Weakly nonlinear ion sound waves in gravitational systems.

Ion sound waves are studied in a plasma subject to gravitational field giving rise to vertically inhomogeneous steady-state plasma conditions. Such systems are interesting by exhibiting a wave growth that is a result of energy flux conservation for pulses propagating in an inhomogeneous system. The increase of the amplitude of a pulse as it propagates along the density gradient in the direction of decreasing density gives rise to an enhanced interaction between waves and plasma particles that can be modeled by a modified Korteweg-de Vries equation. Analytical results are compared with numerical particle-in-cell simulations of the problem. Our code assumes isothermally Boltzmann distributed electrons resulting in a nonlinear Poisson equation. The ion component is treated as a collection of individual particles interacting through collective electric fields. Deviations from quasineutrality are allowed for.

Weakly nonlinear ion waves in striated electron temperatures.

The existence of low-frequency waveguide modes of electrostatic ion acoustic waves is demonstrated in magnetized plasmas for cases where the electron temperature is striated along magnetic field lines. For low frequencies, the temperature striation acts as waveguide that supports a trapped mode. For conditions where the ion cyclotron frequency is below the ion plasma frequency we find a dispersion relation having also a radiative frequency band, where waves can escape from the striation. Arguments for the formation and propagation of an equivalent of electrostatic shocks are presented and demonstrated numerically for these conditions. The shock represents here a balance between an external energy input maintained by ion injection and a dissipation mechanism in the form of energy leakage of the harmonics generated by nonlinear wave steepening. This is a reversible form for energy loss that can replace the time-irreversible losses in a standard Burgers equation.

Transit times in turbulent flows.

Statistics of the motion of passively convected point particles in turbulent flows are studied. The database used is obtained by direct numerical solution of the Navier-Stokes equation. We estimate the probability distribution of the transit times of such particles through reference volumes with given forms and sizes. A selected position within the reference volume is moving with the local flow velocity, thus determining the motion of the entire surface. The transit time is defined as the interval between entrance and exit times of surrounding particles convected through the volume by the turbulent motions. Spherical as well as hemispherical surfaces are studied. Scale sizes in the inertial as well as in the viscous subranges of the turbulence are considered. Simple, and seemingly universal, scaling laws are obtained for the probability density of the transit times in terms of the basic properties of the turbulent flow and the geometry. In the present formulation, the results of the analysis are relevant for chemical reactions, but also for understanding details of the feeding rate of micro-organisms in turbulent waters, for instance.

Collisionless plasma shocks in striated electron temperatures.

The existence of low frequency waveguide modes of ion acoustic waves is demonstrated in magnetized plasmas for electron temperatures striated along the magnetic field lines. At higher frequencies, in a band between the ion cyclotron and the ion plasma frequency, radiative modes develop and propagate obliquely to the field away from the striation. Arguments for the subsequent formation and propagation of electrostatic shock are presented and demonstrated numerically. For such plasma conditions, the dissipation mechanism is the "leakage" of the harmonics generated by the wave steepening.

Numerical simulations of potential distribution for elongated insulating dust being charged by drifting plasmas.

The potential distributions surrounding elongated insulating dust grains being charged by supersonic plasma flows are studied using the particle-in-cell method. The plasma flow introduces an asymmetry in the dust charging. This leads to a complex surface charge distribution on the dust, and to ion focusing in the wake region. We demonstrate that the charge and potential distributions on the dust surface and the wake behind the dust depend on the rod length and dust inclination angle with respect to the flow. The role of the surface charge distribution in the interactions between insulating rods in a plasma is discussed. Our simulations are carried out in two spatial dimensions, treating ions and electrons as individual particles.

Patterns of sound radiation behind pointlike charged obstacles in plasma flows.

The electrostatic potential and plasma density variations around a pointlike charged object in a plasma flow are studied. These objects can represent small charged dust particles, for instance. The radiation patterns can be interpreted as the result of sound waves being radiated by the obstacle. Two limits are considered: one where the electron-ion temperature ratio is large, Te>>Ti , and one where Te/Ti approximately 1 . The former limit can be described by a simple model based on geometrical optics, while the latter requires a kinetic model in order to account for the effects of ion Landau damping. The results are illustrated by numerical simulation using a particle-in-cell code, where the electrons are treated as an isothermal massless fluid, giving a nonlinear Poisson equation. The analytical results are in good agreement with the numerical simulations.

Numerical studies of ion focusing behind macroscopic obstacles in a supersonic plasma flow.

We study the potential and plasma density variations around a solid object in a plasma flow, emphasizing supersonic flows. These objects can be dust grains, for instance. Conducting as well as insulating materials are considered. In a streaming plasma, a dust grain develops an electric dipole moment, which varies systematically with the relative plasma flow. The strength and direction of this dipole moment depends critically on the material. The net charge together with the electric dipole associated with the dust grains gives rise to electric fields, which affects the trajectories of nearby charged particles. The perturbation of ion orbits in streaming plasmas can give rise to a focusing of ions in the wake region facing away from the plasma flow. We study the parameter dependence of this ion focus. Our simulations are carried out in two spatial dimensions by a particle-in-cell code, treating ions and electrons as individual particles.

Wake behind dust grains in flowing plasmas with a directed photon flux.

The wake behind conducting dust grains in a supersonic plasma flow with a directed photon flux is studied by the particle-in-cell method. The electron emission leads to a positive charge on the dust. The resulting plasma wake differs significantly from the case without photoelectrons. This wake is studied for different photon fluxes and different angles between the incoming unidirectional photons and the plasma flow velocity. The simulations are carried out in two spatial dimensions, treating ions and electrons as individual particles.

Experimental studies of occupation times in turbulent flows.

The motion of passively convected particles in turbulent flows is studied experimentally in approximately homogeneous and isotropic turbulent flows, generated in water by two moving grids. The simultaneous trajectories of many small passively convected, neutrally buoyant, polystyrene particles are followed in time by a particle tracking technique. We estimate the probability distribution of the occupation times of such particles in spherical volumes with a given radius. A self-consistently moving particle defines the center of the reference sphere, with the occupation time being defined as the difference between entrance and exit times of surrounding particles convected through the sphere by the turbulent motions. Simple, and seemingly universal, scaling laws are obtained for the probability density of the occupation times in terms of the basic properties for the turbulent flow and the geometry. In the present formulation, the results of the analysis are relevant for understanding details in the feeding rate of micro-organisms in turbulent waters, for instance.

Predator-prey encounters in turbulent waters.

With reference to studies of predator-prey encounters in turbulent waters, we demonstrate the feasibility of an experimental method for investigations of particle fluxes to an absorbing surface in turbulent flows. A laboratory experiment is carried out, where an approximately homogeneous and isotropic turbulent flow is generated by two moving grids. The simultaneous trajectories of many small neutrally buoyant polystyrene particles are followed in time. Selecting one of these to represent a predator, while the others are considered as prey, we obtain estimates for the time variation of the statistical average of the prey flux into a suitably defined "sphere of interception." The variation of this flux with the radius in the sphere of interception, as well as the variation with basic flow parameters is well described by a simple model, in particular for radii smaller than a characteristic length scale for the turbulence. Also the Eulerian counterpart of the problem has been analyzed, and the particle fluxes from the two studies compared.