance was found to follow the trend with respect to z0/r0 observed in the simulations. Experimental efforts indicated that axial modulation on one endplate electrode was required to remove spurious peaks in the mass spectra (caused by higher-order multipole contributions to the trapping electric field), and resulted in mass spectra with full-width-at-half-maximum peaks of 0.4amu.

Calculation of the Magnetic Interaction of Neighboring Magnets for the Future High-Energy Storage Ring at the FAIR Facility

The Forschungszentrum Ju?lich is responsible for the complete design and the construction of the High-Energy Storage Ring HESR , at the future Facility for Antiproton and Ion Research (FAIR) in Darmstadt, Germany. This includes the layout and provision of all magnets where the dipole, quadrupole and sextupole magnets are the most important. All magnets will be iron-dominated and normally conductive. The distance between the magnets is small due to the restricted space in the tunnel. In contrast to isolated magnets, differences are expected for the effective magnetic length as well as the integrated higher-order multipole contributions. In this publication, the results of magnetic-field calculations are presented that assess the magnetic interaction of neighboring magnets.

Non-radiative decay of a dipole emitter close to a metallic nanoparticle: Importance of higher-order multipole contributions

The contribution of higher-order multipoles to radiative and non-radiative decay of a single dipole emitter close to a spherical metallic nanoparticle is re-examined. Taking a Ag spherical nanoparticle (AgNP) with the radius of 5 nm as an example, a significant contribution (between 50% and 101% of the total value) of higher-order multipoles to non-radiative rates is found even at the emitter distance of 5 nm from the AgNP surface. On the other hand, the higher-order multipole contribution to radiative rates is negligible. Consequently, a dipole–dipole approximation can yield only an upper bound on the apparent quantum yield. In contrast, the non-radiative rates calculated with the quasistatic Gersten and Nitzan method are found to be in much better agreement with exact electrodynamic results. Finally, the size corrected metal dielectric function is shown to decrease the non-radiative rates near the dipolar surface plasmon resonance.

Calculation of Surface Plasmon Frequencies of Two, Three, and Four Strongly Interacting Nanospheres

An approximate analytical approach is developed for the calculation of the surface plasmon frequency of a system of interacting nanospheres for arbitrary values of interparticle distances. In addition to having a simple and physically clear form, the final formulae also describe adequately the dependence of the resonance frequencies on the parameters of the problem. The electric field of each of the interacting spheres is approximated by the field of a dipole, placed at a point, with respect to which the tensor of quadrupole moment of the charge distribution vanishes. Because of this procedure, the contribution of higher-order multipoles is effectively suppressed, unlike the case where the multipole moments of interacting spheres are calculated with respect to their centers. It is shown that the derived expressions adequately describe known experimental data on the red shift of the SP wavelength with decreasing interparticle distance. The explicit expression for dependence of the interparticle distance on the SP resonance frequency (“plasmon nanoruler equation”) is obtained for the first time. The results are also compared with known numerical calculations for two, three, and four identical spheres, and excellent agreement is demonstrated even (in the case of two spheres) for interparticle center-to-center distances as small as 1.05 times the particle diameter.

Fabrication and testing of a miniature cylindrical ion trap mass spectrometer constructed from low temperature co-fired ceramics

A novel technique for the fabrication of miniature cylindrical ion trap (CIT) mass spectrometers using a non-conductive substrate has been developed. This technique demonstrated the feasibility of batch fabricating accurate and low-cost CITs. A CIT ring electrode ( r 0 = 1.375 mm) was fabricated using multiple layers of low temperature co-fired ceramics (LTCC) which were punched and then compressed in a ring-electrode die. Uniform compression was achieved, and cracking avoided, by tailoring the thickness of the LTCC stack. The stack was then fired at 850 °C to convert the LTCC into a ceramic ring. Areas to be metallized were patterned photolithographically after the ring was subjected to electroless plating. Stainless steel endplates were affixed to the ring electrode to complete the CIT. The prototype CIT was tested in the mass selective instability mode without axial modulation and produced mass spectra with a typical peak width of 1.8 m/ z. Simulations of operation were also performed in ITSIM 5.0 after SIMION 7.0 was used to calculate the contribution of higher order multipoles to the nominally quadrupole potential inside the CIT.

Coupling of ferroelectric and antiferromagnetic order parameters in hexagonal RMnO3

Second-harmonic generation (SHG) is used as a probe for the coexisting ferroelectric and antiferromagnetic orders in hexagonal RMnO3. SH contributions coupling to the electric and/or magnetic order parameters are identified on the basis of their spectral dependence and the symmetries of the corresponding order parameters. The SH signals from the ferroelectric and antiferromagnetic orders were employed to image the electric and magnetic domain structures separately. The transformation properties of electric and magnetic domains are discussed with respect to the transformation properties of the corresponding order parameters. An investigation of the mutual coupling between the coexisting electric and magnetic orders reveals apparently independent domain structures, which contradicts the symmetry and transformation properties of electric-dipole-induced SHG in this ferroelectromagnetic group of compounds. Apart from higher-order multipole contributions to SHG, interface contributions from clamped electric and magnetic domains can solve the contradiction.

Modeling the fields of magneto-optical devices, including fringe field effects and higher order multipole contributions, with application to charged particle optics

A new method for the calculation of the magnetic field of beam guiding elements is presented. The method relates the calculation to measurement data of the magnetic field in a direct way. It can be applied to single beam guiding elements as well as to clusters of elements. The presented description of the magnetic field differs from the classical approach in that it does not rely on power series approximations. It is also both divergence free and curl free, and takes fringe field effects up to any desired order into account. In the field description, pseudodifferential operators described by Bessel functions are used to obtain the various multipole contributions. Magnetic field data on a two-dimensional surface, e.g., a cylindrical surface or median plane, serve as input for the calculation of the three-dimensional magnetic field. A boundary element method is presented to fit the fields to a discrete set of field data, obtained, for instance, from field measurements, on the two-dimensional surface. Relative errors in the field approximation do not exceed the maximal relative errors in the input data. Methods for incorporating the obtained field in both analytical and numerical computation of transfer functions are outlined. Applications include easy calculation of the transfer functions of clusters of beam guiding elements and of generalized field gradients for any multipole contribution up to any order.

Near-threshold photoionization of hydrogenlike uranium studied in ion-atom collisions via the time-reversed process.

Radiative electron capture, the time-reversed photoionization process occurring in ion-atom collisions, provides presently the only access to photoionization studies for very highly charged ions. By applying the deceleration mode of the ESR storage ring, we studied this process in low-energy collisions of bare uranium ions with low- Z target atoms. This technique allows us to extend the current information about photoionization to much lower energies than those accessible for neutral heavy elements in the direct reaction channel. The results prove that for high- Z systems, higher-order multipole contributions and magnetic corrections persist even at energies close to the threshold.

Radiative Electron Capture Studied for Bare, Decelerated Uranium Ions

By applying the deceleration technique for bare uranium ions at the ESR storage ring we studied the Radiative Electron Capture process in collisions with low-Z target atoms. This allowed us to extend the current information about the time-reversed photoionization process of highly-charged heavy ions to much lower energies than those accessible for neutral heavy elements in the direct reaction channel. The angular differential data obtained prove theoretical predictions that at high-Z higher-order multipole contributions and magnetic corrections play an important role even at energies close to the threshold.

Deviation from the single-particle model in the angular distribution of thorium L3 x rays in proton-impact ionization.

Angular distributions of [ital L][sub 3] x-ray transitions, including electric-dipole-forbidden ones, were measured for 1-, 2-, and 3-MeV proton impact on a thorium target, where the excitation and detection systems were cylindrically symmetric. A sophisticated spectrum-analysis technique was applied, where both the Lorentzian broadening of the transitions and the Si(Li) detector response function with various tailing features were taken into account. The anisotropy-parameter ratios are expected to be independent of the ionization process, and to be characteristic of the x-ray transitions in the independent-particle model. The ratios of the anisotropy parameters of the electric-dipole-allowed transitions were in disagreement with this expectation, even when the higher-order multipole contributions were taken into account. These results follow the same trend as earlier angular distribution and angular correlation measurements. Additionally, the electric-dipole-forbidden [ital Lt]([ital L][sub 3][ital M][sub 2]) and [ital Ls]([ital L][sub 3][ital M][sub 3]) transitions had a [ital P][sub 4](cos([theta])) term, which is not expected within the framework of the single-particle-model predictions. Possible causes for this discrepancy are explored.

Electric field and potential near the plasma resonance cone

The electric field and potential at and close to the resonance cone of an oscillating point charge and dipole in a warm magnetized plasma are investigated theoretically, neglecting ion motion. Approximate expressions are derived for both a drifting and a stationary Maxwellian plasma. The shift in angle of the maximum potential due to plasma drift is shown to be small and dependent on both drift and thermal velocities if the drift velocity is much less than the thermal velocity. For a stationary plasma, a comparison of the potential of a point charge with its electric field and with the potential and field of an arbitrarily-oriented dipole shows that the potential of the point charge has the following distinguishing characteristics: The maximum lies closest to the cold-plasma resonance cone; the angular location of this maximum is least dependent on damping mechanisms in the plasma; the interference structure is the largest. The approximate expression for potential yields results in good agreement with existing experimental results and more rigorous calculations. From the multipole expansion of an arbitrary charge distribution in a stationary Maxwellian plasma, it is shown that higher-order multipole contributions are small if the characteristic source dimension is small compared with the spatial separation between two successive interference maxima.