Approximation of an ideal dipole with a solenoid
Approximation of ideal dipole with a solenoid - dipole field plus error terms
MAGNETIC DIPOLE↗
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Trailing edge noise from hovering rotors
A method has been developed to predict the high frequency broadband noise due to the interaction of convecting turbulent eddies with the trailing edges of a hovering rotor. The trailing edge noise from each blade was modeled as point dipole noise with spanwise loading corrections. This point dipole approximation was checked by applying the concept to a stationary airfoil in a moving medium with excellent results. In order to estimate the strength of the point dipole, the trailing edge noise theory of Amiet was used. The method was applied specifically to blade boundary layer turbulence and compared to incident atmospheric turbulence noise. The results indicate that the relative importance of these two mechanisms is related to the magnitudes of the intensity and of the length scales of the inflow and boundary layer turbulence. The results tend to fall below some available experimental data indicating that in those experiments other broadband noise sources were stronger than boundary layer-trailing edge noise. The approach which was developed is also applicable to other blade-turbulence interaction mechanisms such as local stall and tip noise.
Kim, Y. N.↗
Modeling composite and fluffy grains: The effects of porosity
Recent studies of interplanetary and interstellar dust provide evidence that cosmic dust grains are fluffy, composite objects, highlighting the need for models of the electromagnetic scattering by these grains. Effective medium theory (EMT) with Mie-type series solutions has been used to explore the effects of porosity which would be important in composite dust particles. While this indirect approach is both flexible and computationally efficient, it is not necessarily a good approximation. The need for EMT and its rather restrictive assumptions may be circumvented through a direct computation of the scattering properties via finite element methods, such as the discrete dipole approximation (DDA). Recently, the utility of the DDA method has been advanced significantly through improvements in theory, in numerical algorithms, and in computer hardware. Extensive calculations with the DDA method are used here to examine more directly the effects of porosity. A particular emphasis is placed upon developing a valid methodology. For both solid and porous targets we establish both numerical and physical convergence properties over the range of size parameter that is required for our study. DDA cross sections for grains with a range of porosity are compared to those computed by the EMT/series expansion technique to examine the applicability of several mixing rules, including two extensions of the Bruggeman rule. We show that for particles with Rayleigh vacuum inclusions, the extension proposed by Rouleau & Martin is quite successful. We also investigate the effects of larger, non-Rayleigh vacuum inclusions for various levels of porosity and find that they can be significant.
Wolff, Michael J.↗
The UAH Spinning Terrella Experiment: A Laboratory Analog for the Earth's Magnetosphere
The UAH Spinning Terrella Experiment has been modified to include the effect of a second magnet. This is a simple laboratory demonstration of the well-known double-dipole approximation to the Earth's magnetosphere. In addition, the magnet has been biassed $\sim$-400V which generates a DC glow discharge and traps it in a ring current around the magnet. This ring current is easily imaged with a digital camera and illustrates several significant topological properties of a dipole field. In particular, when the two dipoles are aligned, and therefore repel, they emulate a northward IMF Bz magnetosphere. Such a geometry traps plasma in the high latitude cusps as can be clearly seen in the movies. Likewise, when the two magnets are anti-aligned, they emulate a southward IMF Bz magnetosphere with direct feeding of plasma through the x-line. We present evidence for trapping and heating of the plasma, comparing the dipole-trapped ring current to the cusp-trapped population. We also present a peculiar asymmetric ring current produced in by the plasma at low plasma densities. We discuss the similarities and dissimilarities of the laboratory analog to the collisionless Earth plasma, and implications for the interpretation of IMAGE data.
Sheldon, R. B.↗
Phase-Free Orbital Element Model Designed to Enable Rapid Assessment of Eclipse and Radiation Profiles for Low-Thrust Spiral Transfers Around the Earth
The Gateway Power and Propulsion Element (PPE) will be the first low-thrust solar electric ion propulsion mission to transfer from a highly elliptical Earth-bound orbit to a southern near-rectilinear halo orbit (NRHO) at the Earth-Moon L2 point. Due to the low thrust nature of the transfer orbit, it is desirable to locate viable trajectories that minimize the time spent in the Van Allen radiation belts to reduce solar array degradation and keep radiation dosages below design limits. In addition to radiation, low thrust trajectories which spiral around the Earth will pass through at least one or more seasons of Earth eclipses. The solar electric propulsion system relies on sunlight to generate the power necessary to operate the ion thrusters. Therefore, it is advantageous to find trajectories which also minimize the amount of time spent in eclipse and avoid excessive battery draw-down periods. We present an analytical method which rapidly approximates low-thrust spiral trajectories, fit to high-fidelity simulated data and parameterized to allow for changes in vehicle thrust characteristics, that is post-processed to determine eclipse profiles and time spent in the belts using a novel approach that estimates the geometry of the belts using a first-order dipole approximation of the Earth’s magnetic field. This method can be used to find satisfactory launch dates and orbit orientations that can serve as initial guesses when optimizing such missions in high-fidelity software.
low thrust trajectory design↗
Phase-Free Orbital Element Model Designed to Enable Rapid Assessment of Eclipse and Radiation Profiles for Low-Thrust Spiral Transfers Around the Earth
The Gateway Power and Propulsion Element (PPE) will be the first low-thrust solar electric ion propulsion mission to transfer from a highly elliptical Earth-bound orbit to a southern near-rectilinear halo orbit (NRHO) at the Earth-Moon L2 point. Due to the low thrust nature of the transfer orbit, it is desirable to locate viable trajectories that minimize the time spent in the Van Allen radiation belts to reduce solar array degradation and keep radiation dosages below design limits. In addition to radiation, low thrust trajectories which spiral around the Earth will pass through at least one or more seasons of Earth eclipses. The solar electric propulsion system relies on sunlight to generate the power necessary to operate the ion thrusters. Therefore, it is advantageous to find trajectories which also minimize the amount of time spent in eclipse and avoid excessive battery draw-down periods. We present an analytical method which rapidly approximates low-thrust spiral trajectories, fit to high-fidelity simulated data and parameterized to allow for changes in vehicle thrust characteristics, that is post-processed to determine eclipse profiles and time spent in the belts using a novel approach that estimates the geometry of the belts using a first-order dipole approximation of the Earth’s magnetic field. This method can be used to find satisfactory launch dates and orbit orientations that can serve as initial guesses when optimizing such missions in high-fidelity software.
low thrust trajectory design↗
Computation of Free-Free Transitions in Atomic Physics: Foundations
The amplitude T for "free-free" processes, such as bremsstrahlung or photo- absorption by an electron in the continuum in the presence of an external field, is usually written as the matrix element of the radiation operator taken between two continuum states. However, unlike the case when at least one of the states is bound, as in radiative transitions, electron capture, or the photo-effect, this expression contains an unphysical term, proportional to a delta-function and is not really the physical amplitude Tphys. This continues to be true for both the velocity and length form of the dipole approximation to the amplitude T. We first give an a priori definition of Tphys in terms of the scattering parts of the continuum functions, which has an obvious interpretation in terms of time-ordered diagrams. We then show that when the formal amplitude is modified by a long- distance cutoff, the modified form approaches Tphys as the cutoff is removed. The modified form then serves as a basis for the definition of a physical velocity dipole amplitude and this in turn leads to an equivalent length form of the dipole amplitude. This exercise provides a clear theoretical basis for many extant calculations in which cutoff factors are introduces somewhat ad hoc, as needed.
Bhatia, A. K.↗
APPROXIMATION OF AN IDEAL DIPOLE WITH A SOLENOID
Approximation of a solenoid magnetic field by an ideal dipole field with correction terms
MAGNETIC FIELD↗
Analyses of Cometary Silicate Crystals: DDA Spectral Modeling of Forsterite
Comets are the Solar System's deep freezers of gases, ices, and particulates that were present in the outer protoplanetary disk. Where comet nuclei accreted was so cold that CO ice (approximately 50K) and other supervolatile ices like ethane (C2H2) were preserved. However, comets also accreted high temperature minerals: silicate crystals that either condensed (greater than or equal to 1400 K) or that were annealed from amorphous (glassy) silicates (greater than 850-1000 K). By their rarity in the interstellar medium, cometary crystalline silicates are thought to be grains that formed in the inner disk and were then radially transported out to the cold and ice-rich regimes near Neptune. The questions that comets can potentially address are: How fast, how far, and over what duration were crystals that formed in the inner disk transported out to the comet-forming region(s)? In comets, the mass fractions of silicates that are crystalline, f_cryst, translate to benchmarks for protoplanetary disk radial transport models. The infamous comet Hale-Bopp has crystalline fractions of over 55%. The values for cometary crystalline mass fractions, however, are derived assuming that the mineralogy assessed for the submicron to micron-sized portion of the size distribution represents the compositional makeup of all larger grains in the coma. Models for fitting cometary SEDs make this assumption because models can only fit the observed features with submicron to micron-sized discrete crystals. On the other hand, larger (0.1-100 micrometer radii) porous grains composed of amorphous silicates and amorphous carbon can be easily computed with mixed medium theory wherein vacuum mixed into a spherical particle mimics a porous aggregate. If crystalline silicates are mixed in, the models completely fail to match the observations. Moreover, models for a size distribution of discrete crystalline forsterite grains commonly employs the CDE computational method for ellipsoidal platelets (c:a:b=8.14x8.14xl in shape with geometrical factors of x:y:z=1:1:10, Fabian et al. 2001; Harker et al. 2007). Alternatively, models for forsterite employ statistical methods like the Distribution of Hollow Spheres (Min et al. 2008; Oliveira et al. 2011) or Gaussian Random Spheres (GRS) or RGF (Gielen et al. 200S). Pancakes, hollow spheres, or GRS shapes similar to wheat sheaf crystal habit (e.g., Volten et al. 2001; Veihelmann et al. 2006), however, do not have the sharp edges, flat faces, and vertices seen in images of cometary crystals in interplanetary dust particles (IDPs) or in Stardust samples. Cometary forsterite crystals often have equant or tabular crystal habit (J. Bradley). To simulate cometary crystals, we have computed absorption efficiencies of forsterite using the Discrete Dipole Approximation (DDA) DDSCAT code on NAS supercomputers. We compute thermal models that employ a size distribution of discrete irregularly shaped forsterite crystals (nonspherical shapes with faces and vertices) to explore how crystal shape affects the shape and wavelength positions of the forsterite spectral features and to explore whether cometary crystal shapes support either condensation or annealing scenarios (Lindsay et al. 2012a, b). We find forsterite crystal shapes that best-fit comet Hale-Bopp are tetrahedron, bricks or brick platelets, essentially equant or tabular (Lindsay et al. 2012a,b), commensurate with high temperature condensation experiments (Kobatake et al. 2008). We also have computed porous aggregates with crystal monomers and find that the crystal resonances are amplified. i.e., the crystalline fraction is lower in the aggregate than is derived by fitting a linear mix of spectral features from discrete subcomponents, and the crystal resonances 'appear' to be from larger crystals (Wooden et al. 2012). These results may indicate that the crystalline mass fraction in comets with comae dominated by aggregates may be lower than deduced by popular methods that only emoy ensembles of discrete crystals.
Wooden, Diane↗
Multichannel photo-ionization of atomic systems.
Multichannel photoionization of atomic systems obtained with dipole approximation assuming LS COUPLING, using wave functions
PHOTOIONIZATION↗
Radiating dipole model of interference induced in spacecraft circuitry by surface discharges
Spacecraft in geosynchronous orbit can be charged electrically to high voltages by interaction with the space plasma. Differential charging of spacecraft surfaces leads to arc and blowoff discharging. The discharges are thought to upset interior, computer-level circuitry. In addition to capacitive or electrostatic effects, significant inductive and less significant radiative effects of these discharges exist and can be modeled in a dipole approximation. Flight measurements suggest source frequencies of 5 to 50 MHz. Laboratory tests indicate source current strengths of several amperes. Electrical and magnetic fields at distances of many centimeters from such sources can be as large as tens of volts per meter and meter squared, respectively. Estimates of field attenuation by spacecraft walls and structures suggest that interior fields may be appreciable if electromagnetic shielding is much thinner than about 0.025 mm (1 mil). Pickup of such fields by wires and cables interconnecting circuit components could be a source of interference signals of several volts amplitude.
Metz, R. N.↗
Two-photon ionization of atomic hydrogen with elliptically polarized light
The theory of two-photon ionization of a hydrogenic state in the nonrelativistic dipole approximation is generalized for elliptically polarized light. An application to the metastable 2S state of atomic hydrogen is made. Significant differences in the angular distribution of the outgoing electrons are found depending upon the polarization of the photons. It is claimed that two-photon ionization employing elliptically polarized photons from lasers may provide an additional test for the theories of multiphoton ionization.
Kassaee, A.↗
Electromagnetic wave scattering from some vegetation samples
For an incident plane wave, the field inside a thin scatterer (disk and needle) is estimated by the generalized Rayleigh-Gans (GRG) approximation. This leads to a scattering amplitude tensor equal to that obtained via the Rayleigh approximation (dipole term) with a modifying function. For a finite-length cylinder the inner field is estimated by the corresponding field for the same cylinder of infinite lenght. The effects of different approaches in estimating the field inside the scatterer on the backscattering cross section are illustrated numerically for a circular disk, a needle, and a finite-length cylinder as a function of the wave number and the incidence angle. Finally, the modeling predictions are compared with measurements.
Karam, Mostafa A.↗
Nonadiabatic corrections to the van der Waals potential
Closed-form expressions are derived for the finite-mass nonadiabatic corrections to the van der Waals potential in the electric-dipole approximations in terms of London-analog two-center atomic spectral sums. The nonadiabatic corrections to all orders at threshold energy and also those with first-order energy dependence are given.
Au, C. K.↗
Fractal dust grains around R Coronae Borealis stars
Discrete dipole approximation calculations of the optical properties of random fractal aggregates of graphite spheroids show a UV absorption feature that is too wide and centered at too long a wavelength to fit the observed interstellar 2200-A feature, but which is a good match to the 2400-A feature seen in the hydrogen-deficient R CrB stars reported by Hecht et al. (1984). Graphite fractal grains also match the UV bump and large long-wavelenvth extinction seen in laboratory studies of carbon smoke published by Bussoletti et al. (1987), which are usually attributed to amorphous carbon.
Wright, Edward L.↗
The effects of compositional inhomogeneities and fractal dimension on the optical properties of astrophysical dust
Mathis and Whiffen (1989) have recently suggested that interstellar dust particles are fluffy aggregates of submicron-size particles composed of various astronomical minerals. These dust particles should exhibit optical properties that are quite different from standard dust, characterized by spherical particles of various homogeneous mineral composition. In this paper, the discrete dipole approximation (DDA) method is used to examine the effects of chemical inhomogeneities and spatial structure on the optical properties of interstellar Mathis-Whiffen-type dust particles. The spatial structure of the dust is represented by its fractal dimension, and the chemical inhomogeneities are simulated by randomly assigning the composition of the occupied sites in the structure to be either carbon or silicate. It is found that compositional inhomogeneities are the dominant parameter affecting the shape of the 9.7 and 18 micron silicate bands. Some bands-shape variations can be attributed to the fractal dimension of the dust. The results derived here can be used to explain or constrain variations in these parameters among various astronomical objects.
Bazell, David↗
Radiative properties of visible and subvisible Cirrus: Scattering on hexagonal ice crystals
One of the main objectives of the First International Satellite Cloud Climatology Project (ISCCP) Regional Experiment (FIRE) is to provide a better understanding of the physics of upper level clouds. The focus is on just one specific aspect of cirrus physics, namely on characterizing the radiative properties of single, nonspherical ice particles. The basis for further more extensive studies of the radiative transfer through upper level clouds is provided. Radiation provides a potential mechanism for strong feedback between the divergence of in-cloud radiative flux and the cloud microphysics and ultimately on the dynamics of the cloud. Some aspects of ice cloud microphysics that are relevant to the radiation calculations are described. Next, the Discrete Dipole Approximation (DDA) is introduced and some new results of scattering by irregular crystals are presented. The Anomalous Diffraction Theory (ADT) was adopted to investigate the scattering properties of even larger crystals. In this way the scattering properties of nonspherical particles were determined over a range of particle sizes.
Flatau, Piotr J.↗
Millimeter wave radiative transfer studies for precipitation measurements
Scattering calculations using the discrete dipole approximation and vector radiative transfer calculations were performed to model multiparameter radar return and passive microwave emission for a simple model of a winter storm. The issue of dendrite riming was addressed by computing scattering properties of thin ice disks with varying bulk density. It was shown that C-band multiparameter radar contains information about particle density and the number concentration of the ice particles. The radiative transfer modeling indicated that polarized multifrequency passive microwave emission may be used to infer some properties of ice hydrometers. Detailed radar modeling and vector radiative transfer modeling is in progress to enhance the understanding of simultaneous radar and radiometer measurements, as in the case of the proposed TRMM field program. A one-dimensional cloud model will be used to simulate the storm structure in detail and study the microphysics, such as size and density. Multifrequency polarized radiometer measurements from the SSMI satellite instrument will be analyzed in relation to dual-frequency and dual-polarization radar measurements.
Vivekanandan, J.↗