Astronomy and Space Science Theory Group (ASSTG)

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Gravitoelectrodynamics of Charged Grains in Saturn's F Ring: Encounters with Prometheus and Pandora
(Journal of Physics A, 2003-09-12) Matthews, Lorin Swint.; Hyde, Truell Wayne.
The dynamics of Saturn's F ring have been a matter of curiosity ever since Voyagers 1 and 2 sent back pictures of the ring's unusual features. Some of these images showed three distinct ringlets with the outer two displaying a kinked and braided appearance. Many models have been proposed to explain the braiding seen in these images; most of these invoke perturbations caused by the shepherding moons or kilometre-sized moonlets embedded in the ring and are purely gravitational in nature. These models also assume that the plasma densities and charges on the grains are small enough that electromagnetic forces can be ignored. However, Saturn's magnetic field exerts a significant perturbative force on even weakly charged micron- and submicron-sized grains causing the grains to travel in epicyclic orbits about a guiding centre. This study examines the effect of Saturn's magnetic field on the dynamics of micron-sized grains along with gravitational interactions between the F ring's shepherding moons, Prometheus and Pandora. Due to the differences in charge-to-mass ratios of the various sized grains, a phase difference between different size populations is observed in the wavy orbits imposed by passage of the shepherding moons.
Charged Grains In Saturn's F-Ring: Interaction With Saturn's Magnetic Field
(Advances in Space Research, 2004) Matthews, Lorin Swint.; Hyde, Truell Wayne.
Saturn’s dynamic F-Ring still presents a challenge for understanding and explaining the kinematic processes that lead to the changing structure visible in our observations of this ring. This study examines the effect of Saturn’s magnetic field on the dynamics of micron-sized grains that may become electrically charged due to interaction with plasma in Saturn’s rigidly corotating magnetosphere. The numerical model calculates the dynamics of charged dust grains and includes forces due to Saturn’s gravitational field, the plasma polarization electric field, a third order harmonic expansion of Saturn’s magnetic field, and the F-Ring’s Shepherding moons, Prometheus and Pandora.
A model of coagulation in dust clouds during grain charging
(Advances in Space Research, 2004) Barge, Laura; Matthews, Lorin Swint.; Hyde, Truell Wayne.
Initially uncharged grains in space and laboratory plasma environments become charged due to currents driven by potential differences in the dusty plasma. Certain macroscopic effects such as coagulation of smaller grains into larger ones or fluffy aggregates can be affected during this initial grain charging phase. The charging profiles of micron- and submicron-sized dust grains immersed in such plasma environments are strongly size- and temperature-dependent, and under certain conditions, the dust cloud can have various configurations of charged grains. Using a standard grain charging model along with a modified Barnes–Hut tree code for calculating grain dynamics, this paper examines the effect of including initial grain charging in coagulation of clouds of negative grains, positive grains, and a mixture of oppositely charged grains. The immediate application to coagulation during transient dusty plasma conditions is discussed.
Effect of the Charge-Dipole Interaction on the Coagulation of Fractal Aggregates
(IEEE Transactions on Plasma Science, 2004) Matthews, Lorin Swint.; Hyde, Truell Wayne.
A numerical model with broad applications to complex (dusty) plasmas is presented. The self-consistent N-body code allows simulation of the coagulation of fractal aggregates, including the charge-dipole interaction of the clusters due to the spatial arrangement of charge on the aggregate. It is shown that not only does a population of oppositely charged particles increase the coagulation rate, the inclusion of the charge-dipole interaction of the aggregates as well as the electric dipole potential of the dust ensemble decreases the gelation time by a factor of up to 20. It is further shown that these interactions can also stimulate the onset of gelation, or "runaway growth," even in a population of particles charged to a monopotential where previously it was believed that like-charged grains would inhibit coagulation. Gelation is observed to occur due to the formation of high-mass aggregates with fractal dimensions greater than two, which act as seeds for runaway growth.
Finite coulomb crystal formation
(Advances in Space Research, 2004) Vasut, John; Hyde, Truell Wayne.; Barge, Laura
Dust particles immersed within a plasma environment, such as those found in planetary rings or comets, will acquire an electric charge. If the ratio of the inter-particle potential energy to average kinetic energy is large enough the particles will form either a “liquid” structure with short-range ordering or a crystalline structure with long-range ordering. Since their discovery in laboratory environments in 1994, such crystals have been the subject of a variety of experimental, theoretical and numerical investigations. Most numerical and theoretical investigations have examined infinite systems assuming periodic boundary conditions. Since experimentally observed crystals can be comprised of a few hundred particles, this often leads to discrepancies between predicted theoretical results and experimental data. In addition, recent studies have concentrated on the importance of random charge variations between individual dust particles, but very little on the importance of size variations between the grains. Such size variations naturally lead to inter-grain charge variations which can easily become more important than those due to random charge fluctuations (which are typically less than one percent). Although such size variations can be largely eliminated experimentally by introducing mono-dispersive particles, many laboratory systems and all astrophysical environments contain significant size distributions. This study utilizes a program to find the equilibrium positions of a dusty plasma system as well as a modified Barnes–Hut code to model the dynamic behavior of such systems. It is shown that in terms of inter-particle spacing and ordering, finite systems are significantly different than infinite ones, particularly for the most-highly ordered states.
Dynamics of a Dust Crystal with Two Different Size Dust Species
(Advances in Space Research, 2006) Matthews, Lorin Swint.; Qiao, Ke; Hyde, Truell Wayne.
A self-consistent 3D model for a complex (dusty) plasma is used to study the effects of multiple-sized dust grains in a dust crystal. In addition to the interparticle forces, which interact through a Yukawa potential, the model includes the effects of gravity, the variation of the sheath potential above the powered electrode, and a radial confining potential. Simulations studied various ratios of a mix of 6.5 and 8.9 μm monodisperse particles and compared their correlation functions, electric potential energy of the crystal formations, and the dispersion relations for in-plane and out-of-plane dust lattice wave modes for two different sheath thicknesses. In the 7 mm sheath, the particles formed two layers in the vertical direction by size, and acted as a two-layer crystal with weak correlation between the layers. In the 3 mm sheath, the particles formed an essentially monolayer crystal; however the crystal dynamics showed some characteristics of a bilayer crystal.
Effect of Multi-Sized Dust Distribution on Local Plasma Sheath Potentials
(Advances in Space Research, 2006) Sun, Meihong; Matthews, Lorin Swint.; Hyde, Truell Wayne.
This work investigates the modification of a plasma sheath in a complex plasma due to the presence of dust particles with a specified size distribution. A self-consistent model for the plasma sheath is combined with a self-consistent dynamical code in order to determine the interaction of the dust particles with the local sheath potential and the subsequent effect on the dynamics of the particles. It is shown that the ion density in the region of levitated particles is decreased. The sheath potential in the region of levitated dust particles is also more negative which is qualitatively consistent with the experimental results of Arnas et al. [Arnas, C., Mikikian, M., Bachet, G., Doveil, F. Sheath modification in the presence of dust particles. Phys. Plasmas 7(11), 4418–4422, 2000.].
Formation of Cosmic Dust Bunnies
(IEEE Transactions on Plasma Science, 2007) Matthews, Lorin Swint.; Hayes, Ryan; Freed, Michael; Hyde, Truell Wayne.
Planetary formation is an efficient process now thought to take place on a relatively short astronomical time scale. Recent observations have shown that the dust surrounding a protostar emits more efficiently at longer wavelengths as the protoplanetary disk evolves, suggesting that the dust particles are coagulating into fluffy aggregates, "much as dust bunnies form under a bed." One poorly understood problem in this coagulation process is the manner in which the micrometer-sized charged grains form the fractal aggregate structures now thought to be the precursors of protoplanetary disk evolution. This paper examines the characteristics of such fractal aggregates formed by the collision of spherical monomers and aggregates where the charge is distributed over the aggregate structure. The aggregates are free to rotate due to the collisions and dipole-dipole electrostatic interactions. Comparisons are made for different precursor size distributions and like-charged, oppositely charged, and neutral grains.
Charging and Growth of Fractal Dust Grains
(IEEE Transactions on Plasma Science, 2008-02) Matthews, Lorin Swint.; Hyde, Truell Wayne.
The structure and evolution of aggregate grains formed within a plasma environment are dependent on the charge acquired by the micron-sized dust grains during the coagulation process. The manner in which the charge is arranged on developing irregular structures can affect the fractal dimension of aggregates formed during collisions, which, in turn, influences the coagulation rate and size evolution of the dust within the plasma cloud. This paper presents preliminary models for the charge and size evolution of fractal aggregates immersed in a plasma environment calculated using a modification to the orbital motion-limited (OML) theory. Primary electron and ion currents that are incident on points on the aggregate surface are determined using a line-of-sight (LOS) approximation: only those electron or ion trajectories that are not blocked by another grain within the aggregate contribute to the charging current. Using a self-consistent iterative approach, the equilibrium charge and dipole moment are calculated for the dust aggregate. The charges are then used to develop a heuristic charging scheme, which can be implemented in coagulation models. While most coagulation heories assume that it is difficult for like-charged grains to oagulate, the OML_LOS approximation indicates that the electric potentials of aggregate structures are often reduced enough to allow significant coagulation to occur.
Simulation of dust voids in complex plasmas
(IOP Publishing, 2008-11-04) Goedheer, Willem Jan; Land, Victor
In dusty radio-frequency (RF) discharges under micro-gravity conditions often a void is observed, a dust free region in the discharge center. This void is generated by the drag of the positive ions pulled out of the discharge by the electric field. We have developed a hydrodynamic model for dusty RF discharges in argon to study the behaviour of the void and the interaction between the dust and the plasma background. The model is based on a recently developed theory for the ion drag force and the charging of the dust. With this model, we studied the plasma inside the void and obtained an understanding of theway it is sustained by heat generated in the surrounding dust cloud. When this heating mechanism is suppressed by lowering the RF power, the plasma density inside the void decreases, even below the level where the void collapses, as was recently shown in experiments on board the International Space Station. In this paper we present results of simulations of this collapse. At reduced power levels the collapsed central cloud behaves as an electronegative plasma with corresponding low time-averaged electric fields. This enables the creation of relatively homogeneous Yukawa balls, containing more than 100 000 particles. On earth, thermophoresis can be used to balance gravity and obtain similar dust distributions.
How to make large, void-free dust clusters in dusty
(IOP publishing, 2008-12-18) Land, Victor; Goedheer, Willem Jan
Collections of micrometer-sized solid particles immersed in plasma are used to mimic many systems from solid state and fluid physics, due to their strong electrostatic interaction, their large inertia, and the fact that they are large enough to be visualized with ordinary optics. On Earth, gravity restricts the so-called dusty plasma systems to thin, two-dimensional (2D) layers, unless special experimental geometries are used, involving heated or cooled electrons, and/or the use of dielectric materials. In micro-gravity experiments, the formation of a dust-free void breaks the isotropy of 3D dusty plasma systems. In order to do real 3D experiments, this void has somehow to be closed. In this paper, we use a fully self-consistent fluid model to study the closure of a void in a micro-gravity experiment, by lowering the driving potential. The analysis goes beyond the simple description of the ‘virtual void’, which describes the formation of a void without taking the dust into account. We show that selforganization plays an important role in void formation and void closure, which also allows a reversed scheme, where a discharge is run at low driving potentials and small batches of dust are added. No hysteresis is found this way. Finally, we compare our results with recent experiments and find good agreement, but only when we do not take charge-exchange collisions into account.
Modelling of Voids in Complex Radio Frequency Plasmas
(WILEY-VCH, 2009-06-02) Goedheer, Willem Jan; Land, Victor; Venema, Jan
In this paper hydrodynamic and kinetic approaches to model low pressure capacitively coupled complex radiofrequency discharges are discussed and applied to discharges under microgravity. Experiments in the PKENefedov reactor on board the International Space Station, as well as discharges in which gravity is compensated by means of thermophoresis are simulated with a 2-D cylindrically symmetric hydrodynamic model. Kinetic effects are studied with a 1-D Particle-In-Cell plus Monte Carlo model in which capture and scattering by dust grains is included. Simulations with this model address non-local effects and modulated discharges.
Experimental and computational characterization of a modified GEC cell for dusty plasma experiments
(New Journal of Physics, 2009-06-12) Land, Victor; Shen, Erica; Smith, Bernard (Bernie).; Matthews, Lorin Swint.; Hyde, Truell Wayne.
A self-consistent fluid model developed for simulations of microgravity dusty plasma experiments has for the first time been used to model asymmetric dusty plasma experiments in a modified Gaseous Electronics Conference (GEC) reference cell with gravity. The numerical results are directly compared with experimental data and the experimentally determined dependence of global discharge parameters on the applied driving potential and neutral gas pressure is found to be well matched by the model. The local profiles important for dust particle transport are studied and compared with experimentally determined profiles. The radial forces in the midplane are presented for the different discharge settings. The differences between the results obtained in the modified GEC cell and the results first reported for the original GEC reference cell are pointed out.
Effect of Dipole-Dipole Charge Interactions on Dust Coagulation
(New Journal of Physics, 2009-06-16) Matthews, Lorin Swint.; Hyde, Truell Wayne.
This study examines the effect that dipole–dipole charge interactions between fractal aggregates have on the growth of dust grains. Aggregates in a plasma or radiative environment will have charge distributed over their extended surface, which leads to a net dipole moment for the charged grains. A selfconsistent N-body code is used to model the dynamics of interacting charged aggregates. The aggregates are free to rotate due to collisions and dipole–dipole electrostatic interactions. These rotations are important in determining the growth rate and subsequent geometry (fractal dimension) of the grains. In contrast to previous studies which have only taken charge-dipole interactions into account, like-charged grains are found to coagulate more efficiently than neutral grains due to preferential incorporation of small aggregates into midsized aggregate structures. The charged aggregates tend to be more compact than neutral aggregates, characterized by slightly higher fractal dimensions.
Hydrodynamic and kinetic modelling of complex radio-frequency plasmas
(IOP publishing, 2009-09-18) Goedheer, Willem Jan; Land, Victor; Venema, Jan
In this paper hydrodynamic and kinetic approaches to model low-pressure capacitively coupled complex radio-frequency discharges are discussed and applied to discharges under micro-gravity. Complex plasmas contain dust grains with a large negative charge and are characterized by a strong coupling between the properties of the plasma and those of the dust grains. After a discussion of the physics and methods involved, examples are presented from modelling of experiments under micro-gravity in the PKE-Nefedov reactor on board the International Space Station. These discharges are simulated with a 2D cylindrically symmetric hydrodynamic model. Kinetic effects are studied with a 1D particle-in-cell plus Monte Carlo model in which capture and scattering by dust grains is included. Since experiments are often performed at low pressures, the electron energy distribution function is no longer determined by the local plasma properties. This has consequences for the charging of the dust. Results of simulations with this model are compared with the hydrodynamic results. In addition, we address the behaviour of the dust charge in decaying plasmas.
Dipole-dipole interactions of charged magnetic grains
(IEEE, 2010-04) Perry, Jonathan D.; Matthews, Lorin Swint.; Hyde, Truell Wayne.
The interaction between dust grains is an important process in fields as diverse as planetesimal formation or the plasma processing of silicon wafers into computer chips. This interaction depends in large part on the material properties of the grains (for example, whether the grains are onducting, nonconducting, ferrous, or nonferrous). This paper considers the effects that electrostatic and magnetic forces, alone or in combination, can have on the coagulation of dust in various environments. A numerical model is used to simulate the coagulation of charged, charged-magnetic, and magnetic dust aggregates formed from a ferrous material, and the results are compared to each other as well as to those from an uncharged nonmagnetic material. The interactions between extended dust aggregates are also examined, specifically looking at how the arrangement of charge over the aggregate surface or the inclusion of a magnetic material produces dipole–dipole interactions. It will be shown that these dipole–dipole interactions can affect the orientation and structural formation of aggregates as they collide and stick. An analysis of the resulting dust populations will also demonstrate the impact that grain composition and/or charge can have on the structure of the aggregate, as characterized by the resulting fractal dimension.
Probing the sheath electric field using thermophoresis in dusty plasma
(IEEE Transactions on Plasma Science, 2010-04) Land, Victor; Smith, Bernard (Bernie).; Matthews, Lorin Swint.; Hyde, Truell Wayne.
A self-consistent dusty plasma fluid model has been extended to incorporate all the oble gases as the carrier gas. An analysis of void closure in complex plasma composed of these gases over a wide range of experimental parameters is presented. Driving potential-pressure maps are constructed, which show the range in parameter space where isotropic void-free dust crystals can be expected, where a void is to be expected and where the discharge is expected to extinguish.
Vibrational Modes and Instabilities of a Dust Particle Pair in a Complex Plasma
(IEEE Transactions on Plasma Science, 2010-04-10) Qiao, Ke; Matthews, Lorin Swint.; Hyde, Truell Wayne.
Vibrational modes and instabilities of a dust-particle pair in a terrestrial aboratory complex plasma are investigated by employing an analytical method whereby the plasma wakefield induced by an external electric field is modeled using an image-charge method. It is found that for both horizontally and vertically aligned dust-particle pairs in equilibrium, four normal modes exist. Variations of the confinement parameters cause a single type of instability in the horizontal pair and two types of nstabilities in the vertical pair.
Fluid modeling of void closure in microgravity noble gas complex plasmas
(Physics Review E, 2010-05-12) Land, Victor; Matthews, Lorin Swint.; Hyde, Truell Wayne.; Bolser, Diana
A self-consistent dusty plasma fluid model has been extended to incorporate all the noble gases as the carrier gas. An analysis of void closure in complex plasma composed of these gases over a wide range of experimental parameters is presented. Driving potential-pressure maps are constructed, which show the range in parameter space where isotropic void-free dust crystals can be expected, where a void is to be expected and where the discharge is expected to extinguish.
Modeling Agglomeration of Dust Particles in Plasma
(AIP Conference Proceedings, 2011) Matthews, Lorin Swint.; Land, Victor; Ma, Qianyu.; Perry, Jonathan D.; Hyde, Truell Wayne.
The charge on an aggregate immersed in a plasma environment distributes itself over the aggregate’s surface; this can be approximated theoretically by assuming a multipole distribution. The dipole-dipole (or higher order) charge interactions between fractal aggregates lead to rotations of the grains as they interact. Other properties of the dust grains also influence the agglomeration process, such as the monomer shape (spherical or ellipsoidal) or the presence of magnetic material. Finally, the plasma and grain properties also determine the morphology of the resultant aggregates. Porous and fluffy aggregates are more strongly coupled to the gas, leading to reduced collisional velocities, and greater collisional cross sections. These factors in turn can determine the growth rate of the aggregates and evolution of the dust cloud. This paper gives an overview of the numerical and experimental methods used to study dust agglomeration at CASPER and highlights some recent results.

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