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In a previous paper, the global variation of the magnetic field and solar wind flow parameters in the unshocked region upstream of an outgassing comet was determined using a kinetic treatment for the cometary ions. Two different assumptions were made concerning the cometary ion distribution function: the pickup cometary ions formed either a velocity space gyrotropic ring distribution or a velocity space isotropic shell distribution in the solar wind frame of reference. In the present paper the general case is considered wherein the newly picked up ions are elastically pitch angle scattered from the initial ring distribution to a shell with some characteristic time scale. Using theoretically determined parameters which reflect the conditions expected at Comet Kopff (a typical short-period comet and a possible target for the CRAF/Cassini mission) for various heliocentric distances, how the pitch angle scattering rate affects the global morphology is determined.

Dust grains immersed in plasma become charged. The charge is determined by the plasma characteristics, by secondary and photoemission from the grain, by grain velocity, and at any given instant by the past time history of the charging currents. This charge affects the Coulomb drag on a grain moving through the plasma. It affects the motion of the grain in an electromagnetic field of a planetary magnetosphere, and it is involved in the formation of the spokes in Saturn's rings and in the erosion of the rings by micrometeorites. And finally, it affects the coagulation rate of dust into larger bodies.

The magnetic field and solar wind flow parameters in the vicinity of a weakly outgassing comet are determined using a self-consistent model which treats the cometary ions kinetically. Two different assumptions are made concerning the cometary ion distribution function; the pickup cometary ions from either a velocity space gyrotropic ring distribution or a velocity space isotropic shell distribution in the solar wind frame of reference. The individual currents due to the solar wind and cometary ions, which determine the magnetic field, are calculated in each case. Using theoretically determined parameters which reflect the conditions expected to comet Kopff (a typical short-period comet and one possible target for the future CRAF/Cassini mission) for various heliocentric distances, the way in which global field and flow characteristics are influenced by the nature of the cometary ion distribution function is determined.

Expressions are given for the drag due to Coulomb collisions on a charged dust grain moving through a plasma. The commonly used Chandrasekhar (1943) result does not include large scattering angles or plasma collective effects. An equation given by Morfill et al. (1980) which does include large scattering angles, is limited to one-dimensional plasma particle motion and can give at least an order of magnitude too much drag. This paper also makes use of an analogy between the drag problem and problems in electrostatics. This analogy permits generalization to any isotropic plasma of an observation made by Chandrasekhar for a Maxwellian, namely, that the drag is independent of the presence or absence of plasma particles moving faster than the grain. Finally, the contribution of plasma collective effects to the drag is studied with the inclusion of large scattering angles.

The 'gyrophase drift' phenomenon in Jupiter's fine-dust 'gossamer ring' is presently shown to exceed the plasma-drag drift, and may be able to move small, charged grains either toward or away from synchronous radius. The grain gyrophase drifts toward the higher temperature in the presence of a radial gradient in plasma temperature; gyrophase drift will also occur in conjunction with a radial gradient in the relative concentrations of different plasma ion species, or even due to plasma-grain velocity variation associated with the grain's cycloidal motion through the plasma. The Poynting-Robertson drift is noted to be diminutive by comparison with either the plasma-drag or gyrophase drifts.

An erosional model of Saturn's rings is proposed based on theoretical studies of the high charge-to-mass ratio particles in Saturn's ring plane, and assuming that the B and C rings were initially formed as one ring with the optical thickness of the present B ring. The erosion rate is calculated using data from observed micrometeorite fluxes, and a ring age of 4.4-76 Myr is determined which is inconsistent with the 4.5-Gyr ring lifetime required by the cosmogonic ring hypothesis. The sharpness of the transition between the B and C rings suggests that the principal mass loss is through particles moving at a few m/sec with respect to the parent bodies from which they were eroded.

The theory for the generalized first invariant for adiabatic motion of charged particles in regions where there are large gradients in magnetic or electric fields is developed. The general condition for an invariant to exist in such regions is that the potential well in which the particle oscillates change its shape slowly as the particle drifts. It is shown how the Kruskal (1962) procedure can be applied to obtain expressions for the invariant and for drift velocities that are asymptotic in a smallness parameter epsilon. The procedure is illustrated by obtaining the invariant and drift velocities for particles traversing a perpendicular shock, and the generalized invariant is compared with the magnetic moment, and the drift orbits with the actual orbits, for a particular case. In contrast to the magnetic moment, the generalized first invariant is better for large gyroradii (large kinetic energies) than for small gyroradii. Expressions for the invariant when an electrostatic potential jump is imposed across the perpendicular shock, and when the particle traverses a rotational shear layer with a small normal component of the magnetic field are given.

Frequently, a detector on a spinning spacecraft measures the flux of charged particles whose velocities lie in a plane containing the magnetic field. This flux may be Fourier analyzed as a function of the spacecraft roll angle. Relationships among the Fourier coefficients are derived using the adiabatic solution of the Vlasov equation. These relationships depend only on the fact that the lowest order (in gyroradius) of the distribution function is a function of the magnetic moment and that the first-order term is a function of the lowest order. These relationships may be used to separate the proton from the electron counts registered in Saturn's inner magnetosphere by the University of California's Cerenkov counter on Pioneer 11.

The Cerenkov detector on Pioneer 11 previously observed Crand protons above 600 MeV in Saturn's inner magnetosphere, mixed with a poorly understood background of energetic electrons. The electron count is separated from the proton counts and the first-order angular distributions are established for each species. To do this the theoretical relationships among the harmonic coefficients of the count rate is used as a function of spacecraft roll angle. The majority of the counts were electrons with energy above several MeV; i.e., with drift periods shorter than the satellite orbital resonance. The electrons have isotropic pitch angle distributions, and the protons pancake over most of the region between Nimas and the rings, although there is a small region of dumbbell proton distributions in the vicinity of Janus and Epimetheus.

The potential distribution in a plasma containing dust grains were derived where the Debye length can be larger or smaller than the average intergrain spacing. Three models were treated for the grain-plasma system, with the assumption that the system of dust and plasma is charge-neutral: a permeable grain model, an impermeable grain model, and a capacitor model that does not require the nearest neighbor approximation of the other two models. A gauge-invariant form of Poisson's equation was used which is linearized about the average potential in the system. The charging currents to a grain are functions of the difference between the grain potential and this average potential. Expressions were obtained for the equilibrium potential of the grain and for the gauge-invariant capacitance between the grain and the plasma. The charge on a grain is determined by the product of this capacitance and the grain-plasma potential difference.

Voyager 1 and 2 observations of the Saturnian ring system have led to the discovery of several interesting phenomena associated with its fine dust component. The dust grains are immersed in a plasma. The present paper is concerned with the electrostatics of a dusty plasma, giving particular attention to the capacitance and charge of an individual grain in the presence of neighboring grains and the surrounding plasma. The Poisson equation and gauge considerations are discussed along with a solution of the Poisson equation for several models, taking into account impermeable grains, permeable grains, and a spherical capacitor model. A comparison of potential shapes for three models is conducted, and the effect of neighbors on charging currents is explored.

The newly discovered gossamer ring of Jupiter, composed largely of micron-sized grains, exhibits a significant peak very near the synchronous radius. It is believed that this peak is associated with an unobserved source consisting of large bodies that straddle the synchronous orbit. An alternative evolutionary mechanism is offered, which is the gyrophase drift towards the synchronous orbit, of fine grains, which necessarily are electrostatically charged within the Jovian magnetosphere.

In this paper the theory of charged test particle motion in magnetic fields is reviewed. This theory is then extended to charged dust particles, for which gravity and charge fluctuations play an important role. It is shown that systematic drifts perpendicular to the magnetic field and stochastic transport effects may then have to be considered none of which occur in the case of atomic particles (with the exception of charge exchange reactions). Some applications of charged dust particle transport theory to planetary rings are then briefly discussed.

The sharp, 90-km wide transition from an optical depth of 0.2 in the C ring to 1 in the B ring begins at 91,970 km from Saturn's center. This radius is found to be almost exactly at the inward stability limit of charged particles launched in the ring plane at the local Kepler velocity, provided these particles have large charge to mass ratio. The zonal harmonic models of Saturn's magnetic field from the Voyager data and the gravitational field model from Pioneer data are essential to get the very close agreement between theory and observation. The theoretical stability limits are 91,973 + or - 145 km from Voyager 1 magnetic field data and 91,991 + or 145 km from Voyager 2 magnetic data. The zonal harmonic magnetic field lines are not perpendicular to the ring plane. Therefore, in addition to the magnetic mirror, gravitational, and centrifugal forces, an unknown force must be postulated to produce equilibrium in the ring plane and make the stability calculation meaningful.

Adiabatic equations of motion are derived for the micrometer-sized dust grains detected in the Jovian and Saturn magnetospheres by the Pioneer 10 and 11 spacecraft. The adiabatic theory of charged particle motion is extended to the case of variable grain charge. Attention is focused on the innermost and outermost limits to the grain orbit evolution, with all orbits tending to become circular with time. The parameters such as the center equation of motion, the drift velocity, and the parallel equation of motion are obtained for grains in a rotating magnetosphere. Consideration is given to the effects of periodic grain charge-discharge, which are affected by the ambient plasma properties and the grain plasma velocity. The charge-discharge process at the gyrofrequency is determined to eliminate the invariance of the magnetic moment and cause the grain to exhibit radial movement. The magnetic moment increases or decreases as a function of the gyrophase of the charge variation.

The boundary between the inner and outer parts of Saturn's B ring is located at the theoretical limit of stability of dust grains with large negative charge to mass ratio. A grain inside of this stability limit will move along magnetic field lines and strike Saturn if given a slight velocity component normal to the ring plane. Outside of this marginal stability radius, a perturbed grain merely oscillates back and forth through the ring plane. The theoretical location of the marginal stability radius is at 1.625 Saturn radius. Observations by Pioneer 11 and Voyager 2 in the infared see the boundary as a prominent change in ring brightness at this radius. The occultation of delta-Scorpii by the rings in the ultraviolet seen by Voyager 2 shows about a factor of two change in optical depth beginning very close to this radius.

It is noted that an observed deviation of the angular velocity of spoke features from the Keplerian value can yield the charge to mass (q/m) ratio of spoke particles. Observations in the literature of spoke motion are consistent with q/m in the neighborhood of -10 coul/kg. Since a lower limit on q is one electronic charge, this value yields a lower limit to the size of spoke particles of approximately 0.01 micron. The criteria for electrostatically ejecting small particles from larger parent bodies suggest an upper limit of approximately 1,000 m for the parent bodies. The stability of the grains to electrostatic disruption or field emission yields an upper limit of approximately 3 microns for the spoke particle size. It also leads to the conclusion that the spoke particles must consist of material that is stronger than loose dust balls.

Some aspects of adiabatic drift theory are investigated in the regime where the E x B drift velocity is comparable with or larger than the gyro velocity. Particles undergo five drifts in addition to the E x B gradient, and line curvature drifts have three more terms in the parallel equation of motion. The case of the rapidly rotating rigid magnetic field configuration is found to be an exception due to the corotating particle with a nearly periodic motion. The guiding center drift velocity and parallel differential equation of motion are obtained, and the drift velocity in the rotating frame is found to consist of the expected field gradient and line curvature drift, plus centrifugal and coriolis force induced drifts. It is shown that the second invariant is conserved in the rotating frame by the four drifts, so that a particle slowly drifts around on its drift shell and returns to its original field line. Thus, there is no long term energy change, and any energy change is periodic on the bounce and drift time scale.

The dynamics of micron and submicron sized dust grains moving under the combined influence of planetary gravitation and the electromagnetic forces within the corotating regions of planetary magnetospheres are discussed. Magnetogravitational capture of charged grains in planetary rings is outlined. The adiabatic motion of charged dust is reviewed.

The paper investigates conditions under which a diffusion equation is a valid description of the transport across magnetic field lines of low energy magnetospheric plasma. The case in which the guiding center drift and its fluctuating component are comparable in size to the particle thermal speed is considered. It is concluded that a two-dimensional diffusion equation is valid in the alpha-beta space of the Euler potentials, provided that the fluctuations have a short enough correlation time so that the guiding center drifts remain negligible, and ions in Jupiter's Io plasma torus can thus be described by a diffusion equation if the correlation time is no more than a few rotation periods of the planet.

The theory and technique of Northrop and Thomsen (1980) are applied to the observations of energy spectra and directional anisotropies of 0.61- to 3.41 MeV protons in Saturn's magnetosphere. The observations were made by the Goddard Space Flight Center/University of New Hampshire and University of Iowa instruments aboard Pioneer 11 during the Pioneer encounter with Saturn in August-September 1979. Fourier fits to 15-min intervals of data are combined with spectral indices to yield information about the E x B convection velocity and temporal changes in the particle population. There is a fundamental inability to distinguish unambiguously between the two, but if one can be assumed, the other then follows from these calculations. It is found that although these data do not by themselves allow an unambiguous determination of the extent of corotation in Saturn's outer magnetosphere, they are consistent with exact corotation at the nominal rotation period in the presence of significant but not unreasonable temporal variations in the energetic proton population.

When a spacecraft detector measures particle flux as a function of look direction in a plane (the scan plane), anisotropy is often seen. This anisotropy is caused by spatial gradients, by E x B particle drift, and by various spectral and geometric effects. This paper treats all of these effects systematically, starting from the nonrelativistic Vlasov equation. The general analysis is applied to a simple model of an anisotropic distribution to give a relation between the E x B drift, the gradient and the experimentally observed first, second, and third harmonics of the flux as a function of angle in the scan plane. Even with an assumed model, anisotropy observations in one plane alone do not suffice to determine the E x B drift velocity and the spatial gradient independently. If the E x B velocity is assumed (e.g., the corotational velocity in a rotating planetary magnetosphere), the spatial gradient may be deduced, and from it the time rate of change of flux in a nonrotating frame of reference.

Phenomena associated with the bowshock, such as its thickness, velocity, and associated waves are described. There are transverse waves radiating away from the shock and at times stationary waves fixed to it. Reflected protons generate waves far upstream. Electrostatic waves occur in the shock.

Solar wind, earth's bowshock, and magnetospheric convection and substorms were investigated. Topics discussed include computational physics, multifluid codes, ionospheric irregularities, and modeling laser plasmas.

The maximum count rates of energetic particles are observed earlier on the inbound pass and later on the outbound pass than one would expect if the Jovian magnetodisk moved rigidly with the planet. This lead and lag cannot be explained by the observed azimuthal distortion of the Jovian magnetic field alone. A possible explanation is that the foot of a magnetic field line in the ionosphere slips with respect to Jupiter's surface. The rate of slippage and the electric field necessary for this is estimated. The electric field may be as large as 2 V/m in the Jovian polar ionosphere.

Two different models for the distribution function are fit to the Jovian protons seen by Pioneer 10 inbound. The models reproduce the observed energy and angular distributions. These models are then used to assess the collisionless mirror instability. Because of the pancake proton angular distributions in the equatorial ring current region, the ring current particle population appears to be mirror unstable at times, with instability growth rates of about 10 min. Such a time is consistent with observed proton flux autocorrelation times. An instability such as this (there are other candidates) may be responsible for the previously established proton flux flowing parallel to the magnetic field away from the equatorial region.

The magnitude of the strong flow of 1.79-2.15 MeV protons away from the Jovian magnetic equator is used to estimate the residence lifetimes of these protons in the equatorial source region. The lifetime is approximately 1.2 x 10 to the 5th/(R - 5.8)-squared sec, where R is distance in Jovian radii from Jupiter's center to the equatorial region of interest. At Europa and Ganymede (but not at Io) this lifetime is 1-2 orders of magnitude shorter than sweepup lifetimes by the moons. The fluxes of these protons, integrated over the observed range from 6 to 40 Jovian radii, amount to 3 x 10 to the 23rd particles per second, per degree of longitude and carry away about 9 x 10 to the 17th ergs per second per degree.

One-hour-averaged fluxes of 1.8- to 2.15-MeV protons observed by the LET2 detector on Pioneer 10 on the inbound trajectory showed anisotropies attributable to corotation of Jupiter's magnetodisc only when Pioneer was near the dipole equator. Most of the time the anisotropy greatly exceeded the value expected from corotation. Gradients in the distribution function can be used to account for this excess anisotropy, but the amount of gradient required is unacceptably large by 1-2 orders of magnitude. If they were taken as real, these gradients would predict almost complete disappearance of these protons from Jupiter's magnetosphere in a matter of hours. The remedy is to introduce into the model of the distribution function proton flow along field lines away from the equator into both the southern and the northern hemisphere. The parallel flux at the southernmost latitudes reached by Pioneer can reach 25% of the product of proton density and velocity, i.e., 25% of the maximum possible.

Assuming time stationarity of the one-particle distribution function f on the scale of the bounce motion of particles in a magnetic field, the paper expands the Vlasov equation through O(epsilon) in the adiabatic parameter epsilon, which is the ratio of particle gyroradius to scale length of the magnetic field. Since f is directly proportional to particle flux differential in kinetic energy and solid angle, f is in principle measurable in space experiments, and the present analysis is tailored to be explicitly applicable to space problems. It is shown that the usual expression for the electric field which produces plasma corotation in an axisymmetric system such as a dipole also holds for any nonaxisymmetric but rigidly rotating magnetic field pattern, provided the observed magnetic field is used in place of the dipole field. The analysis is applied to the electric field in a rigidly corotating magnetosphere.

In a static magnetic field, some well-known guiding-center equations maintain their form when extended to next order in gyroradius. In these cases, it is only necessary to include the next order term in the magnetic moment series. The differential equation for guiding-center motion which describes both the parallel and perpendicular velocities correctly through first order in gyroradius is given. The question of how to define the guiding center position through second order arises and is discussed, and second order drifts are derived for one usual definition. The toroidal canonical angular momentum, P-phi, of the guiding center in an axisymmetric field is shown to be conserved using the guiding center velocity correct through first order. When second-order motion is included, P-phi is no longer a constant. The above extensions of guiding-center theory help to resolve the different tokamak orbits obtained either by using the guiding-center equations of motion or by using conservation of P-phi.

The one particle distribution function f on the scale of the bounce motion of particles in a magnetic field B is considered. The Vlasov equation is expanded through O(epsilon) in the adiabatic parameter which is the ratio of particle gyroradius to scale length of the magnetic field. Because f is directly proportional to particle flux differential in kinetic energy and solid angle, f is in principle measurable in space experiments, and the analysis is tailored to be explicitly applicable to space problems. To O(1), f is gyrotropic; its first velocity moment is (if non-vanishing) parallel to B, and hence macroscopic parallel flow is included in this term. The O(epsilon) contribution is non-gyrotropic and macroscopic flow parallel to B plus additional parallel flow results from these terms. The degree of non-gyrotropy and the amount of cross-field macroscopic flow depend on the perpendicular component of the electric field, on curvature and shear in the magnetic field, and on the spatial gradient, pitch angle derivative, and speed derivative of the lowest order distribution function.

Charged-particle pitch-angle distributions at one point on a magnetic drift surface in a rapidly rotating axisymmetric mirroring system (such as Jupiter's magnetosphere would be in the absence of the 10-deg dipole tilt) are related to those at another point by Liouville's theorem. If the distribution function in the rotating frame is gyrotropic; i.e., if it is independent of the phase angle of the gyration, it is gyrotropic at all points on that drift surface. Examples are given of 'pancake', 'dumbbell', and isotropic distributions when they are observed from the nonrotating frame at different points on a drift surface.

The perturbation vectors of waves up and downstream from the region of maximum compression in the bow shock were examined on OGO-5 under particularly steady solar wind conditions. The polarization of the upstream waves was RH, circular and of the downstream waves LH, elliptical in the spacecraft frame. By observing that the polarization of the waves remained unchanged as the shock motion swept the wave structure back and forth across the satellite three times in eight minutes, it was found that the waves were not stationary in the shock frame. A study of the methods of determining the shock normal indicates that the normal estimated from a shock model should be superior to one based upon magnetic coplanarity. The propagation vectors of the waves examined did not coincide with the shock model normal, the average magnetic field, or the plasma flow velocity. However, the major axis of the polarization ellipse of the downstream wave was nearly parallel to the upstream propagation vector.

Stationary waves produced by earth bow shock, calculating cyclotron radiation amplitude and polarization characteristics by thin current sheet model

MHD stability of tangential discontinuities in solar wind flow

Stationary cyclotron waves produced by earth bow shock

Spectrum of plasma wave emission by collisionless shock transition

Bounce averaged rate of kinetic energy change of trapped charged particles in magnetic and electric fields, using second adiabatic theory

Equation describing statistically trapped particle motion under influence of fields varying in time and space

Equation describing statistically trapped particle motion under influence of fields varying in time and space

Charged particle energization by arbitrarily moving magnet

Second term obtained in asymptotic series for second adiabatic invariant of charged particle motion in static magnetic field and found to vanish at mirror points

First correction to second adiabatic invariant of charged particle motion in magnetic field

Adiabatic theory of charged particle motion, considering first-order effects in radius of gyration and Alfven theory