Ppjm Piet Schram

Stationary velocity and charge distributions of grains in dusty plasmas

Within the kinetic approach the velocity and the charge distributions of grains in stationary dusty plasmas are calculated and the relations between the effective temperatures of such distributions and plasma parameters are established. It is found that the effective temperature which determines the velocity grain distribution could be anomalously large due to the action of accelerating ionic bombarding force. The possibility to apply the results obtained to the explanation of the increasing grain temperature in the course of Coulomb-crystal melting by reduction of the gas pressure is discussed.

Three particle hydrodynamic interactions in suspensions

We present an outline of a method to determine the components of the grand mobility matrix of a system of three hydrodynamically interacting spherical particles with arbitrary particle configuration. We present the results of a study of some components of the grand mobility matrix in the case of two special configurations. The results derived for one configuration, with the three particles on a line, are compared with some results from the literature. In the other configuration, we have put the particles on the corners of an equilateral triangle. Besides the study of the mobility matrix, we have derived virial expansions for the translational and rotational self‐diffusion coefficients up to quadratic order in φ, the volume fraction. Three particle contributions are incorporated in these expressions. We also present virial expansions, where three particle hydrodynamic interactions are included, for the translational and rotational sedimentation velocities. There are some results available in the literature in the case of the translational self‐diffusion coefficient and the translational sedimentation velocity, which are different from our results. We discuss these differences. As far as we know, the results of the three particle contribution to the virial expansions of the rotational self‐diffusion coefficient and the rotational sedimentation velocity are new. All the virial expansions mentioned above are compared with experimental results and simulation data from the literature.

Statistical properties and relaxation of dusty plasmas

Statistical and relaxation properties of dusty plasmas are studied numerically and analytically. The fluctuation electrodynamics of dusty plasmas is determined taking into account the dynamics of charging processes associated with plasma currents. The influence of grain charging on the effective interaction between dust particles is discussed. Grain attraction and dusty crystal formation are shown to be possible. The results of numerical simulation of dusty plasma relaxation caused by grain charging and plasma-layer expansion are presented in detail. Monte Carlo simulations are used to prove the existence of dust particle effective attraction within a model with constant grain charge.

Retarded hydrodynamic interactions in suspensions

We extend the method to determine the grand mobility matrix presented in a previous article to the problem of two particles in an unbounded fluid satisfying the time dependent linear incompressible Navier-Stokes equations. Use of this method combined with a generalization of the fluctuation dissipation theorem results in the determination of the correlation matrix. We determine the effect of hydrodynamic interactions on the time dependent diffusion coefficients D11(τ) and D12(τ). Finally we study the effects of the correlation functions on Brownian motion.

Quasistatic hydrodynamic interactions in suspensions

We present a method to determine the grand mobility matrix for a system of N spherical particles, interacting hydrodynamically, with stick boundary conditions in an unbounded fluid. In the case of a system of two spherical particles we compare the results with those obtained from the reflection method. Finally we determine virial expansions for some diffusion coefficients, the translational sedimentation and the rotational sedimentation. We compare some of them with results available from the literature; other results are new, such as the second order virial coefficient of the short time rotational self-diffusion coefficient and the virial expansion of the rotational sedimentation. Our conclusion is that the method is generally applicable and offers a more systematic convergence than e.g. the reflection method. It leads to satisfactory results in the case of the two particle problem.

Evolution of an expanding plasma with dust particles

Abstract The main results of theoretical investigations and computer simulations of a plasma expansion with dust particles as well as the methods used in these investigations are presented in this short review. The hydrodynamic treatment consists of the set of fluid equations for the dust particles and the equation for the dust particle charge according to the orbit limited probe theory. The kinetic treatment consists of the Vlasov equation for dust particles with constant charge together with Boltzmann distributions with constant temperature for the electrons and ions and the condition of quasi-neutrality. Computer simulations are described in the framework of the PIC method taking into account the dynamics of the dust particle charge as well as Coulomb collisions of electrons and ions with dust particles. The results of these investigations show the essential influence of dust particles on the plasma expansion. In particular, dust particles cause the distributions of electrons and ions to deviate from equilibrium due to their selective collection by dust particles.

Electron transport in strongly ionized plasmas

The kinetic theory of the electrons in a strongly ionized, collision dominated plasma is reconsidered. By means of a perturbation expansion combined with a multiple time scales formalism, the kinetic equation for the electron distribution function is solved. The usual integro- differential operator is transformed into a pure differential operator. In a fully ionized plasma this operator reduces to a surprisingly simple form when compared to the original one of Spitzer et al. This greatly simplifies the numerical calculation of the transport coefficients.

Kinetic theory of the charging process in dusty plasmas

On basis of the kinetic equations for dusty plasmas we consider the charging equation for grains. We suggest the local charge approximation, in which the distribution function of the charge variable is a delta function, so the charge becomes a function of position and time. Only with this assumption can the usual form of the charging equation be derived. We also simplify the kinetic equations for dusty plasmas in the case of the local charge approximation and find not only an electrical but also a bombarding force acting on grains. In the case of immobile grains and linear perturbations we find the dielectric function and analyse the influence of the charging process on the wave spectra.

On the theory of Brownian motion in compressible fluids

Within the framework of the theory of hydrodynamic fluctuations the Brownian motion of a spherical particle in a compressible fluid has been considered taking into account the action of a harmonic potential. The general relations for the velocity autocorrelation function and mean square displacement of a Brownian particle have been established by means of the solutions of the generalized Langevin equation. The analysis for the time evolution of the correlations has been performed both on large and small time scales. On a large time scale the asymptotic expansions describing the persistent correlations have been found to arbitrary order in t−n/2. The transition to the system without potential has been studied and the conditions for realization of the diffusion regime of correlations have been clarified. On a small time scale a consistent limit procedure for the velocity autocorrelation function has been used which leads in a straightforward manner to the well-known result given by the equipartition theorem.

Expansion of a bounded plasma with dust particles

The expansion of a bounded plasma with dust particles is investigated by means of computer modelling, taking into account the dynamics of the dust particle charge as well as the Coulomb collisions of electrons and ions with dust particles. The PIC method is used for the computer modelling. The collection of electrons and ions by dust particles is described in a way similar to orbit-limited probe theory. Coulomb interactions are described in the framework of stochastic differential equations. It is shown that the mean distribution functions of electrons and ions are influenced by the dust particles during plasma expansion. The evolution of the ion distribution function leads to a strong deviation from equilibrium. Dust particles also influence the temporal behaviour of the plasma parameters.