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Low‐frequency, flute‐type electrostatic fluctuations propagating across a strong, homogeneous magnetic field are studied experimentally. The fluctuations are generated by the Kelvin–Helmholtz instability. The presence of relatively long‐lived vortexlike structures in a background of wide‐band turbulent fluctuations is demonstrated by a conditional sampling technique. Depending on plasma parameters, the dominant structures can appear as monopole or multipole vortices, dipole vortices in particular. The importance of large structures for the turbulent plasma diffusion is discussed. A statistical analysis of the randomly varying plasma flux is presented.

Conditionally averaged random potential fluctuations are an important quantity for analyzing turbulent electrostatic plasma fluctuations. Experimentally, this averaging can be readily performed by sampling the fluctuations only when a certain condition is fulfilled at a reference position. Alternatively, for time stationary and homogeneous turbulence, analytical expressions, involving higher order correlation functions Rn(r, t) = n(ζ, τ)(r + ζ, t + τ), can be derived for the conditional averages. These expressions have the form of series expansions, which have to be truncated for practical applications. The convergence properties of these series are not known, except in the limit of Gaussian statistics. By applying the analysis to numerically simulated ion acoustic turbulence, we demonstrate that by keeping two or three terms in these series an acceptable approximation is obtained even in cases deviating significantly from Gaussian statistics.

Two-dimensional, incompressible flows are discussed by a generalization of the line-vortex model. A large number of structures are randomly distributed initially. Each individual structure is convected by the superposed flow field of all the others. The statistical properties of the resulting space–time varying random flow are studied. Analytical expressions for both Eulerian and Lagrangian correlation functions are obtained for the limit where the density of structures is large. The analytical results compare favourably with numerical simulations. The study serves as a special test on proposed relations between Eulerian and Lagrangian averages which can be generally valid, i.e. also for three-dimensional, turbulent 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, TeTi , 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.

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.

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.

The charging of the perfectly insulating dust grain in flowing plasmas and in the presence of a directed photon flux is studied using the particle-in-cell numerical simulations. In flowing plasmas a finite size dust grain acquires an electric dipole moment, and the formation of wakes in the potential and plasma density, that are more pronounced for supersonic flows, is observed. The photoelectric effect is important for the dust charging in space, planetary atmospheres and fusion reactors. Recently the possibility of the dust charge manipulation in rf discharges by the UV radiation has also been discussed. We study the total charge and charge distribution on the dust grain for different photon fluxes and different angles of the photon incidence with respect to the plasma flow. We find that the resulting positive charge on the dust surface, together with the photoelectrons, may distort spatial features in plasma in the vicinity of the dust. We compare our results with the case without the photoelectric effect. Our analysis is done in two spatial dimensions, with electrons and ions treated as individual particles.

The three-dimensional incompressible Euler equations are expanded in eigenflows of the curl operator, which represent positive and negative helicity flows in a particularly simple and convenient way. Four different basic types of interactions between eigenflows are found. Two represent an "inverse cascade", the interaction familiar from the two-dimensional Euler equations, in which only modes of the same sign of the helicity interact. The other two interactions mix positive and negative helicity modes. Only these interactions can transport all of the available energy to higher wave numbers. Initial conditions, which lead to the appearance of structures and self-organization, are discussed.

Kinetic effects associated with the electron motion along magnetic field lines in low‐beta plasmas are studied. Using the gyrokinetic description of electrons, a kinetic analog of the reduced magnetohydrodynamic equations is derived, and it is shown that in the strongly nonlinear regime they possess localized solutions in the form of dipolar vortices, which can efficiently interact with resonant electrons. In the adiabatic limit, evolution equations are derived for the vortex parameters, describing exchange of the energy, enstrophy, and of the Poynting vector between the vortex and resonant particles. The evolution equations indicate the possibility of excitation of plasma vortices by electron beams.

Low-frequency, flute-type electrostatic fluctuations propagating across a strong homogeneous magnetic field are studied experimentally. The fluctuations are generated by the Kelvin-Helmholtz instability. The presence of relatively long-lived vortexlike structures in a background of wideband turbulent fluctuations is demonstrated by a conditional sampling technique. It is demonstrated that in spite of the large-scale convection patterns associated with these structures, they can in some cases contribute only modestly to the turbulent plasma flux across the magnetic-field lines.

The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves is investigated in two spatial dimensions by numerical simulations. The long time evolution of the modulational instability shows a quasirecurrent behavior with a slow spreading of the energy, originally confined to the lowest wave numbers, to larger and larger wave numbers resulting in an apparently chaotic or random wave field.

A wave-number-in-cell code was developed for simulation of a model proposed by Vendenov, Gordeev, and Rudakov for studying weak Langmuir turbulence. The model uses a WKB approach for describing the Langmuir wave field. Theoretical results for damping of ion acoustic waves caused by resonant interaction of Langmuir waves with group velocity around the sound speed were confirmed. Simulations corresponding to an initial condition with an intense wave burst demonstrate a formation of almost stationary localized cavities of intense wideband self-trapped Langmuir wave fields. These cavities have features in common with phase-space vortices.

The propagation of a low-density-modulated ion beam with finite cross section in a homogeneous plasma is considered. Analytical expressions describing a Cerenkov-like radiation pattern are obtained. An experimental setup is described that is suitable for investigating these phenomena. The results are in qualitative agreement with the analytical expressions. >

Turbulent diffusion of charged test particles in electrostatic plasma turbulence is reviewed. Two different types of test particles can be distinguished. First passive particles which are subject to the fluctuating electric fields without themselves contributing to the local space charge. The second type are particles introduced at a prescribed phase space position at a certain time and which then self-consistently participate in the phase space dynamics of the turbulence. The latter "active" type of particles can be subject to an effective frictional force due to radiation of plasma waves. In terms of these test particle types, two basically different problems can be formulated. One deals with the diffusion of a particle with respect to its point of release in phase space. Alternatively the relative diffusion between many, or just two, particles can be analyzed. Analytical expressions for the mean square particle displacements in phase space are discussed. More generally equations for the full probability densities are derived and these are solved analytically in special limits.

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.

The motion of point-particles is studied by numerical simulations. We analyze the turbulent particle fluxes to perfectly absorbing spheres, which are moving with the flow. Particular attention is given to the effect of viscosity for the case where the radius of the sphere is comparable to or smaller than the Kolmogorov length scale. By relatively simple model arguments, we arrive at analytical expressions which give a very good agreement with the observed scalings.

Observations from the EISCAT Svalbard Radar, for instance, demonstrate that the symmetry of the naturally occurring ion line can be broken by an enhanced, non-thermal, level of fluctuations, i.e., ...

Charging of individual dust particles in contact with hot plasmas is studied by numerical methods. The dust particle is treated as a rigid solid body, composed by either perfectly insulating or conducting material. The collisionless plasma, consisting of electrons and singly charged ions, is simulated by Particle-in-Cell methods in two spatial dimensions. It is demonstrated that the surface conditions, i.e. roughness, of the dust particles are significant for the charging. 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. We observe also Langmuir oscillations excited in the vicinity of the particles, and analyze the spatial variation of their spectral distribution.

The analysis of low frequency electrostatic waves, drift waves in particular, is generalized to the case where the plasma parameters, the density in particular, have gradient also along magnetic field lines. A few related problems can be solved exactly, others approximately, but still beyond the accuracy of geometrical optics. A set of fully nonlinear basic equations are derived here and solved by a linearized analysis to give the appropriate dispersion relations. One conspicuous feature of such systems is a an amplitude increase that can be misinterpreted as an instability.

Observations of turbulent transport in magnetized plasmas indicate that plasma losses can be due to coherent structures or bursts of plasma rather than a classical random walk or diffusion process. A model for synthetic data based on coherent plasma flux events is proposed, where all basic properties can be obtained analytically in terms of a few control parameters. One basic parameter in the present case is the density of burst events in a long time-record, together with parameters in a model of the individual pulse shapes and the statistical distribution of these parameters. The model and its extensions give the probability density of the plasma flux. An interesting property of the model is a prediction of a near-parabolic relation between skewness and kurtosis of the statistical flux distribution for a wide range of parameters. The model is generalized by allowing for an additive random noise component. When this noise dominates the signal we can find a transition to standard results for Gaussian random noise. Applications of the model are illustrated by data from the toroidal Blaamann plasma.

We discuss general ideas, which can be used for estimating models for coherent time-evolutions by random sampling of data. They turn out to be particularly useful for interpreting data from instrumented spacecraft. These "new methods" are applied to examples of localized bursts of lower-hybrid waves and correlated density depletions observed on the FREJA satellite. In particular, lower-hybrid wave collapse is investigated. The statistical arguments are based on three distinct elements. Two are purely geometric, where the chord length distribution is determined for given cavity scales, together with the probability of encountering those scales. The third part of the argument is based on the actual time variation of scales predicted by the collapse model. The cavities are assumed to be uniformly distributed along the spacecraft trajectory, and it is assumed that they are encountered with equal probability at any time during the dynamical evolution. Cylindrical and ellipsoidal cavity models are discussed. It turns out that the collapsing cavity model can safely be ruled out on the basis of disagreement of data with the predicted cavity lengths and evolution time scales. Application to Langmuir wave collapse is suggested in order to check its reality and relevance.

The feasibility of an experimental method for investigations of the particle flux to an absorbing surface in turbulent flows is demonstrated in a Lagrangian as well as an Eulerian representation. 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 approximately neutrally buoyant polystyrene particles are followed in time. In a Lagrangian analysis, we select one of these as the centre of a “sphere of interception”, and obtain estimates for the time variation of the statistical average of the inward particle flux through the surface of this moving sphere. The variation of the 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. Applications of the problem to, for instance, the question of the feeding rate of micro-organisms in turbulent marine environments are pointed out.

The Third Nordic Symposium on Plasma Physics was organized at Lysebu, Oslo, Norway on 4–7 October 2004, under the auspices of the Norwegian Centre for Advanced Study (CAS). The arrangement was preceded by two similar meetings organized at the Riso National Laboratory in Denmark by one of us (HP): Nonlinear Waves in Plasmas, 13–16 August 1985, and The Second Nordic Symposium on Nonlinear Phenomena in Plasmas and Related Topics, 8–12 August 1988. The proceedings from these two previous meetings were published as Physica Scripta Reprint Series No. 2, and RS 16 (with a few copies still being available). The idea of `Nordic' in the title of this latest meeting was interpreted somewhat liberally, by including also scientific organizations in northern Germany, where a collaboration facing Nordic countries comes naturally, and indeed has solid historical roots pointing also to ongoing activities. We hope that this series of meetings can continue, suggesting that the interval should be kept to a minimum of three years to ensure that all participants present new results. (We hope not to have to wait 16 years until next time, though!) The aim of our meetings is to stimulate collaboration among plasma physicists by creating a forum where the participants can exchange ideas and seek inspiration under relaxed conditions. We have the distinct impression that the meeting was very successful in this respect. Many Nordic institutes have widespread international collaborations, and we were happy to welcome also foreign representatives for some of these activities. Altogether 28 contributed talks were presented by 30 participants. The abstracts of all talks were distributed at the meeting. The present proceedings cover a selection of the contributions. One participant had to cancel, but the contribution is included in these proceedings. All the papers have been refereed according to the usual standards of the journal We, the organizers, thank CAS for the generous financial support and also the staff at the centre for the help we received with the practical arrangements. Also we thank the Norwegian Academy of Sciences for their hospitality by letting us arrange the conference dinner at the academy.

The dynamic behavior of an ion flow around an obstacle in a collisionless plasma is investigated. The obstacle consists here of an absorbing cylinder, and a 2 dimensional electrostatic particle-in-cell simulation is used to study the flow characteristics. The formation of irregular filamented density depletions, oblique to the flow, is observed. The dynamics of these structures depend on the physical parameters of the plasma. The structures form at the edges of the wake behind the obstacle, in a region with a strong velocity shear, and are found to be associated with phase-space vortices, observed specially in the velocity direction perpendicular to the flow. The results can be of interest in the interpretation of structures in space plasmas as observed by instrumented space crafts.

Summary form only given. By simple arguments, we obtain a reduced time series for the sunspot activity. This time series can be argued to represent, approximately, the magnetic flux density at the coronal surface. The reduced sunspot index correctly reproduces also the 22-year solar cycle. Closer scrutiny of the sunspot variation shows that the local frequency of the solar cycle and the energy in the solar magnetic field vary consistently with conservation of action, i.e. local energy divided by local frequency. The analysis is based on the available data for the annual average of the sunspot number, beginning with the year 1700, and analyzed by means of a wavelet transform. The basic results are confirmed also by including other datasets. The observations regarding the action conservation can support an interpretation of the 22-year solar cycle proposed earlier by Gurnett and D'Angelo.

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.

Results on the formation and propagation of electron phase space vortices from laboratory experiments are summarized. The electron phase space vortices were excited in a strongly magnetized Q-machine plasma by applying a pulse to a segment of a waveguide surrounding the plasma. Depending on the temporal variation of the applied pulse, one or more phase space vortices can be excited, and their interaction can be followed in space and time. We were able to demonstrate, for instance, an irreversible coalescence of two such vortices. These results are extended by numerical simulations, showing how electron phase space vortices can also be formed by beam instabilities. Furthermore, a study of ion phase space vortices is performed by numerical simulations. Both codes allow for an externally applied magnetic field in three spatial dimensions. Ion phase space vortices are formed by the nonlinear saturation of the ion-ion two-stream instability, excited by injecting an ion beam at the plasma boundary. By following the evolution of the ion distribution of the velocity perpendicular to the direction of propagation of the injected ion beam, we find a significant ion heating in the direction perpendicular to the magnetic field associated with the ion phase space vortices being formed. The results are relevant, for instance, for the interpretation of observations by instrumented spacecraft in the Earth's ionosphere and magnetosphere.

We present a definition of wavelet bicoherence based on wavelet polyspectra. We propose a simple estimator for wavelet bicoherence, and discuss its statistical properties. In particular it is shown that wavelet bicoherence estimation has a larger number of effective degrees of freedom than traditional Fourier-based bicoherence estimation. The proposed estimator is applied to detection of coherent couplings in rocket measurements from the ionospheric E-region. It is concluded that wavelet bicoherence is a tool well-suited for analysis of non-stationary mode coupling.

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.

[1] Low-frequency electrostatic fluctuations detectedby the instruments on the Rocket and Scatter Experiment (ROSE) rockets inthe E region over northern Scandinavia are analyzed.It is demonstrated that the time-resolved statistical properties of the fluctuationsdeviate significantly from those associated with a Gaussian process. The characteristicsof the fluctuations are analyzed with particular attention to non-Gaussianeffects and phase-coherent mode couplings of electrostatic fluctuations. Non-Gaussianeffects are analyzed by means of the kernel estimator for probability densityfor short data segments. Short-time phase-coherent effects are analyzed andquantified by means of the squared wavelet bicoherence, which has desirablestatistical properties in the frequency regions of interest. The results arecompared with similar results from rocket data obtained over SondreStromfjord in Greenland. The results show a remarkable similarity,indicating that the observed phase coherence is a robust feature of the saturatedstage of the E region instabilities.

The self-consistent description of Langmuir wave and ion-sound wave turbulence in the presence of an electron beam is presented for inhomogeneous non-isothermal plasmas. Full numerical solutions of the complete set of kinetic equations for electrons, Langmuir waves, and ion-sound waves are obtained for a inhomogeneous unmagnetized plasma. The result show that the presence of inhomogeneity significantly changes the overall evolution of the system. The inhomogeneity is effective in shifting the wavenumbers of the Langmuir waves, and can thus switch between different process governing the weakly turbulent state. The results can be applied to a variety of plasma conditions, where we choose solar coronal parameters as an illustration, when performing the numerical analysis., 11 pages, 8 figures

International audience; The formation and propagation of isolated ion phase space vortices are observed in a 3-dimensional numerical simulation. The code allows for an externally applied constant magnetic field. The electrons are assumed to be isothermal and Boltzmann distributed at all times, implying that Poisson's equation becomes nonlinear for the present problem. Ion phase space vortices are formed by the nonlinear saturation of the ion-ion two-stream instability, excited by injecting an ion beam or short ion-bursts at the boundary. We consider the effects of finite beam diameters and the intensity of an externally imposed magnetic field.

The stability of ion velocity distributions in magnetized plasmas is studied under conditions where the plasma has an E0 × B/B2-drift with respect to a neutral background. Charge–exchange collisions can give rise to velocity distributions having the form of a ring or a loss-cone that can become linearly unstable. Sometimes the distributions have distorted forms and a stability analysis is not straightforward. Numerical simulations offer the most convenient method of a stability analysis in such cases. By numerical simulations using a particle-in-cell code that includes collisional interactions we demonstrate the formation of such velocity distributions and study the instabilities associated with them. We observe the saturation of the linear instability by quasi-linear velocity space diffusion. The parameter dependence of the instability conditions is illustrated by examples. The results are relevant for explaining some of the low frequency oscillations observed in the lower parts of the Earth's ionosphere (E- and F-regions), where collisions with neutrals are abundant. The results are important for laboratory experiments as well.

The space-time evolution of an initial step-like plasma density variation is studied. We give particular attention to formulate the problem in a way that opens for the possibility of realizing the conditions experimentally. After a short transient time interval of the order of the electron plasma period, the solution is self-similar as illustrated by a video where the space-time evolution is reduced to be a function of the ratio x/t. Solutions of this form are usually found for problems without characteristic length and time scales, in our case the quasi-neutral limit. By introducing ion collisions with neutrals into the numerical analysis, we introduce a length scale, the collisional mean free path. We study the breakdown of the self-similarity of the solution as the mean free path is made shorter than the system length. Analytical results are presented for charge exchange collisions, demonstrating a short time collisionless evolution with an ensuing long time diffusive relaxation of the initial perturbation. For large times, we find a diffusion equation as the limiting analytical form for a charge-exchange collisional plasma, with a diffusion coefficient defined as the square of the ion sound speed divided by the (constant) ion collision frequency. The ion-neutral collision frequency acts as a parameter that allows a collisionless result to be obtained in one limit, while the solution of a diffusion equation is recovered in the opposite limit of large collision frequencies. © 2013 AIP Publishing LLC.

Low frequency electrostatic turbulence in strongly magnetized, low β-plasmas, is studied in two spatial dimensions. In this limit the guiding center velocity in the direction perpendicular to a homogeneous magnetic field is approximated by the E x B 0 /B 0 2 -velocity. The electron Larmor radius can safely be set to zero for most relevant conditions, but the ion-dynamics are noticeably influenced by finite Larmor radius effects. We analyzed the effects of finite Larmor radius corrections on the ion velocity and density by using a fluid model where these effects are included by a computationally simple filtering operation. The equilibrium spectra are investigated and compared with analytical results. The consequences of finite Larmor radius corrections for the turbulent diffusion of charged particles across magnetic field lines are studied by obtaining the Lagrangian correlation functions for passive test particles convected by the plasma flow.

The density and potential variations at and in the vicinity of a spacecraft in flowing plasmas are studied by numerical simulations. The spacecraft charging, wake formation, and their role for the diagnostics of the ambient plasma are addressed. It is demonstrated that the wake features, such as ion focusing, can be altered by photoemission due to directed sunlight. For multiple ion species, the wakes for ions with different ion masses can be separated, with light ions contributing to the ion focus, and heavy ions giving a geometrical shape of the wake. As a specific case, the Cassini spacecraft approaching Saturn is considered. The simulations are carried out with DiP2D and DiP3D codes, the two- and three-dimensional particle-in-cell codes.

The motions of point particles and virtual surfaces are studied by use of data from direct numerical solutions of the Navier-Stokes equation. A selected particle within a reference volume with given form and size is moving self-consistently with the local flow velocity, thereby determining the motion of the entire surface. We estimate the encounter rates between particles in the surrounding flow and such surfaces. We find also the probability distribution of the transit times of particles through the reference volumes. The transit time is defined as the interval between entrance and exit times of surrounding particles convected through the volume by the turbulent motions. 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 encounter rate as well as the probability density of the transit times in terms of the basic properties of the turbulent flow and the geometry.

Low-frequency electrostatic waves in the ionospheric E region are studied by analyzing data obtained by instrumented rockets. We identify the origin of the enhanced fluctuation level to be the Farley–Buneman instability. The basic information on instability, such as altitude varying spectra and speed of propagation are obtained. Comparison of power spectra for the fluctuations in plasma density and electrostatic potential, respectively, provides information on the electron dynamics. A bispectral analysis gives indications of phase-coherent couplings within the wave spectrum, while higher order structure functions indicate some intermittent features of the turbulence.

The charging of conducting or alternatively insulating dust grains in a supersonic plasma flow with a directed photon flux is studied by the particle-in-cell method. The electron emission modifies the charge distribution on the grain surface and in the surrounding plasma. The charge and potential distributions on and around a dust grain are studied for different photon fluxes and different angles of the incident unidirectional photons with respect to the plasma flow velocity vector. Continuous and pulsed radiations are considered. It is shown that photoemission allows the charge on conducting grains to be controlled, and that interactions between positively charged grains can be strong. The charging of stationary and spinning insulating grains is discussed. The simulations are carried out in two spatial dimensions, treating ions and electrons as individual particles.

Interaction potentials between two insulating elongated dust grains in a supersonic plasma flow are studied by a particle-in-cell numerical method. It is found that the spatial variations of the charge distribution and the plasma potential depend on the orientation and the relative distance of the dust grains. For the case of two grains aligned perpendicular to the flow, a single wake and region of enhanced ion density are observed for small relative distances. The ion flux can be enhanced between such grains. For grains aligned parallel to the flow, the resulting wake is not a linear combination of the wakes behind a single grain, and the grain charge and interaction potentials strongly depend on their relative orientations. The simulations are carried out in two spatial dimensions, treating ions and electrons as individual particles. The case of two spherical grains, with separation vector perpendicular to the plasma flow direction, is considered for comparison.

The motion of small absorbing surfaces is modeled by numerical simulations of turbulent flows with realistic Reynolds numbers. We obtain empirical models for the encounter rate of particles, and in particular the turbulent particle fluxes to given surfaces following the flow. Particular attention is given to the limit, where the particle separations are in the viscous limit, where the scale size of the absorbing surfaces are comparable to or smaller the Kolmogorov length scale. Spherical surfaces represent a special limiting case, but more general shapes are considered as well. The relevance of the problem to the feeding rate of small planktonic organisms in turbulent environments is pointed out in particular, but the results have wider applications. Based on analytical results, we obtain first an empirical expression for the particle flux to a reference spherical surface of interception. This result covers ranges in the universal as well as the viscous subrange. The analysis is then generalized to conica...

With reference to studies of the influence of turbulence on the feeding process of aquatic micro-organisms, we analyze particle fluxes into absorbing surfaces in turbulent flows by numerical simulations. The simultaneous trajectories of many point particles are followed in time in a fully three-dimensional solution of the turbulent flow described by the Navier–Stokes equation. Selecting one of these points to represent a predator, while the others are considered as prey, we obtain estimates for the time variation of the statistical average of particle fluxes into a co-moving “sphere of interception”. The essential restriction in the model, when applied to aquatic micro-organisms, is that self-induced motions are ignored. Particles are assumed to be absorbed when crossing the surface. In this sense, the problem can be analyzed as the one involving a perfectly absorbing surface. The variation of the particle flux with the radius in the absorbing sphere, as well as the variation with basic flow parameters is...

The motion of passively advected particles is studied experimentally in approximately homogeneous and isotropic turbulent flows. The turbulence is generated in water by two moving grids. The simultaneous trajectories of many small passively advected, neutrally buoyant polystyrene particles are followed in time by a particle tracking technique. We estimate the probability distribution of the transit times of such particles in spherical volumes with given radius. A particle which is passively advected by the flow is selected to define the center of a reference sphere, with the transit time being defined as the difference between entrance and exit times of surrounding particles advected through this sphere by the turbulent motions. Simple 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. Also other formulations of the problem have been considered, by assuming, for instance, that particle positions are uniformly ...

The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which is perturbed by a small amplitude incoherent wave–field. The initial evolution is exponential, following the growth of perturbations predicted by linear stability theory. The fluctuations saturate at relatively high amplitudes, by forming a pair of magnetic field aligned vortex–like structures of opposite polarity, i.e. a pair of electrostatic convective cells.

The evolution of nonlinear electron plasma waves in weakly magnetized plasmas is studied for conditions where the principal waves propagate along the magnetic field lines. The analysis is based on an electrostatic fluid model for the waves. Numerical results using a spectral method with periodic boundary conditions demonstrate "quasi-collapsing" solutions for localized initial conditions with sufficiently high amplitude. The possibility of acceleration of electrons by the high-frequency waves is discussed. It is demonstrated that electrons are likely to gain energy in parts of the nonlinear wavepacket and to loose all, or most of, this energy again in other parts.

The properties of low frequency dynamics of electrostatic fluctuations in strongly magnetized plasmas have been studied, with particular attention to localization of the fluctuation amplitudes. A model based on a few isolated vortical structures is analyzed, with particular attention to vortex collapse, where three vortices merge together within a finite time, or to the converse process, i.e. a vortex explosion. Details of these particular types of vortex dynamics depend on the actual model used for describing the electrons, the presence of a Debye shielding in particular. For shielded vortices a "boomerang"-type of interaction is found.

Field and particle data recorded on the geostationary satellite GEOS 2 are used to investigate the electric and magnetic signatures of a substorm characterized by a dispersionless injection of energetic electrons and ions. Three types of field variations are observed: (1) Long-period oscillations with period of ∼ 300 s, interpreted as oscillations of entire field lines. These oscillations develop as second harmonic standing waves and correspond to coupled shear Alfven-slow magnetosonic modes. They grow after the most active period of the breakup. (2) Short-period transient oscillations with periods of ∼ 45–65 s, interpreted as wave modes trapped in a current layer which develops prior to the substorm breakup and is disrupted at breakup. These oscillations also correspond to a coupled shear Alfven-slow magnetosonic mode (coupled via magnetic field curvature effects in a high-β plasma). The short-period transient oscillations are only observed during the most active period of the breakup. (3) A nonoscillatory sharp increase observed on both the parallel magnetic component and the energetic ion flux, averaged over one satellite rotation, interpreted as evidence for the fast magnetosonic mode which in view of the simultaneous large impulsive increase in the azimuthal electric field, appears to propagate radially outwards, transporting the substorm breakup downtail.

Results of laboratory experiment on Bragg backscatter of 3-cm microwaves by turbulent waves driven by the Farley-Buneman and gradient drift instabilities are reported. It is noted that the study is the third in a series of laboratory experiments performed to test, under controlled conditions, prevalent ideas on EM scattering by equatorial and high-latitude ionospheric waves and irregularities. It is shown through separate backscattering from fast and slow ion beam modes that a beam of EM radiation actually provides, in backscatter, information on the spectral content of the scattering medium.

The collapse of electrostatic upper hybrid waves in weakly magnetized plasmas is considered with particular attention to include dispersive low-frequency waves in the equations governing the ion dynamics. Considering a magnetic-field aligned cylindrical collapse we demonstrate that a magnetic field can delay or even prevent a collapse in comparison with the unmagnetized case.