A review of the effects of light scattering on the dynamics of irregularly shaped dust grains in the Solar System

The various aspects of the interaction of electromagnetic radiation with cosmic dust particles are discussed. In particular, attention is paid to discrepancies between optical and physical behavior of realistically shaped particles and volume equivalent homogeneous spheres. The dynamical evolution of morphologically non-identical particles which are driven by gravity, electromagnetic radiation and the Lorentz forces can dramatically differ. Although spherical particles often enable analytical calculations, an orbital evolution of spheres cannot be considered as a representative evolution for real cosmic dust particles. The effect of electromagnetic radiation on the motion of dust grains plays a crucial role here. While irregularly shaped interstellar dust particles may be captured in the Solar System, the spherical particles will not survive due to close encounters with the Sun. Spherical grains can be captured almost only in the evaporation region (in the vicinity of the Sun), where they are destroyed due to high temperatures. The spherical dust particles ejected from comets will monotonously inspiral toward the Sun subject to the Poynting-Robertson effect. However, the non-spherical particles of the same origin may be temporarily stabilized at some heliocentric distances and thus their lifetime may be much longer than that for the Mie spheres. Some dust particles may also be captured in mean-motion resonances with planets (commensurability resonances). While spherical particles are always characterized by the secular decrease of the semi-major axes near mean-motion resonances, this may not be true for non-spherical particles. Resonant captures of arbitrarily shaped dust grains exist for exterior and interior mean-motion resonances with planets.     

Motion of nonspherical dust particle under the action of electromagnetic radiation

Equation of motion of realistically shaped particle in the circumstellar dust shell is derived under the action of electromagnetic radiation including the gravity of central body. The effect is considered to the accuracy , where is particle's velocity in a given inertial frame of reference and c is the speed of light. Equation of motion is expressed in terms of particle's optical properties, standardly used in optics for stationary particles.

Application to nonspherical dust particle in the Solar System with initial orbital elements identical to those of comet Encke is presented as an example. It is shown that the motion of nonspherical submicron- and small micron-sized particle may significantly differ from the motion for spherical particle of an identical volume.     

Radiation force caused by scattering, absorption, and emission of light by nonspherical particles

General formulas for computing the radiation force exerted on arbitrarily oriented and arbitrarily shaped nonspherical particles due to scattering, absorption, and emission of electromagnetic radiation are derived. For randomly oriented particles with a plane of symmetry, the formula for the average radiation force caused by the particle response to external illumination reduces to the standard Debye formula derived from the Lorenz–Mie theory, whereas the average radiation force caused by emission vanishes.     

随机取向非球形沙尘气溶胶粒子的光学特性

利用离散偶极子近似法分析了一种随机取向旋转椭球体沙尘气溶胶粒子模型在尺度参数变化范围为0.1~23时(波长0.55!m对应有效半径为0.01~2!m)的光学特性,研究了沙尘粒子非球形性程度对其光学特性的影响,并考察了非球形粒子的随机取向能否用等体积球体来代替。就随机取向单分散和多分散旋转椭球体沙尘气溶胶而言,粒子非球形特征越明显,消光效率因子、不对称因子和单次散射反照率基本上偏离其等体积球体越大;对于相同的非球形,不对称因子偏离其等体积球体的相对偏差要比消光效率因子和单次散射反照率要大。非球形粒子的随机取向并不能使其光学特性严格等效为其等体积球体的光学特性。如果粒子形状偏离球体较小,则非球形粒子的随机取向的平均效果能使其消光效率因子、不对称因子和单次散射反照率近似用等体积球体的对应光学参量来等效;而如果粒子形状偏离球形较大,仅有单次散射反照率可以近似用等体积球体的单次散射反照率来等效,例如,轴半径比为16的旋转椭球体沙尘粒子的单次散射反照率偏离其等体积球体仅在3%以内。     

Separation of variables method for multilayered nonspherical particles

A separation of variables method based on expansions of the electromagnetic fields in terms of spherical wave functions is expanded at nonspherical (axisymmetric) particles with a rather large number of layers. Commonly used alternative approaches to systems of linear algebraic equations relative to unknown field expansion coefficients for layered particles are considered in some detail. The SVM code developed is compared with the EBCM, GMT and DDA codes designed for multilayered scatterers and some numerical results obtained for nonspherical scatterers with up to 100 layers are presented as illustrations.     

T-matrix formulation and generalized Lorenz-Mie theories in spherical coordinates

There has been recently a growing interest in the development of what is usually known as the T-matrix method (better to be named: T-matrix formulation), in connection with studies concerning light scattering by nonspherical particles. Another line of research has been devoted to the development of generalized Lorenz-Mie theories dealing with the interaction between arbitrary electromagnetic shaped beams and some regular particles, allowing one to solve Maxwell’s equations by using a method of separation of variables. Both lines of research are conjointly considered in this paper. Results of generalized Lorenz-Mie theories in spherical coordinates (for homogeneous spheres, multilayered spheres, spheres with an eccentrically located spherical inclusion, assemblies of spheres and aggregates) are modified from scalar results in the framework of the Bromwich method to vectorial expressions using vector spherical wave functions (VSWFs) in order to match the T-matrix formulation, and to express the T-matrix. The results obtained are used as a basis to clarify statements, some of them erroneous, concerning the T-matrix formulation and to provide recommendations for better terminologies.     

Generation of tunable electromagnetic radiation by a dust ripple in dusty plasmas

It is shown that a pre-existing dust ripple in a dusty plasma may excite tunable electromagnetic radiation. For our purposes, we use the Maxwell equation and the electron equation of motion to derive a Mathieu equation in the presence of a spatially oscillating dust ripple. The Mathieu equation admits instability of an electromagnetic wave. Criteria under which instability occurs are presented. Explicit expression for the electromagnetic radiation frequency and the growth rate are obtained. The possible relevance of our investigation to nonthermal electromagnetic radiation sources from laboratory and cosmic dusty plasmas is considered.     

Multiple components in narrow planetary rings

The phase-space volume of regions of regular or trapped motion, for bounded or scattering systems with 2 degrees of freedom, respectively, displays universal properties. In particular, drastic reductions in the volume (gaps) are observed at specific values of a control parameter. Using the stability resonances we show that they, and not the mean-motion resonances, account for the position of these gaps. For more degrees of freedom, exciting these resonances divides the regions of trapped motion. For planetary rings, we demonstrate that this mechanism yields rings with multiple components.     

Interstellar grains The interaction of light with a small-particle system

Interstellar dust is suggested to be one of the most thoroughly studied of all small-particle systems, whose characteristics have in some ways not been duplicated in our laboratories. The particles are maintained in complete isolation from one another, in ultra-high vacuum and at low temperature, and have been studied spectroscopically from far infra-red to far ultra-violet. Optical properties of the interstellar dust which are surveyed include effects interpreted as due to surface plasmon bands in the ultra-violet, surface phonon bands and other vibrational absorption bands in the infra-red, linear and circular polarization caused by aligned particles, impurity absorption, and defect absorption possibly caused by radiation damage. A discussion of the possible origins for interstellar grains leads to speculation on their relationship to certain meteorites. Absorption and scattering effects from small particles in general are surveyed by way of Mie calculations for a representative insulator, MgO, and a representative metal, Mg. Spectral features revealed by the calculations from far infra-red to far ultra-violet are discussed briefly. Methods of measuring optical constants, necessary for small-particle calculations, are surveyed, and results for several solids of possible importance in astronomy are discussed. Collective resonances associated with plasmons and phonons in small particles are treated, and the effect of particle shape is illustrated with several experimental examples. Various non-collective resonance effects in small particles are presented and situations in which bulk optical constants may not be appropriate are reviewed. Applications are made of all these effects to observed features from interstellar grains. Special emphasis is given to a discussion of the 39 unidentified interstellar bands in the visible spectral region, which comprise the longest-standing spectroscopic mystery in astronomy.     

Microwave scattering properties of sand particles: Application to the simulation of microwave radiances over sandstorms

The single-scattering properties of sand/dust particles assumed to be ellipsoids are computed from the discrete dipole approximation (DDA) method at microwave frequencies 6.9-89.0 GHz in comparison with the corresponding Lorenz-Mie solutions. It is found that the single-scattering properties of sand particles are strongly sensitive to the shapes of the particles. The bulk scattering properties of sandstorms composed of spherical or nonspherical particles are investigated by averaging the single-scattering properties of these particles over log-normal particle size distributions. Furthermore, a vector radiative transfer model is used to simulate microwave radiances. The microwave brightness temperatures in the vertical polarization model are essentially not sensitive to sand particle habit, whereas microwave brightness temperature polarization differences are influenced by particle habit. It is shown that microwave brightness temperatures and brightness temperature polarization differences may be useful for estimating the effective particle sizes and mass loading of sandstorms.     

Electrodynamics and dispersion properties of a magnetoplasma containing elongated and rotating dust grains

The electrodynamics and dispersion properties of a magnetized dusty plasma containing elongated and rotating charged dust grains are examined. Starting from an appropriate Lagrangian for dust grains, a kinetic equation for the dust grain and the corresponding equations of motion are derived. Expressions for the dust charge and dust current densities are obtained with the finite size (the dipole moment) of elongated and rotating dust grains taken into account. These charge and current densities are combined with the Maxwell-Vlasov system of equations to derive dispersion relations for the electromagnetic and electrostatic waves in a dusty magnetoplasma. The dispersion relations are analyzed to demonstrate that the dust grain rotation introduces new classes of instabilities involving various low-frequency waves in a dusty magnetoplasma. Examples of various unstable low-frequency waves include the electron whistler, the dust whistler, dust cyclotron waves, AlfvÉn waves, electromagnetic ion-cyclotron waves, as well as lower-hybrid, electrostatic ion cyclotron, modified dust ion-acoustic waves, etc. Also found is a new type of unstable waves whose frequency is close to the dust grain rotation frequency. The present results should be useful in understanding the properties of low-frequency waves in cosmic and laboratory plasmas that are embedded in an external magnetic field and contain elongated and rotating charged dust grains.     

Growth and form of planetary seedlings: results from a microgravity aggregation experiment

The outcome of the first stage of planetary formation, which is characterized by ballistic agglomeration of preplanetary dust grains due to Brownian motion in the free molecular flow regime of the solar nebula, is still somewhat speculative. We performed a microgravity experiment flown onboard the space shuttle in which we simulated, for the first time, the onset of free preplanetary dust accumulation and revealed the structures and growth rates of the first dust agglomerates in the young solar system. We find that a thermally aggregating swarm of dust particles evolves very rapidly and forms unexpected open-structured agglomerates.     

Measurement of the translational and rotational Brownian motion of individual particles in a rarefied gas

We measured the free Brownian motion of individual spherical and the Brownian rotation of individual nonspherical micrometer-sized particles in rarefied gas. Measurements were done with high spatial and temporal resolution under microgravity conditions in the Bremen drop tower so that the transition from diffusive to ballistic motion could be resolved. We find that the translational and rotational diffusion can be described by the relation given by Uhlenbeck and Ornstein [Phys. Rev. 36, 823 (1930)]. Measurements of rotational Brownian motion can be used for the determination of the moments of inertia of small particles.     

Acoustic radiation force of a Bessel beam on a porous sphere

The possibility of using acoustic Bessel beams to produce an axial pulling force on porous particles is examined in an exact manner. The mathematical model utilizes the appropriate partial-wave expansion method in spherical coordinates, while Biot's model is used to describe the wave motion within the poroelastic medium. Of particular interest here is to examine the feasibility of using Bessel beams for (a) acoustic manipulation of fine porous particles and (b) suppression of particle resonances. To verify the viability of the technique, the radiation force and scattering form-function are calculated for aluminum and silica foams at various porosities. Inspection of the results has shown that acoustic manipulation of low porosity (<0.3) spheres is similar to that of solid elastic spheres, but this behavior significantly changes at higher porosities. Results have also shown a strong correlation between the backscattered form-function and the regions of negative radiation force. It has also been observed that the high-order resonances of the particle can be effectively suppressed by choosing the beam conical angle such that the acoustic contribution from that particular mode vanishes. This investigation may be helpful in the development of acoustic tweezers for manipulation of micro-porous drug delivery carrier and contrast agents.     

Acceleration of charged particles and radiation-reaction in strong plane and spherical waves

A comparison between the acceleration of charged particles in plane and spherical waves including the effect of radiation reaction is given. In strong electromagnetic waves the charged particle stays initially at practically constant phase — “phase locked” part of the motion — and only after it has travelled many wavelengths does the wave overtake the particle. During the phase-locked part of the motion depending upon the initial conditions of how a particle is injected into the wave radiation reaction can lead to both a net energy gain or loss compared to the motion without radiation reaction. In a plane wave however radiation reaction always leads to a net energy gain if it can build up long enough. A test of this latter prediction by means of ultra-strong lasers might be possible.     

Modelling of nanometer scale dust grains in tokamak

Dust poses a serious threat to tokamak operation and safety. It is important to study the behaviour of dust grains under tokamak's discharge conditions, which depends heavily on their size and charge. Existing simulations mainly address issues on dust grains with radii larger than 1 μm, in which case, the drift effect due to electromagnetic fields can be safely ignored. For nanometer scale dust grains, however, the drift effect becomes significant and a new model based on guiding-centre system needs to be established. In this work, the NDS has been done under BOUT++ framework. The simulation contains two parts. Part one, NDS evaluates the charging and ablation processes of the dust grains. In the second part, the guiding-centre orbits of dust particles are tracked in tokamak plasmas, whose parameters are obtained from BOUT++, a highly desirable C++ code package for performing parallel plasma fluid simulations with an arbitrary number of equations in 3D curvilinear coordinates. The orbit of nanodust dynamics is described by guiding centre equations for simplicity, and these equations are numerically solved by conventional fourth-order Runge Kutta method. Simulations provide results such as trajectories and evolutions of dust particles with different sizes and velocities for different tokamak geometries. Results show tungsten dust grains with a radius of a few nanometers launched from outer midplane will oscillate before totally ablated in C-Mod. The oscillation in this case is driven by the ion drag force. Larger Nanodust with a radius of 100 nm, on the contrary, cannot be completely constrained by the electromagnetic field. The high plasma temperature and density in the seperatrix region causes severe dust ablation, resulting in total ablation within several ms.     

On the role of dust in the cometary plasma

The cometary coma consists of neutral gas, plasma, and dust grains. The dust grains can influence both the neutral and charged coma’s constituents. Usually, the presence of dust particles in a plasma results in additional losses of both electrons and ions due to the plasma recombination on the particle surfaces. Solar radiation makes the impact of dust even more complicated depending on the solar flux, the dust number density, the photoelectric properties of the dust particles, the dust particle composition, the distribution of the sizes, etc. We propose a simple kinetic model evaluating the role of dust particles in the coma plasma chemistry and demonstrate that this role can be crucial, resulting in a nontrivial behavior of both the electron and ion densities of the plasma. We show that a coma’s dust particles can be negatively as well as positively charged depending on their composition. These opposite charges of the grains can result in fast coagulation of dust particles, thus, forming complex aggregate shapes of cometary grains. The text was submitted by the authors in English.     

Infrared extinction by homogeneous particle aggregates of SiC, FeO and : Comparison of different theoretical approaches

Particle shape and aggregation have a strong influence on the spectral profiles of infrared phonon bands of solid dust grains. Calculating these effects is difficult due to the often extreme refractive index values in these bands. In this paper, we use the discrete dipole approximation (DDA) and the T-matrix method to compute the absorption band profiles for simple clusters of touching spherical grains. We invest reasonable amounts of computation time in order to reach high dipole grid resolutions and take high multipolar orders into account, respectively. The infrared phonon bands of three different refractory materials of astrophysical relevance are considered—silicon carbide, wustite and silicon dioxide. We demonstrate that even though these materials display a range of material properties and therefore different strengths of the surface resonances, a complete convergence is obtained with none of the approaches. For the DDA, we find a strong dependence of the calculated band profiles on the exact dipole distribution within the aggregates, especially in the vicinity of the contact points between their spherical constituents. By applying a recently developed method to separate the material optical constants from the geometrical parameters in the DDA approach, we are able to demonstrate that the most critical material properties are those where the real part of the refractive index is much smaller than unity.     

A generalized multiparticle Mie-solution: further experimental verification

We further test our electromagnetic multisphere-scattering solution developed earlier by comparing theoretical predictions from the theory with a set of laboratory measurements of microwave analog to light scattering by aggregated spheres. This solution is an extension of Mie theory to the multisphere case, generally applicable to an arbitrary aggregate of spherical and/or nonspherical particles. It is demonstrated once again that the theory is in a uniform agreement with experiment, convincingly confirming the veracity of the multiparticle-scattering formulation. The computer code for the calculation of the scattering by an aggregate of spheres in a fixed orientation and the experimental data havebeen made publically available.     

Anomalous kinetic energy of a system of dust particles in a gas discharge plasma

The system of equations of motion of dust particles in a near-electrode layer of a gas discharge has been formulated taking into account fluctuations of the charge of a dust particle and the features of the nearelectrode layer of the discharge. The molecular dynamics simulation of the system of dust particles has been carried out. Performing a theoretical analysis of the simulation results, a mechanism of increasing the average kinetic energy of dust particles in the gas discharge plasma has been proposed. According to this mechanism, the heating of the vertical oscillations of dust particles is initiated by induced oscillations generated by fluctuations of the charge of dust particles, and the energy transfer from vertical to horizontal oscillations can be based on the parametric resonance phenomenon. The combination of the parametric and induced resonances makes it possible to explain an anomalously high kinetic energy of dust particles. The estimate of the frequency, amplitude, and kinetic energy of dust particles are close to the respective experimental values.