Effects Of Multipoles Research Articles

A density functional approach to freezing transitions in molecular fluids: Dipolar hard spheres

We extend a density functional theory of atomic systems to simple molecules using first-order perturbation theory. We model the hydrogen halides as dipolar hard spheres and consider freezing into two orientationally different fcc lattices. In one of these, the dipoles may align parallel to a single, space-fixed axis while in the other, the dipoles in adjacent faces of the fcc unit cell are constrained to lie perpendicular to one another. The second structure approximates the experimentally observed molecular crystals of HF and HCl, and the phase diagram calculated from this model agrees qualitatively with experiment. At high temperatures, or for weak enough dipole moments, a plastic (orientationally disordered) solid precedes the molecular crystal. The plastic phase is unaffected by the dipolar perturbation but eventually becomes a molecular crystal upon lowering the temperature or increasing the density. We also discuss second-order perturbation theory, the effects of higher multipoles, and some general consequences of the density functional theory of molecular systems.

Tracking Studies on the Effects of Magnet Multipoles on the Aperture of the RHIC Heavy Ion Collider

Tracking studies including the effects of random multipoles resulting from construction errors have been made for RHIC with two independent tracking programs at three different tunes. The studies were made using ten different sets of random errors for each of the programs. The aperture was defined as the worst case, and the results of the two programs are in good agreement. A second set of studies was made for which the number of dipoles was doubled to determine whether doubling the number of independent random errors results in a reduction of the effects or random multipoles. The results for the two cases, one dipole per half cell and two dipoles per half cell, indicate there is little difference in dynamic aperture.

Tracking Studies on the Effects of Random Multipoles in the 6.5 T Lattice of the SSC Reference Designs Study

The acceptance of lattice A (6.5 T) of the SSC Reference Designs Study is determined for ten different sets of random errors as various multipole orders are set to zero. On the basis of 400 turn studies it is concluded that all multipole orders in the dipoles are important. Further studies show that the beam crossing dipoles limit the acceptance--when their multipoles are scaled as r-(n+ l), corresponding to an increased coil radius, the acceptance of the lattice essentially doubles.

On the dielectric theory of fluids

This is the second paper in a series aimed at consistently incorporating the effects of higher multipoles into a molecular theory of dielectric phenomena. In this article we examine the low density limit of the non-linear dielectric response of an arbitrary fluid to an externally applied, and in general non-uniform, electrostatic field. We thus elucidate the physical mechanisms whereby higher multipole moments of single molecules contribute to the dielectric response. An explicit expression for the static dielectric tensor of such systems is obtained, and is found to be independent of the choice of molecular origin with respect to which the multipole moments are referred only if the effects due to orientational anisotropy and electrostriction are considered on an equal footing. We examine the general question of the origin invariance of the Maxwell equations if a truncated multipole expansion of the displacement field is employed. Finally, we consider the possibility of novel experiments to determine the permanent quadrupole moment of dipolar molecules.

Orbit effects of the end field multipoles in superconducting magnets

Two possible effects due to the end field multipoles in superconducting magnets are pointed out. One effect is the sagitta-end-multipole effect in dipoles. A result of this is that the v-shift due to an end multipole is not cancelled by an equal and opposite correction multipole distributed over the central part of the dipole, which complicates the correction of the end multipole effects. A second effect is the aperture-higher-multipole effect. The presence of higher end field multipoles for which there are no correction coils may be reduce the good field aperture. These two effects are illustrated by computing them for the case of the ISABELLE accelerator.

Unsteady Lagally theorem for multipoles and deformable bodies

The Lagally theorem for unsteady flow expresses the forces and moments acting on a rigid body moving in an inviscid and incompressible fluid in terms of the singularities of the analytically continued flow within the body. Previous generalizations of the Lagally theorem, originally given by Lagally (1922) for steady flows, are due to Cummins (1957) and Landweber & Yih (1956), who consider the effect of flow unsteadiness on the forces and moments. In these, the system of image singularities within the body was assumed to consist of isolated or continuous (surface or volume) distributions of sources and doublets. A further extension of Lagally's theorem ie due to Landweber (1967), who derived expressions for the steady forces and moments acting on a rigid body generated by isolated or a continuous distribution of multipoles. The purpose of the present paper is to generalize the Lagally theorem so as to include the effects of multipoles in unsteady flow, and deformability of the body, as well as to present a briefer derivation of the resulting formulae. Two examples, illustrating the application of the force and moment formulae, will be presented.

The conductivity of lattices of spheres I. The simple cubic lattice

We have extended a method devised by Lord Rayleigh to calculate the conductivity of a simple cubic lattice of conducting spheres in a conducting matrix. The extended theory is capable of including the effects of multipoles of arbitrarily high order, and yields excellent agreement with measurements on arrays of perfectly conducting spheres, even when they are close to touching. Calculations and measurements on lossy spheres are also compared. An explicit formula for the conductivity is given which takes into account poles of order 2 7 , and two empirical formulae are discussed.

Investigation ofE2andE3Radiation above the Giant Dipole Resonance inY89(p, γ0)Zr90

New detailed angular distribution measurements are presented for $^{89}\mathrm{Y}(p, {\ensuremath{\gamma}}_{0})^{90}\mathrm{Zr}$ above the giant dipole resonance ($14 \mathrm{MeV}l~{E}_{p}l~27 \mathrm{MeV}$), which show pronounced effects of higher multipoles. Direct-semidirect calculations provide a good description of the data by including $E2$ and $E3$ as well as $E1$ radiation. The sensitivity of the reaction to a $T=1$ giant quadrupole resonance is demonstrated.

Electromagnetic Transmission Characteristics of a Lattice of Infinitely Long Conducting Cylinders

This investigation is primarily concerned with the study of electromagnetic transmission characteristics of a lattice of infinitely long conducting cylinders. Four approaches to the general problem have been employed and the advantages, disadvantages, and realms of validity of each have been studied. Several of these methods constitute a substantial improvement over previous analyses and are supported by wave-guide and free-space experimental work. The four approaches are: (1) A molecular analogy with a consideration of dipole interactions leading to the Clausius-Mosotti relations, (2) A transmission line formulation which considers the thick obstacle for both polarizations, (3) An analysis based on the summation of scattered fields which demonstrates that the Clausius-Mosotti relations are a special case of a more general relation which accounts for the effects of higher order multipoles, and (4) A solution formally valid for all values of spacing and cylinder radius based on integral equation formulation of variational principle.

High Energy Photo-Disintegration of the Deuteron

The disintegration of the deuteron by $\ensuremath{\gamma}$-rays in the range 50-250 Mev is investigated. The lower energy limit is imposed by the neglect of nuclear forces between the neutron and proton after absorption of the photon. Moreover, the effects of retardation and of multipole radiation higher than dipole, the investigation of which constitutes one of the primary purposes of the present work, become apparent only above 50 Mev. The upper limit is imposed by the assumption that the nuclear particles can be treated non-relativistically. It is shown that at the high radiation energies considered it is essential to take into account the range of the nuclear forces in the ground state and that this is the case because of the importance of interference effects (short de Broglie wave-length of the nucleons) which depend very strongly on the "size" of the deuteron. The cross section at 50 Mev is 37\ensuremath{\mu}b(37\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}30}$ ${\mathrm{cm}}^{2}$) and decreases with $\ensuremath{\gamma}$-ray energy up to 150 Mev as ${(\ensuremath{\hbar}\ensuremath{\omega})}^{\ensuremath{-}n}$ where $n$ lies between 4 and 5. Beyond 150 Mev the cross section decreases less rapidly because of a more favorable phase relation between outgoing waves from different parts of the deuteron. The general features of the cross section and of the angular distribution of the particles can be understood in terms of interference; the most important effect of the interference is to favor strongly small momentum for the recoil particle (proton in the case of charge coupling and both proton and neutron in the case of spin coupling). The error caused by neglect of nuclear forces in the final state is estimated, by a consideration of electric dipole transitions, to be less than 30 percent in the worst case (low energy photons). The effects of retardation and higher multipoles are calculated explicitly, and it is shown that these effects are small at 50 Mev and important at 100 Mev. It is also shown that the effect of non-central forces between the nucleons in the ground state introduces negligible error.