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Investigation of the influence of resonant multipole interactions on exchanges of rotational energy in molecular collisions, by means of a simple two-state impact-parameter approximation. It is found that dipole-quadrupole and quadrupole-quadrupole interactions can have a significant effect for molecules with low moments of inertia.
A closed-form solution for the sound radiation from multipole sources imbedded in an infinite cylindrical jet with an arbitrary velocity profile is obtained. It is valid in the limit where the wavelength is large compared with the jet radius. Simple formulae for the acoustic pressure field due to convected point sources are also obtained. The results show (in a simple way) how the mean flow affects the radiation pattern from the sources. For convected lateral quadrupoles it causes the exponent of the Doppler factor multiplying the far-field pressure signal to be increased from the value of 3 used by Lighthill to 5.
A previous analysis of the acoustic radiation from multipole sources is extended to include additional components of the dipole and quadrupole sources. It is found that, unlike the components of the sources considered in the previous paper, the exponent of the Doppler factor now depends on the location of the sources within the jet.
A 30-cm electron-bombardment ion source has been designed and fabricated for micromachining and sputtering applications. This source has a multipole magnetic field that employs permanent magnets between permeable pole pieces. An average ion current density of 1 ma/sq cm with 500-eV argon ions was selected as a design operating condition. The ion beam at this operating condition was uniform and well collimated, with an average variation of + or -5 percent over the center 20 cm of the beam at a distance up to 30 cm from the ion source.
The oxygen plasma oxidation of GaAs was studied in order to obtain extremely high frequency responses with MOS devices. In the multipole system a homogeneous oxygen plasma of high density can easily be obtained in a large volume. This system is thus convenient for the study of plasma oxidation of GaAs. The electrical properties of the MOS diodes obtained in this way are controlled by interface states, located mostly in the upper half of the band gap where densities in the 10 to the 13th power/(sq cm) (eV) range can be estimated. Despite these interface states the possibility of fabricating MOSFET transistors working mostly in the depletion mode for a higher frequency cut-off still exists.
A rectangular ion source particularly suited for the continuous sputter processing of materials over a wide area is discussed. A multipole magnetic field configuration was used to design an ion source with a 5 x 40 cm beam area, while a three-grid ion optics system was used to maximize ion current density at the design ion energy of 500 eV. An average extracted current density of about 4 mA/sq cm could be obtained from 500 eV Ar ions. The difference between the experimental performance and the design value of 6 mA/sq cm is attributed to grid misalignment due to thermal expansion. The discharge losses at typical operating conditions ranged from about 600 to 1000 eV/ion, in reasonable agreement with the design value of 800 eV/ion. The use of multiple rectangular-beam ion sources to process wider areas than would be possible with a single source was also studied, and the most uniform coverage was found to be obtainable with a 0 to 2 cm overlap.
Formulas are derived for the high frequency sound emission from moving point multipole sources embedded in an arbitrary unidirectional transversely sheared mean flow. The results are used to study the sound generated by non-axisymmetric turbulent jets. The effect of the asymmetry in both the mean flow and the source distribution is accounted for by a 'circumferential directivity factor', which is easily calculated from the solution of a second order ordinary differential equation in the general case and from an explicit formula when the mean flow is symmetric but the source location is not. This factor is used to assess the potential of employing asymmetric velocity profiles that redirect the sound upward to reduce the noise radiation below the flight path of a jet aircraft.
It has been customary to assume that ions flow nearly equally in all directions from the ion production region within an electron-bombardment discharge chamber. Ion flow measurements in a multipole discharge chamber have shown that this assumption is not true. In general, the electron current through a magnetic field can alter the electron density, and hence the ion density, in such a way that ions tend to be directed away from the region bounded by the magnetic field. When this mechanism is understood, it becomes evident that many past discharge chamber designs have operated with a preferentially directed flow of ions.
A triple infinite sum of formulas expressed as an expansion in Legendre polynomials is generated by use of computer algebra to represent the potential from the midpoint of two Slater-type orbitals; the charge density that determines the potential is given as the product of the two orbitals. An example using 1s orbitals shows that only a few terms are needed to obtain four-figure accuracy. Exact formulas are obtained for multipole moments by means of a careful study of expanded formulas, allowing an 'extrapolation to infinity'. This Loewdin alpha-function approach augmented by using a C matrix to characterize Slater-type orbitals can be readily generalized to all cases.
The multipole polarizability of the ground state of francium is calculated by utilizing both the variational technique of Davison and the quantum defect theory underlying the Bates-Damgaard method. This approach is also shown to yield reasonable results for other alkali atoms. Second-order Stark shift for the ground state of francium is presented as a function of field strength for possible future experimental comparison.
The oscillating mass 2(exp l)-pole moment, M(sub nl), of a star in a given (normalized) oscillation mode determines the energy that can be absorbed by the mode in a tidal interaction and the power radiated by the mode in gravitational waves, both of which are proportional to (absolute value of M(sub nl))(exp 2). The coefficients in the expansion of the vector fields del(r(exp l)Y(sub lm)(theta, phi)) in terms of the displacement fields of modes of given l and m are proportional to M(sub nl). This expansion leads to a sum rule sum over n(absolute value of M(sub nl))(exp 2) = constant. For stars of weak to moderate central condensation (such as neutron stars), the f-mode is well approximated by the vector field being expanded, and therefore it takes the lion's share of the sum. Thus the multipole moments of all other modes must be small. In there numerical evaluation, it is necessary to know the shape of the eigenfunctions quite precisly, since a small f-mode contamination can significantly increase the obtained values. This contamination occurs in some `hybrid' numerical computations of neutron star oscillations with relativistic equilibrium stars and Newtonian dynamics (e.g., McDermott et al. 1988). In this case, it is due to a slight inconsistency in the models and leads to a large overestimate of the power radiated in gravitational waves by modes other than the f-mode, although their oscillation periods are nearly unaffected.
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 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.
The quality of several atomic charge models based on different definitions has been analyzed using cumulative atomic multipole moments (CAMM). This formalism can generate higher atomic moments starting from any atomic charges, while preserving the corresponding molecular moments. The atomic charge contribution to the higher molecular moments, as well as to the electrostatic potentials, has been examined for CO and HCN molecules at several different levels of theory. The results clearly show that the electrostatic potential obtained from CAMM expansion is convergent up to R-5 term for all atomic charge models used. This illustrates that higher atomic moments can be used to supplement any atomic charge model to obtain more accurate description of electrostatic properties.
The NASA Fast Scattering Code (FSC) is a versatile noise prediction program designed to conduct aeroacoustic noise reduction studies. The equivalent source method is used to solve an exterior Helmholtz boundary value problem with an impedance type boundary condition. The solution process in FSC v2.0 requires direct manipulation of a large, dense system of linear equations, limiting the applicability of the code to small scales and/or moderate excitation frequencies. Recent advances in the use of Fast Multipole Methods (FMM) for solving scattering problems, coupled with sparse linear algebra techniques, suggest that a substantial reduction in computer resource utilization over conventional solution approaches can be obtained. Implementation of the single level FMM (SLFMM) and a variant of the Conjugate Gradient Method (CGM) into the FSC is discussed in this paper. The culmination of this effort, FSC v3.0, was used to generate solutions for three configurations of interest. Benchmarking against previously obtained simulations indicate that a twenty-fold reduction in computational memory and up to a four-fold reduction in computer time have been achieved on a single processor.
An approach that efficiently solves for a desired parameter of a system or device that can include both electrically large fast multipole method (FMM) elements, and electrically small QR elements. The system or device is setup as an oct-tree structure that can include regions of both the FMM type and the QR type. An iterative solver is then used to determine a first matrix vector product for any electrically large elements, and a second matrix vector product for any electrically small elements that are included in the structure. These matrix vector products for the electrically large elements and the electrically small elements are combined, and a net delta for a combination of the matrix vector products is determined. The iteration continues until a net delta is obtained that is within predefined limits. The matrix vector products that were last obtained are used to solve for the desired parameter.
Velocity-of-light, multi-spoke cavities are being proposed to accelerate electrons in a compact light-source. There are strict requirements on the beam quality which require that the linac have only small non-uniformities in the accelerating field. Beam dynamics simulations have uncovered varying levels of focusing and defocusing in the proposed cavities, which is dependent on the geometry of the spoke in the vicinity of the beam path. Here we present results for the influence different spoke geometries have on the multipole components of the accelerating field and how these components, in turn, impact the simulated beam properties.
Effects of RF field asymmetry along with multipoles have been studied in Project X front end cavities. One family of half wave resonators operating at 162.5 and two of spoke resonators operating at 325 MHz have been analysed. HWR and spoke res onators unlike elliptical cavities, do not have axial symmetry, hence a quadrupole perturbation to the beam is present. The purpose of this paper is to explain the approach and the calculation method used to understand and overcome the drawbacks due to th e RF field asymmetry.
Effects of RF field asymmetry along with multipoles have been studied in Project X front end cavities. One family of half wave resonators operating at 162.5 and two of spoke resonators operating at 325 MHz have been analysed. HWR and spoke res onators unlike elliptical cavities, do not have axial symmetry, hence a quadrupole perturbation to the beam is present. The purpose of this paper is to explain the approach and the calculation method used to understand and overcome the drawbacks due to th e RF field asymmetry.