Higher Order Multipoles Research Articles

Bulk flow velocities in the solar corona at solar maximum

We present velocity estimates of bulk motions seen in the solar corona by the Large Angle Spectrometric Coronagraph (LASCO) onboard the Solar and Heliospheric Observatory (SOHO) spacecraft. These estimates reflect the mass-weighted mean outflow of all coronal mass ejections (CMEs) seen during a 1-yr period on the approach to solar maximum. The particular period of interest spans 1999 March 6 to 2000 March 5 and velocities are compared with those obtained previously during an epoch of minimum activity. We use a correlation analysis and we address issues concerned with qualifying this method with regard to its possible limitations. Our method allows us to determine objectively velocity estimates at altitudes from 2 to 30 R⊙ at all latitudes. This represents an increased range over what was possible at solar minimum, and the high number of events has also allowed for much improved statistical accuracy in our estimates. At all latitudes we find outflow speed profiles that are similar in form to those seen in the equatorial region at solar minimum, although overall they are slightly faster. We do not see the large-scale latitudinal dependence of velocity evolution that was apparent at solar minimum and we associate this with the much reduced strength of the solar magnetic dipole relative to higher-order multipoles. We find that a typical kilogram of ejected plasma enters the C2 field at a speed of around 50 km s−1. The typical kilogram of plasma accelerates at a reasonably uniform rate of about 5 m s−2 and eventually reaches the edge of the C3 field with a velocity of ∼450 km s−1. To maintain this trajectory we find that the ejected plasma requires a remarkably constant input of energy, at a rate of around 2.2×106 W kg-1, throughout its entire evolution. In total, we find that a typical kilogram of plasma takes approximately 24 h to traverse the combined field of the LASCO white-light coronagraphs. This is somewhat slower than typically quoted CME speeds and highlights how the velocity associated with the leading edge of an event does not always accurately reflect the motion associated with the bulk of the mass of an event. We compare our velocity profiles with a basic model describing the expansion of an isothermal solar wind and find strong similarities in the flow speed. We suggest that at altitudes as low as 5 R⊙ in the corona the motion of the mass-dominant class of CMEs is governed by their immersion in the surrounding wind flow. We discuss the relaxing of the internal energy requirements of the CME phenomenon associated with their being carried through the lower corona by the solar wind and provide what we believe to be the most reasonably parametrized velocity profiles to be met by models of CME eruption.

A relativistic description of the polarization mechanism of elastic bremsstrahlung

A completely relativistic mechanism for describing polarization bremsstrahlung caused by an elastic collision of a charged particle with a many-electron target was suggested. Multipole expansions for the amplitude and cross section of the process taking into account radiation lag effects were obtained. Including higher order multipoles was shown to result in substantial asymmetry of the angular distribution of emitted photons compared with the dipole case and in a noticeable change in the spectral characteristics of polarization radiation. The cross section of polarization bremsstrahlung was found to increase logarithmically as the energy of incident particles grew.

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.

Analytical solutions for the invariant spin field for model storage rings

We present nonperturbative analytical expressions for the invariant spin field for several storage ring models. In particular, we solve the important models of a ring with one Snake and a single resonance driving term, and a ring with two Snakes and a single resonance driving term. We also treat several other models, all of which contain Siberian Snakes. Our solutions contain some novel features, e.g. in some cases the polarization does not point along the direction of the closed-orbit spin quantization axis. We also include vertical resonance driving terms, and consider the contributions of sextupoles and higher order multipoles to the resonance driving terms, and argue that these can play a significant role in some circumstances. We offer some brief remarks on the so-called Snake resonances. We relate our results to observations of higher-order depolarizing spin resonances for polarized proton beams in a real ring, and offer some suggestions as to how our ideas might be verified.

Failure of local Mie theory: optical spectra of colloidal aggregates

Fully retarded calculations of the optical properties of aggregates of metallic nanoparticles have been performed. Within a local theory, the optical spectra of particles in contact with each other are dominated by a series of resonances below the Fröhlich resonance of isolated spheres. The resonances are shown to be related to surface plasmon polaritons of extremely short wavelength, which are localised at the points of contact of the particles, and are connected with strong field enhancements in the vicinity of the contact point. Standard local Mie theory of the optical properties of interacting spheres does not describe this excitation correctly at finite cut-off multipole orders ⩽30. Intensity distributions and spectra were therefore calculated by means of the semianalytical multiple multipole technique. For small particles, however, a nonlocal refinement of aggregate Mie theory predicts, that the localised surface excitations are strongly damped by the excitation of volume plasmons at the surface. Local Mie theory should therefore not be applied to colloidal aggregates of small metallic particles in contact with each other. The localised surface plasmon polaritons are important, on the other hand, for aggregates of somewhat larger particles, even if nonlocality is taken into account. Employing aggregate Mie theory with a nonlocal dielectric function, we show in addition, that, even for relatively small particles, retardation effects and high-order multipoles must be taken into account.

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.

High order relativistic corrections to Keplerian motion

The first terms of the general solution for an asymptotically flat stationary axisymmetric vacuum spacetime endowed with an equatorial symmetry plane are calculated from the corresponding Ernst potential up to seventh order in the radial pseudospherical coordinate. The metric is used to determine the influence of high order multipoles in the perihelion precession of an equatorial orbit and in the node line precession of a nonequatorial orbit with respect to a geodesic circle. Both results are written in terms of invariant quantities such as the Geroch–Hansen multipoles and the energy and angular momentum of the orbit.

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.

Charge capacity limitations of radio frequency ion guides in their use for improved ion accumulation and trapping in mass spectrometry.

The use of radio frequency (rf) ion guides as "linear" two-dimensional ion traps and ion guides for ion storage and accumulation, respectively, is becoming increasingly important for realizing improved sensitivity in mass spectrometry. Analytical relationships describing the ion accumulation operation mode of rf ion guides are reported. Comparisons are made between the rf quadrupole ion guide, higher-order rf multipoles and rf stacked ring ion guides, in terms of the charge capacity limitations due to the instability of ions, rf focusing efficiency limits, and effects due to rf ion heating (i.e., collisional activation due to rf oscillations of ions). Analytical relations for the stored charge quantity are derived in the low ion energy approximation, which is shown to be reasonable for the systems considered. The ion density spatial distribution is derived, an exponential form of which proved to provide a good approximation for high-order rf multipoles and stacked ring rf ion guides. The limit on the stored charge dependence upon rf is shown to be directly related to the thermal dissociation thresholds for the ions being studied; the limitation is weaker for higher-order multipoles and stacked ring ion guides. These results suggest that rf quadrupoles provide an optimum configuration when accumulation of a moderate ion density is sufficient (below 10(9) elementary charges/m). Alternatively, accumulation of an appreciable density for more fragile species, such as noncovalent complexes, may be realized using higher-order multipoles and stacked ring ion guides.

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.

Evanescent light scattering: The validity of the dipole approximation

In near-field optics the very concept of dipole is often used to represent either an elementary source or a scattering center. The most simple and widely used example is that of a small spherical particle whose polarizability is assumed to conform to the Clausius-Mossotti relation. While in conventional, far-field optics this approximation is known to be valid provided that the object is much smaller than the wavelength, its extension to near-field optics requires some precautions. Indeed, in the case of the scattering, by a spherical object, of an evanescent field generated, for instance, by total internal reflection or by a surface polariton, the strong-field gradient may increase the contribution to the polarizability of multipoles higher than the dipole. Such high-order multipoles are seldom considered in near-field optics because they complicate considerably any scattering calculation. In this paper we derive, for a spherical particle, the contributions of multipole orders up to the hexadecapole. This serves to illustrate the relative importance of each order. Moreover, within the framework of the coupled dipole method, we study, self-consistently, the problem of the scattering of an evanescent field by the sphere. We show that, with an initial field decreasing exponentially, the dipole approximation can be misleading. @S0163-1829~98!01428-3#

Toroidal Equilibrium Equipped with Dipole Divertor

A new type of divertor, a dipole divertor, is described. The dipole divertor is composed of a line dipole and is characterized by a simple configuration and the realization of a double-null separatrix with a small distortion on the equilibrium magnetic surface shape. Various configurations, including a conventional divertor, can also be realized with the basic two current hoops by changing current direction and magnitude. Higher-order multipole divertors such as the quadrupole divertor are also formed by four or more coils. A divertor magnetic field can be further localized in the higher-order multipoles. A possible stabilizing effect through curvature of the field line is discussed.

Focusing of neutrons and 3He atomic beams with hexapole magnets

The focusing properties of hexapole magnets were investigated with a neutron beam using a two-dimensional position-sensitive detector. The results were analysed with the help of computer simulations and values for the dipole and the hexapole field component were determined. Contributions of higher-order multipoles were detected and estimated.

Europa's magnetic signature: report from Galileo's pass on 19 December 1996.

On 19 December 1996 as Galileo passed close to Jupiter's moon, Europa, the magnetometer measured substantial departures from the slowly varying background field of Jupiter's magnetosphere. Currents coupling Europa to Jupiter's magnetospheric plasma could produce perturbations of the observed size. However, the trend of the field perturbations is here modeled as the signature of a Europa-centered dipole moment whose maximum surface magnitude is approximately 240 nanotesla, giving a rough upper limit to the internal field. The dipole orientation is oblique to Europa's spin axis. This orientation may not be probable for a field generated by a core dynamo, but higher order multipoles may be important as they are at Uranus and Neptune. Although the data can be modeled as contributions of an internal field of Europa, they do not confirm its existence. The dipole orientation is also oblique to the imposed field of Jupiter and thus not directly produced as a response to that field. Close to Europa, plasma currents appear to produce perturbations with scale sizes that are small compared with a Europa radius.

Propagation of light in the stationary field of multipole gravitational lens

A rigorous mathematical formalism for calculating the propagation of light rays in the stationary post-Newtonian field of an isolated celestial body (or system of bodies) considered as a gravitational lens having a complex multipole structure is developed. Symmetric trace-free tensors are used in the definition of gravitational multipoles instead of the less convenient (in general situations) scalar and vector spherical harmonics. Two types of perturbations of light rays, caused correspondingly by the mass and spin multipoles, are analyzed in full detail. A new simple method of integration for the equations of light propagation is proposed. This method enables us for the first time to obtain complete expressions both for the relativistic time delay and for the angle of the total deflection of light in any order of multipole perturbations without restriction. The results thus obtained can be applied to the interpretation of the secondary weak gravitational lens effects produced by the solar system bodies, stars, binary pulsars, and galaxies where the influence of higher-order multipoles on the propagation of null rays may be important and measurable. The methods developed in the paper can be also applied to physical optics of multipole electromagnetic lenses and for calculation of propagation of gravitational waves through the curved space–time. As a particular application of the method the generalized equation for a multipole gravitational lens is derived using Cartesian coordinates and symmetric transverse-traceless tensors.

A continuum solvation theory of quadrupolar fluids

We have derived a generalization of Poisson’s equation, a fourth-order partial differential equation, to describe the electrostatic behavior of polarizable, quadrupolar fluids. Our theory is in accord with the approach of Evangelista and Barbero. This equation was solved for the case of multipoles of arbitrary order placed at the center of a spherical cavity in a quadrupolar fluid. Our solution indicates that the quadrupolar portion of the disturbance created by an electrostatic probe in a polarizable quadrupolar fluid is localized to a distance of about a bohr, while asymptotically the fluid behaves as a polarizable medium. Internal field corrections as well as internal field gradient corrections have been computed. Fairly good agreement is found between our theory and the experimentally determined dielectric constant for carbon dioxide. The cavity model solution has been applied toward understanding the solvation of ions and dipolar molecules in supercritical carbon dioxide. We have used our theory to show that ions do not dissolve in supercritical carbon dioxide. Our theory displays improving agreement with data on the solubility of water molecules in supercritical carbon dioxide as pressure and temperature are increased. Ways to enhance agreement with experiments are suggested. We speculate on generalizations of our approach to fluids composed of higher-order multipoles, e.g., methane, whose first nonvanishing moment is an octupole.

Time-dependent multipoles and their application for radiation from volume source distributions

The radiation from a pulsed source distribution is expressed directly in the time-domain using a sum of time-dependent spherical (multipole) wave functions. Two alternative expressions for the time-dependent multipole moments (the excitation pulses) are derived. It is shown how they are related to the time-dependent plane-wave spectrum of the source (obtained via a Radon transform of the source distribution in the four space-time coordinates). Furthermore, the time-dependent multipole moments, and thereby the total time-dependent field outside the source region, are completely determined by the time-dependent radiation pattern. The series convergence is addressed by showing that the high order multipole moments tend to the quasistatic extension of the static multipole moments. This also puts an upper limit on the spatial resolution that can be achieved by a source distribution with specified size and pulse length.

Nonradial Coronal Streamers

The appearance of white light streamers in the outer solar corona is simulated by applying simple extrapolation models to the photospheric magnetic field and taking line-of-sight electron scattering into account. Highly nonradial streamers are obtained when the electrical currents are confined to thin sheets and the photospheric field contains a strong quadrupole (or higher order multipole) component, in addition to the normally dominant dipole. The finite angular resolution of the simulations gives rise to faint, multiple raylike structures or striations, which may mimic the effect of density inhomogeneities in the heliospheric current sheet.

New effective medium models and their applications

Thin films and many surfaces often have complex structures which are conveniently analysed for overall optical response by effective medium models. Examples from new deposition techniques and new exact theory are presented that highlight effects that are not predictable by many of the widely used simple effective medium models. High order multipoles and associated multiple resonances play a key role and alter spectral response and transport properties markedly. The new theories can discriminate the short range forces between neighbouring pairs and longer range forces in chains and arrays. Experimental data on composite films show how changes in component distribution can strongly effect spectral absorptance in ways that are not predictable by standard dipole theories.

A generalized fast multipole approach for Hartree—Fock and density functional computations

The fast multipole method (FMM) and the cell multipole method (CMM) compute charge—charge interactions in a system of N particles with O ( N) scaling. We propose an approach for incorporating CMM or FMM into Hartree—Fock (HF) and density functional theory (DFT) calculations. We show how the rate limiting computation of the Coulomb term in HF and DFT can be efficiently carried out using a generalized fast multipole algorithm applicable to higher-order point multipoles.