Fluctuations of the charge on a dust grain in a plasma

A dust grain in a plasma acquires an electric charge by collecting electron and ion currents. These currents consist of discrete charges, causing the charge to fluctuate around an equilibrium value 〈Q〉. Electrons and ions are collected at random intervals and in a random sequence, with probabilities that depend on the grain's potential. We developed a model for these probabilities and implemented it in a numerical simulation of the collection of individual ions and electrons, yielding a time series Q(t) for the grain's charge. Electron emission from the grain is not included, although it could be added easily to our method. We obtained the power spectrum and the RMS fluctuation level, as well as the distribution function of the charge. Most of the power in the spectrum lies at frequencies much lower than 1/τ, the inverse charging time. The RMS fractional fluctuation level varies as 0.5 |〈N〉|^-1/2, where 〈N〉=〈Q〉/e is the average number of electron charges on the grain. This inverse square-root scaling means that fluctuations are most important for small grains. We also show that very small grains can experience fluctuations to neutral and positive polarities, even in the absence of electron emission     

Three-dimensional wake potential in a streaming dusty plasma

The oscillatory wake potential for a slowly moving or static test dust particulate in a finite temperature, collisionless and unmagnetized dusty plasma with a continuous flow of ions and dust particles has been studied. The collective resonant interaction of the moving test particle with the low-frequency and low-phase-velocity dust-acoustic mode is the origin of the periodic attractive force between the like polarity particulates along and perpendicular to the streaming ions and dust grains resulting into dust-Coulomb crystal formation. This wake potential can explain the three-dimensional dust-Coulomb crystal formation in the laboratory conditions.     

Effect of a longitudinal magnetic field on the excitation of plasma wake waves

The effect of a longitudinal magnetic field on the linear wake fields excited by a relativistic electron bunch in a cold homogeneous plasma is considered. The obtained results prove that the presence of an external magnetic field leads to a dependence of the wake wavelength on the transverse coordinate, to a change in the wave amplitude with increasing distance from the bunch, and to the emergence of anharmonicity. It is found that a strong magnetic field reduces the wave amplitude significantly for narrow bunches and changes the amplitude insignificantly for broad bunches.     

Effect of small total pulse on development of a wake behind the self-propelled bodies

Experimental studies on the wakes behind the self-propelled bodies of revolution have been analysed, and results of stereometric studies on the co-current flows behind autonomous streamlined and bluff bodies of revolution are presented for the times of their development corresponding to the coordinate system of a distant wake of 2400 and 1200 body diameters, correspondingly. Possible modelling of axisymmetric co-currents by the flows generated by a string at its pulse motion along the axis is examined. It is shown that supposed solutions based on the model of interferential development of wakes behind the self-propelled bodies of revolution can approximate both the known results of experimental studies of wakes behind the self-propelled bodies of revolution and the flows generated by corresponding pulse transportation of a string.     

Use of the wake of a small cylinder to Control unsteady loads on a circular cylinder

Simultaneous measurements of lift and drag forces have been performed in order to study passive control of unsteady loads induced on a circular cylinder. For this purpose, an aerodynamic balance has been developed. The balance, developed for a cylinder of 25.4 mm in diameter, was designed to operate in the subcritical regime (Re=32000). This instrument is characterized by its sensitive element that forms a small central part of the cylinder. The static and dynamic calibrations of the balance show the appropriateness of the present design. Moreover, qualification experiments carried out with a single cylinder gave results (mean and rms values of the lift and drag coefficients) that are in good agreement with those found in the literature. The purpose of this paper is to present a passive control experiment performed by means of the wake of a smaller cylinder interacting with a larger one. Firstly, a parametric study was performed by varying the following: i) the diameterdS of the small cylinder for one large cylinder diameterd (7 values in the range 0.047≤d _S /d≤0.125); ii) the center-to-center spacingS/d (11 values in the range 1.375≤S/d≤2.5); and iii) the stagger anglea(0≤a≤90 with a fine angular stepDa fora≤15). A maximum mean drag reduction of about 48% is achieved. Ata=4 to 8, one can observe a peak of mean lift coefficient. Then unsteady fluid forces, vortex shedding frequency and flow pattern were systematically investigated for the small cylinder having a diameterdS=2.4 mm (0.094d). Reductions of 78% and 56% of the rms lift and drag fluctuations respectively were obtained with the small cylinder placed at a slight stagger angle in the range 6<a<9. This leads to an instantaneous force vector that exhibits more steadiness both in angle and amplitude. Moreover, at these stagger angles, the energy of the lift fluctuations at the shedding frequency is significantly reduced compared to the single cylinder case.     

On the variable order dynamics of the nonlinear wake caused by a sedimenting particle

In this work we develop a variable order (VO) differential equation of motion for a spherical particle sedimenting in a quiescent viscous liquid. In particular, we examine the various force terms in the equation of motion and propose a new form for the history drag acting on the particle. We show that the variable order formulation allows for an effective way to express the dynamic transition of the dominant forces over the entire time of the motion of the particle from rest to terminal velocity. The use of VO operators also allows us to examine the evolving dynamics of the wake during sedimentation. Using numerical data from a finite element simulation of a sedimenting particle, we first solve for the order of the derivative that returns the correct decay of the history force. We then propose a relatively simple expression for the history force that is a function of the Reynolds number and particle-to-fluid density ratio. The new history drag expression correlates very well (R²>0.99) with the numerical data for terminal Reynolds numbers ranging from 2.5 to 20, and for particle-to-fluid density ratios of interest in practice (1<β<10).     

Multi-scale energy exchanges between a nonlinear oscillator of Bouc-Wen type and another coupled nonlinear system

The concept of energy exchange between coupled oscillators can be endowed for wide variety of applications such as control and energy harvesting. It has been proved that by coupling an essential nonlinear oscillator (cubic nonlinearity) to a main system (mostly linear), the latter system can be controlled in a one way and almost irreversible manner. The phenomenon is called energy pumping and the coupled nonlinear system is named as nonlinear energy sink (NES). The process of energy transfer from the main system to the nonlinear smooth or non-smooth attachment at different scales of time can present several scenarios: It can be attracted to periodic behaviors which present low or high energy levels for the main system and/or to quasi-periodic responses of two oscillators by persistent bifurcations between their stable zones. In this paper we analyze multi-scale dynamics of two attached oscillators: a Bouc-Wen type in general (in particular: a Dahl type and a modified hysteresis system) and a NES (nonsmooth and cubic). The system behavior at fast and first slow times scales by detecting its invariant manifold, its fixed points and singularities will be analyzed. Analytical developments will be accompanied by some numerical examples for systems that present quasi-periodic responses. The endowed Bouc-Wen models correspond to the hysteretic behavior of materials or structures. This paper is clearly connected with the dynamics of systems with hysteresis and nonlinear dynamics based energy harvesting.     

Potential around a dust grain placed in the plasma sheath

We present a theory for potential distributions around a charged dust grain in a plasma with flowing ions. For this purpose, we account for absorption of ions by the grain surface and derive a kinetic ion density response for ion flow speed lying between the electron and ion thermal speeds. Poisson's equation is then solved to obtain the potential distribution close and far from the dust grain. It is found that at distances smaller than half the Debye radius, the potential remains spherically symmetric, while at large distances the potential becomes assymetric.     

Positron injection and acceleration on the wake driven by an electron beam in a foil-and-gas plasma

A novel approach for generating and accelerating positron bunches in a plasma wake is proposed and modeled. The system consists of a plasma with an embedded thin foil into which two electron beams are shot. The first beam creates a region for accelerating and focusing positrons and the second beam provides positrons to be accelerated. Monte Carlo and 3D PIC simulations show a large number of positrons (10(7) approximately 10(8)) are trapped and accelerated to approximately 5 GeV over 1 m with relatively narrow energy spread and low emittance.     

1D theory of laser plasma wake

In this paper, we get the 1D approximate analytical solution of the plasma electrostatic wake driven by the laser, and get the modified oscillating frequency of this wake. Finally we analyze the longitudinal beam dynamics in this electrostatic wake, and find that the high order terms don’t change the topology of the longitudinal phase space.     

Measurement of dust grain charging in a laboratory plasma

The authors present an experimental system capable of causing dust grains to interact with a plasma in a well-controlled manner and measuring the accumulated charge. Results indicate that the measured charge accumulated on 0.1 μm diameter bismuth particles agrees to the first order with simple charging models. With further refinement of the diagnostic system, it is expected that detailed comparisons can be made with existing models     

Acoustic measurements of the sound-speed profile in the bubbly wake formed by a small motor boat

In situ measurements of the bubble field within wakes generated by a small motorboat show that the bubble field, shortly after the initial turbulent generation period, consists mainly of bubbles with radii between 20 and 200 microm. The subsequent dispersion of the wake field can be described using a model that includes bubble buoyancy and dissolution only, and the air volume fraction within the wakes decay exponentially with an e-folding time of between 40 and 60 s. Simultaneous measurements of sound propagating through the bubbly wake exhibit spectral banding due to waveguide propagation. Inversions using the inverse-square theory developed by Buckingham [Philos. Trans. R. Soc. London, Ser. A 335, 513-555 (1991)] show that this acoustic inversion technique provide a viable means of estimating the low-frequency sound-speed profile in an upward refractive bubble layer when dispersion can be neglected.     

Relativistic nonlinear waves in a magnetised plasma

Relativistic propagation of a nonlinearly-coupled circularly-polarised electromagnetic wave and a Langmuir wave along the applied magnetic field is considered. Analytical solutions are given or are indicated for some special cases like purely transverse waves and purely longitudinal waves. In the presence of an applied magnetic field, the incident circularly polarised electromagnetic wave is found to propagate further into denser regions of the plasma — a result which is in accord with the so-called inverse Faraday effect. Finally, we shall consider general coupled transverse and longitudinal waves for which we give an approximate solution. We investigate whether this system of coupled waves exhibits any internal resonances and consequent energy exchange between them.     

On the theory of nonlinear response in a nonideal plasma

A theory of nonlinear response is developed for studying nonlinear phenomena and nonlinear transport processes in nonideal Coulomb systems. Temporal plasma echo and transformation of waves in a nonideal Coulomb system are studied on the basis of the theory of nonlinear response to mechanical perturbations. General constraints imposed on nonlinear response functions are considered, and the model for determining quadratic response functions is formulated. The conditions for the emergence of temporal plasma echo and wave transformation are determined. It is shown that these nonlinear effects in a nonideal plasma can be initiated by ultrashort field pulses. A theory of transport is developed for determining the Burnett transport properties of a nonideal multielement plasma. A procedure is proposed for comparing the phenomenological conservation equations for a charged continuous medium and equations of motion for the operators of corresponding dynamic variables. The Mori algorithm is used for deriving the equations of motion for operators of dynamic variables in the form of generalized Langevin equations. The linearized Burnett approximation is considered in detail. The properties of the matrices of coefficients of higher-order derivatives in the system of conservation equations in the linearized Burnett approximation, which are important for hydrodynamic applications, are discussed. Various versions of the theory of nonlinear response are compared.     

Strong electron tunneling through a small metallic grain

Electron tunneling through mesoscopic metallic grains can be treated perturbatively only under the conduction that the tunnel junction conductances are sufficiently small. If that is not the case, fluctuations of the grain charge become strong. As a result (i) the contributions of all—including high energy—charge states become important, and (ii) the excited charge states become broadened and essentially overlap. At the same time, the grain charge remains discrete and the system conductance e-periodically depends on the gate charge. We develop a non-perturbative approach which accounts for all these features and calculate the temperature-dependent conductance of the system in the strong tunneling regime at different values of the gate charge. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 12, 953–958 (25 June 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Plasma electron trapping and acceleration in a plasma wake field using a density transition

A new scheme for plasma electron injection into an acceleration phase of a plasma wake field is presented. In this scheme, a single, short electron pulse travels through an underdense plasma with a sharp, localized, downward density transition. Near this transition, a number of background plasma electrons are trapped in the plasma wake field, due to the rapid wavelength increase of the induced wake wave in this region. The viability of this scheme is verified using two-dimensional particle-in-cell simulations. To investigate the trapping and acceleration mechanisms further, a 1D Hamiltonian analysis, as well as 1D simulations, has been performed, with the results presented and compared.