Search NASA⌕ Search

SEARCH · Search NASA

Results for “Dipole approximation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

Trajectory Traces of Charged Particles in the Magnetosphere

The characteristic enhancements of ring current particles with energies of about 1 to 100 keV, associated with magnetospheric substorms, were observed by Explorer 45 around the plasmapause in the afternoon to midnight region, and showed the characteristic structure called a 'nose' in the proton spectrograms. The motion of these particles in the equatorial magnetosphere, under a recently proposed convection electric field and a dipole magnetic field is described. Approximate equations of a bounce period, a second adiabatic invariant, and a bounce-average azimuthal velocity are given with inaccuracies less than about 0.001 for all pitch angles. The complete set of flow patterns of 90 deg pitch angle particles is also presented by means of stagnation lines through which radial drifts and/or azimuthal drifts change their directions. The particle tracings in the magnetosphere give a basic concept to explain the observed nose characteristics.

Ejiri, M.↗

Interactions of the plasma sheet with the lunar surface at the Apollo 14 site

Calculations of the magnetic shadow zones of lunar-based particle detectors are extended to include the effects of local remanent magnetic fields. At the Apollo 14 site, the local magnetic field is approximated as that of a dipole. Numerically calculated open and shadowed zones are shown to be in agreement with quiet-time plasma-sheet observations of the charged-particle lunar-environment experiment. An analysis of three storm-time observations indicates that magnetic shadowing can significantly alter the near-lunar-surface electrostatic potential distribution.

Reiff, P. H.↗

Modeling the thermal structure and magnetic properties of the crust of active regions with application to the Rio Grande rift

Experiments in Curie depth estimation from long wavelength magnetic anomalies are summarized. The heart of the work is equivalent-layer-type magnetization models derived by inversion of high-elevation, long wavelength magnetic anomaly data. The methodology is described in detail in the above references. A magnetization distribution in a thin equivalent layer at the Earth's surface having maximum detail while retaining physical significance, and giving rise to a synthetic anomaly field which makes a best fit to the observed field in a least squares sense is discussed. The apparent magnetization contrast in the equivalent layer is approximated using an array of dipoles distributed in equal area at the Earth's surface. The dipoles are pointed in the direction of the main magnetic field, which carries the implicit assumption that crustal magnetization is dominantly induced or viscous. The determination of the closest possible dipole spacing giving a stable inversion to a solution having physical significance is accomplished by plotting the standard deviation of the solution parameters against their spatial separation for a series of solutions.

Source record↗

An Exact Form of Lilley's Equation with a Velocity Quadrupole/Temperature Dipole Source Term

There have been several attempts to introduce approximations into the exact form of Lilley's equation in order to express the source term as the sum of a quadrupole whose strength is quadratic in the fluctuating velocities and a dipole whose strength is proportional to the temperature fluctuations. The purpose of this note is to show that it is possible to choose the dependent (i.e., the pressure) variable so that this type of result can be derived directly from the Euler equations without introducing any additional approximations.

Goldstein, Marvin E.↗

Thermal conductivity and resonant multipole interactions.

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.

Nyeland, C.↗

Magnetospheric chorus - Occurrence patterns and normalized frequency

Over 400 hours of continuous broadband data obtained by the OGO 3 satellite are analyzed to provide a statistically accurate description of band-limited (magnetospheric) chorus. Certain aspects of the chorus frequency distribution are interpreted in terms of a gyroresonant electron feedback model of generation. An example of high chorus activity during an outbound pass through the noon magnetosphere is examined in detail, the spectral complexity of some chorus is illustrated, and the diurnal variation of chorus occurrence is investigated. The frequency and bandwidth distributions of chorus are analyzed. The results indicate that chorus occurrence depends strongly on local time and dipole latitude, the general region of maximum chorus occurrence approximates the previously reported zone of 'hard' electron precipitation, and the normalized chorus frequency is strongly dependent on dipole latitude. It is shown how a change in the curvature of the whistler-mode refractive-index surface affects focusing of radiation along magnetic field lines and how interference can occur between modes with slightly different ray velocities. It is concluded that most magnetospheric chorus consists of rising emissions which are probably generated by gyroresonant electrons slightly off the equator.

Burtis, W. J.↗

Theoretical studies of photoexcitation and ionization in H2O

Theoretical studies using Franck-Condon and static-exchange approximations are reported for the complete dipole excitation and ionization spectrum in H2O, where (1) large Cartesian Gaussian basis sets are used to represent the required discrete and continuum electronic eigenfunctions at the ground state equilibrium geometry, and (2) previously devised moment-theory techniques are employed in constructing the continuum oscillator-strength densities from the calculated spectra. Comparisons are made of the calculated excitation and ionization profiles with recent experimental photoabsorption studies and corresponding spectral assignments, electron impact-excitation cross sections, and dipole and synchrotron-radiation studies of partial-channel photoionization cross sections. The calculated partial-channel cross sections are found to be atomic-like, and dominated by 2p-kd components. It is suggested that the latter transition couples with the underlying 1b(1)-kb(1) channel, accounting for a prominent feature in recent synchrotron-radiation measurements.

Diercksen, G. H. F.↗

Use of Satellite-Derived Water Vapor Data to Investigate Northwestward Expansion of North Pacific Subtropical High During 1995 Summer: Westward Propagating Moisture Pattern

The spatial and temporal evolution of the moisture field over the subtropical northwest Pacific during the summer of 1995 is investigated using daily total precipitable water from combined SSM/I-TOVS data and pentad upper tropospheric humidity (UTH) data, in conjunction with NCEP reanalysis data. From analysis of the combined water vapor field, the westward movement of a dry airmass is observed along the 20-30 degrees N latitude zone from near the dateline to the south of Japan throughout the summer of 1995. Extended EOF analysis of total precipitable water reveals that the westward moving pattern takes place in conjunction with an expanding North Pacific subtropical high maintaining an oscillatory component exhibiting a period of some 15-25 days. A concomitant dipole-like oscillating anomalous circulation with approximately a 20-day period between the South China Sea and south of Japan appears to influence the westward expansion of the subtropical high. The analysis also suggests that the fluctuations of the North Pacific high are in response to a local Hadley-type circulation which is induced by westward-moving anomalous convection episodes along 10-20 degrees N.

Sohn, Byung-Ju↗

Solar magnetic fields - Extended.

Spacecraft observations of the interplanetary magnetic field have revealed that almost always each solar rotation can be divided into sectors, within each of which the field has a predominant polarity toward the sun or away from the sun. Comparisons of this interplanetary magnetic sector pattern with observations of the photospheric magnetic field have revealed a similar solar magnetic pattern. The boundaries between solar magnetic sectors are approximately in the north-south direction over a wide range of latitudes on both sides of the equator. This solar magnetic sector structure can be described as a rotating dipole whose magnetic axis makes an angle of approximately 90 deg with the axis of rotation. Possible similarities between this solar-sector magnetism and the models derived from observations of stellar magnetism are discussed.

Wilcox, J. M.↗

Modified Coulomb-Dipole Theory for 2e Photoionization

In the light of recent experiment on 2e photoionization of Li near threshold, we have considered a modification of the Coulomb-dipole theory, retaining the basic assumption that the threshold is dominated by asymmetric events in phase space [implies r(sub 1), k(sub 1)) greater than or equal to 2(r(sub 2), k(sub )]. In this region [in a collinear model, 2/r(sub 12) approached + 2/(r(sub 1)+r(sub 2)] the interaction reduces to V(rIsub 1) is greater than or equal to 2r(sub 2) is identically equal to [(-Z/r(sub 2)-(A-1)/r(sub 1)] + [(-2r(sub 2)/r(sub 1 exp 2)] is identically equal to V(sub c)+[V(sub d)]. For two electron emission Z = 2, thus both electrons see a Coulomb potential (V(sub c)) asymptotically, albeit each seeing a different charge. The residual potential (V(sub d)) is dipole in character. Writing the total psi = psi (sub c) + psi(sub d) = delta psi, and noting that. (T+V(sub c)-E)psy(sub c) = 0 and (T+V(sub c))psi(sub d) = 0 can be solved exactly, we find, substituting psi into the complete Schrod. Eq., that delta psi = -(H-E)(exp -1)(V(sub d) psi(sub 0)+V(sub c psi (sub 1). Using the fact that the absolute value of V(sub c) is much more than the absolute value of V(sub d) in almost all of configuration space, we can replace H by H(sub 0) in 9H-E)(exp -1) to obtain an improved approximation psi (improved) = psi(sub c) + psi(sub d) -(H(sub 0)-E)(exp -1) (V(sub c) psi (sub 0) + V(sub c) psi(sub 1). Here's the Green's function (H(sub 0)-E)(exp -1), can be exhibited explicitly, but the last term in psi (improved) is small, compared to the first two terms. Inserting them into the transition matrix element, which one handles in the usual way, we obtain in the limit E approaches 0, the threshold law: Q(E) alpha E + M(E)E(exp 5/4) + higher order (Eq. 1a). The modulation function, M(E), is a well-defined (but very non-trivial integral, but it is expected to be well approximated by a sinusoidal function containing a dipole phase term (M(E) = c sin[alpha log (E) + micron] (Eq. 1b). Experimental results show definite modulations, and are well fitted by Eqs (1).

Source record↗

Theoretical and observational analysis of spacecraft fields

In order to investigate the nondipolar contributions of spacecraft magnetic fields a simple magnetic field model is proposed. This model consists of randomly oriented dipoles in a given volume. Two sets of formulas are presented which give the rms-multipole field components, for isotropic orientations of the dipoles at given positions and for isotropic orientations of the dipoles distributed uniformly throughout a cube or sphere. The statistical results for an 8 cu m cube together with individual examples computed numerically show the following features: Beyond about 2 to 3 m distance from the center of the cube, the field is dominated by an equivalent dipole. The magnitude of the magnetic moment of the dipolar part is approximated by an expression for equal magnetic moments or generally by the Pythagorean sum of the dipole moments. The radial component is generally greater than either of the transverse components for the dipole portion as well as for the nondipolar field contributions.

Neubauer, F. M.↗

Polarizability of molecular hydrogen.

Perturbation theory summation method for calculating molecular hydrogen static dipole electric polarizability, using coupled Hartree- Fock approximation

Taylor, H. S.↗

Saturn radio emission near 1 MHz

Emission from the direction of the planet Saturn was observed by the IMP-6 spacecraft at 15 frequencies between 375 and 2200 kHz during the period April 1971 to October 1972. The Saturnian radio bursts were identified in the IMP-6 data through an analysis of the phase of the observed modulated signal detected from the spinning dipole antenna. Initial data reduction has isolated approximately 12 storms whose occurrence corresponded to times in which the spacecraft had an unobstructed view in the direction of Saturn. These events persisted over periods between one and ten minutes. Over the span of 500 days of data another 10 to 20 Saturnian events may exist, but positive identification is confused by the presence of terrestrial noise as well as a geometric ambiguity with Jupiter. A power spectral analysis of the storm occurrence times indicates a weak periodicity at 10h 30m + or - 5m at some of the observing frequencies. The spectral character of the radiation was found analogous to that of Jupiter.

Brown, L. W.↗

Oscillator strengths and electron collisional excitation cross sections for atomic oxygen

The electron-impact excitations of 12 states of O I are analyzed using a close-coupling approximation. The absorption oscillator strengths for dipole-allowed transitions among the states are calculated. Cross sections for excitation of the states by electron impact in the energy region 13.87 to 100 eV are compared with the data of Smith (1976) and Doering and Gulcicek. It is observed that there is a correlation between the data at energies 13.87, 20, and 30 eV for the (3)P-3p(5)P transition and at energies 13.87 and 16.5 eV for the (3)P-3s(5)S(0) transitions; however, for the dipole-allowed (3)P-3d(3)D(0) and (3)P-3s(prime)(3)D(0) transitions there are discrepancies in magnitude.

Tayal, S. S.↗

The ring arcs of Neptune

After the corotation resonance with an exterior satellite proved inapplicable to the Neptune ring arc confinement, a search for other mechanisms settled on the possible influence of Neptune's magnetic field. The areas of greater optical depth around the ring are much dustier than the low optical depth regions. These particles reside in a plasma; therefore, they must carry some charge. The components of Neptune's magnetic field on the equator at the radius of the ring arcs as a function of Neptunian longitude are shown. The components are those of an offset tilted dipole model. Although the dipole model is probably not a good approximation so close to the planet, the magnitude of the field that is given is probably close to the actual value. The possible importance of the magnetic field on the smallest particles in the ring is indicated by the ratio of the magnetic field on the smallest particles in the ring is indicated by the ratio of the magnetic force to the central gravitation attraction with the field strength of B = 0.01 gauss at the ring distance. A preferred position in the orbit for magnetically perturbed particles seems to require a commensurability between the rotation of the planet and the motion of the particle in the orbit. The period of rotation is assumed to be that of the radio bursts at 16.11 hours. However, without a model for the radio emission, one cannot be absolutely sure. Jupiter's decametric radiation depends on Io's orbital position as well as the rotation, so a synodic periodicity might be appropriate. But the latter radiation is highly directed, whereas Neptune's was seen all along the spacecraft trajectory on the 16.11 hour schedule, i.e., with no shifts in phase relative to a fixed longitude on the planet. The ring orbital period is 10.536 hours which is not commensurate with the rotation period. If the 16.11 hours is interpreted as a synodic period between the rotation and a satellite motion, the closest rotation periods to 16 hours are 15.9 hours if the satellite is 1989N4 and 18.2 hours if the satellite is Triton. The former is near a 3:2 resonance with the ring particle motion. The problem deserves some more thought before a possible herding of small particles by the magnetic field is abandoned.

Peale, S. J.↗

Do large rate coefficients for ion-polar neutral reactions have a serious effect on chemical models of dense clouds?

In order to incorporate large ion-polar neutral rate coefficients into existing gas phase reaction networks, it is necessary to utilize simplified theoretical treatments because of the significant number of rate coefficients needed. The authors have used two simple theoretical treatments: the locked dipole approach of Moran and Hamill for linear polar neutrals and the trajectory scaling approach of Su and Chesnavich for nonlinear polar neutrals. The former approach is suitable for linear species because in the interstellar medium these are rotationally relaxed to a large extent and the incoming charged reactants can lock their dipoles into the lowest energy configuration. The latter approach is a better approximation for nonlinear neutral species, in which rotational relaxation is normally less severe and the incoming charged reactants are not as effective at locking the dipoles. The treatments are in reasonable agreement with more detailed long range theories and predict an inverse square root dependence on kinetic temperature for the rate coefficient. Compared with the locked dipole method, the trajectory scaling approach results in rate coefficients smaller by a factor of approximately 2.5.

Herbst, E.↗

Modeling of Jovian Hectometric Radiation Source Locations: Ulysses Observations

The Unified Radio and Plasma Wave (URAP) experiment on Ulysses has provided unique high latitude measurements of Jovian hectometric radiation (HOM) during its encounter with Jupiter in February 1992. URAP was the first radio instrument in the Jovian environment with radio direction-finding capability, which was previously used to determine the HOM source locations in the Jovian magnetosphere. These initial source location determinations were based on several assumptions, including the neglect of refractive effects, which may be tested. We have, for the first time, combined the measured incident ray-direction at the spacecraft with a model magnetosphere to directly trace the rays back to the HOM source. We concentrate on the observations of HOM from high northern latitudes when Ulysses was at distances less than 15 R(sub j). The three- dimensional ray-tracing calculations presented here indicate that the HOM sources probably lie on L shells in the range 3 less than or approximately equal to L less than 7 (tilted dipole magnetic field model) consistent with previous determinations that ignored the effects of refraction. The ray-tracing results, however, indicate that wave refraction due to the Io torus and the magnetic field can significantly influence the precise source location. We show that constraints on the locations imposed by the gyroemission mechanism suggest that the lo torus density may have experienced temporal and/or spatial fluctuations during the Ulysses observations of HOM. Finally, in the cold plasma approximation we demonstrate that even if the emission were nearly linearly polarized near the source region, almost circular polarization will be observed at Ulysses, in agreement with observations.

Menietti, J. D.↗