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NASA NTRS1988

Catalytic ignition of hydrogen and oxygen propellants

An experimental program was conducted to evaluate the catalytic ignition of gaseous hydrogen and oxygen propellants. Shell 405 granular catalyst and a monolithic sponge catalyst were tested. Mixture ratio, mass flow rate, propellant temperature, and back pressure were varied parametrically in testing to determine the operational limits of the catalytic igniter. The test results show that the gaseous hydrogen and oxygen propellant combination can be ignited catalytically using Shell 405 catalyst over a wide range of mixture ratios, mass flow rates, and propellant injection temperatures. These operating conditions must be optimized to ensure reliable ignition for an extended period of time. A cyclic life of nearly 2000, 2 sec pulses at nominal operating conditions was demonstrated with the catalytic igniter. The results of the experimental program and the established operational limits for a catalytic igniter using the Shell 405 catalyst are presented.

Zurawski, Robert L.↗

NASA NTRS1988

Catalytic ignition of hydrogen and oxygen propellants

Zurawski, Robert L.↗

NASA NTRS2014

Water Delivery and Giant Impacts in the 'Grand Tack' Scenario

A new model for terrestrial planet formation has explored accretion in a truncated protoplanetary disk, and found that such a configuration is able to reproduce the distribution of mass among the planets in the Solar System, especially the Earth/Mars mass ratio, which earlier simulations have generally not been able to match. Walsh et al. tested a possible mechanism to truncate the disk-a two-stage, inward-then-outward migration of Jupiter and Saturn, as found in numerous hydrodynamical simulations of giant planet formation. In addition to truncating the disk and producing a more realistic Earth/Mars mass ratio, the migration of the giant planets also populates the asteroid belt with two distinct populations of bodies-the inner belt is filled by bodies originating inside of 3 AU, and the outer belt is filled with bodies originating from between and beyond the giant planets (which are hereafter referred to as 'primitive' bodies). One implication of the truncation mechanism proposed in Walsh et al. is the scattering of primitive planetesimals onto planet-crossing orbits during the formation of the planets. We find here that the planets will accrete on order 1-2% of their total mass from these bodies. For an assumed value of 10% for the water mass fraction of the primitive planetesimals, this model delivers a total amount of water comparable to that estimated to be on the Earth today. The radial distribution of the planetary masses and the dynamical excitation of their orbits are a good match to the observed system. However, we find that a truncated disk leads to formation timescales more rapid than suggested by radiometric chronometers. In particular, the last giant impact is typically earlier than 20 Myr, and a substantial amount of mass is accreted after that event. This is at odds with the dating of the Moon-forming impact and the estimated amount of mass accreted by Earth following that event. However, 5 of the 27 planets larger than half an Earth mass formed in all simulations do experience large late impacts and subsequent accretion consistent with those constraints.

Planetary dynamics↗

NASA NTRS1995

Fibonacci chain polynomials: Identities from self-similarity

Fibonacci chains are special diatomic, harmonic chains with uniform nearest neighbor interaction and two kinds of atoms (mass-ratio r) arranged according to the self-similar binary Fibonacci sequence ABAABABA..., which is obtained by repeated substitution of A yields AB and B yields A. The implications of the self-similarity of this sequence for the associated orthogonal polynomial systems which govern these Fibonacci chains with fixed mass-ratio r are studied.

Lang, Wolfdieter↗

NASA NTRS1961

An Automatic Terminal Guidance System for Rendezvous with a Satellite

This study includes a consideration of the design philosophy for an automatic terminal guidance system, a derivation of guidance equations required, and an outline of the general type of instrumentation necessary to provide the essential information. A control system for a sample vehicle is analyzed. A representative case, rendezvous with a satellite in circular orbit at 400 nautical miles, was examined. Terminal-stage nominal burning times of 200 and 400 seconds were used. For the 200-second case, initial errors in circumferential displacement of +/- 25,000 feet, in radial displacement of 7,000 to -9,000 feet, and in lateral displacement of +/- 20,000 feet were within the capabilities of the system. Velocity errors of 300 to -400 ft/sec in the circumferential direction, 180 to -200 ft/sec in the radial direction, and velocity offsets of at least 20 (+/- 800 ft/sec) in the lateral direction could also be handled. The 400-second case was capable of correcting larger errors, but limits were not determined. The dependence of required characteristic velocity on initial errors was determined and it was found that increases over the nominal terminal-stage characteristic velocity of the order of 15 percent covered most of the previously mentioned in-plane errors. The requirements were more severe for cases with lateral velocity offsets. A simplified set of guidance equations was tested and produced only slight variations in performance. Overall velocity requirements and mass ratios were determined for terminal-stage burning times of 100, 200, 300, and 400 seconds and for a range of transfer angles by using exact calculations for the terminal stage and an impulsive launching velocity. These results indicated that the shortest burning time consistent with the launch guidance errors expected gave the best mass ratio.

Carney, Terrance M.↗

NASA NTRS1993

Experimental studies on effervescent atomizers with wide spray angles

An experimental investigation was conducted to examine the operating and spray characteristics of two internal-mixing twin-fluid atomizers that were designed to produce effervescent atomization at low air/liquid mass ratios (ALR's). These two experimental atomizers ejected the two phase flow so as to produce a wide spray angle. One atomizer was a plain orifice design that used a four-hole exit orifice which divided and turned the two phase flow just prior to ejection. The other atomizer, called the conical sheet atomizer, ejected the two phase flow through an annular passage in such a way as to form a hollow cone spray. The atomizer operating parameters varied during this investigation were the air/liquid mass ratio, atomizer operating pressure, and, in the case of the conical sheet atomizer, the exit gap width. Studies of spray characteristics included measurements of the spray Sauter mean diameter (SMD), drop size distribution, and, for the conical sheet atomizer, circumferential distribution of the liquid mass within the spray. For both atomizers it was found that SMD decreases with an increase in either ALR or operating pressure. The effect of ALR on SMD diminishes as the value of ALR increases. For the conical sheet atomizer, when operating at low values of pressure and ALR, SMD increases with increase in gap width, but the influence of gap width on SMD diminishes with an increase in either pressure or ALR. At the highest operating pressure of the conical sheet atomizer (552 kPa), SMD is independent of gap width at all ALR's. For both atomizers, changes in operating pressure and ALR have little effect on the distribution of drop sizes in the spray.

Whitlow, J. D.↗

NASA NTRS1994

First measurement of helium on Mars: Implications for the problem of radiogenic gases on the terrestrial planets

108 +/- 11 photons of the martian He 584-A airglow detected by the Extreme Ultraviolet Explorer (EUVE) satellite during a 2-day exposure (January 22-23, 1993) correspond to the effective disk average intensity of 43 +/- 10 Rayleigh (Ra). Radiative transfer calculations, using a model atmosphere appropriate to the conditions of the observation and having an exospheric temperature of 210 +/- 20 K, result in a He mixing ratio of 1.1 +/- 0.4 ppm in the lower atmosphere. Nonthermal escape of helium is due to electron impact ionization and pickup of He(+) by the solar wind, to collisions with hot oxygen atoms, and to charge exchange with molecular species with corresponding column loss rates of 1.4 x 10(exp 5), 3 x 10(exp 4), and 7 x 10(exp 3)/sq cm/s, respectively. The lifetime of helium on Mars is 5 x 10(exp 4) years. the He outgassing rate, coupled with the Ar-40 atmospheric abundance and with the K:U:Th ratio measured in the surface rocks, is used as input to a single two-reservoir degassing model which is applied to Mars and then to Venus. A similar model with known abundances if K, U, and Th is applied to Earth. The models for Earth and Mars presume loss of all argon accumulated in the atmospheres during the first billion years by large-scale meteorite and planetesimal impacts. The models show that the degassing coefficients for all three planets may be approximated by function delta = delta(sub 0) x (t(sub 0)/t)(exp 1/2) with delta(sub 0) = 0.1, 0.04, and 0.0125 Byr for Earth, Venus, and Mars, respectively. After a R(exp 2) correction this means that outgassing processes on Venus and Mars are weaker than on Earth by factors of 3 and 30, respectively. Mass ratios of U and Th are almost the same for all three planets, while potassiumis depleted by a factor of 2 in Venus and Mars. Mass ratio of helium and argon are close to 5 x 10(exp -9) and 2 x 10(exp -8) g/g in the interiors of all three planets. The implications of these results are discussed.

Krasnopolsky, V. A.↗

NASA NTRSDate not supplied

Soluble Organic Matter (SOM) analysis of the Hayabusa2 samples: The first results

The Hayabusa2 spacecraft successfully collected the surface and possible sub-surface materials of the asteroid 162173 Ryugu. Ryugu is a C-type asteroid characterized by a low-albedo surface probably consisting of hydrous minerals and carbonaceous materials. [1] The direct optical and spectral analysis of the returned samples indicates that Ryugu material is dominated by hydrous carbonaceous chondrite-like matter (similar to CI chondrites) [2]. Since carbonaceous chondrites have generally yielded various types of organic matter, the collected Ryugu grains are expected to contain diverse types of organic compounds including bio-related molecules. The occurrence of organic compounds in the Ryugu surface will provide clues to the evolution of prebiotic molecules and their preservations associated with aqueous alteration of the primitive asteroid. The initial analysis of soluble organic matter (SOM) of the Hayabusa2-returned samples has been performed by an international team consisting of 32 members. Because the sample amount available for comprehensive SOM analyses is limited, and because the SOM is expected to be present as a complex mixture of various types of organic compounds with very small concentrations of each compound, high-sensitivity and high-resolution analytical techniques have been developed using carbonaceous meteorites [e.g. 3]. Two aggregate samples of the Ryugu grains (A106 and C107) were allocated for the solvent extractions and bulk carbon (C), hydrogen (H), nitrogen (N), sulfur (S) and oxygen (O) measurements. The A106 sample was collected during the 1st sampling in February 2019 and the C107 sample was collected during the 2nd sampling in July 2019 after the Small Carry Impactor (SCI) operation. They consist mainly of particles smaller than 1 mm in diameter, and each sample mass was 38-39 mg. They were firstly investigated spectroscopically in the near infrared wavelength range by the Stone Team prior to the solvent extractions. Other small grains (A0080 and C0057) were also allocated for this study to investigate the spatial distribution of organic compounds on the sample surface. The extraction and analytical measurements implemented by the SOM Team are summarized in Figure 1. Each powder sample was extracted sequentially with non-polar to polar solvents, i.e., hexane, dichloromethane (DCM), methanol (MeOH) and H2O, for non-targeted analysis to reveal the compound composition. Each solvent extract was analyzed by solution state nuclear magnetic resonance (NMR) spectroscopy [4], Fourier transform- ion cyclotron resonance/mass spectrometry (FT-ICR/MS) with ESI and APPI ionization [5] and by high-resolution mass spectroscopy using Orbitrap MS coupled with nano-liquid chromatography (nanoLC/Orbitrap MS) [6], and using two dimensional gas chromatography/mass spectrometry (GC×GC/MS). The extracted residues were passed to the Chemistry Team for further inorganic element analysis. The other powder sample was subjected to the hot water extraction for amino acid analyses including chiral isomer separation, which was performed by three-dimensional (3D) high-performance liquid chromatography (HPLC) with high-sensitivity fluorescence detection (FD) [7] and by HPLC/FD coupled with quadrupole-time of flight/mass spectrometry (QToF/MS) [8]. After the hot water extraction, the residue was split into two halves. One half was further extracted with hydrochloric acid (HCl) to analyze for amino acids in bound-form. The other half was sequentially extracted with DCM/MeOH (1/1) to analyze semi-polar compounds such as polycyclic aromatic hydrocarbons (PAHs) by GC/MS, followed by further extraction with formic acid to analyze polar heterocyclic compounds, and subsequent extraction with HCl to detect bound-form polar compounds. The extracted residues were passed to the IOM Team for the analysis of insoluble organic matter (IOM). Compound-specific stable isotope analyses will be performed using GC/combustion/isotope ratio mass spectrometry (GC/C/IRMS) if the compound concentration is high enough to enable such an isotopic measurement. All extraction procedures were performed on an ISO 6 (Class 100) clean bench inside an ISO 5 (Class 1000) clean room. Baked serpentine powder was also analyzed as a procedural blank. In situ organic compound analysis with the molecular imaging was performed using desorption electrospray ionization (DESI) equipped with Orbitrap MS [9, 10], followed by spatial imaging of organic compounds using ToF/secondary ion mass spectrometry (ToF/SIMS) [11]. The bulk chemical and isotopic compositions of CNS and HO were determined using nano-elemental analysis/isotope ratio mass spectrometry (nanoEA/IRMS) [12] and EA/pyrolysis/IRMS, respectively. We have identified a variety of indigenous organic compounds in the extracts of both A106 and C107 samples. The Ryugu grains host organic molecules under the high-vacuum and cosmic-ray irradiation environment of the asteroid surface. The analysis of extracted molecules is in progress, and the first results will be presented at the symposium.

Hiroshi Naraoka↗

NASA NTRS1995

Interactive flutter analysis and parametric study for conceptual wing design

An interactive computer program was developed for wing flutter analysis in the conceptual design stage. The objective was to estimate the flutter instability boundary of a flexible cantilever wing, when well defined structural and aerodynamic data are not available, and then study the effect of change in Mach number, dynamic pressure, torsional frequency, sweep, mass ratio, aspect ratio, taper ratio, center of gravity, and pitch inertia, to guide the development of the concept. The software was developed on MathCad (trademark) platform for Macintosh, with integrated documentation, graphics, database and symbolic mathematics. The analysis method was based on nondimensional parametric plots of two primary flutter parameters, namely Regier number and Flutter number, with normalization factors based on torsional stiffness, sweep, mass ratio, aspect ratio, center of gravity location and pitch inertia radius of gyration. The plots were compiled in a Vaught Corporation report from a vast database of past experiments and wind tunnel tests. The computer program was utilized for flutter analysis of the outer wing of a Blended Wing Body concept, proposed by McDonnell Douglas Corporation. Using a set of assumed data, preliminary flutter boundary and flutter dynamic pressure variation with altitude, Mach number and torsional stiffness were determined.

Mukhopadhyay, Vivek↗

NASA NTRS1979

The split comets - Gravitational interaction between the fragments

The gravitational interaction between two fragments of a split comet nucleus in the sun's gravitational field is studied by means of the n-body computer program of Schubart and Stumpff (1966). Patterns of interactions are found for combinations of the masses, mass ratios and densities of the parent nucleus and the fragment, directions of separation, and regions of separation for nucleus separations occurring at perihelion and at true anomalies of +90 deg and -90 deg. It has been found that solar gravitational effects become noticeable about 0.5 to 1 day after separation at perihelion, and about 1 to 2 days after separation at twice the perihelion distance. Mass ratios and bulk density do not appreciably affect the appearance of the calculated trajectories. The calculated patterns vary from zero to very high inclinations, from a prograde to a retrograde sense of motion, and from escape of the companion to its pursuance of periodic quasi-stable orbits around the principal nucleus, terminated in some cases by collision of the fragments.

Sekanina, Z.↗

NASA NTRS1996

An Interactive Software for Conceptual Wing Flutter Analysis and Parametric Study

An interactive computer program was developed for wing flutter analysis in the conceptual design stage. The objective was to estimate the flutter instability boundary of a flexible cantilever wing, when well-defined structural and aerodynamic data are not available, and then study the effect of change in Mach number, dynamic pressure, torsional frequency, sweep, mass ratio, aspect ratio, taper ratio, center of gravity, and pitch inertia, to guide the development of the concept. The software was developed for Macintosh or IBM compatible personal computers, on MathCad application software with integrated documentation, graphics, data base and symbolic mathematics. The analysis method was based on non-dimensional parametric plots of two primary flutter parameters, namely Regier number and Flutter number, with normalization factors based on torsional stiffness, sweep, mass ratio, taper ratio, aspect ratio, center of gravity location and pitch inertia radius of gyration. The parametric plots were compiled in a Vought Corporation report from a vast data base of past experiments and wind-tunnel tests. The computer program was utilized for flutter analysis of the outer wing of a Blended-Wing-Body concept, proposed by McDonnell Douglas Corp. Using a set of assumed data, preliminary flutter boundary and flutter dynamic pressure variation with altitude, Mach number and torsional stiffness were determined.

Mukhopadhyay, Vivek↗

NASA NTRS1994

Dynamics of binary-disk interaction. 1: Resonances and disk gap sizes

We investigate the gravitational interaction of a generally eccentric binary star system with circumbinary and circumstellar gaseous disks. The disks are assumed to be coplanar with the binary, geometrically thin, and primarily governed by gas pressure and (turbulent) viscosity but not self-gravity. Both ordinary and eccentric Lindblad resonances are primarily responsible for truncating the disks in binaries with arbitrary eccentricity and nonextreme mass ratio. Starting from a smooth disk configuration, after the gravitational field of the binary truncates the disk on the dynamical timescale, a quasi-equilibrium is achieved, in which the resonant and viscous torques balance each other and any changes in the structure of the disk (e.g., due to global viscous evolution) occur slowly, preserving the average size of the gap. We analytically compute the approximate sizes of disks (or disk gaps) as a function of binary mass ratio and eccentricity in this quasi-equilibrium. Comparing the gap sizes with results of direct simulations using the smoothed particle hydrodynamics (SPH), we obtain a good agreement. As a by-product of the computations, we verify that standard SPH codes can adequately represent the dynamics of disks with moderate viscosity, Reynolds number R approximately 10(exp 3). For typical viscous disk parameters, and with a denoting the binary semimajor axis, the inner edge location of a circumbinary disk varies from 1.8a to 2.6a with binary eccentricity increasing from 0 to 0.25. For eccentricities 0 less than e less than 0.75, the minimum separation between a component star and the circumbinary disk inner edge is greater than a. Our calculations are relevant, among others, to protobinary stars and the recently discovered T Tau pre-main-sequence binaries. We briefly examine the case of a pre-main-sequence spectroscopic binary GW Ori and conclude that circumbinary disk truncation to the size required by one proposed spectroscopic model cannot be due to Linblad resonances, even if the disk is nonviscous.

Artymowicz, Pawel↗

NASA NTRS1960

Slow-Neutron Scattering by Rotators. II

The methods developed in a previous paper for extending the neutron scattering formalism of Zemach and Glauber to any type of molecular rotator have been employed to derive generalized forms generalized forms of the differential cross sections for rotator scattering. A mass-ratio expansion for the treatment of the high-energy limit is illustrated on the classical cross section and then employed in the treatment of the more general quantum-mechanical expression for the differential cross section. The results apply to an arbitrarily asymmetric rotator. The very low energy approximation is carried out for the symmetric rotator, and the procedure is compared with the explicit summing of the partial cross sections for individual rotational transitions. The inelastic correction to the static approximation for interference scattering is calculated to an accuracy of first order in the mass ratios for the case of the symmetric rotator.

Volkin, Howard C.↗

NASA NTRS1982

Anti-misting additives for jet fuels

The ignition characteristics of sprays, created by wind shear action, of Jet-A fuel containing polyisobutylene additives wee examined over ranges of air velocities from 45 to 90 m/s and of fuel/air mass ratios of 0.20 to 8.0. Ignition was by calibrated sparks of energies up to about 0.5 J and by a butane/oxygen flame at 165 J/s. The polymeric additives studied included the grades L80, L160, and L200 from Exxon Chemical and B200 and B230 from BASF. The ignition suppression ability of the additives, as well as their observed anti-misting (AM) behavior, ranked exactly as their molecular weights (viscosity average, M sub v) with 400-500 ppm of L80 (M sub v = 0.68 x 1,000,000) being required to suppress ignition of a spray at 51 m/s, 1.8 fuel/air mass ratio, by a 0.55 J spark while only 10 ppm of B230 (M sub v = 7.37 x 1,000,000) was required for the same conditions. The additive concentrations (L160) required for ignition suppression increased with increasing air velocity and with increasing fuel/air ratio.

Grens, E. A., II↗

NASA NTRS2022

KMT-2021-BLG-0171Lb and KMT-2021-BLG-1689Lb: Two Microlensing Planets in the KMTNet High-Cadence Fields With Followup Observations

Follow-up observations of high-magnification gravitational microlensing events can fully exploit their intrinsic sensitivity to detect extrasolar planets, especially those with small mass ratios. To make followup observations more uniform and efficient, we develop a system, HighMagFinder, to automatically alert possible ongoing high-magnification events based on the real-time data from the Korea Microlensing Telescope Network (KMTNet). We started a new phase of follow-up observations with the help of HighMagFinder in 2021. Here we report the discovery of two planets in high-magnification microlensing events, KMT- 2021-BLG-0171 and KMT-2021-BLG-1689, which were identified by the HighMagFinder. We find that both events suffer the ‘central-resonant’ caustic degeneracy. The planet-host mass-ratio is q ∼4.7 × 10 −5 or q ∼2.2 × 10 −5 for KMT-2021-BLG-0171, and q ∼2.5 × 10 −4 or q ∼1.8 × 10 −4 for KMT-2021-BLG-1689. Together with two other events, four cases that suffer such degeneracy have been discovered in the 2021 season alone, indicating that the de generate solutions may have been missed in some previous studies. We also propose a quantitative factor to weight the probability of each solution from the phase space. The resonant interpretations for the two events are disfavoured under this consideration. This factor can be included in future statistical studies to weight degenerate solutions.

Micro gravitational lensing↗

NASA NTRS2008

Mergers of Non-spinning Black-hole Binaries: Gravitational Radiation Characteristics

We present a detailed descriptive analysis of the gravitational radiation from black-hole binary mergers of non-spinning black holes, based on numerical simulations of systems varying from equal-mass to a 6:1 mass ratio. Our primary goal is to present relatively complete information about the waveforms, including all the leading multipolar components, to interested researchers. In our analysis, we pursue the simplest physical description of the dominant features in the radiation, providing an interpretation of the waveforms in terms of an implicit rotating source. This interpretation applies uniformly to the full wavetrain, from inspiral through ringdown. We emphasize strong relationships among the l = m modes that persist through the full wavetrain. Exploring the structure of the waveforms in more detail, we conduct detailed analytic fitting of the late-time frequency evolution, identifying a key quantitative feature shared by the l = m modes among all mass-ratios. We identify relationships, with a simple interpretation in terms of the implicit rotating source, among the evolution of frequency and amplitude, which hold for the late-time radiation. These detailed relationships provide sufficient information about the late-time radiation to yield a predictive model for the late-time waveforms, an alternative to the common practice of modeling by a sum of quasinormal mode overtones. We demonstrate an application of this in a new effective-one-body-based analytic waveform model.

Baker, John G.↗

NASA NTRS2022

Fayalite Formation Through Hydrothermal Experiments: Insights into Early Fluid-assisted Aqueous Alteration Processes on Asteroids

In order to understand the effects of the earliest fluid-assisted hydration processes on asteroids, we performed one hydrothermal experiment using three different reactants (FeO-rich amorphous silicates, iron metal powder, and water) at conditions informed by our current state of knowledge of asteroidal alteration. This experiment provides, for the first time, clear evidence that the growth of fayalite can occur during hydrotherma lalteration, as described previously in meteorites. These newly formed fayalite crystals are elongated and porous, similar to the ones described in CV3, CK, and ordinary chondrites. The results show that (1) fayalite could form even if chemical equilibrium was not reached in the experiment, at a water to rock mass ratio (0.4 W/R at the beginning of the experiment) higher than the values calculated to be thermodynamically viable at equilibrium(W/R > 0.2); (2) the composition and the texture of the reactants changed during the hydrothermal alteration process, suggesting that the reactants, especially the amorphous silicates, underwent dissolution and reprecipitation; (3) fayalite can form at low temperature(220°C), which is at the transition between hydrothermal alteration and fluid-assisted metamorphism in chondrites. The results are consistent with previous mineralogical observations and thermodynamic models, which suggest that fayalite crystals are formed on asteroidal parent bodies by the interaction between a hydrothermal fluid and disequilibrium assemblages that compose the pristine materials that condensed in the early solar nebula. This experiment suggests that two variables play a very important role in the formation off ayalite during the hydrothermal growth (W/R mass ratio and the fluid composition). These results are similar to the recent observations of the fine-grained matrix of ordinary chondrites.

E Dobrică↗

NASA NTRS1994

Charged dust in planetary magnetospheres: Hamiltonian dynamics and numerical simulations for highly charged grains

We use a combination of analytical and numerical methods to investigate the dynamics of charged dust grains in planetary magnetospheres. Our emphasis is on obtaining results valid for particles that are not necessarily dominated either by gravitational or electromagnetic forces. A Hamiltonian formulation of the problem yields exact results, for all values of charge-to-mass ratio, when we introduce two constraints: particles remain in the equatorial plane and the magnetic field is taken as axially symmetric. In particular, we obtain locations of equilibrium points, the frequencies of stable periodic orbits, the topology of separatrices in phase space, and the rate of longitudinal drift. These results are significant for specific applications: motion in the nearly aligned dipolar field of Saturn, and the trajectories of arbitrarily charged particles in complex magnetic fields for limited periods of time after ejection from parent bodies. Since the model is restrictive, we also use numerical integrations of the full three-dimensional equations of motion and illustrate under what conditions the constrained problem yields reasonable results. We show that a large fraction of the intermediately charged and highly charged (gyrating) particles will always be lost to a planet's atmosphere within a few hundred hours, for motion through tilted-dipole magnetic fields. We find that grains must have a very high charge-to-mass ratio in order to be mirrored back to the ring plane. Thus, except perhaps at Saturn where the dipole tilt is very small, the likely inhabitants of the dusty ring systems are those particles that are either nearly Keplerian (weakly charged) grains or grains whose charges place them in the lower end of the intermediate charge zone. Fianlly, we demonstrate the effect of plasma drag on the orbits of gyrating particles to be a rapid decrease in gyroradius followed by a slow radial evolution of the guiding center.

Schaffer, L.↗